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Dlsplay Spatlal Lumlnance Nonunlformltles:
Effects on Operator Performance and Perceptlon
bvJennie Jo Decker
Dissertation submitted to the Faculty of the
Wrginia Polytechnic Institute and State University
in partial fulüllment of the requirements for the degree of
Doctor of Philosophy
in
Industrial Engineering and Operations Research
Approved:
Harry L. Snydenäairman
Gr . Bu yoff John G. Casa!
Robert D. Drydeä Paul T. emmerling
August, 1989
Blacksburg, Wrginia
Display Spatlal Lumlnance Nonunlformltles:
Effects on Operator Performance and Perceptlon
bv
Jennie Jo Decker
Harry L. Snyder, Chairman
Industrial Engineering and Operations Research
(ABSTRACT)
This dissertation examined the effects of display spatial luminance nonuniformities on
operator performance and perception. The objectives of this research were to develop
definitions of nonuniformity, develop accurate measurement techniques, determine acceptable
levels of nonuniformities, and to develop a predictive model based on user performance data.
Nonuniformities were described in terms of spatial frequency, amplitude, display
luminance, gradient shape, and number ol dimensions. Performance measures included a visual
random search task and a subjective measure to determine users' perceptions of the
nonuniformities. Results showed that users were able to perform the search task in the presence
of appreciable nonuniformities. lt was concluded that current published recommendations for
acceptable levels of nonuniformities are adequately specified. Results from the subjective task
showed that users were sensitive to the presence of nonuniformities in terms of their perceptions
of uniformity.
Specifically, results showed that as spatial frequency increased, perceived uniformity
ratings increased. That is, users rated nonuniformities to be less noticeable. As amplitude and
display luminance increased, the users' ratings of perceived uniformity decreased; that is, they
rated the display as being farther from a uniform field. There were no differences in impressions
between a sine and triangle gradient shape, while a square gradlent shape resulted in lower
ratings of perceived uniformity. Few differences were attributed to the dimension (1-D versus 2-
D) of the nonuniformity and results were inconclusive because dimension was confounded with
the display luminance.
Nonuniformities were analyzed using Fourier techniques to determine the amplitudes of
the coefficients for each nonuniformity pattem. These physical descriptors were used to develop
models to predict users' perceptions of the nonuniformities. A few models yielded good fits of
the subjective data. lt was concluded that the method for describing and measuring
nonuniformities was successful. Also, the results of this research were in strong concurrence with
previous research in the area of spatial vision.
Acknowledgements
iv
TABLE OF CONTENTS
ABSTRACT ..................................................................................................................... I
ACKNOWLEDGEMENTS ................................................................................................. iv
INTRODUCTION ............................................................................................................. 1
Problem Statement ........................................................................................... 3
BACKGROUND .............................................................................................................. 4
Detectlng Luminance Gradients ........................................................................ 4Nonuniformity Experiments .............................................................................. 1 1
Low frequency luminance nonunilormities ................................................. 11High frequency luminance nonunitormities ................................................. 12
Current Levels of Nonuniformitiy on Displays ..................................................... 17Background Summary and Objectives .............................................................. 20
METHOD ....................................................................................................................... 23
Experimental Design ........................................................................................ 23Human Perlonnance Tasks ............................................................................... 25
Random search task .................................................................................. 25Magnitude estimation task ......................................................................... 25
Subjects .......................................................................................................... 26Measurement Apparatus .................................................................................. 26
Imaging system ......................................................................................... 26Measurement system ....................................................................................... 30Measurement Procedure and Analysis .............................................................. 32
Calibration ................................................................................................ 32Display system gamma .............................................................................. 32Nonuniformity description ......................................................................... 35Photometric measurements ...................................................................... 38Fourier descriptions of the nonuniformities ................................................. 38
Human Performance Apparatus and Stimuli ....................................................... 43Imaging system ......................................................................................... 43Random search task stimuli ........................................................................ 43Magnitude estimation task stimuli ............................................................... 46
Human Performance Procedures ...................................................................... 46Random search task .................................................................................. 50Magnitude estimation task ......................................................................... 50
RESULTS AND DISCUSSION .......................................................................................... 51
Random Search Task ....................................................................................... 51Search time .............................................................................................. 51Correct responses .................................................................................... 59Target confusion ...................................................................................... 66
Random Search Conclusions ............................................................................ 66Magnitude Estimation Task ................................................................................ 72
Results with baseline .................................................................,.............. 73Summary .................................................................................................111Magnitude estimation results, basellne removed ........................................112Summary .................................................................................................129
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Magnitude Estimation Conclusions ...................................................................129Display Iuminance ..................................................................................... 130Amplitude ................................................................................................130Gradient ...................................................................................................131Dimension ............................................................................................... 131
Performance Modelling ....................................................................................131Modelling approach ..................................................................................132Regressor variables .................................................................................. 132Analysis and results .................................................................................. 135
GENERAL DISCUSSION AND CONCLUSIONS................................................................. 144
Human Performance and Current Standards ..................................................... 144Relation to Previous Research ......................................................................... 145
Display failures .........................................................................................145Effects of visual noise ...............................................................................146
Definitions and Measurement ............................................................................147Spatial Wsion .................................................................................................. 148Future Research Needs ................................................................................... 149
REFERENCES ............................................................................................................... 151
Appendix A. Displayed Luminance Modulations for each Condition ................................... 156
Appendix B. Subject Instructions .................................................................................... 242
Appendix C. Procedure for Transformation of Magnitude Estimation Data, After Klingand Riggs (1971) ..........................................................................................246
VITA ..............................................................................................................................247
vi
LIST OF TABLES
Iable ume1. Contrast Levels and Percent Correct Responses for Linear
Gradient Targets (from McCann et al., 1973) .......................................... 13
2. Percent of Correct Responses for Detecting Sinusoidal Targets(from McCann et al.,1973)....................................................................... 14
3. Center and Comer Luminance Levels for a Sun 2/160 Gray Scale Monitor(From Pigion et al., 1986)...................................................................... 19
4. Frequency and Amplitude Settings and Function Generator AccuracyRanges for Each Wave Shape............................................................... 29
5. Display Luminance (DL) Values for One and Two·Dimensional Conditions ....... 39
6. Analysis of Variance Source Table for Search Time ........................................ 52
7. Simple Effect F-test for F x A for One and Two Dimensions - Search Time ........ 55
8. Simple Effect F-test for DL x G for One and Two Dimensions · Search 'Iime ...... 57
9. Simple Effect F-test for DL x Dim for Each Gradient - Search Time ................... 58
10. Simple Effect F-test for Dim at Each Amplitude · Search Time .......................... 61
11 . Newman-Keuls Comparisons for Display Luminance - Search Time ................. 63
12. Analysis of Variance Source Table for Correct Responses .............................. 64
13. Simple Effect F-test for Dim at Each Display Luminance -Correct Responses ............................................................................... 68
14. Symbol Confusion Matrix .............................................................................. 71
15. Analysis of Variance Source Table for Magnitude Estimation,Baseline included .................................................................................. 74
16. Simple Effect F-test for A x DL x DIM at Each Frequency ·Magnitude Estimation ............................................................................ 79
17. Simple Effect F-test for F x DL x DIM at Each Amplitude -Magnitude Estimation ............................................................................ 80
18. Simple Effect F-test for F x A x DIM at Each Display Luminance -Magnitude Estimation ............................................................................ 81
19. Simple Effect F-test for F x A x DL for One and Two Dimensions -Magnitude Estimation ............................................................................ 82
20. Simple Effect F-test for F x A at Each DL · Magnitude Estimation ..................... 85
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21. Simple Effect F-test for F x DL at Each Amplitude - Magnitude Estimation ........ 86
22. Simple Effect F-test for F x G at Each Amplitude - Magnitude Estimation .......... 88
23. Simple Effect F-test for A x G at Each Frequency - Magnitude Estimation .......... 90
24. Simple Effect F-test for G x DL at Each Frequency - Magnitude Estimation ....... 92
25. Simple Effect F-test for G X DIM at Each Frequency - Magnitude Estimation ..... 94
26. Simple Effect F-test for F x G for One and Two Dimensions —Magnitude Estimations ........................................................................... 96
27. Simple Effect F-test for F x DIM for Each Gradient - Magnitude Estimation ........ 97
28. Newman-Keuls Comparisons for A at Each Frequency -Magnitude Estimation ............................................................................ 99
29. Newman-Keuls Comparisons for DL at Each Frequency ·Magnitude Estimation ........................................................................... 101
30. Newman-Keuls Comparisons for G at Each Frequency - Magnitude Estimation.. 104
31. Newman-Keuls Comparisons for G at Each Amplitude - Magnitude Estimation... 106
32. Newman—Keuls Comparisons for G at Each Display Luminance -Magnitude Estimation ............................................................................ 108
33. Comparisons for DL at Each Amplitude - Magnitude Estimation ....................... 1 10
34. Analysis of Variance Source Table for Magnitude Estimation,Baseline Removed ................................................................................ 113
35. Comparison of Significant Effects for ANOVAs With and Vlüthout the BaseIine.. 115
36. Simple Effect F-test for F x A x DL for One and Two Dimensions · MagnitudeEstimation, Baseline Ffemoved ............................................................... 116
37. Simple Effect F-test for A x DL x DIM at Each Frequency - MagnitudeEstimation, Baseline Removed ............................................................... 118
38. Simple Effect F-test for F x A for One and Two Dimensions -Magnitude Estimation, Baseline Flemoved .............................................. 120
39. Simple Effect F-test for A x DIM at Each Frequency - Magnitude Estimation,Baseline Removed ................................................................................ 121
40. Simple Effect F-test for F x G for One and Two Dimensions - MagnitudeEstimation, Baseline Removed ............................................................... 122
41. Simple Effect F·test for G x DIM at Each Frequency - Magnitude Estimation,Baseline Removed ................................................................................ 123
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42. Simple Effect F-test for A x G at Each Frequency - Magnitude Estimation,Baseline Removed ................................................................................ 125
43. Newman-Keuls Comparisons for A at Each Frequency - MagnitudeEstimation, Baseline Removed ............................................................... 126
44. Newman-Keuls Comparisons for Amplitude - Magnitude Estimation,Baseline Removed ................................................................................ 127
45. Newman-Keuls Comparisons for Gradient - Magnitude Estimation,Baseline Removed ...................................................................................... 128
46. Regressor Variable Defintions ...................................................................... 133
47. Best-fit Regression Models for Perceived Uniformity ..................................... 136
48. Best-fit Regression Models for Perceived Uniformity WithSubjects Treated as a Categorical Variable ............................................... 137
49. Best-fit Regression Models for Mean Perceived Uniformity CollapsedAcrossSubjects ........................................................................................... 1 39
ix
LIST OF FIGURES
Esuta1.
Transmission of a signal through a linear system ................................................... 5
2. The modulation transfer function (MTF) ............................................................... 7
3. The contrast threshold function as a function of display Iuminance (fromv an Meeteren et al., 1968, adapted from Snyder, 1980) ...................................... 8
4. Fourier analysis technique for predicting visual detection of a square wavepattem (after Cornsweet, 1970) .......................................................................... 10
5. Experimental design ........................................................................................... 24
6. Block diagram of the imaging system .................................................................... 27
7. Block diagram of the measurement system ........................................................... 31
8. Luminance modulation for each A x DL condition for the vertical andhorizontal function generators ........................................................................... 33
9. Luminance rnodulations forthe combined vertical andhorizontalfunctiongenerators, and the combined vertical and Horizontal
Line Generator (HLG) ......................................................................................... 34
10. The gamma function of the CRT ......................................................................... 36
11. Example of 1-D and 2-D nonuniformity voltage measurements:a) modulation for 1-D pattem, b) modulation for the 2·D pattems,c) displayed 2·D nonuniformity pattem .............................................................. 37
12. LSF and MTF of the CRT ................................................................................... 40
13. Random search task symbols ............................................................................. 44
14. Photograph of a random search pattern with map ................................................ 45
15. Photograph of 1·D and 2-D SINE at 4 c/dw ......................................................... 47
16. Photograph of 1-D and 2-D TRI at 4 c/dw ........................................................... 48
17. Photograph of 1·D and 2·D SQ at 4 c/dw ............................................................ 49
18. The F x A x DIM Interaction for search time .......................................................... 54
x
19. The G x DL x DIM Interaction for search time ....................................................... 56
20. The A x DIM Interaction for search time ............................................................... 60
21. The effect of DL on search time ......................................................................... 62
22. The DL x DIM Interaction for percentage of correct responses ............................. 67
23. The effect of DL on percentage ot correct responses ......................................... 69
24. The effect of F on percentage of correct responses ............................................ 70
25. The F x A x DL x DIM Interaction for magnitude estimationa) DL-1, 1-D b) DL-1, 2-D c) DL-2, 1-D
d) DL-2, 2- D e) DL - 3, 1-D f) DL·3, 2-D ............................................................. 76
26. The F x A x DL Interaction for mean perceived uniformity ..................................... 84
27. The F x A x G Interaction for mean perceived uniformity ....................................... 87
28. The F x G x DL Interaction for mean perceived uniformity ..................................... 91
29. The F x G x DIM Interaction for mean perceived uniformity .................................... 93
30. The F x A Interaction for mean perceived uniformity ............................................ 98
31. The F x DL Interaction for mean perceived uniformity ..........................................100
32. The F x G Interaction for mean perceived uniformity ............................................103
33 The A x G Interaction for mean perceived uniformity .............................................105
34. The G x DL Interaction for mean perceived uniformity ......................................... 107
35. The A x DL Interaction for mean perceived uniformity ..........................................109
36. The F x A x DIM Interaction for mean perceived uniformity, baseiine removed .......119
xi
INTRODUCTION
ln visual displays, systematic changes in luminance or color are used to present picture
details and gray scale rendition. Display luminance uniformity refers to the ability of a display to
present a uniform luminance across the display screen and is important for the appearance of a
continuous picture. Display nonuniformity refers to unintended changes in luminance or color on
the display that may result in image degradation. From a marketing standpoint, displays which
manifest obvious nonuniformities may be esthetically displeasing to the customer. From a
performance standpoint, nonuniformities may directly affect task performance.
Research investigating the effects of display nonuniformities is very limited. Farrell and
Booth (1984) categorized cathode ray tube (CRT) nonuniformities into systematic and
nonsystematic changes in screen luminance. Two examples of systematic nonuniformities are
phosphor bum and the luminance difference from the center to the edge of a CRT screen.
Examples of nonsystematic nonuniformities were described as blemishes and categorized into
four types:
D_y¤am_ic_- blemishes caused by writing or erasing functions.
Static - blemishes not caused by writing or erasing functions.
·blemishes lighter than the background.
- blemishes darker than the background.
Farrell and Booth (1984) gave descriptive examples of different blemishes such as
pattem bums, raster burns, and blue edges (the area near the edge of the screen appears more
blue than the center).
1
lt is not feasible to list and describe all of the different types of nonuniformities that may
exist on each of the different display technologies. Goede (1978, cited by Snyder, 1980)
proposed categorizing nonuniformities into three types:
Large area · luminance or color gradients from one area on the screen to another, such as
edge·to·edge or center·to·center. An example is the center-to—edge luminance difference
commonly found on CRTs. Because CRTs have curved screens, the beam strikes the
phosphor at oblique angles, which is the primary cause of the luminance difference (Farrell
and Booth, 1984).
Small area - luminance or color changes from element to element. Examples of this type of
nonunifonnity are blemishes, dirt specks, and element failures.
Edge discontinuity - luminance or color gradients extending across a boundary resulting in
the impressions of edges or discontinuous figures. For example, some flat panel displays are
manufactured such that several small displays are matrixed together to form one large screen
display. The boundaries where these smaller displays are joined may result in impressions of
edges. Another example is line failures common to some matrix-addressed displays.
While these categories are somewhat useful, they are limited. The definition of "large" or
"small" area is not adequately specified. The extent and type of luminance gradient are also not
defined. The nonuniformities discussed above refer to luminance or color changes that are
inherent in the display technology. Another example of nonuniformities is Moire patterns that may
appear with the introduction of mesh glare filters placed over the display. Also, a digitized image
may result in nonuniform outputs because of the sampling rate used. These types of
nonuniformities do not fall neatly into the above categories.
3
Prob/em Statement
Electronic displays are used for many critical tasks such as photointerpretation,
sophisticated cartographic and symbolic representation for many military systems, computer-aided
design and computer-aided manufacturing (CAD/CAM), and other graphic applications.
Displaying an aocurate oominuous image is often critical to task performance. Although operators
may be able to perform such tasks with displays that exhibit nonuniformities, we do not know how
the nonuniformities may affect performance. Accurate measurement techniques for describing
spatial nonuniformities and reoommendations for acceptable levels are needed.
lt is possble that the effects of luminance nonuniformity will vary with the type of task and
the type of information displayed. Performing the numerous experiments to investigate
empirically the effects of all possible combinations is not feasible. Thus, a more general predictive
metric which relates the nonuniformity to operator performance is recommended. The objectives
of this research are to measure and define nonuniformity and to develop a predictive metric based
on user performance data.
BACKGROLND”
Detecting Luminance Gradients
Research which deals with detecting visual suprathreshold Iuminance gradients
is limited, as most of the literature deals with threshold measurement. Knowledge of the
threshold levels can give an indication of what the observer can detect, although
performance is unlikely to be affected by Iuminance gradients at or near threshold.
Brown and Mueller (1965) reviewed the vision literature dealing with the
ability to detect threshold changes in Iuminance. In these experiments, an adapting
Iuminance (L) was presented to the observer and the Iuminance change (AL) required by
the obsenrer to detect the change was determined. Many different variables were
manipulated and found to influence the ability to detect Iuminance changes. Examples
include task type and stimulus parameters such as size, duration, and shape. Even with
these data, it is difficult to predict quantitatively absolute detection thresholds because
they vary with all these parameters and their interactions.
Another approach to this topic has been to apply the concepts of linear systems
analysis and the mathematics of Fourier transforms. With linear systems analysis it is
possible to determine the extent to which any component or system of components can
transmit a signal. During transmission some of the signal is lost due to limitations of the
system (e.g., limited bandwidth) as illustrated in Figure 1. Modulation is defined as:
Modulaucn (M) = (1)
where Lmax is the maximum luminance and Lmin is the minimum Iuminance. The modulation
4
5
M<>d¤lati¤¤ ln (Mo Modulation out (MO)
imaging systemopticshuman
Modulation Transfer Factor
M (wiTMgco)
where T(w) is the modulation transfer factor at spatial frequency co,and Mo(m) and M|(m) are the output and input modulations, respectively.
Hgure 1. Transmission of a signal through a linear system.
6
transfer factor is the ratio of the modulation out of the system to the modulation into the system as
defined in equation 2.
Mom)(2)
lf the modulation transfer factor values at each spatial frequency are connected,
a oontinuous function is formed, the modulation transfer function or MTF. An example of
an MTF is illustrated in Figure 2. The modulation transfer function or MTF is a
measure of the fidelity in a system. The measurement is made for a sine wave of known
amplitude or modulation. The loss of output modulation generally increases with
increasing frequency of the sine-wave input.
These concepts have been applied to the visual system. An observer is presented
with a known sine-wave pattern that is varied in spatial frequency and he adjusts the
Iuminance contrast (modulation) of the grating to his visual threshold. When the
results are plotted as a function of spatial frequency the function is termed the contrast
threshold function or CTF. Figure 3 illustrates CTFs for different levels of display
Iuminance (van Meeteren, Vos, and Bongaard, 1968, as cited by Snyder, 1980). At
higher levels of display Iuminance the eye is most sensitive to frequencies between 3 and
5 cycles per degree of visual angle. Higher modulations are required as the spatial
frequency decreases or increases. As display Iuminance is decreased, higher modulations
are required for threshold detection and peak sensitivlty shifts to lower frequencies. .
Fourier analysis states that any repetitive waveform can be analyzed into its
sine-wave components with each component frequency having a speciüc amplitude and
phase relationship, such that they can be recombined into the original image. The
1
1 .0
0.8I-$2LI.
Egb 0.6
E1-ä1*: 0.4S
E0.2
00.1 0.5 1.0 5 10 50 100
SPATIAL FFIEQUENCY, CYCLES PER UEGREE
Hgure 2. The moduiation transfer function (MTF).
8
1
20.10 od/m
.1'3E= 2Q 10 wmE .01
.001.1 1 1 0 100
Spatlal Frequency (Cycles/degree)
Hgure 3. The comrast sensitivity function as a function of display luninance from van Meeteren et
al., 1968, adapted from Snyder, 1980).
9
component frequencies of the image can be compared to the CTF of the visual system to
determine whether the frequencies can be detected by the visual system. For example, if
high frequency information is critical to performance then it is important that the high
frequency information be preserved. A Fourier analysis of the displayed information can
be used to determine if the high frequency information is detectable to the observer. If
the amplitudes exceed the observer's threshold, then the information is detectable.
Figure 4 illustrates an example of this concept. The top part of the figure
illustrates the first two components of a square wave. The second figure is a spectrum
which shows the sine wave content of the image. The third figure is the contrast
sensitivity function (CSF) of the visual system, which is the inverse of the CTF. The eye
attenuates the lowest frequency component. The last part of the figure is the spectrum of
the image as seen by the eye.
De Palma and Lowry (1962) measured the threshold response for sine· and
square-wave gratings at different spatial frequencies. Their results indicated that for
both sine and square waves the visual system was most sensitive between 3 and 5 cycles
per degree. They also found that below 6 cycles per degree the square wave required less
modulation for detection than did the sine wave.
This result can be predicted using Fourier techniques. A square wave can be
produced by adding sine waves starting with a sine wave that has the same fundamental
frequency as the square wave and adding additional sine waves with frequencies that are
odd multlples (3X, 5X, 7X ...) of the fundamental frequency with amplitudes that are
1/3, 1/5, 1/7 of the fundamental (Cornsweet, 1970). When the Fourier components
of a square wave and a sine wave that have the same fundamental frequency and peak-to-
peak amplitudes are compared, the amplitude of the fundamental is 4/1: (or 1.273)
10
43
components äof a square §wave E
Ab 4Amplitude
_ modulatlonof the 2object
0
4GTransfer 1 0functionof thevisual 1·°system(relativesensltivity) ¤·2
4d 4Amplitudespectrum 2ot theimage
0
0.15 1.5 15.0 150.0
Spatlal Frequency (cycles/degree)
lägure 4. Fourier analysis technique for predicting visual detection ol a square wave pattem (after
Comsweet, 1970.
11
higher for the square wave than for the sine wave; therefore, the square wave requires
less modulation to detect. The higher order harmonics contribute to detection also, but
only up to a point. The sensitivity of the eye deoreases beyond 5 eycles/degree. lf the
higher order harmonics are beyond 5 cycles/degree they will contribute less to detection
(Snyder, 1980). This relationship was demonstrated by De Palma and Lowry (1962).
Results from studies on oontrast sensitivity indicate that the spatial frequency of
a nonuniformity (luminance gradient) and the type of periodic pattern or waveform of
the nonuniformity will influence how it is perceived. A low spatial frequency or very
gradual change in Iuminance will probably go undetected by the observer. However, it
will depend upon the pattern underlying the gradient (e.g., square, sinusoidal, linear,
etc.). Therefore, rather than defining nonuniformity in terms of large area or small
area, spatial frequency is more descriptive and more likely to be generalized validly to a
variety of display conditions.
Nonuniformity Experiments
Low frequency Iuminance nonuniformities. McCann, Savoy, Hall, and Scarpetti
(1974) investigated continuous linear Iuminance gradients and sinusoidal periodic
patterns. Contrast (defined as (Lmax-Lmin)/Lmax) and retinal gradient were the
independent variables. Retinal gradient referred to the rate of change of flux on the
retina and was defined as (contrast)/(retinal angle between Lmax and Lmin).
ln the first experiment Iuminance was varied linearly in one direction across a
square target 10.2 cm2. The target was constructed using photographie print paper.
Five oontrast levels were used. Targets were placed in an illumination box and
uniformly illuminated from within. All targets were scanned using a telephotometer and
12
the center Iuminance of each target was 527.6 cd/m2. The targets subtended 4.8 degrees
of visual angle and were presented in four orientations, with the maximum Iuminance on
top, bottom, left, or right (i.e., maximum Iuminance to minimum Iuminance).
Observers were asked to identity the dimmest edge and correct responses were reoorded.
ln order to determine the effects of retinal gradient, the targets were also viewed
at distances which yielded a constant retinal gradient. Table 1 summarizes the target
contrasts and results. The percent correct was greatest for the highest Iuminance
contrast condition (i.e., the steepest slope) and progressively lower as target contrast
decreased. When retinal gradient was kept constant results were very similar,
indicating that visibility was not a function of retinal gradient. lf a 50-percent detection
accuracy is defined as the threshold, a contrast between 0.12 and 0.17 was required. A
contrast of 0.33 resulted in 93 percent correct detection rates.
ln the second experiment sinusoidal Iuminance gratings were used and contrast
was kept constant at 0.10. The gratings varied in spatial frequency between 0.5 and 2.8
cycles/degree as indicated in Table 2. Targets were presented in an octagon so that four
orientations were possible. Observers were asked to determine the four orientations of
the gratings. The results (see Table 2) are similar to other experiments dealing with
sinusoidal gratings. As the spatial frequency increased, the visibility increased
monotonically. At 2.8 cycles/degree the subjects responded correctly 100 percent of the
time. At the lowest spatial frequency (0.5 cycle/degree) correct responses were at
chance levels. Fletinal gradient again was not a factor in determining visibility.
High frequency Iuminance nonuniformities. Limited research can be found with
regard to high frequency Iuminance gradients or ”smalI area" nonuniformity, or changes
in Iuminance or color at the elemental or pixel level. Such nonuniformities may include
13
TABLE 1: Contrast Levels and Percent of Correct Ftesponses for Linear Gradient Targets
(from McCann et al.,1973).
Target Contrast % Correct viewed Viewing distance for retinal %Correct at aat 122 cm gradient of 0.12 constant retinal
A 0.0 8 4 1 4 8 9 4 8
B 0.1 2 4 7 2 2 2 5 5
C 0 .1 7 6 8 2 3 4 5 8
D 0.23 8 0 1 8 0 7 7
E 0.33 9 3 1 2 2 9 3
14
TABLE 2: Percent of Correct Responses for Detecting Sinusoidal Targets (from McCann
et al., 1973).
Target frequency % Correct viewed Viewing distance (cm) for % Correct at a(c/deg) at 122 cm retinal gradient of 0.12 constant retinal
0.5 22 74 9 19
0.7 30 472 28
1 .0 60 3 6 8 75
1 .2 70 274 75
1 .7 86 221 86
2.0 95 1 9 6 1 0 0
2. 8 1 0 0 1 2 2 1 0 0
15
blemishes, dirt on the screen, or a change in Iuminance of the pixel. (This definition
does not include the Iuminance change with respect to the element size.) The acceptable
level will also vary with the number of nonuniformities on the screen.
An image can be stored in a computer electronically in digital form. A continuous
tone image is sampled and quantized into different Iuminance levels or bits. These bit
values are converted to analog values and sent to the display. A computer with the
capability of storing 8 bits has 256 intensity levels (28) available that can be displayed
on compatible display hardware. lf the differences between these levels are small enough
and there are enough levels, the Iuminance gradations will appear continuous. Some
displays are only capable of displaying one bit of intensity information (on or off), such
as the typical AC plasma panel; therefore, only two intensity levels can be displayed
which may not be enough to present picture details which require fine Iuminance
gradations without using techniques such as spatial or temporal dithering.
Emissive displays may exhibit Iuminance variations in pixels such that the
Iuminance level is below or above the intended level. In the case of the plasma panel, the
display may fail by having a pixel remain on or off irrespective of the intended state.
Other matrix-addressed or ceII·addressed displays may also have these types of failures.
Effects of display failures have been investigated and the results are relevant to this
topic.
Riley and Barbato (1978) evaluated the effects of discrete element degradation
on the Iegibility of 5 x 7 dot-matrix fonts, including ASCII, Lincoln—MlTRE, Huddleston,
Ellis, and NAMEL fonts. importance values were assigned to each dot which composed a
character. importance values were assigned as a function of the amount of degradation the
character would suffer if the dot was removed. Each character was then degraded by the
16
addition, removal, or both addition and removal of dots. Subjects performed a character
identification task. The removal, addition, of simultaneous removal and addition of dots
did not differentially affect character identification. There were also no differences
among fonts. lt should be noted that this study systematica//y removed or added dots and
that display failures are typically random.
Abramson and Snyder (1984) investigated element failures on an AC plasma
panel display to determine effects on operator reading performance. Two between-
subject variables, font (Lincoln-MITRE, Huddleston, and a font from an HP2621A
terminal), and case (mixed or upper) were investigated along with within-subject
variables of failure type (vertical or horizontal line failures, cell failures), failure
mode (failed on or off), and percent failure (0, 2, 4, 8, 12, 20). Failures were placed
randomly on a screen with a 1024 x 1024 active area. The task was a Tinker speed of
reading test. Response time and the frequency of correct, incorrect, and null responses
were reoorded.
As the percentage of cell failures increased from 0 to 20 percent, response time
increased. This effect was most dramatic for mixed case text. ON cell failures resulted in
significantly slower response times than OFF cell failures. For ON cell failures the
mixed case was significantly slower than upper case. The Huddleston font resulted in the
fastest response times regardless of whether the failure was ON or OFF.
ln terms of response frequency, as the percent failure increased the proportion
of incorrect responses increased. Above 8% the proportion of null responses increased.
The authors concluded that failures below 2% would not result in reading performance
degradation. This conclusion may not hold for more complex task situations in which
reading is not the primary task.
17
Further investigations into the effects of display failures were conducted by
Decker, Dye, Kurokawa, and Lloyd (1988) and Lloyd, Decker, Kurokawa, and Snyder
(1988). Results from both studies supported results obtained by Abramson and Snyder
(1984). In addition, it was found that display failures were more detrimental when
performing a random search task then when performing a Tinker reading task. With a
percent failure of 4%, search performance was degraded 28% and reading performance
was degraded 4% from a no-failure condition. For search type-tasks, ON cell failures
above 1% should be avoided.
The research described above revealed that display failures which cause high
frequency nonuniformities across the screen will influence performance; however,
acceptable levels and quantitative predictive metrics for describing high frequency
nonuniformities are difficult to establish. The spatial frequency of the nonuniformity
was not varied, nor was the degree of Iuminance change (or amplitude of the
nonuniformity). Further research is still needed.
Current Levels of Nonuniformity on Displays
Prior to describing and measuring the effects of display nonuniformities it is
necessary to determine current levels of display nonuniformities in the market.
Unfortunately, without an accurate and standard definition of the term it is difficult to
determine current levels.
Several sources have attempted to address the effects of low frequency Iuminance
changes on displays. Klaiber (1966) measured physical and optical properties of
projection screens. Although no data were presented he stated,
18
"Preliminary studies in our Iaboratory indicate that the Iuminance gradient
across an empty field will be tolerable (when information is later
displayed) if the Iuminance at the field edges is one—third of that at the
center. These results depend greatly on the shape of the Iuminance gradient;
our study is based on a linear gradient.'
Tannas (1985) stated that for television displays center-to-edge gradients of
two—to·one go 'generally unnoticed." He did not lndicate the size of the display;
however, he did indicate that the acceptable levels will depend on the end use of the
display. Unfortunately no data were presented regarding typical levels of nonuniformity
in the current market.
Vogel (1974) measured average Iuminance levels from the center to the edge of
two types of color televisions. He found gradients of 53 to 63 percent from center to
ecge.
Pigion, Decker, Hunter, and Snyder (1986) made center and four corner average
Iuminance measurements on a gray scale Sun 2/160 19-inch CRT monitor. The corner
measurements were made one inch from the corners of the screen. These measurements
were made with all pixels at 0 and full (255) bit levels. The brightness adjustment was
varied until the center Iuminance level reached 80 cd/m2. All measurements were then
made without adjusting the brightness control. Results are presented in Table 3. At 255
bits, the right corners were approximately 6.4 percent greater in Iuminance than the
center, while the left corners were approximately 6.6 percent lower than the center
Iuminance.
19
TABLE 3: Center and Corner Luminance Levels for a Sun 2/160 Gray Scale Monitor
(from Pigion et al., 1986).
Luminance at 0 bits Luminance at 255 bits(cd/m2) (cd/m2)
center 0.2 80.6
top left 0.3 75.2
top right 0.4 87.9
bottom left 0.3 75.4
bottom right 0.4 83.7
20
The research and recommendations seem to indicate that Iuminance gradients
from center to edge on current CFtTs including televisions can be as high as 60 percent,
although some systems are within 10 percent.
The American National Standard for Human Factors Engineering of Visual Display
Terminal Workstations (1988)recommends that the Iuminance variation from the
center to the edge cf the active display area should vary no more than 50% of that of the
center Iuminance. In reference to high frequency spatial Iuminance nonuniformities,
the standard recommends that unintended Iuminance variaticns shall not vary by more
than 50% within an area the size of half a degree of arc, at any position on the screen.
(This value is calculated based on the display design viewing distance.) This last
recommendation ensures that if a 50% Iuminance change does occur, it will not occur
sharply creating the impression of an edge or dark spot. Validation of this standard is
still needed.
Background Summary and Objectives
lt is obvious that quantitative research is lacking to describe the effects of spatial
Iuminance nonunifcrmities on human performance. Validation of current
recommendations is needed. The cbjective of this research is to define nonunifcrmities
in a manner which would allow systematic measurement, and to determine the effects of
nonunifcrmities on human performance.
Underlying this investigation is the concept of the visual system as a Fourier
analyzer in the spatial domain. The techniques of linear systems analysis and Fourier
analysis are powerful analytical tools which can provide a quantitative measurement
framework for describing nonunifcrmities. Also, a large body of literature in the areas
21
of vision and visual display systems postulates a spatial frequency model for describing
human visual responses. Describing nonuniformities in spatial frequencies enables
comparison of results with previous research.
As previously discussed, visual detection thresholds vary as a function of spatial
frequency, modulation, and the shape of the gradient (e.g., sine wave versus square
wave). Therefore, to characterize nonuniformities, these variables will be included in
the investigation. Describing nonuniformities in terms of spatial frequency allows
nonuniformity to be described as a continuous variable, avoiding the discrete arbltrary
definitions of large and small area.
ln addition to the above variables, visual detection thresholds have also been
found to vary as a function of the display luminance (van Meeteren et al., 1968).
Because display luminance is a parameter that display users may adjust, it is important
to include this variable in the investigation. For example, older users or observers who
are viewing under high glare conditions may increase the display luminance.
Nonuniformities may vary in two dimensions on the screen; therefore, the effects
of one- and two-dimensional nonuniformities should also be included in the
investigation. Carlson, Cohen, and Gorog (1976) determined threshold responses for
both 1-D and 2-D sine waves and found no significant difference in thresholds between
the two patterns. However, the authors only reported results for one trained subject.
The stimuli were presented on a CRT which would be limited in the high frequency
ranges as a function of it's MTF. The limitations of the display were not discussed by the
authors.
22
Describing nonuniformities in terms of spatial frequency, modulation, and
gradient shape allows for physical measurement of the nonuniformities using
photometric techniques. Physical measures of the nonuniformities can then be correlated
with human performance. This technique is used in this investigation.
METHOD
Experimental Design
The experimental design was a 7 x 6 x 3 x 3 x 2 complete factorial and is shown in Rgure
5. Seven levels of spatial frequency (F) were evaluated: 4, 8, 16, 32, 64, 128, and 256 cycles per
display width (c/dw). The 256 c/dw condition consisted of waveforms of 2 pixels on and 2 pixels
off. The waveform generators were bandwidth limited beyond this spatial frequency. The lower
frequency value of 4 c/dw was selected based on research by Hoekstra, van der Goot, van den
Brink, and Bilsen (1974), who found that when spatial frequency was held constant, the
number of cycles presented in the grating affected threshold modulations. The critical number of
cycles varied as a function of luminance. For the range of mean display luminance values of
interest in this study, the critical number of cycles is approximately four. The figure also includes
the frequency values in units of cycles/degree of visual angle (c/deg).
The six levels of amplitude (A) in peak·to-peak voltage were 0, 6, 10, 14, 20, and 24 mv.
The A-0 condition was included as a baseline condition. That is, nonuniformities were not
present. The three levels of display luminance (DL) were DL-1 = 0.003, DL·2 = 0.016, and DL-3 =
0.10 candela per square meter (od/m2). Display luminance refers to the mean luminance level of
the nonuniformity and may also be considered as a voltage or luminance DC offset. Three
gradient shapes (G) were investigated: square (SQ), triangular (TRI), and sine (SINE). The
variable dimension (DIM) included one—dimensional (1-D) and two-dimensional (2-D)
nonuniformities. The 1-D nonuniformities were in the vertical direction only. The 2-D condition
consisted of horizontal and vertical nonuniformities summed together.
23
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25
Human Performance Tasks
Random search task. A non-contextual random search task was used in which the
dependent measures were search time (ST) and the peroentage of correct responses (CR). This
task was chosen because research has shown that humans are able to perlorm contextual type
tasks, such as reading tasks, under adverse conditions (Albert, 1975). Lloyd et al. (1988) found
that the random search task was more sensitive to high frequency display failure nonuniformities
than a Tinker Speed of Reading Task. For the random search task the gradient variable (G) was
assigned as a between·subjects variable and all other variables were within~subjects, resulting in
252 conditions for each G. Each condition was repeated five times for a total of 1260 data points
per subject. There were five subjects randomly assigned to each G level.
Magnitude estimation task. Although subjects may be capable of performing an objective
task in the presence of nonuniformities, it is possible that nonuniformities may be esthetically
displeasing. This task was included to determine subjective impressions of the nonuniformities.
The magnitude estimation task required subjects to provide a magnitude rating of the perceived
uniformity; that is, subjects rated how uniform the luminance appeared to them. Note that subjects
were told to rate perceived uniformity rather than nonuniformity because nonuniformity can not be
defined without biasing responses. However, subjects could understand the term uniformity.
Higher numerical values indicated that subjects perceived the display as appearing more uniform.
Instructions for this task are listed in Appendix B. The rating was the dependent variable. During
pilot testing it was detennined that if a rating scale was provided, subjects were unable to üt all their
impressions onto the scale. With the free-modulus technique subjects could provide their own
rating scale, which gave a better indication of their impressions. For this task, the variable DIM was
treated as a between~subjects variable and all others as within-subjects, resulting in 378
26
conditions for each DIM. Each condition was repeated twice for a total ot 756 data points per
subject. Hfteen subjects were randomly assigned to each DIM condition.
Subjects
Forty-five students from Virginia Polytechnic Institute and State University served as
subjects and were paid $5.00 per hour for their participation. Fifteen subjects participated in the
random search task and 30 subjects in the magnitude estimation task. Subjects participated in
the random search task 5 days, 2 hours per day. Subjects participated in the magnitude
estimation task for 2 days, 2 hours per day. All subjects were between the ages ol 18 and 30 with
a mean age ot 20.5. Each subject was screened for normal or corrected 20/22 near and distant
vision, and nomtal lateral and vertical phoria using a Bausch & Lomb Orthorater. Each subject was
also screened for normal near and far contrast sensitivity using a contrast sensitivity test by
Vistech Consultants Inc.
Measurement Apparatus
Imaging system. The imaging system consisted of a 48.3-cm diagonal monochrome
cathode·ray tube (CRT), a video signal generator, two programmable function generators, a
custom built horizontal line generator (HLG), and an lBM·PC AT. Hgure 6 is a block diagram ot the
system.
The CRT monitor was a high resolution GMA~201 manufactured by Tektronix, Inc. (part #
070-5079-00). The monitor was driven at 60 Hz non—interlaced with an addressability of 1024 x
1024 pixels within an active area of 27.94 cm2· The CRT had a standard P4 phosphor and was
interfaced with an OPIX video signal generator produced by Quantum Data. The OPIX was
capable of a 200-MHz pixel rate with a nominal rise/fall time of 1.8 ns.
27
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28
Two programmable function generators (Tektronix, model 5010) produced the
nonuniformities. The generators controlled the A, DL, and F of the nonuniformities. One function
generator was used to produce vertical nonuniformities and one to produce horizontal
nonuniformities. Each generator was capable of a frequency range of 0.002 Hz to 20 MHz and
output amplitudes of 20 mv to 20 v peak-to~peak. The generators were triggered and
synchronized by the OPIX and had a frequency stability of 0.10% (Tektronix, 1982). Table 4 lists
the amplitude and frequency values for both the vertical and horizontal function generators and
the frequency accuracy ranges for each wave shape (Tektronix, 1982).
As illustrated in Figure 6, the vertical and horizontal synch from the OPIX triggered the
vertical and horizomal function generators. The output of the vertical generator was attenuated by
6 dB and the horizontal generator by 10dB (not shown in the figure) before the signal was input to
the custom electronic enclosure. Vertical and horizontal nonuniformities were synchronized using
a sample and hold amplifier (model CLC940A1) by Comlinear Corp. output from both generators
was then sent to a passive mixer. The output from the mixer was then sent to a high speed switch
to be synchronized with the blanking signal from the OPIX. The signal out of the high speed
switch was sent to another passive mixer which added the nonuniformity signal and the OPIX
video output signal. The output from the mixer was amplified by a linear video signal amplifier
(model CLC 100 by Comlinear Corp.) before being sent to the display.
The function generators were not phase·locked to the OPIX or display. When a square
wave shape from the horizontal function generator was presented, the horizontal lines on the
display would flicker on and off. Therefore, a custom built horizontal line generator (HLG) was
used to generate the square-wave shapes for the horizontal signal. The HLG was capable of
controlling the F, A, and DL values and values were set to match the output of the vertical and
29
TABLE 4
Frequency and Amplitude Settings and Function Generator Accuracy Ranges for each Wave
Shape.
Amplltudés (volts) Frequencles (KHz)
Vertical FG Horizontal FG Vertical FG Horizontal FG
0.0 0.0 0.250 354 .00
0.069 0.784 0.484 737 .00
0.1388 1.546 1.031 1403.00
0.232 2.16 1.999 2890.00
0.394 3.14 4.02 5820.00
0.482 4.00 8.01 11120.00
16.04 20000.00
Function Generator Accuracy Ranges
Sszuare Iriaucle Sim
0.002 Hz S f S 1 kHz 1 2.0% 1 2.0% 1 3.0%
1 kHz < f S 100 kHz 1 3.5% 1 3.5% 1 3.50%
100 kHz < f S 1MHz 1 3.5% 1 4.0% 1 3.5%
1 MHZ < f S 5MHz 1 5.0% + 4.0%,- 5.0% 1 5.0%
5 MHZ < f S 10 MHZ 1 5.0% + 4.0%, - 20.0% + 5.0%, -10.0%
10 MHZ < f S 20 MHZ i1Ü.Ü°ß + 4.0%, - 20.0% + 5.0%, -10.0%
30
horizontal function generators. The HLG was controlled manually and was only used for the SQ 2-
D nonuniformities because the 1-D nonuniformities were vertical.
During measurements the IBM·PC AT was used as a terminal to control the OPIX and the
programmable function generators. The function generators and OPIX were interfaced to the IBM-
PC AT using the General Purpose Interface Bus (GPIB) communications system.
Measurement system. Figure 7 is a diagram of the microphotometric measurement
system used to make spatial luminance measurements. The system was composed of a
telemicroscope (GS·2110); photomultiplier tube (PMT) with a photopic correction filter (D46-A);
an x, y, z stage for microscope positioning; a stainless steel optical table; an intelligent radiometer
(GS-4100); and an IBM-PC XT. The telemicroscope, PMT, and radiometer were produced by
EG&G Gamma Scientific. A 1.0X objective lens and a 0.010 mm x 3.0 mm scanning slit aperture
were used for all measurements. The steel optical table was air-cushioned to isolate the
measurement system and display from high frequency noise. The table was produced by
Technical Manufacturing Corporation.
A CS100 hand held spot photometer by Minolta was used to perform area luminance
measurements and to calibrate the CRT. The CS100 had a measurement area of 2 degrees and
was mounted on a tripod during calibration and measurements for stability.
A digital oscilloscope by Tektronix (11042) was connected to the imaging system to
determine the output voltages that were being sent to the display. The oscilloscope was
connected to a special synch function in the OPIX which acted as an oscilloscope trigger. This
allowed observation of a signal during a horizontal scan line at any particular time during the frame
penod.
31
GS-2100 GMA/201Scanning CRT
GS·41 00 Telemicroscope MonitorIntelligentRadiometer
IBM PC-XT
Rgure 7. Block diagram of the measurement system.
32
Measurement Procedure and Analysis
lnitially, cycles of each nonuniformity condition were to be measured on the display using
the microphotometric measurement system to determine the actual output modulations at each
spatial frequency. These values could then be used as input into a Fast Fourier routine to
detemwine the coefficients of the nonuniformity patterns. However, the nonuniformity luminance
(DL) levels used in this study were too low to be measured accurately by the spatial luminance
microphotometric system. instead the description of the nonuniformities in terms of their Fourier
coefficients was determined analytically based on the theories of Fourier analysis and linear
systems analysis as described below.
Ca/ibration. There was a 30-min warm·up period after the imaging system was tumed on.
All units of the imaging system were left on at all times throughout the measurement phase. The
system was calibrated using the CS100 spot photometer. Each DL level was sent to the display
and the output luminance was measured. lf necessary, the luminance output was changed using
the brightness knob on the CRT. Measurements were made for the horizontal and vertical
function generators as well as the HLG.
Figures 8 and 9 illustrate that the vertical and horizontal function generators and the HLG
were calibrated to produce the same outputs. Hgure 8 is the luminance modulation for the DL X A
conditions for the separate horizontal and vertical generator signals. Figure 9 shows the
combined vertical and horizontal generator signal and the combined vertical and HLG signal for 2-
D conditions for each DL x A condition. These graphs illustrate the near-perfect correspondence
in output signals between the function generators and the HLG.
Display system gamma. The display system gamma is the function which relates the input
voltage to the output luminance of the CRT. This function was determined by varying the input
33
1.0
Generator0,7
•-•—Horizontal G•n•r•tor
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0.2
0.1
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—•-—V•rtlo•lG•n•r••or
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Amplitude
Figure 8. Luminance modulation for each A x DL condition for the vertical and horizomal function
generators.
3h
1.0· DL-1
0.8
S 0.62:Li:
§ 0.4
02 —-•— V + H Generator:*0* V Genefller + FLG
0.00 1 2 3 4 5 8
Amplitude
1.0
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S 0.6a:E:•8 0.4E
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0.00 1 2 3 4 5 8
Amplitude
1.0
DL-30.8
cg 0.8E§E 0.4
0.2 —•— V + H Generator:*•—V Generator + HLG
0.00 1 2 3 4 5 8
Amplitude
Figure 9. Lumlnance modulations for the combined vertical and horizontal function generators,
and the combined vertical and HLG.
35
voltages and measuring the output luminance of the CRT with all pixels on. Luminance
measurements were taken with the CS100 spot photometer. Input voltage was manipulated by
changing the bit values into the display. The display was capable of 0 to 255 bit levels and the
voltage levels corresponding to each bit level were displayed on the oscilloscope. Figure 10
illustrates the gamma function of the CRT. As illustrated by this figure, the luminance output of
the CRT as a function of input voltage, for all practical purposes, ls linear in the low luminance
range. Therefore the application of linear systems analysis is viable for the luminance levels (i.e.,
less than 0.33 cd/m2) used in this study.
Nonuniformity description. After obtalning the gamma function, the maximum and
minimum luminance values for each A and DL level were determined. The nonuniformity was
sent to the CRT and the input voltages were displayed on the oscilloscope. After determining the
maximum and minimum voltages for each A level at each DL, the values were then oonverted to
maximum and minimum luminance using the gamma function. In the case of 2-D nonuniformities,
maximum and minimum luminance values were determined for the horizontal nonuniformity, the
vertical nonuniformity, and the added vertical and horizontal nonuniformity as illustrated in Figure
11. Modulation A represents the vertical nonuniformity, modulation B represents the horizontal
nonuniformity, and modulation C represents the added vertical and horizontal nonuniformities
and is the maximum modulation displayed. An example of the final displayed pattern is illustrated
in Figure 11c. Modulations for each A x DL condition were determined using luminance values in
Equation 1.
lt should be noted that the A x DL modulations are different for the 1-D and 2-D cases.
Throughout the course of the experiment, the DL levels were manipulated by setting a constant
offset on each function generator and by sending a constant bit level to the display for each DL
condition. Therefore, the bit level and the output from the generators were added and descrlbe
36
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Figure 10. The CRT‘s gamma function.
37
1-D Wave Form
LMax
Lminal
2-D Wave Form
‘-max tgäf Modulation A0C.9E3EE
.‘-"‘a*
Modulation 6Lmin Lmin
bl2-D Nonuniformity Pattern
Modulation BE il Modulation A
Modulation Ccl
Hgure 11. Example of 1-D and 2—D nonuniformity voltage measurements.
38
each DL level. In the case of the 1-D nonuniformity, the output on one of the function generators
was disabled. Disabling the generator tumed off the constant offset voltage being sent to the
display from that generator; therefore, the DL levels for the 1-D conditions were lower than the 2-
D conditions by the constant amount of 180 mv. Table 5 lists the DL levels in luminance for the 1-
and 2-D conditions. Throughout this report, the DL levels will be discussed in terms of three
levels, DL-1, DL-2, DL-3. The reader should keep in mind, however, that the DL levels did vary
depending on the DIM.
Photometric measurements. The modulation transfer function (MTF) of the display
system was determined through microphotometric measurements. The MTF can be obtained
from the Fouriertransform of a line spread function (LSF). The LSF was determined by scanning a
single vertical line on the CRT. The output from this scan is luminance as a function of distance.
As stated previously, the photometric system was unable to measure the low modulation levels
used in this study; however, at these levels it was assumed that the display system gamma was.
linear. Several LSF measurements were taken of a vertical line set to maximum luminance values
of 0.40 to 1.0 cd/m2. The MTFs from these measurements were compared and found to be
almost identical, supporting the assumption that the display system's output was in fact linear in
these ranges. Therefore, the MTF values for a measurable luminance level could be used in
subsequent analysis. The LSF and resulting MTF for the 1.0 cd/m2 are shown in Figure 12 and
were the MTF values used to describe the display system.
Fourier descriptions of the nonuniformities. The measurement data provided by the
procedures described in the preceding sections were used to determine the Fourier coefficients
for each nonunifonnity condition. The procedure for obtaining the coefficients was analytical and
was based on the Fourier Series, as briefly discussed below for purposes of explanation.
39
TABLE 5.
Display Luminance (DL) Values (cd/m2) for 1- and 2-Dimensional Conditions.
DL 1-Dimensional 2-Dimensional
DL-1 0.0037 0.0215
DL·2 0.0167 0.0752
DL-3 0.1033 0.3352
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41
The general fomt of the Fourier Series is expressed as
x(p)-ao+;(a„cosnw0p+b„sinnwop), (3)
where wo is the spatiai frequency. The components of the series ao, an, and bn describe the
frequency content of the image. The ao coefficient is the average value of the function x(p) over
one period (P) or its DC level. The first component of the series for n-
1 is the fundamental
frequency component. Additional components of the series are integer multiples of the
fundamental and are called hamwonics. The coefücients can be detemnined by
1 Pha„
Ffo x(p)dt, ( )
Pa„-lf x(p)cosn:»„P/dt, (5)
P 0
Pb„=-lf x(p)sannw„P/dt, (6)P o
The Fourier series for common wave forms are widely published . When the coefficients
are evaluated for a square wave, they result in the series;
x(p) -g(coso>„p -%cos3a>0P+%cos5woP ·%cos 7moP......), (7)7l
where wo-
21:/ P, P is one cycle of the wave form, and V is the half-amplifude of the wave form.
For the triangular wave form the series is
x(p) =¥(coso>„p ·%cos 3m„P +écos5w„P —%-cos 7woP......), (8)1E
The Fourier coefticients (in displayed luminance amplitude) for the nonuniformities were
derived from the Fourier series equations. The nonuniformities used in this study were described
42
in terms of F, A, and waveform (or G); therefore, these data can be used in the above equations
to determine the coefficients for each nonuniformity condition. The half amplitudes (cd/m2) for
each A x DL condition were input into the Fourier series equations to determine the amplitude of
the fundamental frequency component and harmonics for each nonuniformity condition. For the
2-D conditions, the half amplitude of the highest modulation on the display was used in this
analysis as illustrated in Hgure 11. If subjects were unable to detect the highest modulation, then
they would be unable to detect the lower modulations.
The MTF describes the display system spatial frequency response; therefore, the
amplitude coefücients at each wo were multiplied by the MTF value at wg to determine the output
displayed Iuminance amplitude. The displayed Iuminance amplitude was then converted to
modulation values using Equation 1.
Appendix A is a series of tables which list the displayed Iuminance modulations (DLM) for
the fundamental and the first three harmonic frequencies of interest for each nonuniformity
condition. Each individual table represents an F x DL x DIM condition. Vfhthin each table are the
DLM values for the A x G conditions. The CTF value listed in the table represents the CTF value
at each particular spatial frequency. lf the DLM is greater than the CTF value, then the frequency
component is visible to the observer, or above his or her visual detection threshold. The row
labeled detection indicates whether the frequency component is visible by indicating Yes or No.
Notice that as F increases, modulations required for detection generally increase, the ability of the
display to pass the modulation decreases, and detection is no longer possible for higher
harmonics as indicated by the No responses in the tables.
The CTF values found in Appendix A were determined from Figure 3, which shows the
CTFs for different display Iuminance backgrounds found by van Meeteren et al. (1968) as
43
reported by Snyder (1980). The CTF for 0.10 cd/m2 was used based on the DL levels used in
this study.
The half amplitudes (cd/m2) are listed at the end ot Appendix A so that exact Iuminance
values can be replicated. Note that the ao value (or DC levels) are included in the Appendix for
each A x DL condition.
Human Performance Apparatus and Stimuli
Imaging system. The imaging system was the same as that described in the Measurement
Apparatus section. A Microsoft Systems mouse was used as an input device and was connected
to the IBM-PC AT.
Random search task stimuli The map pattems and symbols were generated by the OPIX
video signal generator. There were 26 U.S. Army symbols constructed in an 11 x 15 matrix size,
as shown in Hgure 13. The 11 x 15 matrix subtended 19 x 26 arcminutes of visual angle. Numbers
were used as identification tags for the symbols and were created in the upper case 11 x 15
Lincoln-MlTFlE font. The map pattems were generated by an algorithm which drew lines on the
display in a pseudo-random fashion. The lines were 1 pixel wide. Figure 14 is an example ot a
map with symbols. The symbols and maps were presented at a bit level ot 65 which oorresponded
to a Iuminance level ot approximately 4.13 cdlmz. Note, however, that the symbol Iuminance was
added to the DL levels so symbol and map Iuminance values were actually higher. When the
nonunitormities were also added, the Iuminance of the symbols increased more when the symbol
fell on the light portion ot a cycle than when they tell on a dark portion of a cycle. The modulations
ot the symbols and maps varied tor each DL level. For the 1-D conditions the modulations were
approximately 0.998, 0.992, and 0.951 tor DL-1, DL-2, and DL-3, respectively. For the 2-D
hh
Rgure 13. Random search task symbolsR
46
conditions the modulations were approximately 0.989, 0.992, and 0.849 for DL-1, DL-2, and DL-
3.
The nonuniformity pattems were created using the function generators. The parameters
of F, A, G, and DL were sent fo the function generators via the GPIB bus system from the IBM-PC
AT.
Magnitude esfimafion task stimuli. Stimuli consisted of the nonuniformity patterns
generated by the function generators and were the same as those used in the search task. Map
and symbol information were not displayed. Figures 15 through 17 are examples of six
nonuniformity patterns. These patterns represent the SINE, SQ, and TRI wave shapes at an F of
4 c/dw, for 1- and 2-D. Note that the photographs are high contrast examples and do not reflect
the true (lower) modulations displayed on the CRT.
Human Performance Procedure.
At the beginning of each experimental session the display was calibrated using the
CS100 spot photometer. The luminance of the display at each DL level was checked with the
input from each function generator and the HLG. The nonuniformity pattems were also checked
at each spatial frequency to be sure that all generators functioned property. Ambient illumination
was set to produce approximately 0.20 cd/m2 luminance on the back wall.
During the first day of an experimental session, subjects read and signed an informed
consent form. At the beginning of each session the instructions were read aloud by the
experimenter. Instructions for both tasks are listed in Appendix B. Subjects were seated in front
of the display and the height and distance of their chair were adjusted. On the first day subjects
participated in 10 practice trials to become familiar with the procedures.
50
Random search task. Before beginning the experimental sessions, the symbols were
presented on the screen and subjects were given five minutes to become familiar with the
symbols. This also gave subjects a chance to dark adapt. At the beginning of each trial a prompt
was displayed on the screen which stated ”Ready, the next target is _l", with the search
target cüsplayed. When subjects were ready to begin searching they pressed the button on the
mouse input device and the map, 26 symbols, and nonuniformities were displayed. All symbols
were randomly placed on the screen. Symbols and map lines never overlapped. After locating
the target, subjects pressed the mouse button and the nonunlformity and symbols were
removed. A symbol identification (ID) number was displayed in the area to the right of each
symbol position. Subjects reported the symbol ID which corresponded to the target symbol they
had found. The ID number was randomly selected for each symbol during each trial so that
subjects could not memorize a specific ID number associated with a specific symbol. Subject
responses were input to the computer by the experimenter. Responses were timed from the ·
onset of the first button press to the second button press using the IBM-PC clock function. The
clock had a resolution of plus or minus 55 ms. There were 5 trials per condition, resulting in 1260
trials per subject. All trials were presented in random order.
Magnitude estimation task. After reading the instructions subjects were dark adapted for
five minutes. At the beginning of each trial a READY prompt was displayed. When subjects were
ready to give their perceived uniformity ratings they pushed the button on the mouse input
device and a nonunlformity pattern was displayed. Subjects were given as much time as they
needed to report their ratings. The ratings of perceived uniformity were input to the computer by
the experimenter. There were two trials per condition, resulting in 756 trials per subject. All trials
were presented in random order.
RESULTS AND DISCUSSION
Random Search Task
For each subject, the mean of the five trials per condition was calculated and used in
subsequent analyses. Analysis of variance (ANOVA) procedures were then performed on the
dependent variables search time (ST) and percentage of correct responses (CR) over the five
trials/condition using the Statistical Analysis System (SAS, version 5.18) on an IBM 3090. Post-
hoc simple-effect F-tests were performed to evaluate significant interactions, and the Newman-
Keul comparisons test was performed to compare means.
Search time. Results of the 7 x 6 x 3 x 3 x 2 (F x A x DL x G x DIM) repeated—measures
mixed factorial analysis of variance (ANOVA) are listed In Table 6. G was treated as a between-
subjects variable and all other variables as within·subjects. Discussed below are two third·order
effects (F x A x DIM, DL x G x DIM), one second-order effect (A x DIM), and the main effect of DL.
Figure 18 illustrates the F x A x DIM Interaction (p-
0.0562). The results of a simple-
effect F—test by DIM are shown in Table 7. The F x A Interaction is significant (p= 0.0422) tor the 1-
D condition; however, even for the 1-D level, it is difficult to Interpret the F x A Interaction. Higher
levels of A do not necessarily result In longer STs, nor Is there any pattem to the F effect.
Figure 19 shows the DL x G x DIM Interaction (p = 0.0303). This figure illustrates that for
both the 1- and 2-D conditions, STs were faster for SINE waves than for TRI or SQ waves. Also,
as DL Increased, ST in general decreased. A sImpIe—effect F·test (Table 8) Indicated no signiticant
G x DL Interaction for either DIM. Table 9 lists the results of simpIe—effect F-tests for DL x DIM at
each G. A significant Interaction between DIM and DL for the SQ wave was Indicated. For the 2-D
SQ wave there appears to be little difference among the three DL levels, although there is a slight
51
52
Table 6Analysis of Variance Summary Table for Search Time
Source of Variance df MS F p
Gradient (G) 2 1328412.88 1.20 0.3355Subjects(S/G) 12 1109011.59
Frequency (F) 6 18796.59 1.53 0.1793F°G 12 11253.70 0.92 0.5332F*Sub(G) 72 12250.62AmpIitude(A) 5 6034.79 0.38 0.8617A°G 10 9935.24 0.62 0.7886A°(S/G) 60 15956.35Display luminance (DL) 2 255152.94 8.50 0.0016DL°G 4 10562.03 0.35 0.8403DL'(S/G) 24 30033.82
DIITIQHSIOH (DIM) 1 21.24 0.00 0.9786DIM°G 2 1008.81 0.04 0.9650DIM‘(S/G) 12 28218.21F'DL 12 17338.27 1.00 0.4523F°DL°G 24 20420.41 1.18 0.2721F‘DL°(S/G) 144 17342.08
F‘A 30 24707.93 1.34 0.1144F'A°G 60 21500.02 1.16 0.2024F°A‘(S/G) 360 18459.40
F°D|M 6 14029.49 0.81 0.5675F*D|M'G 12 15688.06 0.90 0.5482F°D|M‘(S/G) 72 17374.20
53
TABLE 6 (CONT)
Source of Variance dt MS F p
A’DL10 27014.62 1.68 0.0920
A'DL°G 20 19412.38 1.21 0.2577A°DL'(S/G) 120 16038.59A°D|M 5 37736.41 2.29 0.0568A"D|M°G 10 22369.62 1.36 0.2218A°D|M°(S/G) 60 16470.07DL'D|M 2 1689.47 0.14 0.8666DL‘DIM'G 4 37648.55 3.21 0.0303DL°DIM°(S/G) 24 1 1729.84F‘A'DL 60 15240.46 0.85 0.7800F°A°DL°G 120 16905.46 0.94 0.6454F°A‘DL'(S/G) 720 17898.35
F'A‘D|M 30 24075.10 1.47 0.0562F’A°D|M'G 60 21257.72 1.30 0.0792F‘A°DIM"(S/G) 360 16370.53A'DL°DIM 10 21057.11 1.21 0.2912A'DL°DIM'G 20 16507.27 0.95 0.5282A'DL°DIM°(S/G) 120 17398.84DL‘D|M°F 12 15593.40 0.88 0.5683DL'D|M‘F”'G 24 16486.60 0.93 0.5606DL"D|M‘F‘(S/G) 144 17711.19
F'A°DL°D|M 60 18315.08 1.09 0.3082F°A'DL"D|M‘G 120 17692.60 1.05 0.3481F'A'DL'D|M‘(S/G) 720 16837.33
Total 3779
sh
1-D
4.8A il- A-04.6 A-1g “
—-•·—A·2
8 4.4 —•— A-3g E _^ ' 1l— A·4~·· 4.2 A-sQ'I_§4.0 I·/r-67:1 /4: 3.8 '9n .
3 3.6U)3.4
0 100 200 300
Frequency (c/dw)
2-D4.8
7; A UIIU A-0U 4.6 V U•— A-18 —¤— A-29 4.4 ·‘ —•—-A~3cg /Ä —¤— A~4
"4_2
A-5
I':"°
n' WI \ .|‘,,..: 3.8 Y _
.
Hn
ri
8 3.6UI
3.40 100 200 300
Frequency (c/dw)
Figure 18. The F x A x DIM imeraction for search time.
55
TABLE 7
SimpIe~Effect F-tests for F x A for One and Two Dimensions - Search Time
Source of Variance df MS F p
FxAfor1-D 30 24915.77 1.52 0.0422
FxAfor 2-D 30 2386.72 0.14 1.0000
FxAxD|Mx S/G 360 16370.53
56
1'D
A 4.6Q
——o- 3345r: 4.4 —¤·—· TRI3
——¤— 33Q) 4.2¤ 4.0E" 3.88
·
8 3.40 1 2 3 4
DL
2-D4.6
1;* ——<>— SEE 4.4 -—•— TRI8
*-IT ä
0 4.2QQ 4.0
EI" 3.8SE 3.600‘”
3.40 1 2 3 4
DL
Figure 19. The G x DL x DIM Interaction for search time.
57
TABLE 8
Simple-Effect F-tests for DL x G for One and Two Dimensions · Search Time
Source of Variance df MS F p
DLxGfor1-D 2 27710.47 2.36 0.1160DLxGfor2-D 2 20500.11 1.75 0.1952DLxD|MxS/G 24 11729.84
58
TABLE 9
Simple-Effect F-tests for DL x DIM for Each Gracüem · Search Time
Source ot Variance dt MS F p
DLx DIM for Sina 2 6195.99 0.53 0.5953DLx DIM for Square 2 43503.28 3.71 0.0394
DLx DIM forTriangIe 2 27287.29 2.33 0.1189
DLx DIM x S/G 24 11729.84
59
increase in ST from DL-2 to DL·3. For the 1-D case ST decreased as DL increased. For the SO
wave the highest level of DL for the 2-D condition did not decrease ST probably because the
nonuniformity pattem was beginning to interfere with performance, reducing the benefit of higher
DL levels.
The A x DIM interaction is shown in Figure 20. STs were longer for the 1-D condition in all
but two of the A conditions, A-0 and A-4. Table 10 lists the results of F-tests by A. There is a
significant difference between DIMs for the A-4 condition only. There are no significant
ditferences among A levels for either of the two DlMs.
The main effect of DL is illustrated in Figure 21. ST decreased as DL increased. Table 11
lists the result of a Newman-Keuls test. DL-1 resulted in significantly slower STs than DL-2 or DL-
3.
Results of this analysis indicated that the effect of nonuniformities on search time is
negligible. Subjects were able to perform the task with little interruption in search time
performance. The nonuniformities altered the appearance of a background to the task information
rather than causing an interlerence in the acquisition of task information. Only two effects
appeared consistent. An interaction among G, DL, and DIM indicated that the SQ and TRI waves
were more degrading to ST performance than the SINE wave. A possible explanation may be that
because the modulations of the SQ and TRI wave fundamentals are higher than the SINE; thus,
they are more distracting to subjects. A contributing factor is probably the visible "edges'° of these
waveforms at lower spatial frequencies (Appendix A). The effect of DL was also consistent. DL-1
resulted in slower search times.
Correcf responses. An analysis of variance (ANOVA) on the percentage of correct
responses (CR) was performed and the results are listed in Table 12. The DL x DIM interaction
60
4.2A —-¤— A·0
A-1: —-•— A·2g 4.1 —•.
A.3ä
—•— A·4v —¤-— A-5
°4.oE
I-S2 3.9QGIlb
3.81-D 2-D
Dimension
ügure 20. The A x DIM Interaction for search time.
61
TABLE 10
Simple-Effect F·tests tor DIM at Each Amplitude — Search Time
Source ot Variance df MS F p
DIM at Amplitude 0 1 9192.07 0.56 0.4572
DIM at Amplitude 1 1 48444.25 2.94 0.0916
DIM at Amplitude 2 1 8899.59 0.54 0.4653
DIM at Amplitude3 1 1914.40 0.11 0.7413
DIM at AmpIitude4 1 96134.28 5.84 0.0187
DIM at Amplitude 5 1 24118.72 1.46 0.2317
Ax DIMx S/G 60 16470.07
62
4.3
TE·¤ 4.2G
80 4.1UIü
¤ 4.0.§I-
3.9S0ln$ 3.8U)
3.70 1 2 3 4
DL
Hgure 21. The effect of DL on search time.
63
TABLE 11
Newman-Keuls Compaiisons for Display Luminance · Search Time
Meanßltst (Sl0 4.22 A
1 4.05 B
2 3.93 B
Note: Means aocompanied by the same letter are not significantly different, p Z .05
64
TABLE 12
Analysis of Variance Summary Table for Correct Flesponses
Source of Variance dl MS F p
Gfadiéflf (G) 2 0.1298 0.71 0.5108Subjects within Gradient (S/G) 12 0.1826
Frequency (F) 6 0.0123 2.10 0.0636F'G 12 0.0047 0.81 0.6393F"(S/G) 72 0.0059Amplitude (A) 5 0.0054 0.95 0.4571A"G 10 0.0020 0.34 0.9648A°(S/G) 60 0.0057DL 2 0.0200 2.61 0.0941DL"G 4 0.0002 0.03 0.9981DL°(S/G) 24 0.0077Dimension (DIM) 1 0.0018 0.43 0.5236DIM'G 2 0.0013 0.32 0.7344D|M‘(S/G) 1 2 0.0041F‘DL 12 0.0058 1.38 0.1836F°DL°G 24 0.0031 0.72 0.8202F'DL'(S/G) 144 0.0042
F‘A 30 0.0049 0.98 0.5038F°A°G 60 0.0062 1.23 0.1307F'A'(S/G) 360 0.0051F’D|M 6 0.0039 0.82 0.5607F°DIM°G 12 0.0060 1.25 0.2671F°D|M"(S/G) 72 0.0048
65
TABLE 12 (CONT)
Source of Varlance df MS F p
A'DL 10 0.0032 0.69 0.7339A°DL"G 20 0.0048 1.03 0.4368A‘DL‘(S/G) 120 0.0047A*D|M 5 0.0079 1.43 0.2279A°D|M'G 10 0.0035 0.63 0.7821A°D|M*(S/G) 60 0.0055DL°D|M 2 0.0156 3.05 0.0659DL°D|M*G 4 0.0059 1.16 0.3549DL'DlM°(S/G) 24 0.0051F'A'DL 60 0.0050 0.90 0.6860F‘A'DL°G 120 0.0062 1.13 0.1803F°A'DL°(S/G) 720 0.0055F*A"D|M 30 0.0062 1.25 0.1768F"A"DlM°G 60 0.0059 1.19 0.1709F*A"D|M°(S/G) 360 0.0050A*DL'DIM 10 0.0058 1.16 0.3279A°DL'D|M"G 20 0.0046 0.92 0.5650A‘DL‘D|M°(S/G) 120 0.0050DL‘DIM°F 12 0.0056 1.05 0.4073DL"D|M°F"G 24 0.0056 1.05 0.4072DL°D|M°F'(S/G) 144 0.0053F°A'DL°D|M 60 0.0051 0.97 0.5407F°A'DL'DlM'G 120 0.0050 0.95 0.6271F'A*DL°DlM*(S/G) 720 0.0053
Total 3779
66
(p= 0.0659) is illustrated in Hgure 22. F-tests by DIM were performed and the results are in Table
13. No significam differences between DIMs were obtained, as might be expected from the p-
value of the DL x DIM interaction.
The main effects of DL (p-
0.0941) and F (p = 0.0636) are illustrated in Figures 23 and
24, respectively. As DL increased, the mean CR increased and the increase in performance is
consistent with ST data. The effect of F indicated a dip in CRs at 32 c/dw; however, the nature of
this function is not meaningful. Since both effects have somewhat high p·values and show very
small percent correct response differences, they should probably be ignored.
CR was not expected to be a highly sensitive measure because subjects were asked to
search umil they found the target; therefore, few errors were made.
Target confusrbn. The symbols used in this study were U.S. Army symbols which were
originally designed for hard copy. Many of the symbols were very similar, with single lines or dots
used to represent the differences among the symbols. Therefore, errors may not have been a
function of the nonuniformities, but of confusion among symbols. Errors were analyzed in terms
of confusion among symbols. lf the errors were due to the introduction of nonuniformities the
confusions should be random. Table 14 shows the target confusion matrix. It is obvious that
certain symbols were confused with other symbols consistently. Redesign of these symbols is
recommended if they are to be used for specific applications.
Random Search Conclusions
Nonuniformities were found to not significantly impact random search performance.
Subjects were able to perform the task with no degradation even with the added nonuniformities.
The lack of performance differences may be explained by several factors. First of all, the
luminances of the nonuniformities were added to the symbol luminances; therefore, the symbol!
67
100
2tn ·—¤—— DL—1§ 99 —•— ou.-23- '*l*' DL-30°’¢
98tl00L'°
97O•-•
5 96Qh00.
951 ·D 2-D
Dlmenslon
Egure 22. The DL x DIM Interaction for percentage of correct responses.
68
TABLE 13
Simple—Effect F·tests for DIM at Each Display Luminance - Correct Flesponses
Source of Variance df MS F p
DIM for Display Luminance 1 1 0.0249 1.60 0.2180
DIM for Display Luminance 2 1 0.0081 0.52 0.4778
DIM for Display Luminance 3 1 0.00003 0.0019 0.9656
Dx DIMxS/G 24 0.00156
69
100
3tn 99CQ13g 98i0°h
SO 97Ol!C02 96Q0.
951 2 3
DL
Figure 23. The effect of DL on percentage of correct responses.
70
100
Cb0UI§ eeEUI0E
3 980L nu- „ .„0O*6 97 U
U!0•e
E es0a-0E
950 1 00 200 300
Frequency (c/dw)
Figure 24. The effect of F on percentage of correct responses.
71
TABLE 14.Symbol Confusion Matrix. Table Entries are Number ol lnoorrect Response:.
Repenee1 2 3 4 5 6 7 8 91011121314151617181920212223242526
Target
1 0 2 2 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 5 O 0 02 9 0 0 4 1 1 0 1 0 O 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 03 2 0 0 7 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 26 O 04 0 3 6 0 0 0 0 1 0 0 0 0 O 1 0 1 0 0 0 0 0 0 0 0 0 O5 0 0 1 1 0 3 6 0 O 0 1 0 0 0 0 0 0 0 0 0 O 0 0 0 8 06 0 1 0 0 2 0 0 6 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 07 0 0 0 0 4 0 0 3 0 1 0 0 0 0 0 0 0 0 O 0 0 0 0 3 0 218 0 0 0 4 O 1 1 4 0 0 1 0 0 0 0 0 O 0 0 0 0 0 0 0 1 0 09 0 0 0 0 0 1 0 0 O 6 0 0 0 0 O 0 2 0 0 0 0 0 0 0 0 O10 0 0 0 0 0 1 0 0 9 0 1 0 1 0 0 0 0 1 O 0 0 1 0 0 1 01 1 0 0 O 0 0 0 0 0 0 0 0 26 2 1 0 0 0 0 0 0 0 0 0 0 0 01 2 0 O 0 1 0 0 0 0 0 0 1 0 0 0 3 1 1 0 0 0 1 0 1 0 1 O 01 3 1 0 1 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 0 014 0 3 1 0 0 O 0 0 0 0 1 0. 1 2 O 0 O 0 0 0 0 0 1 0 0 0 01 5 0 0 0 0 0 O 0 0 0 0 1 0 0 O O 1 2 2 1 0 0 0 0 0 1 0 01 6 0 0 0 0 0 0 0 0 0 0 1 0 0 1 22 0 1 8 0 0 0 0 0 0 1 01 7 0 0 0 0 0 0 0 1 0 0 1 0 0 0 4 2 0 9 0 0 0 0 0 0 0 018 0 O 0 1 0 0 0 0 O 0 0 O 0 1 0 9 1 9 0 0 1 0 0 1 1 0 01 9 0 0 0 0 0 O 0 0 0 O 0 0 0 0 0 0 0 0 0 1 2 6 1 0 1 0 020 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 1 10 0 1 1 1 0 1 0 021 0 0 0 0 1 0 1 0 1 0 0 0 0 0 0 O 2 0 7 0 0 1 2 0 0 0 022 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 5 2 1 8 4 0 0 0 0 023 8 1 O 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 O 3 0 O24 0 0 27 1 0 1 5 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 O O25 0 0 0 1 4 5 1 0 O 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 426 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 2 1 0
w
72
background modulations were always above recommended (e.g., ANSI, 1988) levels. That is, the
nonuniformities did not degrade the symbol modulation. Also, the nonuniformities were
systematic and had the appearance of a background to the map and symbols. Perhaps subjects
were able to ignore the nonuniformities. lf nonuniformities were random it may have been more
difficult to visually separate the nonuniformities from the symbols.
Another possible explanation is that the nonuniformities, which can be considered as
noise, were always at spatial frequencies below the spatial frequency of the targets and maps
which were one pixel wide; therefore, masking effects did not occur.
Although subjects were able to perform the search task in the presence of
nonuniformities, many subjects commented that the nonuniformities were annoying and
fatiguing. Some subjects also commented that the SINE wave shapes were blurry. Long term
performance with a display which exhibits nonuniformity levels used in this study may induce eye
fatigue and strain over many hours.
Tasks which require extraction of information from a literal image where gray scale is used
to present picture details (for example, a digitized picture) may be more sensitive to
nonuniformities. ln these tasks, the nonuniformities may not appear as a background, but as an
intemiption in the cominuity of the image.
Magnitude Estimation Task
For this task the free-modulus technique was employed. The free-modulus technique
allows subjects to select their own scale to describe the stimuli presemed. The data are then
transformed to place ratings of perceived uniformity on the same scale. The data were
transformed using the method described by Kling and Fliggs (1971); this method is presented in
Appendix C. Before scaling, a constant of 101 was added to each rating of perceived uniformity
73
for all subjects to bring the range into the positive domain. The range of the subject mean
perceived uniformity scores was 11 to 301. These values were used in the analyses.
After scaling, two separate analysis of variance (ANOVA) procedures were performed.
One analysis included the A-0 condition which was a baseline; that is, nonuniformities were not
presented (other than those inherent in the display itself). The baseline was an important variable
which gave an indication of how far from a uniform screen the subjects estimated the
nonuniformities to be. It also served as a check to the reliability of subjects' perceptions. Subjects
would be expected to rate the A-0 condition the same throughout the study. In addition, an
analysis without the baseline was included because it was often difficult to determine whether
significant effects were being unduly weighted by this A-0 condition. Results of both analyses are
presented below.
Results with baseline. Results of the ANOVA are shown in Table 15. Results indicated a
significant fourth·order interaction (F x A x DL x DIM), four significant third-order interactions (F x A
x DL; F x A x G; F x G x DL, F x G x DIM), and six significant second-order interactions (F x A; F x
DL; F x G; A x G; G x DL; A x DL). All main effects were significant and will be discussed in the
context of the interactions to avoid redundancy. Post~hoc simple-effect F-tests and Newman-
Keuls comparison tests were conducted to further evaluate significam effects.
The F x A x DL x DIM interaction is illusfrated in Hgure 25. This interaction is divided into
three three-way interactions for presentation. Note that large values of perceived uniformity
indicate that subjects rated the condition as being more uniform in luminance. Simple-effect F-
tests were conducted on each variable and are listed in Tables 16 through 19.
The A x DL x DIM interaction is significant for the 128 c/dw condition only. In Figure 25,
comparing the 1- and 2-D conditions at DL·1 and DL-2, the ranges in perceived uniformity across
74
TABLE 15
Analysis ot Variance Summary Table for Magnitude Estimation, Baseline Included
Source ot Variance df MS F p
Dimension (DIM) 1 1635.74 0.27 0.6098Subjects within Dimension 28 6138.68
(S/DIM)
Frequency (F) 6 131604.13 20.65 0.0001F’D|M 6 977.33 0.15 0.9882F°(S/DIM) 168 6373.91
Amplitude (A) 5 157289.88 23.78 0.0001A°D|M 5 395.01 0.60 0.7011A‘(S/D|M)) 140 6613.07Display Luminance (DL) 2 24568.34 23.68 0.0001DL°DlM 2 133.77 0.13 0.8793DL'(S/DIM) 56 1037.70G 2 18723.40 11.42 0.0001G‘DIM 2 3518.10 2.15 0.1266G'(S/DIM) 56 1640.00
F'DL 12 1057.84 7.60 0.0001F°DL'D|M 12 73.35 0.53 0.8971F°DL°(S/DIM) 336 139.33F°A 30 5774.28 17.07 0.0001F"A‘DIM 30 272.26 0.80 0.7632F°A‘(S/DIM) 840 338.36F'G 12 1776.56 7.72 0.0001F‘G°D|M 12 394.55 1.71 0.0624F°G°(S/DIM) 336 230.24
75
TABLE 15 (CONT)
Source ot Varlance dl MS F p
A*DL 10 1714.34 17.76 0.0001A‘DL'D|M 10 34.03 0.35 0.9653A°DL'(S/DIM) 280 96.52A‘G 10 827.41 7.44 0.0001A°G°DIM 10 161.81 1.46 0.1557A'G‘(S/D|M)) 280 11 1.14DL'G 4 464.07 6.30 0.0001DL'G‘D|M 4 51.28 0.70 0.5964DL'G°(S/DIM) 112 73.71F*A"DL 60 70.34 21.4 0.0001F*A'DL'D|M 60 47.68 1.45 0.0151F°A°DL'(S/DIM) 1680 32.92F'A‘G 60 116.10 3.33 0.0001 ‘
F*A‘G'DIM 60 41.68 1.19 0.1497F‘A'G°(S/DIM) 1680 34.90
A°DL'G 20 32.73 1.31 0.1639A°DL'G°D|M 20 20.21 0.81 0.7023A°DL°G°(S/DIM) 560 24.94DL‘G'F 24 50.54 1.75 0.0153DL'G‘F‘D|M 24 29.26 1.01 0.4478DL°G‘F°(S/DIM) 672 28.92F°A°DL’G 120 24.34 1.06 0.3080F*A‘DL'G°D|M 120 26.38 1.15 0.1285F‘A*DL'G'(S/DIM) 3360 22.93
Total 11339
76
DL·1; 1-D
160>•2E*6 150
140 .·¤ 'QGQ Ä·0
'ö 130 / "*‘* ^·2U ; Z ?•-A3•-{
I/. ——|-A4
120 A-5Q .G)
= 1100 100 200 300
8) Frequency (c/dw)
DL-1; 2·D
160>•.2E . « .....2- -5 150 F .2Q .
140 _/’A•0
Z Ä KO- A•18 1:-10 V _ , *'* ^·2A~3¤- Vj V ; -I—
A-4
8: 120 F;} —°" ^'5N
•
°
•
E•
1100 1 00 200 300
b) Frequency (c/dw)
Hgure 25. The F x A x DL x DIM Interaction for mean perceived uniformity. a) DL-1, 1-D
b) DL-1, 2·D c) DL-2, 1-D d) DL-2, 2-D e) DL-3, 1-D f) DL·3, 2-D.
77
DL•2; 1-Ü
160>•1:E*• 1506 ,„„ ,, „ .1P: 1 L
140 //-·¤ ./Q 1 —¤— A-0E 130
—•-—· A-1E _/ . —¤-— A-20 _
-—•-- A3¤' A-4F A-s6 J'
1100 100 200 300
c) Frequency (c/dw)
DL·2; 2-Ü
>. 1602E . .,3 150
“ ‘.
P:
1402,2. —¤— A.0
— -—I-— A-2¤. '
·-—•—- A-3
c 120 ——•— A-4A-5E 110
11
0 100 200 300
d) Frequency (c/dw)
Figure 25 cont.
T8
DL·3;1~D'
EL
§ 150 ...4.. ¤ „ „ —C
= .U1400·2
3 100 _ .“°“‘
^·°A•1
A·2c 120 ' *°" ^·30 uf: —•—
A4°
L' —¤— A-5E110
0 100 200 300e) Frequency (c/dw)
160
0 1507; .
g140 _
E .„/T5 13;;
I*|—
A-0ä l
‘ A•1¤_. ' ".*' A·2
120 ^·3S . [ —•—
A40 -0- A.5E 1100100 200 300
0 Frequency (c/dw)
Figure 25 cont.A
79
TABLE 16
Simple-Effect F-tests for A x DL x DIM at Each Frequency — Magnitude Estimation
Source of Variance df MS F p
A x DLx DIM 1or4cycIes/dsplay 10 17.03 0.52 0.8771
Ax DLx DIM for8 cycles/display 10 49.39 1.50 0.1332
A x DL x DIM for 16 cycles/dsplay 10 40.31 1.22 0.2729
A x DL x DIM for 32 cycles/display 10 16.54 0.50 0.8909
A x DL x DIM for 64 cycles/display 10 46.52 1.41 0.1696
A x DL x DIM for 128 cycles/display 10 127.31 3.87 0.0003
A x DL x DIM for 250 cycles/display 10 22.98 0.70 0.7271
A x DL x F x (S/DIM) 1680 32.92
80
TABLE 17
Simple-Effect F-tests tor F x DL x DIM at Each Amplitude - Magnitude Estimation
Source ol Variance df MS F p
Fx DLx DIM for Amplitude 0 12 5.44 0.16 0.9951
Fx DLx DIM torAmplitude1 12 44.51 1.35 0.1836
Fx DLx DIM for Amplitude 2 12 34.16 1.04 0.4086
Fx DLx DIM for Amplitude3 12 62.93 1.91 0.0292
Fx DLx DIM for Amplitude4 12 75.76 2.29 0.0069
Fx DLx DIM forAmpIitude5 12 90.32 2.74 0.0011
Fx DLxAx S/DIM 1680 32.92
81
TABLE 18
SImpIe·Ef1ect F-tests for F x A x DIM at Each Display Luminance - Magnitude Estimation
Source of Variance df MS F p
FxAx DIM for DL-1 30 81.53 2.48 < 0.0001FxAx DIM for DL -2 30 118.07 3.59 < 0.0001FxAxD|MforDL·3 30 168.01 5.10 < 0.0001FxAx DLxS/DIM 1680 32.92
82
TABLE 19
Simp|e—Effect F-tests for F x A x DL for One and Two Dimensions ~ Magnitude Estimation
Source of Variance df MS F p
FxAxDLfor1-D 60 59.50 1.81 0.0002FxAxDLfor2-D 60 58.51 1.78 0.0003FxAx DLxS/DIM 1680 32.92
83
the differem levels of A (at 128 c/dw) are smaller for the 1-D condition. This difference in range is
not apparent at DL·3. As previously discussed, the DL levels for the 2-D condition are higher
than those for the 1-D condition and may be oontributing to this effect. Results of the F x DL x DIM
tests by A, listed in Table 17, indicate that this interaction is signiflcant for A·3, A-4, and A·5. The
F·tests by DL and DIM indicate that all interactions are significant for these variables. Therefore,
these tests add little to describing the effect.
In general, the fourth-order effect described above indicates the following general trends
in the data.
(1) As F increased, perceived uniformity increased; that is, subjects reported
that the display appeared more uniform, irrespective of levels of DIM and A.
(2) As A increased, perceived uniformity decreased.
(3) As DL increased, perceived uniformity decreased.
(4) At A·0, no differences existed, thus proving the constancy of the 'control"
condition.
The F x A x DL interaction is illustrated in Figure 26 and is represented as three two—way
interactions. F-tests by DL are presented in Table 20. Results indicated that the F x A interaction
was significant at each level of DL. F-tests by A are presented in Table 21. The F x DL interaction
was significant for all but the baseline condition, indicating that the baseline may be causing this
triple interaction to reach significance. This issue is explored in the next analysis. Results of the
interaction are the same as those for the four·way interaction discussed previously; that is, as F
increases perceived uniformity increases and as A and DL increases perceived uniformity
decreases.
Figure 27 lllustrates the F x A x G Interaction and is presented as three two-way
interactions. Results of F-tests at each A are listed in Table 22. The F x G interaction was
8h
>_ DL-1.: 160
A·Org 150 = 1 _ *°" 2-·‘€ ,///
""·'* 2:6 A . _,.1, 1w —•- ÜA-5E =¤¤ .//°a. 1/.N *,3-/“
120 [°*ä -'0*
Mo 100 200 300Fr•qu0ncy(cldw)
>_ DL·2ä 160nö 1N—• A-0: 160 1 *°* ^"C ——•— A-2=’
/” —-•-— A-6
A4A-5E *=·=· I// 1
.1 120;.%/.§ _··
3 1105 0 100 200 600Fr•qu0ncy(c/dw)
B DL-3g 160*6
—•··—A-0
=·1 10-• A·1
S150 —•— A-2
/-—•- A-:}g M / -•- A6
E” _ ?Q—•
A·5g1606,/
IL 120 n _/=
E 0 100 200 600Fr0qu•n0y(c/dw)
Hgure 26. The F x A x DL interaction for mean perceived unif0rmity.
85
TABLE 20
SimpIe·Ehect F-tests for F x A at Each DL - Magnitude Estimation
Source of Variance df MS F p
FxAfor DL—1 30 2148.04 65.25 < 0.0001F x Afor DL-2 30 1996.52 60.65 < 0.0001
FxAfor DL·3 30 177041.00 53.78 < 0.0001
FxAxDLxS/DIM 1680 32.92
86
TABLE 21
Simple-Effect F·tests for F x DL at Each Amplitude · Magnitude Estimation
Source of Variance df MS F p
Fx DL for Amplitude 0 12 5.44 0.16 0.9995F x DL for Amplitude 1 12 328.65 9.98 <0.0001F x DL for Amplitude 2 12 302.74 9.20 <0.0001Fx DL forAmp|itude3 12 210.71 6.40 <0.0001F x DL for Amplitude 4 12 274.79 8.35 <0.0001F x DL for Amplitude 5 12 287.22 8.73 <0.0001
FxDLxAxS/DIM 1680 32.92
87
SINE;~ 100E ·—•— A-0* 150 ~ ·-•— A-1
:» 140 —•-— A-:·—•—#4
E 1¤¤ g —•— A-0ä .
„ 1103z 100 0 100 200 :00
Fr•qu0ncy(c/dw)
TRIANGLEG? 160E —•·— A-0g 150 —•— A·1= ·
—•— A·2S 140 —•— A-:—•— #4
ä 1//'s12¤H-¤ 110IO’
100 0 100 200 000Fr•qu•ncy(c/dw)
SQUARE;· 100E —•— A-0E
15O 2G +1 A,-1
S 140 —•—.1}- A-415 1=¤ 5/ -„- M
E 120 '/ '&
;*-’G 110 _·
= 100’0 100 200 :00
Frequency (c/dw) ‘
Hgure 27. The F x A x G interaction for mean perceived uniformity.
88
TABLE 22
Simple-Effect F-tests for F x G at Each Amplitude · MagnitudeEstimationSource
ot Variance df MS F p
F x G tor Amplitude 0 12 3.68 0.11 0.9999Fx Gfor Amplitude1 12 471.42 13.51 < 0.0001F x G for Amplitude 2 12 520.65 14.92 < 0.0001F x G for Amplitude 3 12 582.20 16.68 < 0.0001F x G for Amplitude 4 12 439.78 12.60 < 0.0001F x G tor Amplitude 5 12 339.36 9.72 < 0.0001
FxGxAxS/DIM 1680 34.90
89
significant at all A levels except the baseline condition. Table 23 lists the results of F~tests across
F. The A x G interaction was significant at all but the two highest F levels, 128 and 256 c/dw.
Perceived unifomtity was lower for the SQ wave than for the SINE and TRI wave conditions. Also,
the range in perceived uniformity across A and F appears larger for the SQ condition. These
results are consistent with the research hndings of De Palma and Lowry (1962), who reported that
lower modulations were required to detect square waves at lower spatial frequencies because of
the higher amplitude of the fundamental frequency and because the harmonics of the square
wave contribute to detection when spatial frequencies are low. As spatial frequency increases
even higher levels of modulation are required for detection of the fundamental and harmonics.
The modulations of the harmonics are not high enough to contribute to detection in the 128 and
256 c/dw condition, as shown in Appendix A. At the higher spatial frequencies, the cuwes
converge simply because there is no appreciable visual discrirnination across the G or A variables.
Figure 28 illustrates the F x G X DL interaction which is presented as three two-way
effects. Simple-effect F-test results across F levels are listed in Table 24. The G x DL interaction is
not significant for the 128 and 256 c/dw conditions, which is consistent with the results discussed
above for the F x A x G interaction. Perceived uniformity is lower for the SQ wave at the lower
spatial frequencies. Perceived uniformity ratings for the SINE and TRI wave shapes are very
similar. The trends for F and DL are consistent with previous findings: as F increases perceived
uniformity increases and as DL increases perceived uniformity decrease.
Figure 29 illustrates the F x G x DIM (p = 0.0624), interaction presented as two second-
order effects. SimpIe·effect F-test results for the G x DIM contributions are listed in Table 25. The
G x DIM interaction is significant for 4, 8, and 16 c/dw. Perceived uniformity was lower for the 2-D
SQ wave at each of these F levels.
90
TABLE 23
Simple-Effect F-tests for A x G at Each Frequency - Magnitude Estimation
Source of Variance df MS F p
A x G for 4 cycles/display 1 0 675.66 19.36 < 0.0001
A x G for 8 cycles/display 10 341 .83 9.79 < 0.0001
A x G for 16 cycles/display 10 236.29 6.77 < 0.0001
A x G for 32 cycles/display 10 126.02 3.61 < 0.0001
Ax Gfor64cycIes/display 10 108.75 3.12 0.0006
A x G for 128 cycles/display 1 0 26.75 0.77 0.6580
A x G for 256 cycles/display 1 0 8.73 0.25 0.9908
Ax Gx FxS/DIM 1680 34.90
91
SINE150
gI
= 140¢3
E IN __ _-
E 1N¤3‘
1160 100 200 300
Fr•qu•ncy(c/dw)
TRIANGLE2: 150
E§146c
3
E ==•¤.1
•ß- 120c3l 110
0 100 200 300F1·•qu•ncy(c/dw)
SQUARE
2: 150Eg 140c3
E 130
E• Ih“·120 1
c2I s
1100 100 200 300
Frequency (0/dw)
Hgure 28. The F x G x DL Interaction for mean perceived unitormity.
92
TABLE 24
SimpIe·Effect F-tests for G x DL at Each Frequency - Magnitude Estimation
Source of Variance df MS F p
G x DL for 4 cycles/display 4 168.98 5.84 <0.0001G x DL for 8 cycles/display 4 69.27 2.39 0.0496G x DL for 16 cycles/display 4 128.65 4.45 0.0015
G x DL for 32 cycles/display 4 92.22 3.19 0.0131G x DL for 64 cycles/display 4 278.15 9.62 < 0.0001G x DL for 128 cycles/display 4 27.29 0.94 0.4402
G x DL for 256 cycles/display 4 2.72 0.09 0.9856
GxDLx Fx S/DIM 672 28.92
93
1-D150
g /g140cD
-
3 130 __
84.
8IhE120 1·__TRI
ä —•- m0E 110
0 100 200 300
Frequency (c/dw) ·
2'D>_ 150.2
1401:D·¤
/”
-3 130 __/·3 ——o— 555Q _ -·-t-- TRI¤~ 120 . —I·- $t:00E 110
0 100 200 300
Frequency (c/dw)
Hgure 29. The F x G x DIM Interaction for mean perceived uniformity. »
94
TABLE 25
Simple-Effect F-tests for G x DIM at Each Frequency - Magnitude Estimation
Source of Variance df MS F p
G x DIM for 4 cycles/display 2 2474.92 10.75 0.0003
G x DIM for 8 cycles/display 2 1480.81 6.43 0.0018
G x DIM for 16 cycles/display 2 1400.21 6.08 0.0025
G x DIM for 32 cycles/display 2 361.93 1.57 0.2096
G x DIM for 64 cycles/display 2 151.02 0.66 0.5175
G x DIM for 128 cycles/display 2 13.07 0.06 0.9417
G x DIM for 256 cycles/display 2 3.42 0.01 0.9900
GxFxS/DIM 336 230.24
95
Results of an F-test of F x G at each DIM are listed in Table 26. A significant F x G
interaction was found for the 2-D condition, indicating that there were no differences in perceived
uniformity for G shapes as a function of F for 1-D conditions. As illustrated in Figure 29, these
three G functions are very similar and parallel.
Table 27 lists results for F—tests of the F x DIM interaction, which is significant for each
wave shape. Perceived uniformity is lower for the 2-D wave shapes across F levels 4 - 64 c/dw,
with the largest difference occurring for the SQ wave. The differences in 1- and 2-D perceived
uniformity is very possibly an effect of DL differences, as described earlier.
Analysis ot the seoondbrder effects shows that the data trends are consistent. The F x A
interaction is signiücant and is illustrated in Figure 30. A Newman-Keuls comparison test was
performed on the A means at each F level and results are listed In Table 28. As A increases,
perceived uniformity decreases. As F increases, the curves converge and the number of
significant differences among A levels decreases. At 256 c/dw, there are no significant
differences in perceived uniformity as a function of A. At this level, subjects rated all A levels as
appearing the same in terms of their perceived uniformity. The modulations passed by the display
at this F are not high enough for subjects to determine differences among the A conditions, as
shown in Appendix A.
Figure 31 illustrates the F x DL interaction. There is a significant effect of DL at all F levels
except 4 c/dw. Newman-Keuls test results on the DL means at each F are reported in Table 29.
Perceived unifomrity at all three DL levels are significantly different from one another at all F levels
except 4 c/dw. As DL increases, perceived uniformity significantly and consistently decreases.
These results follow the shape of the CTF. The effect of DL is greater at the middle F levels. The
effect of DL decreases as F increases or decreases.
9 6
TABLE 26
Simple-Effect F-tests for F x G for One and Two Dimensions - Magnitude Estimation
Source of Variance df MS F p
FxGfor1-D 12 345.29 1.50 0.1221FxGfor 2-D 12 1825.81 7.93 < 0.0001Gx FxS/DIM 336 230.24
97
TABLE 27
Simple-Effect F-tests for F x DIM for each Gradient - Magnitude Estimation
Source of Variance df MS F p
Fx DIM for SINE 6 507.63 2.20 0.0427Fx DIM for SO 6 548.90 2.38 0.0289
Fx DIM forTFII 6 709.89 3.08 0.0060GxFx S/DIM 336 230.24
98
160
EE 150 · ‘b
°2:D 140¤
u
2-6
-I—A-0
E 130 *°"' ^·‘es —•— A·2°- - —•- A-65
_ —•— A4e 120 ‘ *‘°* ^·5D c
1100 100 200 300
Frequency (0/dw)
I'-Tgure 30. The F x A interaction for mean perceived uniformity.l
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al 139 ·—•— DL·2—•— DL·3
t: ,8 „.E
1200 100 200 300
Frequency (c/dw)
Hgure 31. The F x DL interaction for mean perceived uniformity.
101
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102
Rgure 32 illustrates the F x G interaction. Newman-Keuls comparisons for G at each F are
listed in Table 30. Perceived unitormity was significantly lower for the SQ wave at all but the two
highest F levels, 128 and 256 c/dw. Results are consistent with those previously discussed.
That is, at the higher F levels the modulations are not high enough for subjects to determine
differences among Gs.
The A x G interaction is presented in Rgure 33. Results of the Newman-Keuls tests are
listed in Table 31 and indicate that perceived unilormity was significantly lower for the SO wave
condition than either the SINE or TRI condition for all levels of A except the baseline condition, as
should be the case. Less modulation is needed to detect the SO wave, and the SO wave is
perceived as being more nonuniform than SINE or TRI waves. However, the imeraction between
A and G would not be significant if the baseline condition were not present. This will be disoussed
in the next section.
The G x DL interaction is shown in Hgure 34. Newman-Keuls results for G at each DL are
listed in Table 32. This effect also illustrates the differences among the SO, SINE, and TRI waves.
Again, the SQ wave results in significantly lower perceived unifcrmity ratings than the SINE or TRI
wave. Overall, as DL increases, perceived unitormity consistently decreases; however, the effect
that DL has on perceived unifcrmity is greater for SQ nonuniformities.
The A x DL interaction is shown in Rgure 35. Newman-Keuls test results are presented in
Table 33. Perceived unifcrmity was significantly different among all DLs at each A level other than
A-0. lt appears that this interaction reached signilicance because of the inclusion of the baseline
condition. For the baseline condition, DL-3 resulted in significantly higher estimations. That is,
subjects rated DL-3 as appearing more uniform than DL-1 or DL-2 when nonuniformities were not
present, perhaps because the Instructions stated that subjects were to rate how uniform in
103
150
E3 1402F ..D /'S “Z 130UQ SIE{ —•-
mnc 120 '—" QN0E
1100 1 00 200 300
Frequency (c/dw)
Figure 32. The F x G imeraction for mean perceived uniformity.
10h
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>•Lé -—o— SIE=-Q150G
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Amplitude
Figure 33. The A x G interaction for mean perceived uniformity.
106
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111
"luminance" the screen was. At lower DL levels they may not have detected "luminance," and so
gave lower ratings.
Summary. The above analyses indicate very strong trends in the data and results are
summarized below.
(1) As F increases, subjects report higher ratings of perceived uniformity; that is, they rate
the screen as appearing more uniform in lumlnance.
(2) In general, as A increases perceived uniformity decreases. At the highest F level
(256 c/dw), subjects' ratings of perceived uniformity are not significantly different among the A
conditions. At this F, the ability of the display to pass modulation is limited by the MTF of the
display. In addition, higher modulations are required for observers to detect higher frequencies.
Both these factors contribute to the reduced perceptions of the nonuniformities.
(3) As DL increases perceived uniformity decreases; that is, subjects report that the
pattems appear more nonuniform. At higher DL levels, less modulation is required for observers
to detect gratings.
(4) The effect of DL also interacted with F and effects can be modelled after the CTF. The
effect that DL has on perceived uniformity is greatest for the middle F levels, and decreases as F
either increases or decreases.
(5) There are no signiücant differences in perceived uniformity between the SINE and TRI
wave shapes. The SQ wave results in significantly lower ratings of perceived uniformity than the
SINE or TRI waves. That is, subjects rate the SQ wave as appearing more nonuniform. However,
the effect of the SQ wave on perceived uniformity is not significant at 128 and 256 c/dw. This
finding is consistent with that of De Palma and Lowry (1962), who found that lower modulations
are required to detect square waves at lower spatial frequencies. As previously discussed, this is
a function of the higher amplitude of the fundamental frequency for the square wave and the
contribution of the harmonics of the square wave. At higher spatial frequencies the harmonics are
112
at spatial frequencies that observers are unable to detect. Also, at these frequencies the display
cannot pass the modulations required for detection.
(6) The effect of DIM Is difficult to Interpret because of the confound with DL. The effect of
DIM statistically significant In only one Interaction, F x A x DL x DIM (p = 0.0063), and almost
reaches signiücance in the F x G x DIM imeraction (p = 0.0624). At DL-1 there was a difference In
the range of perceived uniformity ratings, as a function of A, between the 1- and 2-D conditions at
128 c/dw. This F level corresponds to 3.66 cycles/degree of visual angle where the eye Is most
sensitive. The difference between DlMs may actually be a function of DL rather than a difference
in the sensitivity to 2-D pattems.
Magnitude estimation results, baseline removed. An analysis of variance was conducted
on the same data with the baseline (A-0) removed. Results of this analysis are listed In Table 34.
This analysis revealed that the effects discussed in the preceding section were strong and thatV
excluding the baseline condition did not radically change the results; that Is, the trends were the
same. Each significant result was reanalyzed using the same post-hoc tests. This section will
discuss any differences between the two analyses.
For comparison, Table 35 lists the significant effects and corresponding F~test and
probability values for the analyses with and without the baseline. Three effects ( F x A x DL, A x DL
and A x G) that are significant in the first analysis are no longer significant (p > .05) when the
baseline Is removed. One third-order effect reaches significance in the second analysis (F x A x
DIM). ln some cases, the effects are still significant and the trends the same; however, some
differences among means occurred and these differences will be discussed.
The F x A x DL x DIM Interaction Is Illustrated In Figure 25. Table 36 lists the results for the
F·test of F x A x DL, which is significant only for the 2-D condition. The previous analysis has
113
TABLE 34
Analysis of Variance Summary Table for Magnitude Estimation, Baseline Removed
Source of Variance dt MS F p
Dimension (DIM) 1 1635.74 0.27 0.6085Subjects within Dimension 28 6138.68(S/DIM)
Frequency (F) 6 131604.13 19.16 0.0001F-‘DIM 6 977.33 0.15 0.9881F°S/DIM 168 6373.91Amplitude (A) 4 157289.88 13.19 0.0001A°DIM 4 395.01 1.56 0.1904A'S/DIM 112 6613.07Display Luminance (DL) 2 24568.34 23.03 0.0001DL'D|M 2 133.77 0.10 0.9090DL°S/DIM 56 1037.70Gradient (G) 2 18723.40 10.82 0.0001G°D|M 2 3518.10 2.10 0.1321G'S/DIM 56 1640.00F°DL 12 1057.84 7.51 0.0001F°DL"D|M 12 73.35 0.52 0.8995F'DL°S/DIM 336 139.33F°A 24 5774.28 5.66 0.0001F'A°DIM 24 272.26 2.62 0.0001F'A°S/DIM 672 338.36F'G 12 1776.56 7.30 0.0001F"G°D|M 12 394.55 1.73 0.0591
1 14
TABLE 34 (CONT)
Source of Variance dt MS F p
F"G°S/DIM 336 230.24A‘DL 8 1714.34 1.80 0.0777A*DL'D|M 8 34.03 1.00 0.4332A'DL‘S/DIM 224 96.52A‘G
8 827.41 0.81 0.5932A°G°DIM 8 161.81 0.82 0.5840A'G'S/DIM 224 111.14DL°G 4 464.07 5.65 0.0004DL°G'D|M 4 51.28 0.68 0.6058DL°G°S/DIM 1 12 73.71F'A*DL 48 70.34 0.82 0.8006F°A°DL*D|M 48 47.68 1.60 0.0063F°A'DL"S/DIM 1344 32.92F'A°G 48 116.10 1.77 0.0011F'A*G°D|M 48 41.68 0.99 0.4994F‘A’G'S/DIM 1344 34.90A°DL'G 16 32.73 1.02 0.4340A‘DL°G*D|M 16 20.21 0.80 0.6872A°DL°G‘S/DIM 448 24.94DL'G*F 24 50.54 1.64 0.0289D‘G"F°D|M 24 29.26 1.00 0.4591DL°G°F'S/DIM 672 28.92F*A'DL‘G 96 24.34 1.04 0.3711F*A'DL*G"D|M 96 26.38 1.17 0.1306F‘A*D‘G'S/DIM 2688 22.93
Total 9449
115
TABLE 35
Comparison of Significant Effects for ANOVAs \Mth and Without the A-0 Baseline
Basellne Included Basellna RemovedSource of Variance F p F p
F 20.65 0.0001 19.16 0.0001A 23.78 0.0001 13.19 0.0001DL 23.68 0.0001 23.03 0.0001G 11.42 0.0001 10.82 0.0001F°DL 7.60 0.0001 7.51 0.0001F°A 17.07 0.0001 5.66 0.0001F’G
7.72 0.0001 7.30 0.0001A"DL 17.76 0.0001 1.80 0.0777A'G 7.44 0.0001 0.81 0.5932DL"G 6.30 0.0001 5.65 0.0004F'A°DL 21.40 0.0001 0.86 0.8006F"A°DIM 0.80 0.7632 2.62 0.0001F°G°DIM 1.71 0.0624 1.73 0.0591F'A°G 3.33 0.0001 1.77 0.0011F'G*DL 1.75 0.0153 1.64 0.0289F‘A°DL'DIM 1.45 0.0151 1.60 0.0063
116
TABLE 36
Simple-Effect F·tests for F x A x DL for One and Two Dimensions - Magnitude Estimation,
Baseline Removed
Source of Variance df MS F p
FxAx DLfor1-D 48 37.35 1.13 0.2535FxAxDL1or2-D 48 52.09 1.58 0.0076
F x A x DLx S/DIM 1344 32.92
117
shown that the effects of DL strongly influence the perception of the nonuniformities and may be
causing the differences in estimations for the 2-D condition.
Table 37 lists the results of F-tests on the A x DL x DIM interactions. As In the previous
analysis, there is a significant imeraction among A, DL, and DIM for the 128 c/dw condition. The
Interaction is also significant at 8 c/dw in this analysis. At 8 c/dw there is a slight drop In perceived
uniformity ratings from 4 to 8 cycles for the 2-D condition. It is difficult to determine the influence
of DIM because of the oonfound with DL. The results may be a combination of both DIM and DL.
ln the previous analysis the F x A x DL Interaction was significant at p = 0.0001. As
expected, this Interaction Is no longer significant when the baseline is removed from the analysis.
Vlüthout the baseline the F x A x DIM Interaction reached significance and is Illustrated in
Figure 36. Simple-effect tests by DIM listed In Table 38 indicate a significant F x A imeraction for
the 2—D case only. Table 39 indicates that the A x DIM Interaction Is significant at 4, 8, and 16 c/dw.
Notice that In the 1-D case the F x A Interaction closely tollows the CTF. There Is a larger range in
perceived uniformity ratings at the middle F levels where the visual system is more sensitive. In
the 2-D case, the lower F levels result in a larger range of perceived uniformity ratings. lf this effect
was only a function of the higher DL levels in the 2—D condition, then the results should still follow
the CTF; thus, the results suggest the 2-D pattern is also oomributing.
In the previous analysis the F x G x DIM Interaction reached a probability level of p =
0.0624. Removing the baseline only changed the probability to 0.0591. Table 40 lists the F—test
results by DIM. The F x G Interaction is significant for the 1-D case at p < .05 and for the 2-D case
at p < .01. Recall that F x G is not significant for 1-D when the baseline is included. For both 1- and
2-D the SQ wave results in lower ratings of perceived uniformity than the SINE or TRI waves.
Table 41 lists the results by F. Again, the G x DIM Interaction is significant at the lower Fs: 4, 8,
1 18
TABLE 37
SImpIe—EIfect F-tests for A x DL x DIM at Each Frequency · Magnitude Estimation, Baseline
Removed
Source of Variance df MS F p
Ax DLx DIM for4cyIces/display 8 22.55 0.68 0.7095
A x DL x DIM for 8 cycles/display 8 65.75 2.00 0.0432
A x DL x DIM for 16 cycles/display 8 51.92 1.58 0.1260
A x DL x DIM for 32 cycles/display 8 16.96 0.51 0.8496
A x DL x DIM for 64 cycles/¤1spIay 8 59.75 1.81 0.0711
A x DL x DIM for 128 cycles/display 8 156.42 4.75 < 0.0001
A x DL x DIM for 256 cycles/display 8 22.86 0.69 0.7007
FxAx DLxS/DIM 1344 32.92
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120
TABLE 38
SimpIe·Eftect F-tests for F x A for1~D and 2-D · Magnitude Estimation, Baseline Removed
Source of Variance df MS F p
FxA for1-D 24 138.12 0.41 0.9948F x A for 2-D 24 879.65 2.60 < 0.0001
FxAxS/DIM 672 338.36 '
121
TABLE 39
Simple-Effect F-tests for A x DIM at Each Frequency - Magnitude Estimation, Baseline Fiemoved
Source of Variance df MS F p
A x Dim for 4 cycles/display 4 2281 .73 6.74 < 0.0001
A x Dim for 8 cycles/display 4 1531.32 4.53 0.0013
A x Dim for 16 cycles/display 4 886.31 2.62 0.0340
A x Dim for 32 cycies/display 4 718.35 2.12 0.0767
A x Dim for 64 cycles/display 4 350.62 1.04 0.3856
A x Dim for 128 cycles/display 4 56.75 0.17 0.9537
A x Dim for 250 cycles/display 4 67.23 0.20 0.9383
Ax Fx S/DIM 672 338.36
122
TABLE 40
SimpIe~Effect F—tests for F x G for One and Two Dimensions - Magnitude Estimation, Baseline
Removed
Source of Varlance df MS F p
FxGfor1-D 12 401.95 1.75 0.0554FXG fol'2-D 12 2350.41 10.21 < 0.0001
FxGxS/DIM 336 230.24
123
TABLE 41
SimpIe·Effect F-tests for G x DIM at Each Frequency - Magnitude Estimation, Baseline Removed
Source of Variance df MS F p
G x DIM for 4 cycles/display 2 3341.02 14.51 < 0.0001
G x DIM for 8 cycles/display 2 1920.60 8.34 0.0003
G x DIM for 16 cycles/display 2 1784.00 7.75 0.0005
Gx DIM for 32 cycles/display 2 455.14 1 .98 0.1397
G x DIM for 64 cycles/display 2 215.59 0.94 0.3916
G x DIM for 128 cycles/display 2 9.57 0.04 0.9608
G x DIM for 256 cycles/display 2 4.13 0.02 0.9802
GxFxS/DIM 336 230.24
124
and 16 c/dw. At these F levels, the perceived uniformity ratings for the 2-D SQ wave are lower
than the perceived uniformity ratings for the 1-D SQ wave. These results are consistent with
results reported in the description of the F x A x DIM interaction above.
The F x A x G interaction is illustrated in Hgure 27. The F·test results by F, listed in Table
42, indicate that the A x G interaction is significant at 8, 16, 32, and 64 c/dw. The perceived
uniformity ratings for the SQ wave at each A level were lower than those for the SINE and TRI wave
shapes. ln the previous analysis, the interaction was significant also at 4 c/dw. These results
support the previous research findings of De Palma and Lowry (1962) who found that lower
modulations were required to detect square-wave gratings at lower spatial frequencies.
The F x A interaction is again significant and is illustrated by Figure 30. Results of a
Newman·Keuls test, listed in Table 43, indicate that perceived uniformity is significantly different
among A levels at all but the highest F level (256 c/dw). In the previous analysis, there was a
significant difference among A levels at 256 c/dw, which indicates that the A—0 condition was
contributing to the significant effect of A at 256 c/dw. Therefore, subjects could detect
nonuniformities at the highest F level, although they could not determine the difference among A
levels. This can be predicted by examining Table A-37 - A-42 in Appendix A which shows that the
modulation for 256 c/dw is visible but the harmonics are not.
The A x G interaction is not significant without the baseline. As A increases, perceived
unifonnlty ratings increase for all G shapes at the same rate. There are significant main effects tor
A and G. Tables 44 and 45 list results of Newman-Keuls tests forthese main effects. Perceived
uniformity is significantly lower for the SQ wave. The main effect of A indicates that the lowest A
(A—1) results in perceived uniformity ratings that are signiücantly higher (i.e., more uniform) than
those for A-2 through A-5.
125
TABLE 42
Simple-Effect F-test for A x G at Each Frequency · Magnitude Estimation, Baseline Removed
Source of Variance df MS F p
Ax G for4cycIes/display 8 18.96 0.54 0.8269A x G for 8 cycles/display 8 88.88 2.55 0.0093A x G for 16 cycles/display 8 107.19 3.07 0.0020A x G for 32 cycles/display 8 63.88 1 .83 0.0675A x G for 64 cycles/display 8 88.23 2.52 0.0101A x G for 128 cycles/display 8 23.97 0.69 0.7707A x G for 256 cycles/display 8 9.23 0.26 0.9784A x G x Fx S/DIM 1344 34.90
126
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TABLE 44
Newman-Keuls Compansons tor Amplitude · Magnitude Estimation, Baseline Removed
Amnlituda MBU.1 1 35 .64 A
2 131 .45 B
3 1 29.31 B C
4 1 26.63 C D
5 1 24.90 D
Note: Means aooompanied by the same letters are not significantly different, p > .05
1 28
TABLE 45
Newman—Keuls Comparisons for Gradient - Magnitude Estimation, Baseline Ftemoved
Gradient MBL1TRI 133 .31 A
SINE 131 .02 A
SQ 1 26.43 B
MPU - mean perceived uniformityNote: Means accompanied by different letters are not signiticantly different, p > .05
129
The A x DL interaction is also no longer significant when the baseline is removed.
Perceived uniformity ratings increase as A increases at the same rate for all DL levels.
An analysis of the third~order effect of F x G x DL and the second—order effects of F x G,
and G x DL, indicates that trends are the same when the baseline is removed; therefore, results
will not be repeated here.
Summary. When the baseline condition is removed and the data are reanalyzed, the
overall results are essentially the same. The trends remain unchanged. Listed below are
summaries of the major changes in the results which oocur when the baseline is removed.
(1) The F x A x DL interaction is not significant when the baseline is removed. When DL
increases perceived uniformity ratings increase with increasing F at the same rate for each A level.
(2) The F x A x DIM interaction reaches significance. The F x A interaction is only
significant for the 2-D condition although trends are similar for the 1-D condition.
(3) The A x G and the A x DL interactions are no longer significant when the baseline is
removed. As A increases, perceived uniformity ratings decrease at the same rate for all G shapes,
and at the same rate for all DL levels.
(4) Removal ot the baseline shows that subjects can detect the difference between an all-
pixel-on uniform screen (baseline) and the highest F level, 256 c/dw (2 pixels on 2, pixels off).
Magnitude Estimation Conclusions
Many of the effects of the magnitude estimation task are both statistically significant and
meaningtul. Although subjects' random search performance is not detrimentally influenced by
nonuniformities, subjects are sensitive to the nonuniformities. Defining nonuniformities in terms
of F, A, DL, G, and DIM was successful, and the effects on the perception of uniformity as caused
by each variable are discussed briefly below.
130
Display Iuminance. DL is an influential variable and interacts with many of the other
variables. In general, as DL increases, perceived uniformity decreases (when nonuniformities are
presem). When nonuniformities are not present (baseline condition), subjects rate DL-3 as being
more uniform in Iuminance than the lower DL levels, which may be a function of the instructions
which stated that they were to rate how uniform in "luminance" the screen appeared. Subjects
may have been looking for Iuminance although they were instructed not to rate the screen based
on how "bright" it appeared.
DL also interacts with F. The effects of DL are stronger at middle F levels and these
results resemble the CTF of the visual system. Also, the effect of DL is greater for SQ than for
SINE or TRI nonuniformities. This effect is also consistent with previous research in spatial vision
which shows that lower modulations are required to detect SQ waves.
Amplitude. As A increases, perceived uniformity decreases and the effect of A interacts
with F. As F increases, the effect that A has on perceived uniformity decreases. Again, these
results can be explained by models of spatial vision. The tables in Appendix A are predictive of
these results. These tables illustrate that as F increases the modulations of the fundamental
frequency and harmonics do not reach visual threshold detection levels. At 4, 8, and 16 c/dw the
fundamental and 3rd, 5th, and 7th harmonics (for the SQ and TRI wave) have modulations above
detection thresholds. At 32 c/dw, the 7th harmonic is no longer detectable for many of the A
levels. At 64 c/dw the 5th harmonic is beginning to be undetectable. At 128 cdlw, detection of
the 3rd harmonic is limited. At 256 c/dw, the modulation passed by the display for the
fundamental frequency is 88% of the modulation passed at 4 c/dw and all harmonics are
undetectable. These results verify previous vision research investigating the CTF of the visual
system to SQ wave forms.
131
Gradient. Subjects consistently rated the TRI and SINE waves the same even though the
TRI wave had harmonics that were visible at the lower F levels. The SQ wave resulted in
slgnificantly lower ratings of perceived uniforrnity than SINE and TRI waves. Also, the harmonics
of the SQ wave are more visible (i.e., higher modulatlons) than the harmonics ot the TRI wave as
Illustrated in tables located In Appendix A. For certain combinations of F, A, and DL, harmonics of
the TRI are not visible while harmonics of the SQ wave are. As F increased, the harmonics of the
SQ wave did not reach threshold detection levels as discussed above. At 128 and 256 c/dw
subjects could not tell the difference among G shapes at their viewing distance (45.7 cm). The
tables in Appendix A are predictive of these results. The effect of the SQ shape decreased as the
harmonics became undetectable. These results also verify previous vision research investigating
the CTF of the visual system for SQ wave forms.
Dimension. The effect of DIM is difficult to interpret. It is obvious that DL is an influential
variable. Therefore, it is not unlikely that DL played a prominent role in the effect of DIM due to the
confounding of the variables. Additional research Is necessary to determine the difference
between 1— and 2-D nonuniformities. lf DIM was strongly influencing perceptions, then DIM
probably would have interacted with more variables.
Performance Model/ing
Developing a model which can successfully relate physical measures of nonuniformities
to human performance data will allow human factors engineers and display deslgners to determine
if nonuniformities present in the display system will interfere with performance without having to
conduct numerous performance studies. A performance modelling approach was used in an
attempt to predict human performance in the presence of nonuniformities. Results of the analysis
discussed in the preceding section indicated that ST and CR performance are not slgnificantly
influenced by the presence of nonuniformities; therefore, modelling the prediction of ST and CR
132
would not be meaningful. Instead, models for predicting perceived uniformity of the
nonuniformities were constructed and evaluated.
Modelling approach. Multiple linear regression techniques are used for human
performance modelling. The approach taken in this analysis is to compare alternative models
based on multiple criteria for selection of the best models. Models were examined for
multicollinearity using the diagnostic techniques of variance inflation factors (VIF) and variance
proportions for each regressor. Also, an examination of residuals was performed. For each model
the coefficient of determination (R2), Mallows Cp-statistic (an estimate of bias), and the mean
square error (MSE) were examined. Models were developed with the data set that did not include
the baseline because the baseline data would influence the regression and prediction of
subjective impressions of a uniform screen was not the objective.
The SAS procedures MAXR and STEPWISE were used to determine subsets of models
for further evaluation. The stepwlse techniques choose variables to enter into the model based
on an increase or decrease in the value of R2 and perform significance tests for each entering
variable. However, R2 will increase as the number of regressor variables entering the model
increases, introducing the possibility of overfitting the model. The selection procedures in
stepwlse regression can also result in underestimation of the true model error. Therefore, the
significance levels for the tests on entering variables may not be valid. A high criterion (0.50) for
the entering variables in forward selection was used to combat this problem. The MAXR
procedure also uses R2 for variable screening but significance tests on the variables are not
performed on the entering variables, so this procedure considers all possible models. That is, this
procedure selects one model for each number of regressor variables.
Flegressor variables. The regressor variables selected for model building are listed in
Table 46. variables were selected that would describe the nonuniformities in physical temts. The
133
TABLE 46
Regressor Variable Definitions
FUNDF Fundamental Frequency.
FUNDF2 Square of the Fundamental Frequency.
F(SF) Function of Spatial Frequency, the CTF value at each fundamental frequency.
[F(SF)]2 Square of Function of Spatial Frequency.
F3 Frequency of the 3rd harmonic for SQ and TRI wave shapes.
F5 Frequency of the 5th harmonic for SQ and TRI wave shapes.
F7 Frequency of the 7th hamwonic for SQ and TRI wave shapes.
MODSINE Displayed luminance modulation for the SINE at the fundamental frequency.
MODSQ Displayed luminance modulation for the SQ at the fundamental frequency.
MODTRI Displayed luminance modulation for the TRI at the fundamemal frequency.
MOD3SQ Displayed luminance modulation for the SQ at the 3rd harmonic frequency.
MODSSQ Displayed luminance modulation for the SQ at the 5th harmonic frequency.
MOD7SQ Displayed luminance modulation for the SQ at the 7th harmonic frequency.
MODSTRI Displayed luminance modulation for the TRI at the 3rd harmonic frequency.
MOD5TRl Displayed luminance modulation for the TRI at the 5th harmonic frequency.
MOD7TRl Displayed luminance modulation for the TRI at the 7th harmonic frequency.
G1 Categorical variable to describe the variable G. TRI wave was ooded as 1, SINEand SQ as O.
G2 Categorical variable to describe the variable G. SQ wave was ooded as 1, SINEand TRI as 0.
DIM Categorical variable to describe the variable DIM. 1-D pattems are ooded as 0,2-D patterns are coded as 1.
134
spatial frequencies of the nonuniformities were described by the fundamental frequency (FUNDF)
in cycles/degree of visual angle. The 3rd, 5th, and 7th harmonic frequencies (3F, 5F, 7F) of the
SQ and TRI wave were also included. A function of spatial frequency F(SF) was also defined, and
is the CTF value at each fundamental frequency or CTF(w). The CTF values were taken from the
CTF curve determined by van Meeteren et al. (1966) and is illustrated in Hgure 3.
The results presented in the previous ANOVA section indicate that there is a curvilinear
trend in the data for the variable FUNDF. This is a function of the visual system's response to
spatlal frequency. Quadratic terms FUNDF2 and F(SF)2 were also included in an attempt to
account for this curvature.
The A and DL levels were described by modulation. The modulations at each
fundamental and harmonic frequency were included, where modulation is defined by Equation 1.
These modulation values can be found in tables in Appendix A. MODSIN, MODSQ, and MODTRI
refer to the modulations for the fundamental frequencies for the SINE, SQ, and TRI waves,
respectively. MOD3SQ, MODSSQ, and MOD7SQ refer to the modulations at each harmonic for
the SO shape, and modulations for TRI are defined similarly.
Note that the SINE waveform does not have hamwonics; therefore, the variables F3, F5,
and F7 for the SINE conditions were coded as zero in order to complete the matrix. In reality they
are nonexistent. A similar coding scheme is used for the modulation variables. MODSINE is
coded as zero for SQ and TRI conditions, MODSQ is coded as zero for SINE and TRI conditions
and so forth. The same is true for the modulation variables describing the harmonics. In order to
use the models specified in this study the same coding scheme must be applied. Other coding
schemes were tested but resulted in problems of multicollinearity which caused instability in the
coefficients, and results were uninterpretable.
135
The variables G and DIM were included as categorical variables. G had three levels (SINE,
TRI, and SO) and required two variables to describe the categories. These variables were termed
G1 and G2. Inclusion of G1 would indicate that TRI influences the regression. Inclusion of G2
would indicate that SO influences the regression. If neither G1 nor G2 are included, SINE is
intluencing regression. DIM had two levels and required only one variable to describe the
categories. Inclusion of the variable DIM would indicate that the 2-D case was important in the
model.
Analysis and results. A regression analysis was first performed using the variables
described above. The best-fit models are listed in Table 47. Overall, modelling was not very
successful. A large proportion of the variance is unaccounted for by the models. Large MSE and
small Cp values indicate poor prediction and fit. The most optimal fit ot the estimation data Is the 9·
variable model. As expected, modulation variables have negative slgns indicating that as
modulation increases, perceived uniformity decreases. Modulations ol the 7th harmonic for the
SQ wave and the 5th hamwonic for the TRI wave are also included In the model. Inclusion of these
variables support the theory that It modulations ot the higher harmonics are above the subject's
visual thresholds, they will influence subjective Impressions ol the nonuniformities. Inclusion of
7F and MOD7SO indicates that the 7th harmonic for the square wave Is intluencing estimations.
However, use of these models for prediction is not teasible since most ot the variance (over 70
percent) Is unaccounted for by the models.
An inspection of the ANOVA results in Table 34 showed that a large proportlon ot
variance is contributed by diflerences among subjects, which is unexplained by the models
described above. To determine It the between-subjects variance could account for part ot the
unexplained variance, subject (SUB) was included In the analysis as a categorical variable. The
best fitting model is shown in Table 48 and Is an undertit as indicated by the large Cp statistic. In
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TABLE 47Best-fit Regression Models for Perceived Uniformity
Nlne-Variable Model
lntercept 125.6150 07F 1.0648 0.8841DIM 4.6042 0.1126MODSIN -16.1796 -0.1806MODSQ -8.8411 -0.1256MODTRI -13.4234 -0.1214MOD7SQ -126.6289 -0.1942MODSTRI -37.9093 -0.0544F(SF) -0.5551 -0.4944
R2 = 0.2941 MSE = 295.5118 Cp = 8.562 N = 9450
Ten-Variable Model
INTERCEPT 126.2926 07F 1.0640 0.8835DIM 4.6040 0.1126G2 -2.0100 -0.0463MODSIN -17.4936 0.1952MODSQ -6.7003 -0.0952MODTRI -15.0657 -0.1363MOD7SQ -127.4869 -0.1955MOD5TRI -37.7642 -0.0542FUNDF2 -0.5547 -0.4940
R2 = 0.2944 MSE = 295.3901 Cp = 5.67 N = 9450
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TABLE 48
Best-fit Regression Model for Perceived Uniformity with Subject as a Categorical Variable.
Twelve-Variable Model
INTERCEPT 125.5421 0FUNDF 7.7486 0.9191GFIAD2 -1.9898 -0.0459DIM 3.6826 0.0900MODSIN -17.1603 ·0.1915MOD5SQ -130.5509 -0.2811MODSTBI -77.4318 -0.1852FUNDF2 -0.6209 -0.5530SUB2 19.1872 0.1684SUB21 8.8967 0.0781SUB26 2.4951 0.0219SUB30 2.4274 0.0213
R2 = 0.3267 MSE = 281.9434 Cp = 12.71 N = 9450
138
this model four subjects were included. An examination of raw data indicates that these subjects
had large ranges in their estimations, particularly SUB2 and SUB21. When all SUB variables were
included in the regression, R2 increased to 0.3292 from 0.3267 and the additional SUB
parameters did not contribute signiticantly to the model.
A large proportion of the variance is still unexplained by the model described above.
When SUB is entered as a categorical variable only the between-subject variance is accounted
for. The ANOVA results listed in Table 34 indicated that SUB is interacting with the other variables
(i.e, large MSE values for error terms). Also, when SUB is included as a categorical variable the
model is speciüc to the individual subjects in the experiment and is not easily generalizable. The
objective of model building is to develop a model to predict overall impressions of
nonuniformities. Therefore, the next step was to predict the mean perceived uniformity across all
subjects for each condition.
Best-fit models using mean perceived uniformity are shown in Table 49. This modelling
approach was more successful than previous attempts. A greater proportion of the variance is
accounted for by the models as indicated by the higher values of R2 and lower MSE. Modulation
variables have negative coefticients as expected. FUNDF and the quadratic term FUNDF2 are
also included in all models. ln general, the models are either overfit or undertit as indicated by the
Cp Values. The first 10·variable model listed in Table 49 is perhaps the optimum model although it
is an underüt (Cp is too large) and is therefore biased. Substituting MOD7SQ for MODSSQ and
MOD5TRl for MOD3TRl in the second 10·variable model increased R2 by only .002 but the model
becomes an overfit as indicated by the low Cp statistic. The 11-variable model is an overfit, andthe increase in R2 and decrease in MSE are minimal as coefficients are added to the regression.
Although the first 10·variable model does not account for 16% of the variance, the .
coefficients in this model are meaningful. As expected, frequency variables (FUNDF and
139
TABLE 49
Best-fit Regression Model for Perceived Uniformity Collapsed Across Subjects
Elght·varIable Model
INTERCEPT 126.2970 0FUNDF -7.7486 1.5557GFIAD2 -1.9898 -0.0776DIM 4.3731 0.1810MODSIN -17.1603 -0.3241MODSSO -130.5509 -0.4758MOD3TFII -77.4318 -0.3135FUNDF2 -0.6209 -0.9360
B2 = 0.8403 MSE = 23.6182 Cp = 14.19 N = 630
Nlne·VarIabIe Model
INTERCEPT 126.3175 0FUNDF 7.7970 1.5654GFIAD2 -2.4521 -0.0957DIM 4.4556 0.1844MODSIN -17.6107 -0.3326MODTFII -9.1898 -0.1407MODSSO -127.4514 -0.4645MOD3TRI -44.8689 -0.1817FUNDF2 -0.6143 -0.9269
R2 = 0.8411 MSE = 23.5334 Cp = 12.93 N = 630
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TABLE 49 (CONT)
Ten-Varlable Model (1)
INTERCEPT 126.1049 0FUNDF 7.8882 1.5837GRAD2 -1.8331 -0.0715DIM 4.6001 0.1904MODSIN -17.6953 -0.3342MODSO -3.5033 -0.0843MODTRI -1 1.4847 -0.1758MODSSQ -110.9931 -0.4045MODSTRI -36.3324 -0.1471FUNDF2 -0.6157 -0.9282
R2 ¤ 0.8416 MSE = 23.4920 Cp = 12.83 N = 630
Ten-Varlable Model (2)
INTERCEPT 126.2919 0FUNDF 7.4501 1.4958GRAD2 -2.0096 -0.0784DIM 4.6040 0.1905MODSIN -17.4937 -0.3304MODSQ -6.6998 -0.2307MODTFII -15.0647 -0.1611MOD7SQ -127.4926 -0.3309MODSTRI -37.7712 -0.0978FUNDF2 -0.5549 -0.8365
B2 = 0.8436 MSE = 23.1943 Cp = 4.93 N = 630
141
TABLE 49 (CONT)
EIav6n·VarIabIe Moda!
INTEFICEPT 126.37.58 0FUNDF 7.1883 1.4432GFIAD2 -2.1777 -0.0850DIM 4.6088 0.1907MODSIN -17.4089 -0.3288MODSO -9.8321 -0.2365MODTRI -16.6612 -0.2551MODSSO 83.8890 -0.3657MOD7SO -216.1321 -0.5609MOD7TRI -39.5841 -0.0677FUNDF2 -0.5139 -0.7746
R2 = 0.8441 MSE = 23.1683 Cp = 5.25 N = 630
142
FUNDF2) are included in the model and, as indicated by the beta weights, contribute substantially
to explanation of the variance. Note that the signs on the beta weights indicate the direction of
the effect, not the magnitude of the weight; that is, relative magnitude of the beta weights are
obtained by comparing absolute values. The MOD variables of the fundamental frequencies for
each wave shape are also included in the model. The MOD variables describe the A and DL levels
of each nonuniformity condition. As modulation increases perceived uniformity decreases; that
is, the display appears more nonuniform to subjects. The coefficiems for MODSSO and MOD3TRl
are also important in the model and support the theory that if modulations of the harmonics are
above visual threshold, they will impact Impressions of the nonuniformities. inclusion of these
variables also add support to the theory that the visual system behaves as a Fourier analyzer in
the spatial domain. Note that correlations among MOD variables for harmonics indicate that
different hannonic values could be used instead.
The effect due to the categories G2 and DIM are significant in partial-F tests at g < 0.0001.
inclusion of G2 in the model indicates that perceived uniformity is influenced by the SQ wave
shape and also that wave shape is an important variable in defining nonuniformity as originally
expected. The inclusion of the coefficient DIM indicates that 2-D nonuniformities influence
estimations of perceived uniformity, although it is not possible to determine if the effect is due to
the pattem or the higher DL levels. lt should be noted that categorical variables influence the
intercept of the regression line by a constam amount but do not alfect the rate of change or slope
of the regression line. lf a SO wave shape is not to be predicted, then the coefficient can be set to
0.
The nonuniformities for the 1- and 2-D conditions are completely described by the MOD
terms, which take into account DL levels; therefore, the variable DIM should not be important to
143
the model. inclusion ot this variable may indicate that the 2-D pattem is influencing perceived
uniforrnity beyond the three modulation measures.
GENERAL DISCUSSION AND CONCLUSIONS
Human Performance and Current Standards
The results of this research indicate that very noticeable spatial lumlnance nonuniformlties
do not appreciably affect performance for search type tasks. The American National Standard for
Human Factors of Visual Display Terminal Workstations (1988) recommends that the lumlnance
variation from the center to the edge of the active display area should vary no more than 50% of
that of the center luminance. ln reference to high frequency spatial lumlnance nonuniformlties,
the standard recommends that unintended lumlnance variations shall not vary by more than 50%
within an area the size of half a degree of arc, at any position on the screen. (This value is
calculated based on the display design viewing distance.) The nonuniformities in this study
exceeded these recommendations and search performance was relatively unaffected. The ANSI
standard is written in reference to displays that are to be used for alphanumeric or word
processing and reading type tasks. This research indicates recommendations are also appropriate
for search tasks with non·alphanumeric symbols. Results of this type will most likely apply to
reading type tasks because it has been found that subjects are able to perform reading tasks or
contextual tasks under adverse conditions (Albert, 1975; Lloyd et al., 1988).
The type of task performed is an important consideration. There is limited research
investigating the sensitivity of different task types for research involving presentation of
information on visual displays (Decker et al., 1987). Research which correlates performance
among diflerem tasks to predict results across task types is also Iacking. Photointerpretation tasks
or information extraction from literal images, such as medical imagery, will most likely show different
results.
144
145
Although subjects were able to perform the random search task in the presence of
nonuniformities, results from the magnitude estimation task indicate that subjects were sensitive
to nonuniformities in terms of their impressions of perceived uniformity. Sensitivity fo the
nonuniformities was noted during the random search task. While performing the search task,
many subjects complained about the images and found them annoying. Some subjects
commented that the SINE waveforms appeared blurry and that performing the task was fatiguing.
Focusing on the SINE wave is difficult because there are no edges.
Most displays currently on the market do not exhibit the levels of nonuniformity used in
this study. However, nonuniformities may be caused by components or processes of a display
system other than the display hardware. Possible causes of nonuniformities which may result in
high levels of nonuniformities include signal processing techniques necessary for transfomiation
of signals so they can be displayed or enhanced, or coding techniques such as spatial dithenng or
half·toning. _
Relation to Previous Research
Display failures. As pointed out in the literature review there is limited research
investigating the effects of nonuniformities. Abramson and Snyder (1984), Decker et al. (1988),
and Lloyd et al. (1988) investigated the effects of display failures which can be considered as
high frequency nonuniformities. Cell and line failures were introduced onto the display and
results indicated that these types of nonuniformities were degrading to both search and reading
performance. The high frequency nonuniformities in the current study were not detrimental to
search performance. A possible explanation for the difference in results is that in the previous
research the failures introduced onto the display were random, while the nonuniformities in this
study were not. In fact, the nonuniformities had the appearance of a background to the task
information rather than an interruption in the image and apparently subjects were able to ignore
146
the nonuniformities. The failures on the other hand, degraded the information by removing parts
of the images or adding extra cells or lines resulting in the appearance of visual noise.
The nonuniformities used in this study were additive. When the display luminance was
increased the symbol luminance increased. Therefore, the modulations of the symbols and maps
remained above recommended levels of modulation (e.g., ANSI, 1988). Introduction of failures
degrade the image and change the modulation of symbols or characters as well. Introduction of
nonuniformities that are not additive will probably result in further degradation of the image and
performance will deteriorate.
Effects of visual noise. A significant amount of research has been conducted in the past
investigating the effects of visual noise on detection of targets, including detection of sine-wave
pattems. Noise ls defined as an unwanted signal or disturbance in a system which can obscure
information of interest (Cohen and Lashly, 1986). Results of research on this topic indicate that
performance is affected by the type of noise (e.g., random), the bandwidth of the noise,
amplitude, and frequency (Carter and Henning, 1970; Pollehn and Roehrig, 1970; Snyder,
Keesee, Beamon, and Aschenbach, 1974; Stromeyer and Julesz, 1972), and that noise has
detrimental effects on performance. The differences in findings among studies investigating
noise and this research can be explained by several factors. As mentioned prevlously, the
modulations of the symbols in this study were not degraded by the nonuniformities, whereas
research investigating noise effects has shown degradation in the symbol modulations (Snyder et
al., 1974). In addition, the noise presented in past research contains a band of spatial frequencies
(i.e., broad band noise or narrowband noise) and the noise is often random noise where there is
equal power at all spatial frequencies. Noise masks targets whose spatial frequencies are around
the center frequency of the noise. In this study nonuniformities were centered at only one spatial
frequency (for the given condition) with power at that spatial frequency. The targets were always
147
at a spatial frequency higher than the nonuniformities. Targets and maps were created using one
pixel width lines, and the highest frequency nonuniformity was 2 pixels on and 2 pixels off.
Also, broadband random noise is unstructured. Mitchell (1976) found that higher
thresholds are necessary for detection of unstructured pattems than structured pattems. .lf
subjects can determine the structure of a pattem they may find it easier to Ignore.
Definitions and Measurement
One of the objectives of this research was to determine a method for describing
nonuniformities such that they can be measured. Each of the variables chosen to characterize
the nonuniformities was found to be important. These variables were chosen so that Fourier
analysis techniques could be used to describe the nonuniformities in terms of their sine wave
componems. A regression model was developed to predict subjective impressions of perceived
uniformity based on the sine wave content of the image. These results indicate that developing
models based on Fourier analysis is a viable technique for describing and measuring display
spatial nonuniformities.
Several researchers have utilized Fourier analysis to derive optimal dither or halftone
pattems to minimize unwanted textures (Allenbach and Liu, 1976; Bayer, 1973; Kemisch and
Boetling, 1973). Spatial dithering is a coding technique which uses fixed size dots (or pixels)
coded as on or off and arranged spatially in a fixed array. An image with multiple intensity levels
can be encoded into fewer intensity levels or a binary image (2 levels or 1 bit). Half-toning is a
technique used in printing and photography where the dot size and shape are manipulated to
obtain a binary output image (Bryngdahl, 1978). These approaches are relevam to the topic of
nonuniformity because these techniques are presenting nonuniformities into the image and
relying on the visual system to integrate out the nonuniformity. Flesearchers have been
148
interested in determining the best dither patterns and halftone patterns to minimize textures,
contouring, Moire pattems, and the perception of the dither patterns.
Allenbach and Liu (1976) used a random quasiperiod halftone process to try to eliminate
Moire effects that can be introduced when halftone screens are used. They used Fourier
techniques to describe the output image and compared a periodic image with a quasiperiodic
image. Although authors did not use observers to rate the different patterns in any subjective or
objective manner, they did illustrate that Fourier analysis can be used to describe the images. The
nonuniformities used in the current study were periodic; however, nonuniformities may also be
random, or quasiperiodic due to the signal processing or coding technique used.
Although researchers have been using Fourier analysis techniques to describe dither
and halftone patterns, they have not validated the method using objective or subjective
performance evaluations. Therefore, it was not possible to determine nonuniformity
recommendations based on research in the area of dither or half-toning. This research bridges a
gap between research which only mathematically describes dither pattems and performance. This
research shows that knowledge of the Fourier coefficients of nonuniformity pattems and the CTF
of the visual system can be used to predict subjective Impressions. Further research is still
needed to determine if objective performance can also be predicted and whether objective
performance can be predicted from subjective impressions. Also, empirical data relating Fourier
coefficients and Impressions of dither and halftone pattems are still needed.
Spatial Vision
The results of this investigation are in strong concurrence with previous research In the
area of spatial vision which theorizes that the visual system behaves as a Fourier analyzer in the
spatial domain. De Palma and Lowry (1962) found that threshold detection is lower for a square
149
wave than sine waves. As previously discussed, the fundamental frequency of the square wave is
4/1: or 1.273 higher than that of the sine wave, and the harmonics of the square wave contribute
to detection. The application of Fourier analysis is formed on the basis of research on spatial
frequency models. A competing theory in vision research is that the visual system contains edge
detectors which could be contributing to the difference in detection between the sine and square
waves. The purpose of this study was not to compare spatial frequency filter models with edge
detection models for describing how the visual system processes spatial information. A complete
understanding of the underlying visual processes is not complete. However, Fourier techniques
and the spatial frequency approach can be applied to describe the nonuniformities and predict
performance and have also been successfully applied to other research in the area of visual
displays (Snyder, 1980). Whether the CTF can be described by spatial frequency models or edge
detectors er both, researchers do agree on the curves of the CTF.
The results of the subjective impressions of perceived uniforrnity follow the CTF of the
visual system. In many cases, previous researchers have only reported results using one or two
well·trained subjects. This research, with a much larger subject population, validates previous
research in terms of the CTF. This indicates that smaller subject pools can be successfully used in
research of this kind.
Future Research Needs
Research investigating the effects of nonuniformities is still needed. The role of 1- versus
2—dimensionaI nonuniformities was not adequately assessed. Also, the nonuniformities in this
study were added to the symbol Iuminances; therefore, modulations were always well above
recommended levels. Nonuniformities will not always be additive and effects of nonuniformities
which change the information presemed should be investigated. If the same techniques used in
150
this study are also used to define and measure nonuniformities in future studies then prediction
across studies would be possible.
It would be interesting to predict subjects' impressions of dither or halftone pattems which
have been described in terms of their Fourier components in the literature. After predicting
impressions and parhaps objective performance, the prediction could then be validated by
performing empirical research using the images. Unfortunately, such measurement requires a
capability beyond the currently available commercial state of the art.
The measurement and analytical technique used in this study to describe the
nonuniformities should ba validated through photometric measurements of the nonuniformities.
Photometric measurements of each condition were not possible in this study because the
measurement system was not sensitive enough to measure the levels used in this study .
ln addition to the Fourier analysis technique used in this study, other quantitative
approaches should be investigated. A technique which quantifies the difference between the
original image and the same image after nonuniformities have been lntroduced may be a useful
measure for predicting performance. In addition, an altemative coding schema for describing the
variables to ba used in multiple regression models should be investigated. To use the prediction
model in this study the same coding schema is necessary.
lt is recommended that research be conducted which investigates the effects of
nonuniformities on perfomwance with other tasks. If performance from objective tasks can be
correlated with subjective task perfonnance, information from subjective performance can be
used in the design processes. Objective performance data are often more costly to obtain than
subiective data. Predicting across different types of tasks would also be beneücial to design of
visual display systems.
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APPENDIX A
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APPENDIX B
SUBJECT INSTRUCTIONS
Random Search Task- Day 1
In this experimem you will be presented with a map and symbols. You will be asked to
search for a specified symbol on the map from among other symbols. At the beginning of
each trial you will be presented with the prompt "READY, THE NEXT TARGET IS ."
This will be the target you will search for during that trial. The target will appear in only one
position on the screen.
Examine the symbol and when you are ready to begin searching press the right
button on the mouse input device. A map with symbols will be displayed to you. After you
have located the target, press the left button on the mouse input device. A symbol
identification (ID) number will appear to the right of each symbol, however, the symbols will be
erased. Verbally report the symbol ID to the experimenter. The ID you report should
correspond to the target you located.
During the course of this experiment please respond as QUICKLY AND
ACCURATELY as possible, BOTH ARE IMPORTANT.
Your chair height and distance from the screen has been adjusted to your normal
sitting position. Therefore, during the experiment please remain in your normal position and
do not lean forward.
Throughout the experiment you will hear two tones. One tone will occur at the
beginning of each trial with the READY prompt. This ls to inform you that a trial will begin.
Another tone will occur less frequently and is a prompt to the experimenter. You can ignore
this tone.
242
243
On the first day of the experiment you will participate in 10 practice trials to become
familiar with the procedure. There will be üve sessions, one per day, and each session wlll last
approximately two and one·half (2 1/2) hours. You will be given the opportunity to take short
breaks at speciüed intervals.
Before beginning the experiment you will be given 5 minutes to become familiar with
the symbols. Each symbol is presented on the screen. Many of the symbols are very similar,
therefore, please note their differences. For example, for every symbol type, one symbol is
drawn with all dots and another with missing dots (symbols 1 and 2). These should be
considered as separate symbols. Also notice that diamonds are similar to circles (first eight
symbols versus last four symbols). Please take 5 minutes to examine these symbols.
Random Search Task - Day 2~5
Thank you for your continuing participation in this experiment. As you may recall, you
will be presented with a map and symbols. You will be asked to search for a specified symbol
on the map from among other symbols. At the beginning of each trial you will hear a tone and
be presented with the prompt "READY, THE NEXT TARGET IS ". This will be the target
you will search for during that trial. The target will appear in only one position on the screen.
Examine the symbol and when you are ready to begin searching press the right
button on the mouse input device. A map with symbols will be displayed to you. After you
have located the target, press the left button on the mouse input device. A symbol
identiücation (D) number will appear to the right of each symbol, however, the symbols will be
erased. Verbally report the symbol ID to the experimenter. The ID you report should
correspond to the target you located.
Please remember to respond as QUICKLY AND ACURATELY as possible,
BOTH ARE IMPORTANT.
244
Also remember not to lean forward but to remain in a norrnal seated position.
The session will again take approximately two and one-half (2 1/2) hours, but will be
given the opportunity to take short breaks at specified intervals.
Before beginning the experiment, you will be given 5 minutes to refarniliarize yourself
with the symbols and note again their differences. Take 5 minutes now to examine these
symbols.
Magnitude Estimatrbn Task - Day 1
ln this study you will be presented with a series of stimuli in random order. At the
beginning of each trial you will see the prompt °‘F«lEADY". A tone will indicate when the
"READY" prompt is presem. When you are ready, press the right button on the mouse input
device and a stimulus will be presented.
For this task you will tell the experimenter how ymqgn the luminance on the display
screen appears to you by assigning a number to the stlmulus condition. A ynjtogn screen is
one that is unchanging or unvarying in luminance across the screen. Xgn an-; ngt Latingngntgngnt tng sgtggnts. Call the first stimulus any number that seems appropriate to you. Then
assign successive numbers in such a way that they consistently reflect your subjective
impression. For example, if a stimulus seems 20 times as ttnltggm in luminance as the first
stimulus, assign a number 20 times as large as the first. lf it seems one-fifth as gnjjgg;1 in
luminance, assign a number one·filth as large and so forth. Use whole number, decimals, or
fractions, but make each assignment as proportional to the of the screen as
possible.
At times it may appear that there is no stimulus on the screen, however, one is
present. Just estimate that screen accordingly. Also, occasionally you will hear an additional
245
tone to that which teils you to begin a trial. This tone is a prompt to the experimemer and you
may ignore it.
To begin you will participate in 10 practice trials to become familiar with the procedure.
The session will last approximately two hours. You will be given the opportunity to take short
breaks at specified intervals. Do you have any questions?
Magnitude Estimation Task - Day 2
Thank you for continuing your participation in this experimem. As you may recall you
will be presented with stimuli on the screen and your task is to assign a number which reflects
your subjective impression of how ugßggm (i.e., unchanging or unvarying) the luminance on
the display screen appears to you. When the "READY' prompt is displayed, press the right
button on the mouse input device and a stimulus will be presemed.
Before beginning the experimemal trials you will be shown examples of stimuli that
you saw yesterday and you will be told what number you assigned. This is to remind you of
the scale you were using. Press the right button on the mouse when you see the 'READY"
prompt and the stimulus will be displayed. After examining the stimulus, tell the experimenter
when you are ready to see the next stimulus.
Do you have any questions?
APPENDIX C
PROCEDURE FOR TRANSFORMATION OF MAGNITUDE ESTIMATION DATA,
AFTER KLING AND RIGGS (1971)
Step 1. Convert all scores to log 10.
Step 2. Take the mean of the log sccres for the subjects' responses in each conditicn.
Step 3. Determine the mean of each individual subject's estimations across all condition levels.
Step 4. Determine the mean of all values obtained in Step 3. This is the log value of the grand
mean of all responses.
Step 5. Subtract the mean obtained in Step 4 from each value obtained in Step 3.
Step 6. Subtract the values obtained in Step 5 from the values obtained in Step 2.
Step 7. Take the analog of the data obtained in Step 6.
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