Optical transfer function bench for aerial cameras

Hartmut Ziemann, P. Douglas Carman, Manfred Paulun, and Ian P. Powell

An optical bench has been constructed specifically for the evaluation of image quality in aerial survey camerasof up to 23- X 23-cm format and focal lengths to 310 mm. It is able to study the full field of super-wide-anglecameras without auxiliary arrangements. Line spread functions are measured directly, recorded digitally,and converted to OTF by computationfirst results presented.

1. Introduction

For many years, tests for image quality of aerialcameras at the National Research Council of Canadahave been made by measurements of resolving powerfor low-contrast annular targets of the camera com-bined with one or more of the commonly used photo-graphic films.12 While closely related to practical use,this method had several disadvantages: (1) It depend-ed on the subjective evaluation of the photographicimages by an observer; maintenance of consistent cri-teria by an observer, or among different observers, overmany years was difficult. (2) Introduction of a differ-ent type of film required complete retesting of allcameras or at least all camera types. (3) Consistencyof results depended on consistent properties of the film(and consistent processing) over many years; this fac-tor was beyond the control of the testing laboratory.

Because of these disadvantages, and because of theadvantages of increased information, it was decided toprovide a facility for the testing of image quality ofaerial cameras by objective (physical) methods-methods which provide data on the performance of thecamera alone, without film, such as optical transferfunction, line spread function, point spread function,or edge trace. The facility was to maintain the formerclose relationship to practical use.

II. Design Considerations

The four modes of data presentation listed above aremathematically related.3 4 One of them, line spreadfunction, was chosen as the form in which data would

The authors are with National Research Council of Canada, Divi-sion of Physics, Ottawa KA R6.

Received 10 December 1985.0003-6935/86/081284-06$02.00/0.

Design considerations are given, system components described, and

be directly acquired. It does not provide as completeinformation as does the 2-D point spread function, butit is quicker to use and relatively free of signal-strengthand signal-to-noise problems. It also has the advan-tage of providing directly the data on image asymme-try which is of particular importance in photogramme-try.

The system's spectral response was to simulate thatof a common film (or films) to daylight. The image-analyzing slit in the camera image plane was to be onglass with a refractive index close to that of photo-graphic emulsion so that light assessed would be thatwhich would enter on emulsion. The instrument wasto be capable of testing super-wide-angle as well aswide and normal angle cameras without auxiliary ar-rangements. The instrument was to be based on thesame optical bench and collimator previously used forresolving power measurements.

111. Bench and Lens Cone Holder

The bench, a Lens Testing Instrument Pob 125made by Askania, had been acquired by the NationalResearch Council around 1950 and had already beenmodified to increase the camera swing from 50 to±950 . The collimator and illumination system hadearlier been raised by 150 mm to raise the axis to that ofrotational camera mounts. It was recently raised an-other 30 mm to accommodate the largest lens conetypes now in use in Canada.

A holder was made for Universal Aviogon lens conesfor Wild RC8 aerial cameras, providing rotation aboutthe camera's optical axis so that both diagonals can bestudied. Holders for other lens cones are being made.These holders consist of two parts, a cradle attached tothe swinging arm of the bench and a camera mountholding the lens cone to be tested. The holder can bemoved along the arm to allow setting the entrancepupil of the lens into the arm's axis of rotation.

The swinging arm also carries a separate holder forthe ways carrying the image slit system, so that the

1284 APPLIED OPTICS / Vol. 25, No. 8 / 15 April 1986

image slit can be set in the plane of the face of the waysin its normal attitude of use and then moved only ashort distance to its position of use on the camera andits holder.

The modified bench s shown in Fig. 1. Visible inthe foreground is the holder for the ways carrying theimage slit system with that system in place. Furtherback is visible the cradle attached to the swinging armwith the holder for a Wild Universal Aviogon Lenscone with such a lens cone in place.

IV. Collimator

The collimator lens is an f/15 apochromat of 1873-mm focal length and 125-mm diam. Foucault andartificial star tests showed it was performing poorly.This was traced to decentering due to cell rusting.After cleaning and optimization of centering it per-formed excellently over the central 75 mm of its aper-ture, all that would be used for testing up to a 300-mmf/4 lens. The only significant aberration, secondarycolor, was evaluated approximately by Foucault test-ing with interference filters and is illustrated in Fig. 2.

V. Slits

The line spread function is measured by placing anilluminated object slit at infinity (in the focal plane ofthe collimator) and scanning its image formed by thecamera lens in the camera's film plane with a secondslit while a photocell system measures the light trans-mitted. Ideally the slits would be infinitely narrowlines, but finite width is needed to transmit enoughlight for accurate measurement. A 2-,um nominalwidth has been chosen for the film-plane slit, and theobject slit width was chosen to give approximately thesame value for its geometrical image width in the mostcommon 153-mm focal length camera. The scanningis actually done by moving the object slit for reasons ofmechanical convenience. Computational correctionsare made for both slit widths and for the motion whileeach reading is taken.

VI. Object Slit Motion

The 23,um wide object slit is moved in a directionperpendicular to its length on a Velmex UnislideB2509K 10-cm slide with a 1-mm pitch screw driven bya 1-rps synchronous motor through a gearbox withavailable ratios of 1:1, 1:2, 1:4, 1:10, 1:30, and 1:60.Total travel in use is 21 mm. The motion is linear to±8 Am corresponding to +0.7 um at the axial focus of a153-mm focal length camera. A stroboscopic checkestablished that the synchronous motor drive pulledinto synchronism in -1/10 s and did not cause devi-ations from the nominal slit positions (hunting) ex-ceeding about ±1 Am (±0.1 Am at the camera focus).

VIl. Image Slit Positioning

The image-slit assembly is moved in the film planeon cast iron (Meehanite) ways, optically worked toprovide a flatness of motion of +1 ,um in the plane ofthe camera's register frame to the positions corre-sponding to various field angles obtained by rotating

Fig. 1. Askania lens testing instrument Pob 125 with modifica-tions.

is

16

cm

.50

A45

.40~~~~~1.05 _ 0_

g 21 ,^^ a_ x_ no--

Fig. 2. Secondary color of the f/15 apochromat of the Askania Pob125. This collimator lens has a 1873-mm focal length and a 125-mmdiameter. The shown values were obtained for a 75-mm aperture ata draw tube setting of 12.95 cm. The ordinate values are distancesfrom the end of the draw tube. The horizontal line represents theweighted mean position chosen as the location for the object slit.

the camera about its entrance pupil. Fine adjust-ments provide three mutually orthogonal motions anda rotation about the collector axis for slit positioning.Setting the slit in the plane of the face of the wayswhich contacts the register frame is achieved with anauxiliary microscope fitted with a 47.5X apochromaticobjective of 0.95 N.A. Hence its theoretical depth offocus is 0.7 ,um, and it can be set consistently to +0.5Am. It is first focused on the surface of an optical flaton which its mechanical feet rest.

Vil. Light Source and Condenser System

The illumination system is required to provide ahigh brightness (radiance) that is reasonably suitablespectrally to permit correcting the system to be equiv-alent to daylight with an aerial film, being uniformover both the area covered by the slit travel and thecamera entrance pupil.

15 April 1986 / Vol. 25, No. 8 / APPLIED OPTICS 1285

400 bW W nm

Fig. 3. Condenser and relay system used to illuminate the object slit. The locations of spectral correction filter and object slit are indicated.

A 500-W quartz-iodine projection lamp type EHAwas chosen. Its filament structure is 8 X 8.5 mm,biplane, backed by an internal mirror.

This lamp has a nominal color temperature of 3300K and life of 75 h when operated at its rated voltage of120 V. For the present use it was necessary to cali-brate individually the lamps for color temperature.All were set to 3113 K, which happened to be thehighest color temperature standard available. Thetheoretical reduction in output to 60% of nominaldoes not seem to be a problem. It is offset by a theoret-ical life of 8 times nominal.

The condenser and relay system used with it is illus-trated in Fig. 3. The first three elements are a special-ly designed high-aperture aplanatic system to mini-mize brightness fall-off toward the edges and toprovide the first stage of magnification needed to over-fill the collimator objective. These elements are ofquartz to survive heat from the lamp. The remainderof the system is conventional with the addition of thetwo narrow-angle diffusers shown. These are groundglass with the ground surface covered by a cover glasscemented on with a nonmatching index of refraction.5They provide just enough diffusion to break up thefilament-image structure that would otherwise appearat the collimator objective. Brightness uniformityover the collimator aperture of 125 mm drops to 95%at the edges but is good to ±1% over a 153-mm f/4entrance pupil and ± 1.5% over a 300-mm f/4 entrancepupil.

IX. Spectral Correction Filtration

It was desired to adjust the product of the sourcespectral radiance, the spectral transmittance of thebench's optical system, and the photomultiplier's sen-sitivity, say B, to match the product of daylight andthe spectral sensitivity of one or more selected aerialfilms, say, F. 6-8 To evaluate the correction needed, aset of Ditric three-cavity narrowband interference fil-ters (20-nm steps and 20-nm passbands) was spec-trophotometered from 250 to 700 nm in 5-nm steps andfrom 650 to 2450 nm in 20-nm steps and each throughits passband in 1-nm steps. The transmission of eachfilter was then calculated for F, giving, say TCA, andmeasured on the bench giving TM,. The necessarycorrection filter transmission is then given by TF =TC,/TMx. (To preserve the optical geometry for

nmFig. 4. Designed and actually obtained transmission curves for the

spectral correction filter covering the range from 400 to 720 nm.

these measurements, a simple telescope doublet lenswas used to form the slit image in place of an aerialcamera. The spectral transmission of this small lenswas also measured by spectrophotometry and is in-cluded in F)

Interference filters to meet the requirements TFxwere then designed and fabricated at NRC.9 It wasfound desirable to make two because the one coveringthe whole range from 400 to 720 mm had to have a widerange of transmissions and hence a low overall trans-mission to obtain enough light (relatively) in the blueregion. A second one covering only 470-720, which isadequate for any camera fitted with a yellow or darkerfilter, gave 5 times the transmission and hence bettersignal strength. The spectral fit achieved by the firstfilter is shown in Fig. 4.

X. Light Collecting System

The film-plane slit, a clear line in a chromium coat-ing on a borosilicate-crown glass 1 mm thick is coupledby microscope immersion oil to a specially designedcollector lens of 1.0 N.A. resembling a scaled-up oil-immersion microscope objective, whichis shown in Fig. 5. The index of the glass disk is closeto that of a photographic emulsion, so that acceptanceand reflectance at the surface are similar to film. Thelens collects all the light that enters the slit at any

1286 APPLIED OPTICS / Vol. 25, No. 8 / 15 April 1986

Fig. 5. Collector lens.

angle. It images about half of this light through abeam splitting prism to a conventional microscopeeyepiece, thus permitting visual adjustment of the sys-tem. The other half is reflected from the beam splitterto a relay lens which images the collector system's exitpupil on a diffusing prism in front of the photocathodeof a side-on photomultiplier tube (RCA4840 for pan-chromatic film simulation or RCA4832 for IR filmsimulation). The prism has entrance and exit facesground for diffusion, and its sides have reflecting alu-minum coating. Thus it acts as an integrating cube toreduce the variation in the distribution of illuminationon the photocathode as the used portion of the collec-tor lens exit pupil varies with field angle. This must bedone because the sensitivity of the photocathode var-ies over its area. Completeness of diffusion competeswith transmission efficiency which affects signalstrength. Hence a compromise was needed. For con-stant input at various pupil positions, the signal dropsfrom 100% at the center to 84% at the edge. However,for any one camera field angle, the variation over theused part of the collector aperture is less than ±2%.

Xi Electronics

The high-voltage regulated power supply for thephotomultiplier tube is a Fluke 412B.

Electrical output current from the photomultipliertube is fed to a current-to-voltage transforming headamplifier using an LHOO52.

Its output voltage is read by a Hewlett-Packard3478A integrating digital multimeter on commandfrom an HP9816 microcomputer at a selectable timeinterval and recorded by the computer for processing.If desired, an auxiliary circuit injects a reference tim-ing pulse, triggered by a microswitch at the movingobject slit, to provide for comparing scans made with,for example, different spectral bandpass filters.

The voltmeter can be read at an interval as short as0.23 s when using an integration time of 1/6 s and at aninterval as short as 0.05 s when using an integration of1/60 s that is integrating over one power supply cycle.

Power for the light source is regulated by a Sorensenpower supply model 1001 set by a W1OM Variac vari-able autotransformer and monitored by a Fluke Digi-tal Multimeter 8050A accurate to 0.6% true rms.

XII. Use of Bench

The first lens cone used for system evaluation wasthe Wild UAg R-10 cone equipped with a front-pro-jected reseau, which is located on a plane surface re-

cessed from the image plane -160 gim. It was notedthat a ghost image of the slit was being recorded with-1.5-2% of the energy of the main image and displacedfrom it by an amount proportional to the off-axis angle.It was found to be due to an interreflection between theimage slit's chromium surface and the reseau glass.Its small effect can be adequately eliminated computa-tionally. Another ghost was found at the on-axis posi-tion. It was due to an interreflection through thecamera lens between the chromium surface and theantivignetting filter. It can be avoided by taking on-axis readings slightly (1 mm) off-axis. Alternativelythe filter could be tilted slightly for the test.

The central parts of seven line spread functionswhich were measured on a bench are shown in Figs.6(a) and (b) for tangential and radial slit orientation,respectively, at 0, 15, 30, and 45. All readings weretaken at the same constant time interval of 0.23 s,which resulted in the following distance steps in theimage plane:

0.

15'tangential150 radial300 tangential300 radial45° tangential450 radial

1.87 ,um,2.00 /um,1.94 /Am,2.49 ,um,2.16 ,um,3.74 /im,2.65 ,im.

The 128 points located on each side of the center ofgravity which was also used as a reference point forplotting Figs. 6(a) and (b) were selected from the 913points read for each line spread function and used forthe fast Fourier transforms. Visible in Fig. 6(a) arealso the ghosts caused by the camera reseau at 15 and300.

Figures 7(a) and (b) show the modulation transferfunctions derived from the line spread functions ofFigs. 6(a) and (b), respectively, and Figs. 8(a) and (b)the corresponding phase transfer functions. Theasymmetry in the line spread functions for off-axisscans in radial direction [Fig. 6(a)] causes pronounceddirectional changes in the phase transfer functions forfrequencies between 25 and 8 lp/mm. These frequen-cies correspond approximately to the resolution ob-tained with this lens type when Kodak Double-X Aero-graphic film (2405) is used. It was found desirable tocommence the fast Fourier transform at the point with.the maximum reading rather than the center of gravityof the line spread function to position the phase trans-fer functions into the vicinity of the 0° axis.

The line spread functions for off-axis scans in tan-gential direction are, as expected, symmetrical andproduce line spread functions without pronounced di-rectional changes for 15 and 300 and for a modulationexceeding -5%. The scan in tangential direction at450 [Fig. 6(b)] confirms the formation of a doubleimage which is clearly visible if a thin radial line isphotographed with this lens; the line spread function issymmetrical and has two pronounced peaks. The cor-responding phase transfer function shows repeatedcontrast reversals, while the modulation transfer func-tion indicates spurious resolution.

15 April 1986 / Vol. 25, No. 8 / APPLIED OPTICS 1287

VOLTS

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30 IIII

25 III

___________________________I' ____I, ________

15°L 300 - - - - - -A 5'

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(b)Fig. 6. Line spread function obtained for a Wild Universal Aviogon mapping lens equiped with a front-projected reseau.

XIll. Conclusions

Development of a facility for determination of opti-cal transfer functions for aerial photographic lenseswill enable an improved assessment of the imagingquality done in the past by resolution tests. The newfacility will provide data needed to enable a systemanalysis of the mapping process based on aerial pho-

tography. The data to be gathered with the facilitywill also be used in support of the development of anISO application-oriented OTF standard.

The authors would like to acknowledge the contri-butions from the Mechanical and Optical ComponentsLaboratories of NRC's Division of Physics, which areheaded by H. M. Pink and B. E. Roberts, respectively,

1288 APPLIED OPTICS / Vol. 25, No. 8 / 15 April 1986

.30

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II

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in

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Fig. 7. Modulation transfer functions derived from the line spreadfunction shown in Fig. 6: (a) tangential slit orientation; (b) radial

slit orientation.

Fig. 8. Phase transfer functions derived from the line spread func-tion shown in Fig. 6: (a) tangential slit orientation; (b) radial slit

orientation.

by C. Dodd, R. C. Find, and D. Gignac of the Photome-try and Radiometry Section, and by J. A. Dobrowolski,F. C. Ho, and P. Brennan of the Length and Mechani-cal Standards Section of that Division. Generous fi-nancial support was made available by the Surveys andMapping Branch of the Canadian Federal Departmentof Energy, Mines and Resources in Ottawa.

References1. L. E. Howlett, "Photographic Resolving Power," Can. J. Res. A

24, 15 (July 1946).2. P. D. Carman and H. Brown, "Resolution of Four Films in a

Survey Camera," Can. Surv. 24, 550 (1970).3. R. L. Lamberts, G. C. Higgins, and R. N. Wolfe, "Measurement

and Analysis of the Distribution of Energy in Optical Images,"Opt. Soc. Am. 48, 487 (1958).

4. R. L. Lamberts, "Relationship between the Sine-Wave Responseand the Distribution of Energy in the Optical Image of a Line," J.Opt. Soc. Am. 48, 490 (1958).

5. M. C. King and D. H. Berry, "Small-Angle Diffusing Screens forPhotolithographic Camera Illumination Systems," Appl. Opt. 11,2460 (1972).

6. P. D. Carman, "A Light Source for Sensitometry of Aerial Films,"Photogr. Sci. Eng. 13, 376 (1969).

7. CSA Standard Z7-3-2-1-1969, "Sensitometry of Monochrome Ae-rial Films," Canadian Standards Association, 178 Rexdale Blvd.,Rexdale, Ontario, Canada.

8. P. Moon, "Proposed Standard Solar Radiation Curves for Engi-neering Use," J. Franklin Inst. 230, 583 (1940).

9. J. A. Dobrowolski, "Optical Interference Filters for the Adjust-ment of Spectral Response and Spectral Power Distribution,"Appl. Opt. 9, 1396 (1970).

15 April 1986 / Vol. 25, No. 8 / APPLIED OPTICS 1289

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