summary report for grant nag/i/1476 engineering design of

NASA-CR-194573/'/J-_ 7- c _....

Summary Report for Grant NAG/I/1476

Engineering Design of Sub-Micron Topographies for

Simultaneously Adherent and Reflective Metal-Polymer Interfaces

Principle Investigator: Christopher A. BrownMechanical Engineering

Worcester Polytechnic Institute100 Institute Road

Worcester, MA 01609

submitted: October 29, 1993

(NASA-CR-194573) ENGINEERINGDESIGN OF SUB-MICRON TOPOGRAPHIES

FOR SIMULTANEOUSLY ADHERENT ANDREFLECTIVE METAL-POLYMER INTERFACES

(Worcester Polytechnic Inst.) 56 p

N94-15700

Unclas

G3/21 0190559

INTRODUCTION

The approach of the project is to base the design of multi-function, reflective topographies

on the theory that topographically dependent phenomena react with surfaces and

interfaces at certain scales. The first phase of the project emphasizes the development of

methods for understanding the sizes of topographic features which influence reflectivity.

Subsequent phases, if necessary, will address the scales of interaction for adhesion and

manufacturing processes.

A simulation of the interaction of electromagnetic radiation, or light, with a reflective

surface is performed using specialized software. Reflectivity of the surface as a function

of scale is evaluated and the results from the simulation are compared with reflectivity

measurements made on multi-function, reflective surfaces.

METHODS

Simulation

In this work a numerical simulation of light interaction with a surface is compared with

reflectivity measurements made at NASA with a Perkin-Elmer Lambda5 scatterometer.

Light is emitted from a source, reflected by a surface and then intersects a detector.

Topography

In the simulation, we represented the topography with a 200 x 200 grid of points acquired

by a scanning tunneling microscope (STM), where the points are located in a grid in x and

y with a height z. The STM work was performed at NASA Langley on a Digital

Equipment Nanoscope II. Six topographies were scanned at three scan sizes, 201.tm x

201.tm, 2_tm x 21am, and 200nm x 200nm (see Table 1).

The large, topographic data sets, used to represent the surface, are analyzed by the

patchwork method where the surface, represented by the data points, is tiled with

triangular patches (Brown et al. 1992). The topography is evaluated over a range of

scales, or patch sizes, by tiling over the surface with decreasing patch sizes. In the

simulation each patch represents a reflective facet, atomically smooth and a perfectreflector.

The triangular patches are placed on the surface in two directions: parallel and

perpendicular to the STM scan direction. Reflectivity calculations are made for each

direction and the results of the simulation are the average of the two calculations.

Lambda5 Scatterometer ..

We created a computer model of the Perkin-Elmer Lambda5 scatterometer from optical

path representations of the scatterometer and reflectivity assembly which were provided

by Perkin-Elmer. The incident angle of the light is user-defined, and the detector was

modeled as a rectangle at the position and orientation defined by the optical schematic.

The size of detector was defined from an engineering drawing of the detector which was

J i- '_

provided by Hammamatsu (part number R298 HA). The output of the detector was

assigned a value of unity for any intersection of a reflected ray with the detector.

Table 1 STM Scan and Reflectivity Measurements

SURFACE STM FILENAME MATERIAL POINT SPACING

X x Y • Z (nm)

REFLECT %

20 DEGREES

531 nm

A NASA22 TTM1R-P 1 100 69.1

A NASA23 T7MIR-PI 10 69.1

A NASA24 TTMIR-P I 1 69.1

B NASA25 P4H1R I00 46.7

B NASA26 P4HIR 10 46.7

B NASA27 P4HIR I 46.7

C NASA16 D25M2R-P30 I00 44.7

C NASA17 D25M2R-P30 10 44.7

C NASA18 D25M2R-P30 I 44.7

D NASA19 TTH3R 100 44. I

D NASA20 T7H3R 10 44. I

D NASA21 T7H3R 1 44.1

E NASAl3 D25HIR-P30 100 15.2

E NASA14 D25HIR-P30 10 15.2

E NASA15 D25HIR-P30 I 15.2

F NASAl0 P4M1R 100 14.1

F NASAl I P4M1R 10 14. I

F NASA12 P4MIR 1 14.1

The lighL emitted by the source was modeled as set of parallel rays that originate from the

source, travel to the surface and are reflected by the center of each patch. One ray is

generated for each patch. The direction of the reflected ray is calculated from the incident

ray direction and the normal of the patch. From the center of the patch, the ray is

reflected off of an optical wedge, a concave, spherical mirror and then it is determined if

the ray intersects the detector.

The output of the Lambda5 is percent reflection relative to a known reference sample, in

this case the reference sample was a stainless steel mirror provided by Perkin-Elmer. The

reflectivity measurements are expressed in terms of a percentage of the measured

reflectance from the reference sample.

Reflectivity Simulation

We ran the computerized simulation on the 18 STM data sets with an incident angle of 20

degrees. The simulation generated the incident rays, reflected them off the patches and

counted the rays which rays intersected the detector. The output of the simulation R, or

absolute percent reflectivity, is defined as the number of incident rays that intersect the

detector is divided by the total number of rays reflected by the surface. R is calculated for

each patch size and is plotted versus log(patch area). RR, or relative reflectivity, iscalculated from R as

RRA.n = (RA-KB)/R_A [eq. 1]

where RA>RB.

The simulation was modified to account for the effect of patch orientation on the intensity

of the incident rays. The intensity of the incident ray, initially equal to one, is multiplied by

the cosine of the angle between the patch normal and the incident ray. The ray is then

reflected by the patch and the simulation records the number of rays and their intensities

that intersect tlie detctor. The output of the weighted reflectivity simulation, Rw, is

R w = (E intensity collected rays) / number of reflected rays. [eq. 2]

Reflectivity Results

We combined the simulation's reflectivity results from the three scans sizes into one larger

set of results using Matlab, a matrix-based software program. The large set of results,

combined for each of the six surfaces, covered a range of patch areas of 7 orders of

magnitude, from 0.5 nm 2 to 3p.mL Table 2 shows the range of scale for each of the three

scan sizes and the data point spacing of the scans.

Table 2. Large and Small Patch Sizes for Three STM Scan Sizes

Scan Size Large Patch Size Small Patch Size Point Spacing

20um x 20um 3 l.tm 2 5000nm 2 lOOnm

2 um x 2 um 5000nm 2 50 nm 2 10rim

200 nm x 200nm 50 nm 2 0.5 nm 2 lnm

When the scan sizes were combined, the magnitudes of R did not correspond at the joining

patch size. The values of R were shifted by the difference between the scans so as to

match at the joining patch size. The R values of the largest scan size (20urn x 20urn) were

used as the zero shift scan when the scans were shifted up, and the R values of the two

scans (21xm x 2_tm and 200nm x 200nm) were shifted up to the zero shift scan. When the

scans were shifted down, the smallest scan size (200nm x 200rim) was the zero shift seart,

and the two larger scans were shifted down to it. The shifted results were used to

generate plots of absolute reflectivity vs. log(patch area).

Relative reflectivity results were calculated from the shifted scans for shifted up results,

and plots of relative reflectivity vs. log(patch area) were generated. Calculation of relative

reflectivity (RIO, from eq. 1, was designed to factor out the dependence on the reference

sample. Surface A, which has the largest reflectivity measuremen.t, was used as the

referencein theplots. A negativevalueofR R indicates that the reflectivity of the surfaceis greater than surface A.

Scale of Interaction

The results of the reflectivity simulation are compared to experimental results, obtained

from NASA Langley's Lambda5, to calculate a scale of interaction of the light with the

surface. The scale of interaction was defined as the square root of the patch area, from

the reflectivity simulation, where the corresponding magnitude of R is equal to the

reflectivity value measured by NASA on the Lambda5. Figure 1 shows how a scale of

interaction is found from the simulation and experimental results.

REFLECTIVITY (ABSOLUTE) vs SCALE

L" 100%

U

111m

"d =_

(D

¢t

0%

region 3 region 2

Yregion 1

scale of Interaction

LOG(Scale of Measurementor Triangle Patch Size)

Filzure 1- Schematic of Calculation of Scale of Interaction from Idealized, Absolute

Reflectivity vs. Scale The intersection of the measured reflectivity is found, and the scale

of interaction is calculated from the corresponding patch size. The scale of interaction is

shown to occur in region 2.

RESULTS

Relative Area

The STM data sets were analyzed by the patchwork method and a representative scale-

area plot is shown in figure 2 (Brown et al. 1993). The scale-area analyses were

conducted on each of the three scan sizes separately. All of the scale-area plots are foundin Appendix A.

4

Absolute Reflectivity

Absolute reflectivity as a function of scale, or patch area, was calculated by the reflectivity

simulation. Shifted up an shit_ed down results for surface A are shown in Figures 3 and 4.

Absolute reflectivity plots for the six surfaces are found in Appendix B.

Cosine Weighting - incident angle

Absolute, cosine-weighted reflectivity as a function of scale, for surface B, is plotted with

non-weighted results in Figure 5. Cosine-weighted results for the six surfaces are found in

Appendix C.

Relative Reflectivity

Relative reflectivity as a function of scale, for surface B relative to A, is shown in figure 5.

Relative reflectivity plots for surfaces B through F, relative to A, were generated using

shifted up results. The plots are found in Appendix C.


A scale of interaction was calculated from the absolute reflectivity plots. Table 3 lists the

scales of interaction found using the absolute reflectivity results. The reflectivity

measurements did not intersect the relative reflectivity results, and no scales of interaction

were found.

xdataxlanglegxnasall200 relative areas calculated

Average/Patch Size 8 Surface CoverageRelative Surface Area vs. Patch Area

Ouadrant (1,1) of (1,1)Crossover lou: 205

Crossover high: 2.01e+03Data-dependant

1.07

1.06

1.05

w 1.04>

1.o3

O_

1.02

1.01

1.00m-

I00ri=0.863423

g =-0.031859x+0.0946446.186e+01 to 6.186e+02

=w

-Ioo

°° I='°Oo.°°°°° _

t, ooo t o,_oo 1oo.oooPatch Fu'ea (nm =)

Fi_Ltre 2 - Scale-Area Plot of Surface A_ The 2mm x 2ram scan size is shown for

surface A. The relative area begins to increase (crossover) at a patch area of 2810 nmL

5

REFLECTIUIT¥ (ABSOLUTE) vs SCALE - SHIFTED UP

1(38SU_VACE. ! ! ! !

_ 6eo

e

48 ..........................•............".............:.........................*.........:..._............

e0

ao

28 .............:.............,............:.............".......................................,............

:8 ............_.............:............;.............t .......................................;............

; i • ; ;18-_ 18 Q 18 £ [82 183 184 18 S 186 18 ?

LOG(Pa%ch Area) |n sq. n.

(Fi_,ure 3 - Shifted Up Absolute Reflectivity Results for Surface A The percent

reflectivity is 100% at large patch areas and decreases to about 53% at the fine patch

sizes. The largest scan size was used as the no shill scan.

,,iooe

o

I:e0

@

188

8e

REFLECTIUITY (ABSOLUTE) vz SCALE - SHIFTED DOUH

SURFACE A _

.E_SUa_D _rL_CTIVXTV:69_Ix

............ J ............. 1 ............ [ ............. _ ......................... _............. _ ............

6B ............ • ............. • ............ e............. .. ............

48

8

18-J.

Z8 !!!!!!!!iii!!ii!iiiiiI !!!!!l! I I I I I I

180 10,1L 182 18S 184 . 18_S 186 187

LOG(Pa%ch Area) 1. eq. nm

Figure 4 - Shifted Down Absolute Reflectivit7 Results for Surface A. The percent

reflectivity is about 48% at large patch areas and decreases to about 0% at the fine patchsizes. The smallest scan size was used as the no shill scan.

6

18B

REFLECTIUITY (_tBSOLUTE) va SCALE - SHIFTED" UP

o i+ i80 HEI_SURED ]_FLECT IV I TY=4? ."TX _ ....... _............. _ ............

f;

68 __ "+ ............ " ............. !': ..........

..... .'" i

i

40 ............ -.:............. _ ............ : ...................................... _ ............. : ............

ZO ...... ":.......................... _".......................... I ............ ":............. ; ...........

...... .:............ ; ............ .: ............. _ ............ ; ............ .:.............. ; ...........

e ...... i ", i ; ; ; ;E-J. 188 18 t 16 z 183 1B 4 165 186 16 ?

.@

,puo

.-4

0U

0

LOG(Pa(ch Area) Ln 8q. nm

Figure 5 = Incident Angle Cosine-Weighted and Non-Weighted Absolute Reflectivity

Results for Surface B. The difference between the cosine weighted and unweighted

results is shown. Cosine weighting shifts the set of results down by a factor of 0.94

(a multiplier of cosine 20°), or shifting the results down by 6%. The results are shifted by

an equal percentage at all scales.REFLEC'rIUITY (RELATIUE) vz -RCALE - SHIFTED UP

! ! ! ! | !6.2 t

_IE_SUREI_ REL_TI.UE REFLECTIOITV; = 0.3_2!

.1 _u.PAc_i(n-.)]0_ ... ....

0

-8.1

-8.2

: • c .... +'_ ...... _ ...........-8,3 ............ • ............................... , , • •

-8.4 .......... ":............. ; ............ • ........... "_............ : ............ _"............. ; ............

-8.5 ......

OID

0I>

II

ID

f I i I I I

-8"_8-x 16o 18 x 18 z 18 a 184 185 186 18 ?

LOG(Patch Aeoa) In a q. nn

Figure 6 - Relative Reflectivit7 Results for Surface B Relative to Surface A. The

maximum relative reflectivity value is about. 15 which is less than the measured result. R R

is negative at patch areas less than about 500 nm 2-

¢, i . II

Table 3 Scales of Interaction from Absolute Reflectivity Results. Surface A is the

surface with a scale of interaction from the shifted up results. The scales from the shit_ed

down differ by about I order of magnitude.

Surface Scale of Interaction (nm) Scale of Interaction (nm)

shifted up shifted downA 39 x

B x x

C x 102

D x 164

E x 13

F x 18

DISCUSSION

Relative Area

The scale-area plots show that the reflective topographies are complex at fine scales, and

the relative areas, a measure of complexity, increase with decreasing patch size. The

difference between the relative areas of the three scan sizes is clear: the maximum,

relative areas of the 200nm x 200nm scan size are approximately 2 orders of magnitude

larger than that of the 2 lam x 21am scan size and approximately three orders of magnitude

larger the smallest scan size.

Absolute Reflectivity

The plots show three distinct regions over a range of scale. In region 1, occurring at

patch sizes down to 105 nm 2, the percentage reflectivity (R) remains constant over a range

of patch sizes. Decreasing patch size does not change the amount of reflected light that

reaches the detector, and R is largest in this region.

In region 2, occurring at patch sizes from 105 nm2to 100 nm 2, R decreases with

decreasing patch size. Decreasing patch size decreases the amount of reflected light that

reaches the detector, and R in this region is less than region 1 and greater than region 3.

In region 3, occurring from a patch size of 100 nm 2 to 0.5 nm2,+R remains constant.

Decreasing patch size no longer decreases the amount of light that reaches the detector,

and R is lowest in this region.

The material properties of the surfaces, i.e., conductivity, absorbtivity and transmissivity,

were not considered in the simulation, and would shift the plots down from the shifted up

condition. The downward shift would increase the calculated scale of interaction, and,

depending on the size of the shift, would cause the measured reflectivity results tointersect the simulation's results.

Incidentanglecosineweighting shiftsthe reflectivity simulation results down for all of the

surfaces, and the percentage shift is constant for all scales. It is speculated that the

percentage shift is constant at all scales because the collector is small, and only rays close

to the direction of specular reflection are collected. Reflected rays with a weighting

factor close to zero would reduce the results by more than 6%, but these rays, with a small

weighting factor, will not be reflected close to the specular direction, and will not intersect

the detector. The weighting factors of the collected rays are close to cosine (20°), and

shift the results down by 6%.

Relative Reflectivity

The measured results do not intersect the relative reflectivity results at any scale, which

may be because the scale of interaction theory is wrong or because we are misinterpreting

the results of the reflectivity measurements. It was expected that all relative values would

be positive, at least at one scale, because the calculations were made relative to the surface

with the largest reflectivity measurement, surface A, and that this scale would correlate

with the reflectivity measurements. The plots show that surface A is less reflective than

most of the other surfaces and that the surface with the largest R R changes with scale.

The reflectivity measurements made by NASA are expressed as a percentage reflectivity of

a stainless steel reference sample. It is not yet clear how we should interpret this

representation of reflectivity compared to the computer simulation. Relative reflectivity

plots were generated to factor out the dependence on the reference sample, but we have

not been successful. Including conductivity and absorbtivity of the reference sample in the

computer simulation may provide a truer representation ofNASA's reflectivity method.

Also, more information about how the Lambda5 processes the output signal from the

photo multiplier tube may give a better understanding of the equipment's output.


Joining the three scan sizes effects the scale of interaction calculation; shifting up

decreases the scale and shifting down increases it. Possible causes of mismatch at joining

patch areas are the patch placement algorithm, differences in the STM scan parameters for

the three scan sizes or variability in material properties over the different scan areas.

The current algorithm places a small number of patches at the large scales (large with

respect to data point spacing), and may provide a poor representation of the topography.

Since the topography may be more precisely represented with decreasing patch size, the

joining patch size may be thought of as a boundary separating regions of high and low

precision.

Changes in material properties of a surface will also change how the tip interacts with the

topography. Efforts were made to minimize the effect of local changes in material

properties, but the scans may have been effected to some degree.

Future Work

The work will be continued under a NASA training grant, grant number NGT-51107. In

future work other reflectivity methods, such as total integrated scattering (TIS), will be

investigated as a means for better understanding the amount of energy reflected by the

surfaces. Reflectivity samples will made from homogeneous materials to reduce the

complexity of the reflectivity simulation by eliminating multiple layer materials and

distributed reflective particles. Random patch placement algorithms will be investigated

that may better represent the interaction of light with the surfaces.

CONCLUSIONS

1. The scale-area plots show that the reflective topographies are complex at fine scales,

and that the relative areas, a measure of complexity, increase with decreasing patchsize.

. Simulation of a reflecting surface as a collection of triangular mirrors and decreasing

the size on each repetition results in a steady decrease in the amount of light arriving

at a detector, indicating increasing scatter or diffuse reflection at finer scales.

. Ranking of the surfaces based on reflectivity calculated from the current algorithm

does not correspond at any scale, to the ranking from reflectivity measurement, as

they are currently interpreted.

4. The scales of interaction calculated from the current algorithm do not share a

common region of reflectivity with the measured values.

REFERENCES

C.A. Brown, P.D. Charles, W.A. Johnsen, S. Chesters, "Fractal analysis of topographic

data by the patchwork method",WEAR, 161, 61-67, (1993).

10

Appendix A

Scale-Area plots

, i

\dataxlangleyxnasalO200 relative areas calculatedRverage/Patch Size & Surface Coverage

_elative Surface Rrea vs. Patch Area

Quadrant (1,1) of (1,1)Crossover Iou: 1.33e+04

Crossover high: t. Ite+05Data-dependant

tO

%..

_E

>,_,'4

rY

1.001

t.O00

r_=0.819703y =-0.000499x+0.0023295.133e+03 to 5. t33e+04

• ,,, ,-.°'.° °.°

Ioo,ooo i,oo6,ooo

°

• • °

io,boo

Patch Area (nm _)

xdataxlanglegxnasa11200 relative areas calculatedAverage/Patch Size & Surface Coverage

Relative Surface Area vs. Patch Area

Quadrant (1,1) of (1,1)Crossover lou: 205


(I=

3

1.07

1.06

1.05

1.04

1.03

1.02

1.01

1.00._n=-0.0319 L

• • .•

IO0r_=0.863423g =-O.031859x+O.0946446. t86e+Ot to 6,186e+02

I

I, 000 to,ooo too;oooPatch Rrea (rim:)

,,data,,langley,,nasa12200 relative areas calculatedAverage/PatchSize _ Surface Coverage

_elative Surface f_reavs. Patch Qrea

Quadrant(1,1) of (1,1)Crossover lou: 2.16


2Q;

QJ

).o.-i

CZ

I

1r2=0.737951y =-0.159053x+0.6395341.297e+03 to 1.297e+04

, -,-"

16oPatch Area (nm 2)

I

!• •, | •,

i .. • ..* !i. ,.. ., :

1,000 10,000

"'.L"#_,_" "-

",b

\dataxlanglegxnasa13 Quadrant (Ipi) of (I_i)200 relative areas calculated Crossover low: 6.76e+03Rverage/Patch Size & Surface Coverage Crossover high: t.95e+05

#etative Surface Rrea vs. Patch Rrea Data-dependant

1.001

i_ i . • " j

0: 1 " ". i

i " .i.. "',-.i i ' - .-..o .

0 0004 _. "_

l.O00 . ;..:10, 000 lO0;O00 l,000, OOO

r _=0.628521q =-0.000398x+0.001966 Patch Area (nm _)71136e+03 to 7. 136e+0"{ "_'s,"_m_ "_'-"

\dat a\l angl ey-,nasa 14200 relative areas calculated

Rverage/Patch Size & Surface Coverage[_elative Surface Rrea vs. Patch Rrea

Quadrant (l,l) of (1, I)Crossover lou: 200

Crossover high: 6e+03

Oat a-dependant

eJ

_E

rr

1.t

._=-0.0312t.O _ .:

tO0r_=0.915981

g =-0.031221x+0.1021326.096e+01 to 6.096e+02

!

1,000

"°@,

tO, 000 I00,:000

Patch Area (nm 2)

\dat a\l anglegxnasa15200 relative areas calculatedAverage/PatchSize & Surface Coverage


Quadrant (1,1) of (t,1)Crossover lou: 2.02

Crossover high: 3.22e+03Oata-dependant

1.9

1.8

1.7

1.6t8

_- 1.5<E

_b 1.4>

...4

1.3

O_

1.2

1.1

1.0:

r _=0.998551

i

_=-o.ioio F

10

g =-0.100961x+0•2581765.076e-0 to 5.076e+00

16oPatch Area (nm _)

"-'----:4.%,.1,000 10, 000

xdata\langlegxnasa16200 relative areas calculated

average/Patch Size & Surface CoverageRelative Surface area vs. Patch area

Quadrant (1,1) of (1,1)Crossover low: 6.72e+03


t@@J

k.

>

¢@

n"

1.001

1.000

r_=0.780745

g =-0.000692x+0.0032005.052e+03 to.5.O52e+04

'' °,

F

100,:000 I, 000,000I0,000

Patch area (nm 7)

"._-'__t" •"-

\data\langle_\nasa17200 relative areas calculated

Rverage/Patch Size & Surface Coverage_elative Surface Rrea vs. Patch Area



tU

_E

Q;

>

r_"

l.l

(

1.o_---o.o_t O0 l, 000

r 2=0.846938

y =-0.069470x+0.2031806.098e+01 to 6.098e+02

• 0,

lo,boo loo/oooPatch Rrea (nm=)

\dat axlangiegxnasa18200 relative areas calculated

F_verage/Patch Size _ Surface CoverageRelative Surface Area vs. Patch Area

Quadrant (t,t) of (t,t)Crossover Iou: 2.04 .

Crossover high: 590Oata-dependant

tlJ

Q;

Q;

>

rr

t

r_=O.gS5tgO

,_=-0.2248 _-"i P

t;g =-0.224827x+0.4522982.499e+00 to 2.499e+01

• °,• .

ioo t,ooo to,oooPatch Area (nm _)

"._-I#_,_-t- •'--

%dataxlangleyxnasa19200 relative areas calculatedRverage/PatchSize & Surface Coverage

Relative Surface Rrea vs. Patch Rrea

Quadrant (1,1) of (i,I)Crossover lou: d.72e+03

Crossover high: 6.01e+04Oat a-dependant

l.OOl

rY

1.000:

r_=0.849912

g =-0.000427x+0.0019985.052e+03 to 5.052e+04

@

• _o0=

ir_ ' "''" "°'"'"'°'°='" ""

!

I0,000 tO0, 000 1,000,000

Patch Rrea (nm 2)--" -_--n_,,I_ •'-"

\dataxlanglegxnasa20200 relative areas calculatedAverage/PatchSize & Surface Coverage

Relative Surface Rrea vs. Patch Rrea

Quadrant (1,1) of (1,1)CrossoVer lou: 200


1.1

CO

L |<E " • i

Q;

>°,-i

n-

,J_=-0.03571.0 'j...;

100r ==0.861"{22

g =-0.035737x+0.1103256.096e+01 to 6.096e+02

: . . .:

I, 000

"•° •

I0, _]00 100,: 000

Patch Area (nm:)

\data\langtey\nasa2l200 relative areas calculatedAverage/Patch Size & Surface Coverage

Relative Surface Area vs. PatchArea

Quadrant (lit) of (1, t)Crossover lou: 2

Crossover high: t 12Oat a-dependant

3

rV

_: 2

:>

C£

1

i

i .

,a_=-O. 2341 L

q = P

tO

•0

iI, I

"°'°,l._°w_ I

t,6oo to,ooor_=0.999792

y =-0.234t34x+O.5081673.18te+00 to 3. t8te+Ot

Patch Area (nm _)

\dat a\l angl egxnasa22200 relative areas calculatedAverage/Patch Size & Surface Coverage


Quadrant (1,1) of (1,1)Crossover lou: 7.02e+03


<I:

>

tU

rY

1.001

'10'3 _00r2=0.877183g =-0.000424x+0.0021195.316e+03 to 5.316e+04

"'. m

=-0.0004 _ _'_"_-._'_.1.000:: , . .P .... i

I00, 000 1,000,000

Patch Area (nm _)-&.._. _.-_- • ,.-.

-, r

\dat axlangl egxnasa23200 relative areas calculated

F_verage/Patch Size & Surface Coverage_elative Surface f_rea vs. Patch Area


Crossover high: 1.12e+04

Oat a-dependant

to

$.

>

tO

rr

I.I

_=-0.0513l.O • ,--,

lOOr_=0.891796LJ =-0.051281x+0. 1591"{75.096e+Oi to 6.095e+02

.

iLC

1,000

• -°.,

: - . . J

I0, bOO i00, OOO

Patch Area (nmD

\dataxlangleg\nasa24200 relative areas calculated

Qverage/Patch Size & Surface CoverageRelative Surface Qrea vs. Patch Qrea

Quadrant (ipl) of (1,1)Crossover lou: 2.06

Crossover high: 1.21e+03

Data-dependant

Q;>

°,-4

r_

6

5

4

3

2

l

r_=0.992119

g =-0.331929x+0.9464541.890e+01 to 1.890e+02

"" " "_';-'L.._,__.,._i:_ ! '-:-," I(30 1, (300 10, ()00

Patch Area (nm _)._.._.--,,_ • .,--

\dat a\l angI eg\nasa25200 relative areas calculatedAver age/Pat ch Size & Sur (ace Cover age

_elative Surface Qrea vs. Patch Area

Quadrant (1,1) of (1,1)Crossover lou: 1.32e+04


tUQI

_Z

(#>

.,-4

rr

1.008

1.007

1.006

1.005

1.004

1.003

1.002

1.001

1.000

r_=0.873382g =-0.002704x+0.0136865.499e+03 to 5.499e+04

i • "

-_ °

10,000 iO0;O00 1,000,000

Patch Area (nm 7)-_.#.._,_-_,_.,.,.,.,.,.,.,.,._•,,--

\dataxlangleyxnasa26200 relative areas calculatedAverage/Patch Size & Surface Coverage

Relative Surface Area vs. Patch Rrea



r0eJk.

Q;>

(brr

t"100

rz=0.960182g =-0.147334x+0.7078162.082e+03 to 2.082e+04

1,600

,_..: ,.-:.

h ,,5 b

._=-O. 1473 i -._i ........ , .'_ " : "'_"_-"-_--

t

i0, DO0 IDOl 000

Patch Area (nm 2)

xdata\langleyxnasa27200 relative areas calculatedRverage/Patch Size & Surface Coverage

_lative Surface Rrea vs. Patch Rrea

Quadrant (I,t) of (1,1)Crossover lou: 2.15

Crossover high= 2.26e+03Data-dependant

tU2

<IZ

rr

.i

._=-0.1467

r_=0.997406y =-0.146713x+0.4476664.338e+00 to 4,338e+01

• e w°" . ,_l

",o

t6o 1,6ooPatch Rrea (nm _)

w

10, C)O0

#

Appendix B

Absolute Refleetivity vs. Patch Area

g_

I

¢-N

<I:

l-,

N=¢

[..,eOf.d

f.d

'/E : : : : :

.'< ! ". i i i iv'.i : • : : " :

,.-, : - : - :............................... •: ............................ .:°o

E-,

GO T=

,PI

I I

N

_D

_D

,.4_D

?,el

E

o

,,,m

i-i

c_

I

_J

i,-i

Q

<_

i..,iI,--I

l, iI

Ib,.lr_

b.l

................................ ,.o...o+oo.°ooooooo,o

........ %+..............

,,,.j

I'-4

-e.

I

o

m

i-4

: : : ,i-4

.............................. "............... :............... :............... ... II_

x i ". i i ! i

..... ,..,_....... ._............... - ...... ._. _...: .............. .:.............. .:...i,-i

¢,,3 I_,<Z: _i

,,._° ._ ........ • ....... ...,.,.,..,,+,,+,.I

(d ,I-,

,e-I

.... +.oo°_°°°o° oo.++,,° °,.+o°+°.,° •..+.. o,+-I

_ 03 ,,,,,o,i,-4

£

o

o

l-I

.._

I

0

.!-4

.............. _ .............. %.... °.°..°°oo.° o°°°°°.°° ................. °°%°°°

......................i.............i....._ ........!......"......._.............._..............._...............i...

II : . : _ _

: " i i i..... _ ....... 2.............. _..' .......... _.............. _.............. _---

............_..............i............._.............._..............i-- °

_

_.._ ........ . .............. _ ........... _ ............... ...............

Go _d3

: : :::

! I I

_:l.TaTl.OaI ,_ot[ :l-UOO0eo_I

o.laa_

M

,,,4

•j ,,

I:_

I

P,

Of_

l-t

× i "- i i i iN : • : : : :

..... _ ....... .............. ............. ............... .............. 2"'"

: i . i i i• . ; • ,

.....m:......."................:.........................."..................

<= _ • .

I I f

(33 _ _,4 N

%v'4

v.4

_e

f:

¢.1

N

-I

,.4I

r._

r._

t

r._

o

:)

[-4

o

M

::>

r_

r_r_

....... .,°,,°°_ .......... .°.o_ .............. ,, .......... ...°_ ...... . ....... ._.°.

........... ,.., ...... .° .... ,.%.° ....... .,. °,, ° ° ° ° °, °,,,.,, ° o,,,, .. °, o. °,., °,'o,.

0r._

r._ _°1_;. -_ ....... ..".............. ; .............. .."....

r,_ I"

!

co (_ coc0 _ ,q_

In

o

o

(. °oo.o...°..,°..,,,.o...°...

o

I

q'j

!-i

oC_

I,-,I

I-i

IL,

0

o

I

o

m

v

i.-iM

!-I

I4

I,Q

allI1

1 I I

ii...... _ ........ : ...... ° ....... ,.° ..... .o°,°°°,_.oo°°o,°° ..... ..°°° ........ °. .,.°

_ :

....._ ..................... :............... _............ ..: .................

_.._ ........ _ ............... ................ . .............. •.............. _..

_E

I I I I I

(30

-i-30

t_

I

ot_

ot_

j.40

............................. • .................................. 0 ...... 0,,

iiiiiiiiiiiiiiiiiii iiii°II

_q

..... g ....... _ .............. _,o00,_,,,,,,0,_,00,,0,.,0o,0,,_00,00_.0000_0_ ...

...... oo,°,,°°_.,o', .......... 6, .............. _.°,._°..°°°°° .... _

"t_'"_ ........ °'°°°°°°°°°'°°_' '°°°'''°°°°°°°' '°°°°''°°''°°'%*°°'''°'°°°°°°° _.°

_ _ •r,_ E :

I I I I l-C_

c_c_

£

o

I--4

I

c_

oc_m

E_i-,4

C.1

I-1

..... _ ....... : .............. .:.............. : .............. : ..........

_ : i i !..... _ ....... .:.............. .:.............. J.............. .:..........

-_.._.°°...° oo.... °°.°, ,,,,,%o,.,..,n.,,,,-.,.gl_..,i, ,,.°%,,°,.°.,,,,,.,

I I

C_ CO _ _ NCO CD

Z

o

I

co

o

E-I

r_

• 0 ............... ,o.0°oo,oo. .... ,o°

........... ;oo

f

o

"to-

O

I

J-1

m

[4

i-i

(-)

_.1 54

._.._ ..... .....,. ..... • ...... 0 .............. _ ...............................

E

I I I

E5:

(I)

o

Appendix C

Cosine Weighted and Non-Weighted Absolute Reflectivity vs Patch Area

: J

,,_t_

I

D-1

t_

0

,m

0t_m<C

f_l,,.,4

:)P.-I

,r4

....... 0°_ .............. _ .............. _ ........... 0.o_ ........... 0oo_.°.w

£

0

0,-I

,el

1.4

fiil.lnll, oli I ,FOil _.u_o,_

I

c0

A

ov

k.4

! II ,-tI

OO ,,-t,,0

,r4

___ ....................... i °'°°°*°'°°°°°°'°'°°*°i ....! °°°°° ....... i _.... ........... i "''_ _

A

v

Fi_taT_OOl J_8 _uoo_ZOd

.=I

f_

A

<I:

=,w

:>

I,.4(3

iiii ,i iiiiiiiiiiix: . ! i ! i "-'

=,,i. • . "IFw: • ! " : " fJ

......................... •:...............:.............._.. N,-_: _;) l:q

O- (._r.,;: o

,'_ ,.4:• r,w:+) r_• o o

....._",_ "m;'......................................

,,.,w.(.,)i::i. ,_MF._ _) ,.I:;r._:u 3 _n m:: L ....

<: | "' _i

{n Z 0:=:

,i-I

. ,_(

,.(I ! I

Ir4,,.1

{4

=,

i.,i

0

<3:

E_

Ur_

........ °%°,°°°°.°,, ..... .00.0..0..0.0°°, .0 ..... 0..... 0 ..... 0

_.o.i

......... _.............. _............................................ _...

,-4

aD

_O

O0

CO

£

(I.1

U

0

Appendix D

Relative Reflectivity vs. Patch Area

rJ.

<= IZ::

.. IE... r/J.: ......... _......... _ ......... •

i w

I I

......... :. ...... ,,., ....... J

I

I I I

,,t-I

q-I

£

IZ°_,.4

I-4

¢==4

-r_p

5_

:>

G,I

v

C.)5d

f_

-._ .....:............................., ...............

::3 _:

--_:

_.. C_.:.........•........._.........s.........:....

N

I I!

I I I I I

G_!_T_OOTJO_ o_To _

w-I

£t:::

t_

tD

w.-I

K_

!

o_

L",-_3,rl

r,,r,,1

i

r._

P,,'4

(,,.1

r,_r.,,,lIx

t"4

_3

-._ ...... : : _ ,.......... :,......... :.......... :......... . .........

('q . : _: : : . : :

! i i ! i : iit : : : i _ i i..... "_......... ! ......... ! ........ i ......... _........ "......... "........

: : ; : • : :

i : : : : :[.-, i i i i _ "': :r,.,p : : : : : ." : :

-. r.,_...... :......... :._ ..... .:........

: : : : i i :I_ : : : : : • ".

_._ ..... "... : : : : : :_:":. ...... ; ......................................\: : : • . .

,,.-1 I_: . - : : : _r,,,,1 I. : : " : :

i:3:; ,._. : : : : :

-._ ..... .."......... _ ......... : ......... [ ......... " ........ ._................r.,,,,1: • : : : :

i_ r,,.). : : : - : :¢2:: : : : : :

¢,_ r,,_: : : : : :

_:3: . . . : :_.r..._.- ......... _......... i ......... -; : :

I

co r4

<z:

,,c;0

r,,po,,,-,1

,,.4_3,!-I

I I ,=II

I I I I I I

I

CDI

,r-(

• °oo_oooo .....

I I

£

,._¢,I

0

I,-i...... " ......... • ....... 0°I ......

.... °o+o.,..00°.

i I i

I

..... °.o ......... • ........

_+!+|+oo[+o_ oA++e[m_

-I,.4

U

v

summary report for grant nag/i/1476 engineering design of

Documents