NASA Technical Memorandum 88219 

NASA-TM-8821919860019258 

A Simple Antireflection Overcoat 

fori Opaque Coatings in the 

Submillimeter Region" 

Sheldon M. Smith 

April 1986 

NI\S/\ 

National Aeronautics and 

Space Administration 

~. 

LANGLEY R£S::i\f<CH CENTER 

Ll8RARY, NASA 

H~.r'.7?TONi V!RGI~HA 

1111111111111 1111 ~IIII 1111111111 1111111111111 

NF00936 
NASA Technical Memorandum 88219 

A Simple Antireflectiion Overcoat 

for Opaque Coatings in the 

Subm illimeter Region 

Sheldon IVI. Smith, Ames Research Center, Moffett Field, California 

April 1986 

NJ\S/\ 

National Aeronautics and 

Space Administration 

Ames Research Center 

Moffett Field, California 94035 
A simple antireflection overcoat for opaque coatings in the 

submillimeter region 

Sheldon M. Smith 

NASA Ames Hesearch Center, Moffett Field, CA 94035 

Abstract 

An antireflection overcoat for opaque baffle coatings in the 

FIRlsubmillimeter region has been made from a simple Teflon spray-on 

lubJricant. The Teflon overcoat reduced the specular reflectance of four 

different c,paque coatings by nearly a factor of two. Analysis, based on 

the interfElrence term of a reflecting-layer model, indicates that in the 

submillimeter region the reduced reflectance depends primarily on the 

reflractive index of the overcoat and very little on its thickness. 

I. Introduction 

As illustrated by an earlier paper 1 (hereafter called Paper I), the 

need for ICIW reflectance baffles inside far-infrared (FIR) space telescopes such as SIRTF (the Space Infrared Telescope Facility) has stimulatl~d a sur'vey of FIR absorbing materials. Another way to achieve low 

reflectanCE! is by means of an antireflection coating. The technique for 

dOing this in transmission with smooth, nonabsorbing substrates is wellkno,m,2 however the method used in reflection with smooth, absorbing 

coaUngs i::1 not as well known. The antireflection technique used in 

reflection has been referred to by the terms gradual-transition 

absorber,3 multilayer absorber,4 and multilayer coating.5 The purpose 
'"",', 

of such a coating is to match the optical constants of free space, which 

are relatively small, with those of the substrate, which are very 

large. A similar problem occurs in acoustics. At optical wavelengths 

Heavens6 suggested a film whose refractive index varied continuously 

from one medium to the other, and Jacobss~n and Martensson7 have ~ctually succeeded in making such a graded-index film. In the microwave 

region the wavelength is long enough that layers of material can be used 

to approximate a continuous transition. Thus in a multilayer coating 

the refractive index increases Irregularly from the outside inward 

(hence the surface reflectance of the outermost layer is the least). 

This paper describes a simple, single-layer antireflection overcoat for 

rough, high':'index, baffle coating's. 

Both polyethylene and mylar have been used to make FIR antireflection coatings8 in transmission. Teflon (polytetrafluoroethylene) is 

somewhat similar chemically, but with a lower index of refraction. 

Because of its low index, four IR-opaque baffle coatings described in 

Paper I were sprayed with Teflon to see whether it would have an antireflectIon effect in reflection. The material used was Teflon Wet Lubricant (the Du Pont Co., Wilmington, DE 19898), and a "heavy" spray was 

applied in an effort to produce a thick layer. Specular reflectance 

spectra (asdesc~ibed in Paper I) were made of the four coatings both 

before and after they were sprayed so that any changes measured would be 

attributable to the Teflon overcoat. 

The analysis which follows uses the Teflon refractive index 

obtained by Chamberlain and Gebbie9 because their value is quite close 

to that obtained by Alvarez, Jennings, and Moorwood'O after a 5.5% 

temperature shift observed in the latter's polyethylene data was applied 
tOI their Teflon data. The value found by Birch et a1. 11 is only. 3.5% 

higher. :Beyond 65 pm, Chamberlain and Gebbie show that the absorption 

coefficient of Teflon is negligible. The optical constants of the four 

combination coatings were estimated' in Paper I and they will be used 

here (Table I) with the comment that they are sufficiently accurate for 

a first-order analysis. 

II. Observations 

Figures 1, 2, 3, and 4 present reflectance spectra made near normal 

incidence of four combination coa.tings both before and after they were 

sprayed with Teflon Wet Lubricant. The thickness, d, and roughness, 0, 

of each cl)ating are given in parenthesis (d,o) in the figure captions 

together with the sample number a.nd coating description. In Fig. 1, the 

short wavelength data have been smoothed during replotting at the scale 

of the longer wavelength data. The reflectance levels shown in Figs. 2, 

3, and 4 are considerably below those in Fig. 1 because the coatings in 

the lattelr figures are much thicker. For that reason, and also because 

a thinner beam splitter was used, the short wavelength spectra of Fig. 4 

are noisy; however, they still show two clearly separated reflectance 

levels beyond 80 pm. 

Two lDajor effects of the Teflon overcoat are apparent in the strong 

spectra of fig. 1. First, the peak at 77 pm is shifted (8 pm) toward 

longer wa'ITelength, and second, the reflectance at wavelengths beyond 

300 pm is reduced by a factor close to two. In Fig. 2 both the reduced 

reflectance and the wavelength shift occur at the same feature. The 

spectra in Figs. 3 and 4 are of quite rough coatings and they demonstrate significantly reduced reflectance in two different regions of the 

3 
spectrum. To summarize, these observations demonstrate an approximately 

50% reduction of the reflectance of each sample tested, and two samples 

show the shift of a spectral feature to longer wavelength. 

III. Analysis 

The two effects demonstrated in the preceding section appear large 

enough and simple enough to be amenable to a first-order analysis. 

Smith12 has shown that as the wavelength increases from 10 to about 

350 ~m the reflectance of many optical-black coatings increases rapidly 

because the coating's exponential absorption coefficient (4'1rkd/,,) 

decreases almost linearly. Concurrently, interference between the 

specular reflections from the upper (coating) and lower (metal) surfaces 

produces characteristic fringes which have been called "channelled" 

spectra. 13 The peaks in Figs. 1 and 2 are examples of such fringes. In 

the absence of the Teflon overcoat indicated in Fig. 5, the unshifted 

peaks are due to constructive interference largely between beams Band C 

of the figure. (Multiple internal reflections are rapidly attenuated in 

such thick, absorbing coatings.) When an overcoat is present as shown, 

the shifted peaks are then due to interference largely between beams A 

and C. 

The simple analysis just described is suggested by two observations: first, the shift to longer wavelength of interference features 

is consistent with a larger path difference created by the overcoat; and 

second, the changes observed are only simple modifications of the 

original interference pattern which indicates that just two beams are 

still involved. If"an additional beam were significantly involved, 

additional features such as shoulders, plateaus, or other peaks would be 

4 
apparent. Thus it will be assumed that after an overcoat has been 

applied, the principal interference interaction occurs between beams A 

and C and any further interaction with beam B can be neglected in a 

first-order analysis. 

Because interference features apparently dominate the FIR spectra 

of these :rough coatings, the interference term of the reflecting-layer 

model can be used to evaluate them. The second term of Eq. (18) of 

Ref. 12 glves 

where n±lk is the complex refractive index of the coating, d is its 

thickness, A is the wavelength, a1 is the rms roughness of the upper 

surface, lind Rl is its Fresnel reflectance as given by the usual 

formula, 

(n - 1)2 + i 

R1 = 2 2· 

(n + 1) + k 

(2) 

In Eq. (18) of Ref. 12, we have set R2 = 1 and a2 = 0 for a smooth 

metal sub:3trate, and n - o - for air (see Fig. 5). The presence of 

interference fringes indicates that the wavelength is sufficiently long 

that diffuse transmission through the upper surface can also be 

neglected, hence 

(3) 

5 
Figure 5 shows the situation when the basic coating has been covered 

with a nonabsorbing overcoat of thickness df and (real) refractive 

index nf' For simplicity, it is assumed that the overcoat does not 

change the roughness, 01' 

The first-order effect of a nonabsorbing overcoat on the normal 

incidence specular refleqtance can be calculated from the ratio formed 

by Eq. (1) evaluated with an overcoat (beams A and C), divided by 

Eq. (1) evaluated without the overcoat (beams Band C). The evaluation 

involves substituting a new optical path, nd·sec(S/n) + nfdf·sec(S/nf}, 

for the original path nd·sec(S/n} in the cosine factor, inserting the 

appropriate refractive index throughout, and selecting the appropriate I, 

wavelength. The sec(S/n) factors provide small corrections for notquite normal Incidence. 

In the ratio so formed different factors cancel depending on 

whether the evaluation is done at the peak of an interference fringe, 

which will specify different wavelengths, or whether "it is done at an 

arbitrarily selected single wavelength. In the former case, called 

Technique I, phase is constant and the cosine factors cancel leaving 

Tech I: 

R . Wl 

Rwo = 

R1/2(1 

lA 

R1/2(1 

lB 

exp -(~) 2 

exp _(4::1 )

2 

where R1B is the Rl ofEq. (2), and 

·6 

1/2 

(

-4Wkd sec<S/n}) exp A 

A 

(

-4Wkd SeC(S/n}) exp A 

B 

(4) 

(5) 
The peak wavelengths are 

(6) 

where 6;\ is measured on Figs. and 2. Note that Eq. (4) is independE!nt of df , the thickness of thE~ overcoat. In the latter case, called 

TE!chnique II, the exponential factors cancel because H is zero and 

TElflon is nonabsorbing. Thus 

TEIch II: 

= _R-:-:~ ~~2_( _1 _-_R_1:..:.:A;....) _co_s...JI[o:.;:~_n_{_n_d __ s_e_c...,.,.(_al_n..,..)_+_n,...:f~....,-d~f_s_e_c_( a_l_n-=..f_) ..::..}] 

1/2 cos 4nnd sec(a/n) R1B (1 - R1B) ;\ -

By equating phase factors at; the interference peaks, the optical 

thickness of the overcoat can be related to the wavelength shift, 

yi.elding 

n

f d

f sec( a/nf ) 

nd sec(a/n) 

( 7) 

(8) 

Substituting Eq. (8) into (7) produces a second equation also independelnt of the overcoat thickness: 

RWi 

r= 

wo 

R1/2(1 

1A R1A)COs~{n sec(a/n) + n' sec(a/n') i;}] 

R1/2(1 ) 4nnd sec(a/n) 1B - R1B cos ;\ 

where n' is the value of n measured at AB. 

(9) 

Examination of Eqs. (4), (7), and (9) indicates that as the wavelelngth becomes large, the only factors that do not explicitly approach 

7 
unity are those involving the surface reflectance coefficients,R1A and 

R1B . Since these coefficients depend only on optical constants which in 

the submillimeter region change quite slowly, it appears that the sub .. 

millimeter reflectance ratio approaches a nearly constant value given by 

R1/2{1 

1A (10) 

which is independent of the thickness of the overcoat. Even at shorter 

wavelengths, one would still expect the reduced reflectance to be 

strongly governed by this value. Substitution of Eqs. (2) and (5), 

followed by some algebraic manipulation yields 

( 11) 

This complicated relation has a nonlinear dependence on the optical 

constants., but for the expected values of n ~ 1 and k ~ 0.3, its 

dependence on nand k is small. The numerator, however, has a regular 

dependence on nf and it goes to zero as nf decreases to 1. Thus the 

most significant parameter of the reduced reflectance in the submillimeter region ~ppears to be the index of refraction of the overcoat, and 

not: its thicknes.s. Contrary to what might be expected from analogy to 

antireflection coatings in transmission, the reflectance in this case 

decreases regularly with decreasing overcoat index. 

8 
IV. Calculations 

In this section, Eqs. (4), (7), (8), and (9) are applied. For 

these calculations the roughness and thickness of the IR-opaque coatings 

are taken from Paper I together with the estimates of their optical 

cClnstants. The dispersion of Teflon is so small in the FIR that the 

value of the refractive index given by Chamberlain and Gebbie 9. 1•384, 

is: essentially independent of wavelength. The angle of incidence on the 

coating was 17° and the significant wavelengths are indicated in Figs. 1 

and 2. The ratios Rwi/Rwo were measured in Figs. 1 through 4. These 

da.ta are listed in Table I together with the results of the 

ca.lculations. 

The first two calculations apply Eq. (4) to the spectral peaks, 

shown in Figs. and 2. Considering the approximations made and the 

estimated nature of the optical constants of the coatings, the calculations show good agreement with measurement. The large differences' in 

applied w,3.velength, in the measured reflectances and reflectance ratios, 

and in coating thicknesses between the two applications indicate that 

Technique I is valid over a wide range of FIR wavelengths. It was also 

evident during the calculations that the ratio of reflectance coefficients, R1A and R1B , contributed more to the final result than did the 

other factors, as suggested by Eq. (10). 

The third calculation applies Eq. (9) to sample 1145 at 400 ~m by 

utilizing the wavelength shift of' the short wavelength feature at 

, 

77 }.1m. This process required an evaluation of the optical constants of 

the combination coating at two wi.dely separate wavelengths. Considering 

this, the difference of 23% between calculation and measurement is not 

considered poor. 

9 
In the absence of a spectral feature, Technique II can be applied 

if the thickness of the overcoat is known. Considering the success of 

the first two calculations, the thickness of the overcoat on those two 

coatings was calculated by Eq. (8). The results gave 4.3 ~m on #45 and 

24 JJm on #32. In view of the absence of any control on the thickness of 

the overcoat, this large spread in values is not too surprising. A 

simple average of these two values was then taken to obtain a representative value (15 ~m) of overcoat thickness to use in applying Eq. (7) to 

.).' . 

samples #30 and 1125. It should be noted here that these two combination 

coatings are not homogeneous (the SiC particles are isolated facets) 

hence their estimated optical constants are more uncertain than those of 

the previous samples. Using the value of 15 ~m for df , Eq. (7) 

calculates a reflectance ratio for sample 1130 at 400 ~m that is only 26% 

different from the value measured on Fig. 3. 

Finally, with df initially equal to 15 ~m, Eq. (7) was applied to 

saIl1pie #25 (Fig. 4) at 100 ~m. It was quickly found that with such a 

thick coating at short wavelength that the cosine factors oscillate so 

fast the calculated ratio can take on any of a large range of values 

depending on the specific values of d, df , or L This result is supported by the long wave half of Fig. 4 which has much more the appearance of channelled spectra than of noise. Although this first-order 

analysis breaks down in this case, it should be noted that the calculated ratio based on just the reflectance coefficients (Eq. (10» is of 

the correct order, 0.66, when compared to the value of,0.5 obtained from 

. . 

smooth curves estimated through the spectra of Fig. 4. 

10 
V. Summary and Conclusions 

A simple antireflection overcoat for FIR-opaque baffle coatings has 

bElen made by spraying the coatings with Teflon Wet Lubricant. The 

specular reflectance of four different coatings was reduced by approximaltely a factor of two in the F'IH/submillimeter region. A first-order 

analysis based on the interferenoe term of a reflecting-layer model was 

used to calculate the reduced reflectance to within 26%. This analysis 

indicates that in the submillimeter region the reduction in specular 

rEtflectance depends primarily on the refractive index of the overcoat 

and very little on its thickness. 

11 
References 

1. S. M. Smith, "Survey of Material for an Infrared-Opaque Coating," 

to be publisned as NASA TM-88204, Dec. 1985. 

2. M. Born and E. Wolf, Principies of Optics, (Pergamon Press, Oxford, 

1910) 4th Ed., p. 64. 

3. K. Walther, "Reflection Factor of Gradual Transition Absorbers for 

Electron and Acoustic Waves," LR.E., AP-8, 60B-621 (1960). 

4. A. R. Jones and E. R. Wooding, "Multilayer Microwave Absorber," 

IEEE, AP-12, 50B-509 (1964). 

5. J. R. Grammer, L. J. Bailin, M. D. Blue, and S. Perkowitz, "Absorbing Coatings for the Far Infrared," Proc. Soc. Photo-Opt. Instrum. 

Eng., 251, 192-195 (1980). 

6. o. S. Heavens, Optical Properties of Solid Thin Films (University 

Microfilms, Ann Arbor, Mich., 1964), p. 20B. 

1. R. Jacobsson and J. O. Martensson, "Evaporated Inhomogeneous Thin 

Films," Appl. Opt., 2., 29 (1966). 

8. K. R. Armstrong and F. J. Low, "FIR Filters Utilizing Small Particle Scattering and Anti-Reflection Coatings," Appl. Opt.,.u, 421 

(1914) . 

9. J. E. Chamberlain and H. A. Gebbie, "Dispersion Measurements on 

Polytetrafluoroethylene in the Far Infrared," Appl. Opt., 2., 393 

( 1966) . 

10. J. A. Alvarez, R. E. Jennings, and A. F. M. Moorwood, "IR Measurements of Selected Optical Materials at 1.6°K," Infrared Phys., .12., 

45 (1915). 

12 
11. J. R. Birch, J. D. Dromey, and J. Lesurf,· "Optical Constants of 

Some Low-Loss Polymers between 4 and 40 cm- 1," Infrared Phys., £1, 

225 (1981). 

12~. S. M. Smith, "Specular Reflectance of Optical-Black Coatings in the 

Far Infrared," Appl. Opt., ?3, 2311-2326 (1984). 

13. R. W. Ditchburn, Light (Blackie and Son, Glasgow, 1953), p. 141. 

13 
t-' 

..,... 

Table I. Comparison of Calculations with Measurements of the Reflectance Ratio 

Sample Combination Technumber coating nique d(~m) cr1(~m) AB(~m) 

lJ5 ECP/CB/TlBr I lJO 3 77 

32 Chemg/CB/TlBr I 210 7.5 357 

lJ5 ECP/CB/TlBr II 40 3 400 

30 Chemg/CB/SiC II 160 30 400 

25 ECP/CB/SiC II 215 25 100 

b.A/A n/k 

0.10lJ 1 .lJ5/0. 3 

0.OlJ8 3.5011.1 

O. 1 olJ 2.90/1.1 

(df==15~m) 2.9511.1 

(df==15~m) 1.35/0.5 

RwilRwo 

Calu- MeaDifference 

from 

measurement lated sured 

0.93 1.0 -7% 

0.59 0.53 +11% 

0.36 0.47 -23% 

0.58 0.46 +26% 

-0.66 -0.5 
Figure Captions 

Ftg. 1. Sample 45: TIBr and carbon black in ECP-2200, (40,3). 

Fi.g. 2. Sample 32: TIBr and carbon black in Chemglaze Z-306, 

(~!10, 7l>. 

Fi.g. 3. Sample 30: Number 80 SiC grit and carbon black in Chemglaze 

Z··306, (160,30). 

Fi.g. 4. Sample 25: Number 80 SiC grit and carbon black in ECP-2200, 

(~!15, 25) • 

Flg. 5. Schematic view of overc()at of a combination coating on a 

rE!flecting substrate. 

15 
\ 0 

0 

III 

\ 

\ 

\ 

\ :5 \ ..,. \ 

\ 

\ 

\ 

, 0 

, ~ 

, 

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I- !'" 0 

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::;)Z ..... 00 ..... :I:..J ..... 1-11. ..... -w ..... 5:1- ,. 0 " 0 

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, 

I 

, 0 

0 I N 

I 

I 

0 

III 

... 

(30N3010NI oLL) 30N'If.L031:131:f l:f'lfln03dS 

l6 
.10 -w 

(.) 

Z 

w 

Q 

~ .08 

0 -

.... 

... 

~ .06 

z « 

... 

(.) 

w it .04 

w 

a: 

a: 

« 

.J .02 ::J 

(.) 

W 

Q. 

en 

0 250 300 350 

A,llm 

Fig. 2 

17 

400 450 500 
w 

(.J 

.14 

.12 

z 

w 

o .10 

(.J 

z 

o 

..... 

... - .08 

w 

(.J 

z 

<t 

t-

(.J 

~ .06 

LL 

W 

a: 

a: 

<t .04 

..J 

::;) 

(.J 

W 

Q. 

en 

.02 

O~-----,-------·--_I~--------.~I--------~I 

350 400 450 500 

A, J,tm 
.10 

--w 

(J .08 2 

w 

Q 

-(J 

2 

0 .06 ,... 

0-

W 

(J 

2 

« .04 ... 

(J 

W 

..J 

u.. 

w .02 

a: 

a: 

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..J 

::J 

(J 0 

w 

Co 

en 

-.02 

20 ·40 60 80 

A, 11m 

Fig. 4 

19 

100 120 140 
n = 1 o 

------------~~+---------~------a1 OVERCOAT Of 

-------+-+-------:r-,r-- G1 

COMBINATION 

COATING 

METAL. 

Fig. 5 

20 

n ±ik d 
1. Report No. I 2. Government Accession No. 3. Recipient's Catalog No. 

NASA TM-88219 

4. Title and Subtitle 5. Report Date 

A SIMPLE ANTIREFLECTION OVERCOAT FOR OPAQUE COATINGS April 1986 

IN THE SUBMILLIMETER REGION 6. Performing Organization Code 

7. A.,thor(sl 8. Performing Organization Report No. 

Sheldon M ..Smith A-86074 

10. Work Unit No. 

9. Performing Organization Name and Address 

Ames Research Center 

11. Contract or Grant No. Moffett F:ield, CA 94035 

13. Type of Report and Period Covered 

12. Sponsoring Agency Name and Address Technical Memorandum National Aeronautics and Space Administration 

Washington, DC 20546 14. Sponsoring Agency Code 

159-41-06 

15. Supplementary Notes 

Point of Contact: Sheldon Smith, Ames Research Center, MS 245-6, 

Moffett Field. CA 94035 (415) 694-6264 or FTS 464-6264 

16. Abstract 

An antireflection overcoat for opaque baffle coatings in the 

FIRlsubmillimeter region has been made from a Simple Teflon spray-on 

lubricant. The Teflon overcoat reduced the specular reflectance of four 

different opaque coatings by nearly a factor of two. Analysis, based on 

the interference term of a reflecting-layer model, indicates that in the 

submillimeter region the reduced reflectance depends primarily on the 

refractive index of the overcoat and very little on its thickness. 

11. Ke·v Words (SU!lgested bV Author(s) I 18. Distribution Statement 

Anti-reflection, Opaque coatings, Unlimited 

Submillimeter 

Far-infrared 

Subject category - 74 

19. Security Classif. (of this reportl 20. Security Classif. (of this pagel 21. No. of Pages 22. Price' 

Unclassified Unclassified 23 A02 

'For sale by the National Technical Information Service, Springfield, Virginia 22161 
End of Document