Absolute reflectometer for the mid infrared region

Dan Sheffer, Uri P. Oppenheim, and Adam D. Devir

An absolute reflectometer for the 0.8-5.5-ptm wavelength region is described. It is based on integratingspheres and uses the third Taylor method in the 70/d configuration. An improved theory for the reduction ofthe data is presented, and results for several diffuse gold samples are given.

1. Introduction

The problem of measuring diffuse spectral reflec-tance of surfaces and objects is not new. Over theyears many reflectometers have been built and de-scribed in the literature.' However, few reflectome-ters are of the absolute type and fewer still operate inthe infrared. Most reflectometers use an integratingsphere to carry out diffuse reflectance measurements.The disadvantage of the relative type of reflectometeris that a standard of known reflectance is required.This standard has to be stable both chemically andoptically over long periods of time. Several well-known standards for the visible have become estab-lished such as BaSO4 powder, BaSO4 paint, and vari-ous types of opal glass. However, without thepossibility of recalibration in the laboratory, the user isnever certain if the standard has retained its originalreflectivity. An absolute reflectometer is thereforecalled for, yet only few of these exist and these operatemostly in the visible.

While several absolute measurements have beenpublished for standards such as BaSO4 in the 0.8-2.5-gm region, there is considerable disagreement betweenresults.

This paper describes a method for making absolutereflectance measurements in the 0.8-5.5-gm region,the theory for reduction of the measured reflectiondata, and some experimental results.

II. Third Taylor Method

The third Taylor method for absolute reflectancemeasurements with an integrating sphere in the a/dconfiguration consists of two steps: First, the sampleis placed against the sample port of the sphere and

The authors are with Technion-Israel Institute of Technology,Physics Department, Haifa 32000, Israel.

Received 8 March 1989.0003-6935/90/010129-04$02.00/0.© 1990 Optical Society of America.

illuminated by the entering beam. The sphere is de-signed so that the first reflection from the sample isprevented from reaching the area viewed by the detec-tor during this measurement (but the area viewed bythe detector is illuminated by multiple reflectionsfrom the sphere wall). Second, the sphere wall isilluminated by the entering beam and now the areaviewed by the detector does receive the first reflectionfrom the sphere wall. The ratio of the signal in thefirst measurement to that in the second measurementis calculated. The value of the signal ratio enables oneto calculate the absolute reflectance of the sample. Adescription of this method is given by Buddel andBudde and Dodd.2

11. Apparatus

The experimental system is that of the absolutereflectometer built at the Electro-Optical ResearchCenter (EORC) of the Technion-Israel Institute ofTechnology and has been described previously.3

It consists of several interchangeable sources, circu-lar variable filters (CVFs), integrating spheres, anddetectors. By making various combinations of theseelements the operator can choose different wavelengthregions for measurements (see Fig. 1). Recently thesystem was improved and extended to include the 2.5-5.5-,m region.

IS, and IS2 are integrating spheres using the thirdTaylor method in the 70 /d configuration. Each sphereconsists of two hemispheres which can be rotatedabout a common vertical axis (see Fig. 2). To performa measurement, the upper hemisphere is held fixed,while the lower one is turned about the axis AA' toobtain the first signal I, (sample illumination, with thebaffle shielding the area seen by the detector fromdirect irradiation by the sample). In the second mea-surement the lower hemisphere is rotated until thesample is moved to the dotted position in Fig. 2 and thewall is illuminated directly, while the baffle is out ofthe way. This measurement produces I2. The ratioK = I11I2 of the two signals is then calculated. Moredetails can be found in Ref. 3.

1 January 1990 / Vol. 29, No. 1 / APPLIED OPTICS 129

(

S2*o M4

,k

C.V. E1

CH ,

L I .

/

e S.M.

C.V.F2

GB

N,

I1T

K

0.80

I .X1.5.1

IS. 2

Fig. 1. Optical system for absolute reflectance measurements inthe infrared region (schematic): S2 , projection lamp; M3 ,M4,M 7 ,plane mirrors; M5 ,M6 , spherical mirrors; GB, globar; I.S.1 ,I.S.2 , abso-

lute integrating spheres; C. V.F.1 ,C.V.F. 2, circular variable filters.

DETECTOR

ILLUMINATING DETECTORXBSEAM PORT

FIXED,. | \ HEMISPHERE

ENTRANCEPORT - - …

SAMPLE

ROTATINGa\ - iHEMISPHERE -_~v X

AREASEEN ST B AFLE

DETECTOR

A

Fig. 2. Integrating sphere for the absolute measurement of diffusereflectance (schematic).

IV. New Theory for Data Reduction

In the past, several theories have been published forcalculating the absolute reflectance of the sample, us-ing the signal ratio K,2,4 the most recent one being thework of Budde and Dodd,2 which takes into accountthe finite size of the sphere ports. According to thelatter theory, the absolute diffuse reflectance of thesample r is given by Eq. (1) below, where AO is the totalarea of the wall of the sphere, Al is the area of thesample port, A2 is the net area of the wall of the sphere(excluding the total area of the sphere ports), r, is thereflectance of the sample, and r2 is the reflectance ofthe wall of the sphere:

AO-Al (r1 -r2 ) (1)

r1K(Al +A,)

Strictly speaking, this theory applies to measurementsmade in the dIO configuration (diffuse illumination,normal viewing), but according to the Helmholtz reci-procity theorem,5 it can also be applied to the presentsystem operating in the O/d configuration (a beingvery small). An approximate result is given by Eq. (2)which is exact if r, = r2 but can be used with 0.01accuracy for calculating r, if Al/A2 < 0.01:

K A, (2)(A, + A2)

The integrating spheres used in the present study werespecifically designed so that A1/A2 < 0.01 and there-

0.751

0.5 1.0 1.5WAVELENGTH (m)

2.0 2.5

Fig. 3. Measured K values for NIST (formerly NBS) standardreference material No. 2019b.

0.90

0.85

wI.)z

-J

U-w0.80

0.75

0.5 1.0 1.5WAVELENGTH (m)

2.0

Fig. 4. Reflectance of NIST standard reference material No. 2019bas calculated at EORC according to Budde's2 theory using the Kvalues of Fig. 3, compared with the reflectance values provided by

the NIST.

fore Eq. (2) could be expected to yield 1% accuracy.However, when Eq. (2) and the experimental setupdescribed above were used, large discrepancies wereobserved between measurements made at EORC andat the U.S. National Institute of Standards & Technol-ogy (formerly National Bureau of Standards), on thesame standard reference sample, which was suppliedto EORC by NIST (NBS). Figures 3 and 4 illustratethe results obtained by EORC and by NIST on thesame sample, which was standard reference materialno. 2019b of NIST. Even more disturbing was the factthat realignment of the optical system at EORC result-ed in different results for the signal ratio K, the devi-ations being of the order of ±0.02 in the value of K.Clearly, Eq. (2) could not be applied in this case. Theintegrating sphere used had a diameter of 10 cm andwas coated with BaSO4 paint.

Accordingly, a new theory for data reduction wasdeveloped at EORC. Using the new theory good

130 APPLIED OPTICS / Vol. 29, No. 1 / 1 January 1990

signal from detector, sample illumination

- ~~ ~~~K Si sgnal rom detector, wall illumination

i '- _ _ _ 7_S

_~~~~~~~ \

\ _ -

_ ~~~~~~~~~~~measured(Budde's theory) '

| ~, I I

08. . . . . . . . . . . . . . . . ., ,

I M

II

F

n __

I I,, ,, I,,, I, I

0.90-

present results(new theory)

0.85 -I

0 PlC' I I I I NBS -

Q 80f I Il I l l I I l l I _ .0.5 1.0 1.5

WAVELENGTH (m)2.0 2.5

DETECTOR

ILLUMINATINGBEAM

SAMPLE

Fig. 5. Reflectance of NIST standard reference material No. 2019bas calculated by the new theory, using the K values of Fig. 3 (dotted

curve). The full curve shows results provided by the NIST.

agreement between the measurements at EORC and atNBS was achieved using the same K values as before(see Fig. 5).

The rigorous development of the new theory which isbased on an extension of the theory of Budde andDodd2 is beyond the scope of the present discussionand will be published in a subsequent paper. A briefsummary of it is given below.

Reference will be made to Fig. 6 where the relevantphysical quantities are illustrated schematically. Inaddition to the quantities r, r2, AO, A1, and A2 intro-duced above, A5 designates the area shaded by thebaffle when the sample is illuminated. According tothe new theory, r, can be calculated by solving Eq. (3)for rj:

E-r3+F. rl+ G r +H= 0,

Fig. 6. Schematic drawing of an integrating sphere using the thirdTaylor method for making absolute reflectance measurements, illus-trating the various physical quantities appearing in Eqs. (3) and (4).

1.0

wzI-C-)w_-JE-

0.9

0.8

0.7

(3)

where E = Al/Ao; F = Ajr2(A2 + A5)/Ao; G = r2(A2 - A5+ A2A5r2/Ao) and H = -A0 Kr2.

If r, = r2 (i.e., a sample identical to the wall of thesphere is measured), Eq. (4) can be used:

a -r2+ b-r2 + = 0, (4)

where a = (A1 + A 5 ) * (Al + A2)/A2; b = (A2 - A5)/Aoand c = -K.

In principle, both theories call for two sets of mea-surements: First, r2 is measured by placing a samplewhich is identical to the sphere wall on the sample port.In this case both theories give simple and exact equa-tions for calculating r2 [Eqs. (2) and (4), respectively].Second, the unknown sample is measured, and boththeories use another equation to calculate rl, since r2 isnow known [Eqs. (1) and (3), respectively].

A few important points must be noted:(1) The new theory gives one and only one real

solution for rl, although it uses an equation of the thirdorder.

(2) In the new theory r, is strongly dependent bothon A5, the area shaded by the baffle, and on r2, thereflectance of the sphere wall. No such dependence isfound in the old theory. In the old theory r, has only aweak dependence on r2 and none on A5.

It can be shown that the dependence of r, on r2 wasthe main cause for the large discrepancies between the

1.0 2.0 3.0WAVELENGTH (m)

4.0 5.0

Fig. 7. Absolute reflectance values of several diffuse gold samplesin the 0.8-5.5-jAm region. Most of the error bars have been omitted

for clarity. For explanation of the symbols see text.

NIST and EORC measurements, while the depen-dence of r on A5 was responsible for the variation inthe K values each time the optical system was re-aligned. Introducing the dependence of ri on r2 has abeneficial result: it allows the use of diffuse coatingsfor integrating spheres, without concern about thecoating being of constant reflectance with respect towavelength.

V. Measurements in the 3-5.5-,Am Region

Using the new theory, we attempted to make abso-lute reflectance measurements in the 3-5.5-gum region.In this region no published results of absolute reflec-tance measurement are known at present. To thatend a sulfur-coated integrating sphere of 5-cm diame-ter designated by I.S., in Fig. 1 was built. Figure 7shows the results obtained for a few diffuse gold sam-ples.

Sample G4 is a diffuse gold sample supplied toEORC by Epner Technologies Co. Sample 60m wasfabricated by sandblasting an aluminum plate, and

1 January 1990 / Vol. 29, No. 1 / APPLIED OPTICS 131

lI I I I I I

GPL

_W = -

- IA'

I ERROR BAR

I I I I I I I I

then evaporating on it successively a nickel layer and agold layer. Sample Gsp is made of gold-plated sandpa-per and sample Gpj is a diffuse gold sample fabricatedby plasma coating gold on an aluminum substratewhich was first coated by a ceramic coating.

An interesting feature of Fig. 7 is the pronounced dipin the reflectance curve of Gpj and of G4 in the 2.5-4.0-,m region. Such a dip is not expected on the basis ofknown reflectance data for samples of specular gold6

and is of unknown origin. The other diffuse goldsamples, Gsp and 60m, do not exhibit such behavior inthis region, nor do other diffuse gold samples preparedby evaporating gold on sandpaper of varying grain size.A sandblasted aluminum sheet does not have such afeature either. One might conclude that, in view of thedata given above and considering the widespread useof diffuse gold samples as reflectance standards in theIR region above 2.5 ,um, further investigation of thereflectance properties of such samples is needed.

VI. Summary

An absolute method for making reflectance mea-surements in the 0.8-5.5-,Mm region is described. Anew theory for data reduction is presented and abso-lute reflectance data for various diffuse gold samples

are given. The results suggest that the spectral reflec-tance of such samples in the 3.0-5.5 gm region is not'always flat as expected from specular reflectance mea-surements, and that further investigation of such sam-ples is needed before they can be used as reflectancestandards with reasonable confidence.

The skillful technical help of S. Ariov in building theintegrating spheres is gratefully acknowledged.

References1. W. Budde, "Calibration of Reflectance Standards," J. Res. Natl.

Bur. Stand. Sect. A 80, 585-595 (1976).2. W. Budde and C. X. Dodd, "Absolute Reflectance Measurements

in the d/0 Geometry," Die Farbe 19, 94-102 (1970).3. D. Sheffer, U. P. Oppenheim, D. Clement, and A. D. Devir,

"Absolute Reflectometer for the 0.8-2.5-um Region," Appl. Opt.26, 583-586 (1987).

4. C. H. Sharp and W. F. Little, "Measurement of Reflection Fac-tors," Trans. Illum. Eng. Soc. 15, 802-810 (1920).

5. F. J. J. Clark and D. J. Parry, "Helmholtz Reciprocity: ItsValidity and Application to Reflectometry," Light. Res. Technol.17, 1-11 (1985).

6. W. L. Wolfe and G. J. Zissis, Eds., The Infrared Handbook(Environmental Research Institute of Michigan, Ann Arbor,1978), Chap. 7, pp. 7-81.

132 APPLIED OPTICS / Vol. 29, No. 1 / 1 January 1990