Absolute reflectance measurement at normal incidence

Absolute reflectance m e a s u r e m e n t at normal incidence R.S. RAM, O. PRAKASH, J. SINGH, S.P. VARMA A simple reflectometer for measurement of the absolute reflectance of plane specularly reflecting surfaces at normal incidence without using any reference standard is described. Results obtained for samples of high as well as lowreflecting surfaces using a HeNe laser source are reported. KEYWORDS: reflectometers, reflectance (normal incidence), reflectance (absolute)

Introduction Accurate measurement of spectral reflectance is required in the development of multilayer dielectric coatings, laser mirrors, reflectance standards, interference filters and selective coatings for solar collectors. Reflectance is affected by illuminating radiation, surface texture, surface flatness, angle of incidence and other properties of the sample -- so precise measurement of reflectance is a problem. Spectral reflectance at normal incidence has particular advantages such as (i) the measurement is free from polarization effects, and (ii) reflectance has a simple relationship to optical constants, n and k (given b y g = R s =Rp = [(n - 1)2 + k2]/[(n + 1)2 + k2]; where Rs is the perpendicular component, and Ro the parallel component of reflectance). Spectral reflectance and its applications have been discussed at length in several books 1-5 and other publications 6-14. Most of the reflectometers discussed in literature 6, 10. t l. ~3,~4 require a reflectance standard which necessitates the standard to be stable both chemically and optically over long periods of time. The standard also needs to be calibrated periodically to account for any variation in its reflectance value. A few reflectometers described in literature 7.8.9. 12 do not require any reflectance standard but they are based on a "SAMPLE IN' and 'SAMPLE OUT' technique for absolute measurement of reflectance. These subsequent measurements also lead to inaccuracy because of either (i) any fluctuation in the source intensity and/ or (ii) any drift in detector and processing electronics with time. In this article, the design of a simple double beam reflectometer capable of measuring the absolute The authors are with the Infrared Standard Section, Division of Standard, National Physical Laboratory, Dr K.S. Krishnan Road, New Delhi 110012, India. Received 2 4 February 1989. Revised 1 November 1 9 8 9

value of specular reflectance at norm~/l incidence without using either a reflectance standard or following a 'SAMPLE IN' and 'SAMPLE OUT' technique has been described. It incorporates only a single detector and two beam-splitters. The performance of the reflectometer has also been evaluated by measuring both high and low reflectances from various samples.

Working principle The complete optical schematic and functional diagram of the reflectometer is shown in Fig. 1. The parameters for the optical set-up are given in Table 1. B~ and B2 are two optically identical beamsplitters. The monochromatic radiation from a HeNe laser (in the present case) is finally incident on detector D2 through a diffuser D1. As shown in the ray diagram of Fig. 2, the sample SA is so placed that the radiation is incident normally on its surface and the optical path lengths of sample and reference beams (PNPQX and PDCY respectively) are equal. The reflectance of the sample is the ratio of intensities of sample and reference beams and is given by:

RIr(1

r)2/Ir(1

-

r) 2

-

(1)

This ratio leads directly to the reflectance R of the sample. Similarly, the beams (PQLGW and PDCEFV) reflected from the back surfaces of the beam-splitters may also simultaneously be incident on the detector D 2 through diffuser Di and the ratio of their intensities is given by: R/F3(1

-

r)2/Ir(l

-

r) 4 =

Rr2/[(1 - r)2l

(2)

The variables used here are defined later. It can be emphasized that this discussion is valid only for opaque, front plane surface metallic films and for other samples such as those that are:

0 0 3 0 - 3 9 9 2 / 9 0 / 0 1 0 0 5 1 - 0 5 © 1990 Butterworth Et Co (Publishers) Ltd Optics Et Laser Technology Vol 22 No 1 1 9 9 0

51

B2

I

rf, 0,

l

tH

,<,-,,, ~ 7 / ~ I

V

,t

W

I

I

~

Reference beam

Rlr(1_r)2

Fig. 2

F,%

i

f2 X

MA

\

V Y

The detailed ray diagram of proposed reflectometer

CH

These values are tabulated in Table 2 with various parameters defined below: I

Ap

Fig. 1 Optical schematic of proposed reflectometer. S A is the sample, B 1 and B2 are t w o optically identical beam-splitters, i A is a mask, / is beam intensity, fl and f2 are frequencies, CH is the dual frequency optical chopper, L 1 and L 2 are identical lock-inamplifiers tuned to frequencies #'1 and f2, RA is a ratiometer, RE is a recorder, D 2 is a detector and D 1 is a diffuser, and Ap is an aperture

Table 1. Typical design parameters Separation between two beam-splitters Distance between beam-splitters and detector Distance between sample and first beam-splitter B1 Thickness of each beam-splitter B1 and B2 Angle of incidence of radiation on beam-splitters Angle subtended by beams QX and CY on detector Material of beam-splitters

70 mm

intensity of radiation falling on beam-splitter B1 Rto t total reflectance value at normal incidence R single surface reflectance value at normal incidence from sample-air interface R' single surface reflectance value at normal incidence from sample-substrate interface R" single surface reflectance value at normal incidence from substrate-air interface a absorption value of sample a' absorption value of substrate l thickness of sample l' thickness of substrate r single surface reflectance of beam-splitters at the angle of incidence

42.5 °

It is also evident from Fig. 1 that the experimental set-up requires processing electronics which consists of two identical lock-in amplifiers L1 and L2 (tuned to the frequenciesfl and f2 respectively of the dual frequency optical chopper CH), a ratiometer RA and a recorder R E. The signal from detector D2 is processed by lock-in amplifiers and the ratio of their dc outputs is read by the ratiometer. The reading may be subsequently recorded on the recorder.

10 ° Glass

As discussed earlier the ratiometer reads the value of reflectance of the sample directly.

402 mm 35 mm 10mm

Results and discussions (i) transparent with both partially reflecting surfaces, (ii) absorbing with partially reflecting surfaces, (iii) absorbing with partially reflecting surfaces on an opaque substrate, (iv) transparent with both partially reflecting surfaces on an opaque substrate, and (v) absorbing with partially reflecting surfaces on an absorbing and partially reflecting substrate as the reflectance is being seen at normal incidence there will be contributions from the substrate and other surfaces. We will call this Rtot and it will correspond to the experimentally determined reflectance value.

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As the reflectometer consists of many optical components, the optical alignment is critical and any slight error in alignment will lead to inaccuracy in the measurement. In the present case, the minimum number of optical components have been used to enable easier optical alignment and better accuracy in the measurement. Still, the design suffers from some limitations and it can give accurate measurement if suitable precautions are taken to eliminate the systematic errors. The beamsplitters BI and B2 must be optically identical. This is achieved by taking beam-splitters from the same Optics 8 Laser Technology Vol 22 No 1 1990

Table

2.

Total

value

of

reflectance

I

Various

cases

Value of total reflectance

Conditions

Sample

I

Sample- transparent Absorption, Thickness

2R R tot = I+R

o=0 =/

tot

Sample

R

R]

I I R tot

Sample

R'

R I IR

tot

Sample- absorbing

= R + R ( 1 - 2 R ) e -2al

Absorption = a Thickness =I

tot

Sample- absorbing Absorption = a Thickness = I Substrate- opaque A b s o r p t a n c e , a ' = oo

Thickness

R

1-R 2 e - 2 a l

R + (1-2R) R ' e - 2 a l

tot

I - R R ' e -2al

=I'

LSubstrate

Sample

I R'

R

I IR

tot

Sample- t r a n s p a r e n t A b s o r p t i o n , a= 0 Thickness =l S u b s t r a t e - opaque A b s o r p t a n c e , a' = oo Thickness = I'

R

=R + (1-2R} R' tot

1-RR'

Substrate

Sample R"

R'

R

I [R

tot

Sample-absorbing Absorption = a T h i c k n e s s =l Substrate- absorbing A b s o r p t i o n = o' T h i c k n e s s =/'

ZSubstrate i

R

tot

R"

=R4 R'(1-R)2e-2al -2al 1-RR'e

(I-R)2 (l-R')2e-2a'l'e-2al

1-RR" (1-R')

2 -2a'l' -2al e e

i

melt of optical glass and by polishing them together in a block, in order to have identical surface finishes, the beam-splitters are not coated with reflecting materials because any variation in their Optics Et Laser Technology Vol 22 No 1 1 9 9 0

film thickness may lead to error in the measurement. Experimentally it was observed that by interchanging these beam-splitters, no change in the reflectance value of the sample was noticed. In

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order to minimize the error it is also essential that the angles of incidence of the beams should be equal at both the beam-splitters. It has been found from the computation that for an angle of incidence of 45 ° and for beam-splitters having a refractive index of 1.5 a variation of 24 minutes of arc in angle of incidence at beam-splitters B1 and BE leads to an error of 0.01 in R value. It is evident from Figs 1 and 2 and also (2) that the reflectometer gives the reflectance value of the sample directly when only front surface reflections from the beam-splitters are received at the detector and the back surface reflections are not made to exactly overlap at the diffuser plane. This is achieved by (i) using sufficiently thick beam-splitters to ensure that there is no overlap between the two reflected beams and (ii) suitably placing a mask M A in front of the detector. Thus, the precautions taken during experimentation are: (i) to maintain the same angle of incidence on the two beam-splitters, (ii) to ensure that the same area of the detector is illuminated, and (iii) to introduce the sample normal to the sample beam. The possibility of any asymmetry in the response by placing a diffuser just in front of the detector at the plane overlap of the beams is further defined by an aperture Ap. Table 3 shows the values of reflectance measurements at normal incidence carried out on a variety of samples having low as well as high reflectances. It is evident from this table that in most of the cases the measured values are close to the reported/computed reflectance values of the sample. However, in the case of fused quartz there are different reflectance values for rectangular and circular shaped fused quartz samples. This is because these two plates had different wedge angles so that in the case of the rectangular sample the reflections from the front as well as the back surfaces could be resolved and, having nearly the same intensities, it led to the same reflectance value. In the case of the circular sample these reflections could not be resolved and it led to Rtot (corresponding to case I of Table 1). Any other Table 3. Experimentally measured reflectance values for various surfaces

0.05

e.-

0.04

o~

"~ 0.03

-i

0.02

.~ 0.01 <( 0

Fig. 3 time

I

I

I

I

I

10

20

30 Time (rain)

40

50

60

The variation in reflectance value of fused quartz with

deviation in the measured reflectance value from the computed or reported value might be due to the optical characteristics of the particular sample and/ or the scattering losses from the beam-splitters, sample surface and the detector window. The drift in reflectance with time was evaluated by recording the output of the ratiometer for a quartz (rectangular shaped) sample on a strip chart recorder. The recording over 60 mins shown in Fig. 3 shows that the reflectance value of 0.0346 is almost constant and neither source-intensity fluctuation nor any drift in the detector and processing electronics, as expected for a double beam reflectometer, had any effect in this case. Photometric linearity in a reflectometer indicates the photometric accuracy of the system 15. If the reflectometer is linear between its two limits, that is 0% and 100% reflectances, it clearly indicates that contributions due to stray radiation, extraneous radiation and non-linearity in the detector and the processing electronics are almost negligible. In the present case, the photometric accuracy of the entire set-up for reflectance measurement was evaluated by measuring the sample beam output while the intensity of the incident radiation was varied by introducing a set of neutral density filters between the laser source and the beam-splitter B1. In a separate experiment the varied power of the laser beam was measured with a radiometer which had calibration traceable to NBS (USA) Standards. Fig. 4 shows a plot of the incident power and the system output for the sample beam in the case of fused 0.03

Sample No

Sample

1

Fused quartz (rectangular shape) Borosilicate crown glass BK-7 glass Fused quartz (circular shape) Sapphire PTB plane front surface mirror Laser mirror (aged) Laser mirror (freshly coated)

2 3 4 5 6 7 8

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Reflectance value

E

o_ 0.02

0.0346 0.0423 0.0546

i.

0.01

0.0740 O. 1226

o

x/xj I

0.8850 0.9550 0.9950

o

I XI

I

I

I

I

I

2.0

1.0

Incident power (roW) Fig. 4 A plot between the system output for the sample beam and the incident power

Optics ~ Laser Technology Vol 22 No 1 1 9 9 0

to any spectral range with the proper selection of beam-splitters, detectors and source. 0.040

Acknowledgements 0.035

X

X

X

0.030

i

X

X

l

,

X

l

i

1

i

1.0 Incident power (mW)

l

I

t

2.0

Fig. 5 Absolute reflectance value of fused quartz at varied incident power of the source

quartz (rectangular shaped with calculated R values of 0.0346 for n = 1.457). The reflectance values determined for varied incident powers are shown in Fig. 5. It can be seen that the reflectance values are almost the same for all incident powers and the average value corresponds to the reported/computed value of reflectance for fused quartz. Any deviation in the system output from the average line drawn in Fig. 5 might be attributed to the source intensity variation because the two measurements (one of the sample beam output by the reported system and the other of power by radiometer) were not simultaneous.

Conclusions The optical alignment of beam-splitters, sample and detector was very critical and due precautions were taken following methods reported in the literature9, 12. The reflectometer measures the absolute value of reflectance of the sample in the form of front surface opaque films without requiring any standard. For other samples as discussed in Table 2 the reflectometer will yield the value of reflectance of the sample when its absorption value is determined by other methods 16. It has been assumed throughout the discussion that the sample does not fluoresce in the spectral range of interest. The measurement on the reflectometer may be extended

Optics 8- Laser Technology Vol 22 No 1 1 9 9 0

The authors are thankful to the Director, and Head of the Physico-Mechanical Standards Division, National Physical Laboratory for their constant encouragement and permission to publish this work.

References 1 Wendlandt, W.W., Hecht, H.G. Reflectance Spectroscopy, John Wiley and Sons, (1966) 2 Bennett, H.E., Bennett, J.M. 'Precision Measurements in Thin Film Optics', Physics of Thin Films, (ed. G. Hass and R.E. Thun), 4, Academic Press, (1967) 3 Wendlandt, W.W. 'Modern Aspects of Reflectance Spectroscopy', Plenum Press, New York, (1968) 4 Korttlm, G. 'Reflectance Spectroscopy, Principles, Methods, Applications', Springer Verlag, New York, (1969) 5 Lavin, E.P. 'Specular Reflection', No 2 Monographs on Applied Optics, Adam Hilger, London, (1971) 6 Weeks, R.F. 'Simple wide range specular reflectometer', J Opt Soc Am, 48, (1958) 775-777 7 Bennett, H.E., Koehler, W.F. 'Precision measurement of absolute specular reflectance with minimised systematic errors' J Opt Soc Am, 50, (1960) 1-6 8 Shaw, J.E., Blevin, W.R. 'Instrument for the absolute measurement of direct specular reflectance at normal incidence', J Opt Soc Am, 54, (1964) 334-336 9 Boivin, G., Theriault, J.M. Reflectometer for precise measurement of absolute specular reflectance at normal incidence, Rev Sci Inst, 52, (1981) 1001-1003 10 Hass, G. "Reflectance and preparation of front surface mirrors for use at various angles of incidence from the ultraviolet to the far infrared', J Opt Soc Am, 72, (1982) 27-39 11 Darcie, T.E., Whalen, M.S. 'Determination of optical constants using pseudo-Brewster angle and normal incidence reflectance measurements', Appl Opt, 23, (1984) 1130-1131 12 Bittar, A., Hamlin, J.D. 'High accuracy true normalincidence absolute reflectometer', Appl Opt, 23, (1984) 4054--4057 13 Sheffer, D., Oppenheim, U.P., Clement, D., Devir, A.D. 'Absolute reflectometer for the 0.8-2.5 pm region', Appl Opt, 26, (1987) 583-586 14 Ram, R.S., Om Prakash "Reflectivity Measurement', J Opt (India), 16, (1987) 27-30 15 Stewart, J.E. 'Infrared Spectroscopy, Experimental Methods and Techniques', Marcel Dekker, New York, (1970) 16 Mackechnie, B., Bezuidenhout, D.F. "Determination of thin-film absorption coefficients from photoacoustic data', J Mod Opt, 34, (1987) 1025-1030

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