ABSOLUTE MEASUREMENT OF OPTICAL ATTENUATION USING PHOTOTHERMAL LASER-BEAM-DEFLECTION SPECTROSCOPY

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ABSOLUTE MEASUREMENT OF OPTICAL ATTENUATION USING PHOTOTHERMAL LASER-BEAM-DEFLECTION SPECTROSCOPY

G. Wetsel, Jr, S. Stotts

To cite this version:

G. Wetsel, Jr, S. Stotts. ABSOLUTE MEASUREMENT OF OPTICAL ATTENUATION USING PHOTOTHERMAL LASER-BEAM-DEFLECTION SPECTROSCOPY. Journal de Physique Collo- ques, 1983, 44 (C6), pp.C6-215-C6-219. �10.1051/jphyscol:1983633�. �jpa-00223192�

ABSOLUTE MEASUREMENT OF O P T I C A L ATTENUATION U S I N G PHOTOTHERMAL LASER-BEAM-DEFLECTION SPECTROSCOPY

G.C. Wetsel, Jr. and S.A. Stotts

Department o f Physics, Southern Methodist U n i v e r s i t y , DaZlas, Texas 75275, U.S.A.

Rhsum6

-

Abstract - A method of absolute measurement of optical attenuation using photo- thermal spectroscopy has been developed. Its range of applicability is

characterized by a theoretical model.

We have discovered that laser-beam-deflection spectroscopy (LBDS) can be used for the absolute measurement of wave or particle-beam attenuation.' In this paper we report: 1) the successful+application of LBDS to the absolute measurement of optical attenuation, 6 , in u 3 :CaFz, 2) comparison of the LBDS results to deter- mination of B by enclosed-cell-microphone-detection photoacoustic spectroscopy

(ECMD PAS) and by measurement of transmitted and reflected light, and 3) the results of a theoretical model developed to explain the experiment and characterize its range of applicability.

An exponential decrease of the intensity of a wave or parti le beam with distance (z] along the direction of wave propagation, I(z) = I0e-", where lo is the intensity at z = 0, is characteristic of any loss process for which the spatial rate of change of intensity is linearly proportional to the intensity. If the photo- thermal lascr-beam deflection signal is linearly proportional to I(z), than a semi- logarithmic plot of that signal versus z will be a straight line the slope of which is equal to - B . Such a measurement provides a direct, absolute value of attenu- ation - - by the definition of attenuation. This method contrasts to indirect methods in which transmitted intensity is measured or in which intensity-dependent signals are compared to a reference signal (relative measurements), and to absolute-attenu- ation measurements that require precise theory and knowledge of material parameters to infer 6 from the data.

The application of laser-beam-deflection measurements to spectroscopy or photo- thermal laser-heam-deflection spectroscopy (PTLBDS), was first reported by Boccara, et a1 .', who measured relative optical absorption as a function of wavelength for several solid samples. In subsequent studies PT1,BDS was utilized to measure the optical absorption coefficient in weakly absorbing and condensed" samples.

The deflection signal was calibrated in the former study using a gaseous mixture of known 6 and in the latter study using solid and liquid samples that had previously been characterized with a spectrophotometer. Photothermal laser-beam deflection has also been employed to measure thermal images of surface5 and subsurface6 structure.

The+concept of ahsolute-attenuation measurement using I.BDS was tested using a chopped A r laser "pump" beam and a tfe-Ne laser "probe" beam. The pump beam at a wayelength of 514 nm was directed at normal incidence into a 0.7 x 0.7 x 1 cm

u3 :Car2 c r y ~ t a l . ~ The probe beam at 633 nm, a wavelength for which the sample is weakly absorbing, was directed perpendicular to the pump beam through the region of refractive-index gradient produced by the heat of the absorbed pump beam. Both

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983633

C6-216 JOURNAL DE PHYSIQUE

p a r a l l e l ( 2 ) and p e r p e n d i c u l a r 0.) d e f l e c t i o n s i g n a l s were d e t e c t e d by a t w o - d i - n e n s i o n a l p o s i t i o n s e n s o r . As t h e sample was s c a n n e d p a r a l l e l t o z u s i n g a s t e p p i n g n o t o r , t h e a m p l i t u d e and p h a s e o f t h e d e f l e c t i o n s i g n a l were measured by a l o c k - i n - a n a l y z e r . The e x p e r i m e n t was c o n t r o l l e d and d a t a a u t o m a t i c a l l y a c q u i r e d u s i n g a computer.

The p o s i t i o n - s e n s o r s i g n a l c o r r e s p o n d i n g t o t h e component o f t h e probe-beam d e f l e c t i o n p a r a l l e l t o t h e d i r e c t i o n o f pump-beam p r o p a g a t i o n i s shown i n F i g . 1 a s a f u n c t i o n o f 2 f o r f = 25 H z . The d a t a r a n g e e x t e n d s from a p o i n t n e a r t h e pump- beam e n t r a n c e s u r f a c e t o a p o i n t i n t h e b u l k o f t h e s a m p l e . The s e m i l o g p l o t o f t h e d a t a i s w e l l c h a r a c t e r i z e d by a s t r a i g h t l i n e e x c e p t n e a r z = 0 ( n e a r t h e i n p u t s u r f a c e ) . A l e a s t - s q u a r e s f i t o f t h e s e d a t a t o a s t r a i g h t l i n e y i e l d s t h e s l o p e , and h e n c e , 6. S i m i l a r r e s u l t s were o b t a i n e d f o r r e p e a t e d measurements o f t h e p a r a l - l e l component o f d e f l e c t i o n and f o r mcasurenients o f t h e component o f d e f l e c t i o n p e r p e n d i c u l a r t o t h e d i r e c t i o n o f pump-beam p r o p a g a t i o n . Based on t h e s e v a r i o u s m e a s u r e m e n ~ s , t h e most p r o b a b l e v a l u c o f B o b t a i n e d by t h e PTLBDS method i s 10 cm-' f o r t h e U ~ C sample a t 514 nm. ~ F ~ I t s h o u l d be mentioned t h a t a p o s i t i o n - s e n s o r v o l t a g e o f 100 pV c o r r e s p o n d s t o a d e f l e c t i o n a n g l e o f 5 x l o - ' r a d i a n s .

Measurements on t h e same sample were made u s i n g two o t h e r i n d e p e n d e n t methods f o r p u r p o s e s o f comparison w i t h t h e PTLBDS r e s u l t . Measur.ements o f i n c i d e n t , r e - f l e c t e d , and t r a n s m i t t e d power a t 514 nm were made u s i n g a p h o t o d e t e c t o r and a c a l i - b r a t e d o p t i c a l a t t e n u a t o r . With t h e a s s u m p t i o n t h a t t h e r e i s no s u r f a c e a t t e n u a t i o n f o r t h i s s a m p l e , a v a l u c o f 11 cm-I was i n f e r r e d from t h e r e f l e c t i o n - t r a n s m i s s i o n measurcmcnts. P r e v i o u s l y , t h e a t t e n u a t i o n i n t h i s sample had been d e t e r m i n e d from ECMD-PAS The ECMD-PAS s i g n a l was measured a s a f u n c t i o n o f choppjng f r e q u e n c y and t h e d a t a were f i t t o t h e t h e o r y o f McDonald and w e t s e l q u s i n g a com- p u t e r s e a r c h p r o c e d u r e and a p r o v i s i o n f o r s u r f a c e a t t e n u a t i o n . Assumin a v a l u e f o r s u r f a c e a b s o r p t i o n e x t r a p o l a t e d from t h e d a t a o f Hordvik and S k o l n i k k o f o r CaP2, t h e v a l v e e s t i m a t e d f o r B was a b o u t 12 cm-l. A t h e o r e t i c a l model h a s been d e v e l o e d t h a t d e s c r i b e s t h e t e m p e r a t u r e g r a d i e n t s produced by p h o t o t h c r m a l c o n v e r s i o n o f t i e

3

8

B

m

m

m

d d

. d d d d Z < ) ( I L L I ) o

F i g . 1. P o s i t i o n - s e n s o r a m p l i f i e r o u t p u t v o l t a g e v s . z f o r O,, : f = 25 HZ, wavelength = 514 nm, l J 3 + : c a ~ > .

i s s i m i l a r t o t h a t f o r t h e c a s e s o f p h o t o t h e r m a l imaging o f s u r f a c c and s u b s u r f a c e s t r u c t t i r e 6 , ", and f o r PTLBDS when t h e p r o b e beam i s o u t s f d e t h e s a m p l c l l , 1 2 , o r propa!ating i n s i d e t h e sample p a r a 1 l e l t o t h e pump beam.

'-

Fm

where y = i n i t i a l p o s i t i o n o f probe beam r e l a t i v e t o c e n t e r o f pump beam, A = ( ~ B I ~ ~ ~ / ~ K ~ ~ ) (an/a'I') , a = f r a c t i o n o f a b s o r b e d l i g h t c o n v e r t e d i n t o h e a t , r = Gaussian pump-beam r a d y u s , ~ = t h c r m a l c o n d u c t i v i t y , n o = e q u i l i b r i u m r e f r a c t i v e i n d e x , (an/aT) = e q u i l i b r i u m r e f r a c t i v e - i n d e x g r a d i e n t , u = ( l + j ) a & , a=(ppC ,'r)

'/:

g.

The most i m p o r t a n t f e a t u r e o f

Ig&

z > z where z = 2 . 3 / ( ~ -8) l . Numerical i n t e g r a t i o n o f ( 1 7 f o r r a wide r a n g e o f

'l

a p p r o p % a t e p a r a s e t e r s v E r i f i e s t h a t t h e above i n e q u a l i t i e s p r o v i d e a good measure o f a p p l i c a b i l i t y o f t h e method.

C a l c u l a t i o n s o f 8" a s a f u n c t i o n o f z u s i n g ( 1 ) f o r zci: g i v e a d e v i a t i o n from a s t r a i g h t l i n e on a s e m i l o g p l o t o f t h e same g e n e r a l s h g p c a s t h a t o f t h e d a t a i n F i g . I ; howevcr, p a r t o f t h e r o l l o v e r i n t h e d a t a n e a r z = 0 i s due t o t h e f i n i t e d i a m e t e r o f t h e p r o b e beam (W.8mm). Comparison o f experiment;tl and t h e o - r e t i c a l v a l u e s o f O,,(Z) i n v o l v e c o n s i d e r a t i o n s 1 s i m i l a r t o t h o s e f o r 3,, ( z ) , above.

As f u r t h e r e v a I u a t i o n s o f t h e model,O1 andOA were measured a s a f u n c t i o n o f yo. The r e s u l t s f o r t h e a m p l i t u d e o f 8" a r e shown i n F ~ P . 2 a l o n g w i t h t h c p r c - d l c t i o n s o f ( 1 ) . 'l'he agreement i s e x c e l l e n t c o n s i d e r i n g t h a t t h e pump beam i s p r o b a b l y n o t e x a c t l y Gaussian. The e x p e r i m e n t a l and t h e o r e t i c a l v a r i a t i o n s o f t h e p h a s e o f 0~ w i t h y o were a l s o i n good agreement e x c e p t f o r

1

k h e r e a s t h e f r e q u e n c y dependence o f $U a s i n d i c a t e d by (1) a p p e a r s t o be com- p l i c a t e d , i t i s dominated hy a f dependence, a s i s most ~ ~ h o t o t h e r m a l phenomena.

The d e f l e c t i o n a n g l e i n c r e a s e s \ < i t h i n c r e a s i n g B u n t i l s a t u r a t i o n o c c u r s ; t h e p r e - d e c t i o n s o f (1) f o r CaF2 a r e shown i n F i g . 3.

In summary, we have d e v c l o p e d a method o f a b s o l u t e measurement o f Nave o r p a r t i c l e - b e a m a t t e n u a t i o n u s i n g l a s e r - b e a m - d e f l e c t i o n s p e c t r o s c o p y . The e x p e r i - mental mcthod and i t s r a n g e o f a p p l i c a b i l i t y have been c h a r a c t c r i z c d by a t h e o - r e t i c a l model o f PTLBDS t h x t i s i n e x c e l l e n t agreement w i t h t h e d a t a f o r t h e t e s t s a m p l e , a c r y s t a l of u " : c ~ F ~ . 'I'he v a l u e of 6 o b t a i n e d by P'l'LI3I)S was compared w i t h t h e v a l u e s o b t a i n e d From two i n d e p e n d e n t methods. The v a l u e o f B i n f c r r c d from.

t r a n s m i s s i . o n - r e f l e c t i o n measurements i s s u b j e c t t o e r r o r s d u e t o s u r f a c e a t t e n u a t i o n and inhomogeneity i n t h e s a m p l e , and t o c a l i b r a t i o n e r r o r s i n t h e o p t i c a l a t t e n u - a t o r s . The v a l u e o f @ i n f c r r c d from ECMD-PAS measurement^^^^^^" i s s u b j e c t t o e r r o r s due t o s u r f a c e a t t e n u a t i o n arid i n h o m o ~ e n e i t y i n t h e s a m p l e , i m p r e c i s e knou-

l e d g e o f t h c m a t e r i a l p a r a m e t e r s o f t h e sample, and some u n c e r t a i n t y a b o u t t h e

C6-218 JOURNAL DE PHYSIQUE

Y ~ I L L I E T E R S )

F i g . 2 . Normalized 4, v s . y o f o r z = 1 . 0 mm, f = 25 Hz (+)

.

-3

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d N m t V ) m PI

LOG [ B E T A

<l/r)l

F i g . 3 . ' T h e o r e t i c a l Gu v s . 6 : f = 25 142, z = B - ~ , ⁼ 0 , I, = 1 . 0 w / m 2 , r = 1 . 0 mm, Car2.

o n l y t h e d i s t a n c e ( z ) c a l i b r a t i o n i s r e q u i r e d . I t i s a p p l i c a b l e t o s a m p l e s t h a t a r e n e a r l y t r a n s p a r e n t a t somc ( p r o h c - b e a m ) w a v e l e n g t h and f o r w h i c h somc f r a c t i o n o f t h e a b s o r b e d e n e r g y is c o n v e r t e d i n t o h e a t ; y e t , t h e m e a s u r e d a t t e n u a t i o n f a c t o r , B, i s c h a r a c t e r i s t i c o f p r o c e s s e s t h a t remove e r i e r g y from t h c pump beam. Thc method i s l i m i t e d on t h e low-13 e n d o f t h e r a n g e o f a p p l i c a b i l i t y by n o i s e and by t h e s a m p l e l e n g t h r e q u i r c d ( ~ 6 - I ) ; l t i s l i m i t e d on t h e h i g h - 6 e n d by t h e c h o p p i n g - f r e q u e n c y d e p e n d e n c e o f t h e s i g n a l a n d h e n c e e v e n t u a l l y n o i s e , a n d by t h e a v a i l a - b i l i t y o f s u f f i c i e n t l y - s m a l l z - s t e p s i z e and probe-beam d i a m e t e r . We e x p e c t t h a t t h i s r a n g e i s from t r a n s p a r e n t t o q u i t e o p a q u e f o r t y p i c a l m a t e r i a l s .

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