DETERMINING THE ATTENUATION FACTOR OF AN

AQUEOUS MEDIUM BY A PHASEMETER TECHNIQUE

A. P. Ivanov and V. D. Kozlov UDC 535.32

A new phasemeter technique for measur ing the optical cha rac te r i s t i c s of scat ter ing media was pro- posed in an ear l ie r a r t ic le [1]. It was shown, specifically, that when a sinusoidally modulated beam of light is sent through a medium of uniform depth and the scat tered light is recorded by the "candlepower me te r " a r r angement [2], the emitted signal and the received signal will be related to the equations

q~ =arctg --c~ ; G = 1 2" (1)

Here ~0 is the phase shift between the light signal launched in the medium and the light signal reflected back by the medium, the amplitude of both of which is modulated sinusoidally at the angular f requency co; G is the var ia t ion in the percentage modulation of the received signal re la t ive to the emitted signal; c is the speed of light t r ave r s ing the medium in question; a is the attenuation factor. The value of ~ can be de te r - mined with ease by Eq. (1), when either ~p or G is varied.

Results of an experimental ver i f icat ion of the phasemeter ing technique a re advanced in the present ar t ic le .

For a number of technical considerat ions, the optical a r r angement of the sys tem we fabricated dif- fered f rom the a r rangement discussed in [1] (see Fig. 1). Here the optical axes of the receiving sys tem and emitting sys tem do not coincide, and instead in tersect at a cer ta in point, at an angle ~ = 40' . This method makes it possible to keep s t ray light reflected by the equipment parts out of the receiving device, and at the same time enhances the accu racy of attenuation factor measurements . But Eqs. (1) become in- valid in that case, and new relat ionships linking ~, G, and a a re then required.

Let us consider this problem more closely.

The emitting device, which includes the LG-106 laser 2 operating at 510 nm wavelength, the u l t ra - sonic diffraction type modulator 3 and col l imator 4, fashion a parallel beam of light whose power var ies with with the t ime t in obedience to the law

F 0 = a + b sin cot, (2)

where a and b a r e respec t ive ly the constant component and the amplitude of the var iable component of the intensity of the radiat ion emitted.

The light beyond the tank i l luminator 11 impinges on the aqueous medium, where it experiences a t - tenuation in obedience to the law

F = e- eff J

Here Z is the path t r ave r sed by the light; aeff is the effective attenuation factor , which takes into account the fact that a part of the radiat ion is sca t tered in direct ions close to the direct ion of propagation of the d i rec t light. Clearly, the luminous intensity resul t ing f rom scat ter ing of the p r imary flux in an elemental

Transla ted f rom Zhurnal PriMadnoi Spektroskopii, Vil. 11, No. 1, pp. 109-113, July, 1969. Original a r t ic le submitted November 28, 1968.

�9 1972 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. All rights reserved. This article cannot be reproduced for any purpose whatsoever without permission of the publisher. A copy of this article is available from the publisher for $15.00.

791

. ' ~ - - ? ,9 Z IO~A' - - - - - - - -

Fig . 1. B a s i c l a y o u t of p h a s e m e t e r i n g d e v i c e fo r m e a s u r i n g a t t e n u a t i o n f a c t o r : 1) GD-300 p h a s e m e t e r ; 2) LG-106 l a s e r ; 3) u l t r a s o n i c d i f f r a c t i o n type m o d u l a t o r ; 4) c o l l i m a t o r ; 5) b e a m - s p l i t t i n g p l a t e ; 6) r e f l e c t o r ; 7) r e c e i v e r fo r s c a t t e r e d s igna l ; 8) r e c e i v e r fo r r e f e r e n c e s igna l ; 9) d i a p h r a g m ; 10) ob j e c t i ve ; 11)

t ank i l l u m i n a t o r .

l a y e r of t h i c k n e s s dl a t a dep th I in t he d i r e c t i o n t o w a r d the r a d i a t i o n s e n s o r i s

d I = 1 p(180O)e_eff a ~ - b s i n cot-- dt, (4) 4z~

w h e r e p (180 ~ i s t he s c a t t e r i n g i n d e x f o r s e a t t e r i n g a t 180 ~

W e now d e l i n e a t e the cone ABC in s p a c e . Th i s cone i s f o r m e d a s fo l lows : i t s he igh t m a t c h e s t he o p t i c a l a x i s of the r e c e i v i n g s e n s o r w h i l e p a s s i n g t h rough the c e n t e r 10 of the o b j e c t i v e and a p e r t u r e d i a - p h r a g m 9 p l aced a t the foca l d i s t a n c e f r o m the o b j e c t i v e 10. One of i t s b a s e s i s the o b j e c t i v e c r o s s s e e - t ion AC. The a n g l e a t the v e r t e x i s equa l to the a p e r t u r e a n g l e 27 of the r a d i a t i o n s e n s o r . It should be po in ted out tha t a l l the f lux s c a t t e r e d into the cone ABC at a n g l e 180 ~ r e l a t i v e to the d i r e c t i o n of p r o p a g a - t ion of the p r i m a r y ang l e , in a so l id a n g l e d e t e r m i n e d by the v a l u e of 27,* f a l l s on the r a d i a t i o n s e n s o r 7 p l a c e d on the o t h e r s i d e of the d i a p h r a g m 9. S ince the p o r t i o n o f the f lux F f a i l i ng into the cone ABC i s a p - p r o x i m a t e l y equal to 1/ l o on the i n t e r v a l 0 <_ 1 <- lo, a s can b e e s t a b l i s h e d e m p i r i c a l l y , and i s equal to un i ty on the i n t e r v a l l 0 -< l _</max, we f ind, upon r e c a l l i n g Eq. (4), p lus the f ac t of the a t t e n u a t i o n of the s e a t - t e r e d l igh t on pa ths of l eng th l, tha t the s i g n a l r e c o r d e d i s p r o p o r t i o n a l to

lo

-i-e-(%fI+8}' a@ b sin mt---T2~ dl I = o

lmax

H e r e A (t) and B(t) a r e func t ions of the t i m e ; ~ i s the p h a s e sh i f t of the s c a t t e r e d r a d i a t i o n r e l a t i v e to the o r i g i n a l r a d i a t i o n . The e x p o n e n t i a l func t ion a p p e a r i n g in the i n t e g r a n d con t a in s , in a d d i t i o n to eeff, t he exponen t i a l t e r m e. The l a t t e r t e r m i s a c c o u n t e d fo r by the f ac t tha t the s c a t t e r e d l igh t a r r i v i n g a t the r e - c e i v i n g s e n s o r i s p e r c e i v e d wi th in a s m a l l a n g l e (27 = 15 ' ) , and is t h e r e f o r e a t t e nua t e d in o b e d i e n c e to t h e law e -E/.

I t can be shown tha t , in s t e a d y s t a t e (t ~ oo), when A and B a r e func t ions of t, a n d / m a x = 0%? tha t

r ----- 2r - - %, (6)

w h e r e 0)

r = arctg - - ; ebgC

21oc0 e-2~bg,t~ sin c eeff+ e

(P2 = arctg - - ; - - (7) 1 - - e -2e bg4 cos 2l~176 e bg" 2 '

C

* T h e s c a t t e r i n g a n g l e m a y be c o n s i d e r e d equa l to 180 ~ fo r a l l p r a c t i c a l p u r p o s e s , i n a s m u c h a s the ang le i s v e r y s m a l l . ? T h a t the c o n s t r a i n t / m a x = oo i s p e r m i s s i b l e b e c o m e s c l e a r when we a s s u m e e - ( e e f f + e ) / m a x << 1.

792

%g

2

/

F ig . 2

%g

/,5 3

g

1o . . . . . . . . ;A

Fig . 3

F ig . 2. D e p e n d e n c e of ebg on ~ a t d i f f e r e n t A: 1) A = 0.6; 2) 0.7; 3 ,4) 0.9.

F ig . 3. D e p e n d e n c e of r a t i o ~ / a bg on A: 1) c a l c u l a t i o n s b a s e d on Eq. (8); 2) c a l c u l a t i o n s b a s e d on Eq. (9); 3) e x p e r i m e n t s .

wh i l e the v a r i a t i o n in the dep th of m o d u l a t i o n

V ( 2c~176 ) 2+ e-'4~bgl~176176 2 c2 1 - - e-2ebg t~ cos - G - B/A _ bg c c (8)

b/a (e~gC ~ @ co 2) (I - - e-2%g z,)

It should be e m p h a s i z e d that , in the l i m i t a s l 0 ~ 0, Eqs . (6) and (8) b e c o m e t r a n s f o r m e d into Eqs. (1).

The ebg v a l u e f o r the w a t e r in a t ank s i z e d 10 • 2 • 2 m was d e t e r m i n e d wi th the a r r a n g e m e n t a s f a b r i c a t e d above , by m e a s u r i n g the p h a s e sh i f t only. The p a r a m e t e r s of the e x p e r i m e n t a l a r r a n g e m e n t w e r e the fo l lowing: a n g u l a r m o d u l a t i o n f r e q u e n c y co = 2~r. 10 7 H z ; 10 = 0. 5 m; l m a x = 5 m; g, = 40 ' ; 2T = 15 ' ; o b j e c t i v e d i a m e t e r D = 0.08 m. The o p t i c a l p a r a m e t e r s of the w a t e r a r e the a t t e n u a t i o n f a c t o r a and the s u r v i v a l p r o b a b i l i t y of the photon A = e / a (e i s the s c a t t e r i n g index) , wh ich a r e a l l ow e d to v a r y by add ing m i l k and n i g r o s i n e dye in a p p r o p r i a t e p r o p o r t i o n s . In each m e a s u r e m e n t of abg by m e a n s of the p h a s e - m e t e r , the v a r i a b l e s a and A w e r e c o n t r o l l e d i n d e p e n d e n t l y by o t h e r m e t h o d s . S p e c i f i c a l l y , a was a l s o d e - t e r m i n e d by m e a n s of a c l a s s i c a l t r a n s p a r o m e t e r b a s e d on s u c c e s s i v e c o m p a r i s o n of the i n t e n s i t i e s of the l igh t t r a v e r s i n g the w a t e r - f i I I e d t e s t c e l l s on pa ths of d i f f e r e n t l eng ths . The a p e r t u r e a n g l e s of the e m i t t i n g and r e c e i v i n g d e v i c e s did not exceed 20 ' , t h e r e b y g u a r a n t e e i n g the a b s e n c e of s c a t t e r e d l i gh t on the r a d i a - t ion s e n s o r of the t r a n s p a r o m e t e r when i t was u sed to m e a s u r e d i r e c t r a d i a t i o n .

The photon s u r v i v a l p r o b a b i I i t y A w a s found f r o m the f o r m u l a

% g t § emgm A = ~Vt + ~mVm+ enVn" (9)

H e r e ~w and ~w a r e the a t t e n u a t i o n f a c t o r and s c a t t e r i n g index of p u r e w a t e r in the t ank o c c u p y i n g the v o l u m e Vt; a m and a n a r e the a t t e n u a t i o n f a c t o r s of the o r i g i n a I m i l k and n i g r o s i n e s o l u t i o n s * ; V m and V n a r e the v o l u m e s of the m i l k and n i g r o s i n e s o l u t i o n s i n t r o d u c e d into the a que ous m e d i u m of the tank.

T h e v a l u e s of aw, am, a n w e r e d e t e r m i n e d wi th the t r a n s p a r o m e t e r m e n t i o n e d e a r l i e r , wh i l e ~w was d e t e r m i n e d by a m e t h o d d e s c r i b e d e l s e w h e r e [3].

F i g u r e 2 shows how abg v a r i e s wi th the a t t e n u a t i o n f a c t o r a m e a s u r e d on a t r a n s p a r o m e t e r a t d i f - f e r e n t A v a l u e s . I t i s c l e a r f r o m the d i a g r a m tha t ebg < e c o n s i s t e n t l y , and tha t the d i f f e r e n c e b e t w e e n t h e m i n c r e a s e s wi th i n c r e a s i n g A. T h i s p h e n o m e n o n can be a c c o u n t e d fo r qu i t e r e a d i l y . The p r o b l e m i s t ha t the v a r i a b l e a e f f a p p e a r i n g in the equa t ion fo r abg i s a l w a y s l e s s than ~. The r e a s o n i s t ha t the i l l u m i n a t i o n in a n y c r o s s s e c t i o n of the cone ABC (Fig . 1) p a r a l l e l to the b a s e of tha t cone i s d e t e r m i n e d not s o l e l y by d i - r e e t l igh t but a l s o by s c a t t e r e d l ight . The b r o a d e r the cone, the g r e a t e r the s u r v i v a l p r o b a b i l i t y of the photon, t he f u r t h e r the s c a t t e r i n g i n d i e a t r i x of the e l e m e n t a l v o l u m e i s ex t ended f o r w a r d , the g r e a t e r wi l l be the c o n t r i b u t i o n m a d e by the s c a t t e r e d l igh t , the s m a i l e r aeff w i l l be , and c o n s e q u e n t l y the s m a l l e r abg

* The v a l u e of a m i s p r a c t i c a l l y equa l to the s c a t t e r i n g index of m i l k , and the v a l u e of E n i s p r a c t i c a l l y equa l to the a b s o r p t i o n i n d e x of the n i g r o s i n e dye .

793

will be. It can be shown readi ly that when pract ical ly all of the scat tered light is concentrated within the cone, we have

e 1 - - , (10)

ebg 1 - - 0,5A

and that when only the diffract ion component is concentrated within the cone, we have instead

e 1 ebg 1 - - 0.25A" (11)

It is clear f rom Eq. (10) that, under the least favorable conditions, when the medium is a purely sca t - ter ing medium, ~bg will be ~-fold smal ler . There can be no grea ter difference between the two, in pr in- ciple. Moreover , e and ~bg differ by a significantly smal le r amount in rea l situations.

Figure 3 shows the experimental dependence of e / e b g on A. Here theoretidal curves were plotted on the basis of Eqs. (10) and (11). It is evident in the d iagram that the experimental data fit on the graph in between the data predicted by Eqs. (10) and (11).

The concentrat ion in the objective diameter in the receiving sensor is a threefold one, occur r ing in cases where the equipment sensi t ivi ty allows for that variant, and shows that the value of ebg drew con- sistently c loser to the value of ~ because of the increase in Cell-

This indicates that the experimental investigations confirmed the validity of the phasemeter ing method for measur ing the attenuation factor. The observed slight difference in the value of e, in principle always in existence when this method is used, falls within the limits of those assumptions held to be viable in p rac - t ice in many cases .

The authors express their thanks to Yu. V. Popov for Mndly maMng the GD-300 rangefinder available to us, and for most helpful technical consulation, and also thank I. L. Katsev for his participation in the work and discussion of the resul ts .

1o 2. 3.

L I T E R A T U R E C I T E D

A. P. Ivanov, Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. i Okeana, 4, 224 (1968). A. A. Gershun, Dokl. Akad. Nauk SSSR, 51, 595 (1946). I. M. Levin and A. P. Ivanov, Opt. i Spektr., 18, 920 (1965).

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