Optical analog of a non-redundant array

Volume 32A, number 7

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PHYSICS

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T (K) 1. A plot of (R/SR)2/3 (where 5R = R n -R ) v e r s u s T. The solid lines are plots of eq. 1 for a whisker with = 74 nm and a r e a of 1.3 ~tm 2 at the best fit value of 5. The AL theory (corrected for the 1.3 ~ m c r o s s s e c tion) predicts the dashed line.

LETTERS

7 September 1970

p r o p o r t i o n a l to T - 3 / 2 in the A L l i m i t , we p l o t [ R / ( R n - R ) ] 2/3 v e r s u s T in fig. 1 to d i s p l a y the d i f f e r e n c e b e t w e e n t h e s e r e s u l t s and the A L theory. S i n c e the c h a n g e s in r e s i s t a n c e w e r e r a t h e r s m a l l , l a r g e c u r r e n t d e n s i t i e s , J , had to be u s e d . T y p i c a l l y J w a s 104 A / c m 2. T h e r e s i s t a n c e w a s c u r r e n t d e p e n d e n t in a r a n g e not e x c e e d i n g 100 m K a b o v e T c , and w i t h i n t h i s r a n g e the d a t a d o e s not fit t h i s t h e o r y . W e h a v e m e a s u r e d t h e s e e f f e c t s in w h i s k e r s of p u r e Sn and a l s o of Sn a l l o y e d w i t h Cd o r In. T h e c o h e r e n c e l e n g t h s v a r i e d f r o m 70 to 150 nm and the a r e a s f r o m 0.4 to 2.0 ( ~ m ) 2. T h e r e s u l t s w e r e a l l in a g r e e m e n t w i t h t h i s t h e o r y and had b e s t fit 5 o ' S r a n g i n g f r o m 2 × 10 -3 to 4 × 10 -3.

Fig.

rent) 2/3 versus temperature curve. Since long drift in the measured resistance was large compared to the decrease in resistance due to these fluctuations, the resistance was not measured as a function of temperature. Instead, the resistance at several temperatures was measured as a function of magnetic field. Since a' is

OPTICAL

ANALOG

OF

References [1] J. E. Crow, R. S. Thompson, M. A. Klenin, and A. K. Bhatnagar, Phys. Rev. Letters 24 (1970) 371. [2] W. W. Webb and R. J. Warburton, Phys. Rev. L e t t e r s 20 (1968) 481. [3] L. G. Aslamazov and A. I. Larkin, Phys. Letters 26A (1968) 238; Fiz. Tverd. Tela 10 (1968) 1104. [4] R. S. Thompson, Phys. Rev. B1 (1970) 327. [5] K. Maki, l>rogr. Theoret. Phys. (Kyoto) 40 (1968) 193. [6] D. R. Overcash, M . J . Skove and E. P. Stillwell, Phys. Rev. 187 (1969) 570.

A NON-REDUNDANT

ARRAY

F. G O R I and G. G U A T T A R I Istituto di Fisica, Facolta' di Ingegneria, Universit~ di Roma, Italy Gruppo Nazionale di Struttura della Materia del C.N.R. Received 17 June 1970

An optical analog of a non-redundant a r r a y is used to synthesize a full aperture. Experimental results are shown.

Optical aperture synthesis has recently rec e i v e d c o n s i d e r a b l e i n t e r e s t [1,2]. A p e r t u r e s y n t h e s i s t e c h n i q u e s a r e t r a n s l a t e d into o p t i c s f r o m r a d i o a s t r o n o m y [3,4]. A s i g n i f i c a n t e x a m p l e of s y n t h e s i s in r a d i o a s t r o n o m y i s that of f o u r non e q u a l l y s p a c e d a e r i a l s [5]. T h e i m p o r t a n c e of t h i s a r r a y l i e s on the f a c t that it c o m p l e t e l y r e moves redundancy. 446

In t h i s l e t t e r we r e p o r t an e x p e r i m e n t in which an o p t i c a l a n a l o g of the a r r a y d e s c r i b e d in ref.[5] (fig. l a ) i s u s e d to s y n t h e s i z e a f u l l a p e r t u r e (fig. lb). In i n c o h e r e n t i l l u m i n a t i o n the s y n t h e s i s is p o s s i b l e b e c a u s e only the m u t u a l i n t e n s i t y f u n c t i o n i s of i n t e r e s t in the pupil p l a n e . T h a t f u n c t i o n d e p e n d s on d i s t a n c e s b e t w e e n p a i r s of p u p i l p o i n t s and the p u p i l of fig. l a c o n t a i u s e v e r y d i s -

Volume 32A, number 7

P HYSI C S L E T T E R S

function and then the s a m e i m a g e . It must be noted, h o w e v e r , that f i l t e r i n g i s needed only to apodize the s p r e a d function. As apodization does not i m p r o v e s i g n i f i c a n t l y r e s o l u t i o n l i m i t s when the i m a g e d o b j e c t i s highly c o n t r a s t e d , f i l t e r i n g is u n n e c e s s a r y in this c a s e . T h e s e c o n c l u s i o n s have been e x p e r i m e n t a l l y v e r i f i e d . An i n c o h e r e n t l y i l l u m i n a t e d r e s o l u t i o n bar t a r g e t was i m a g e d through the s y n t h e s i z i n g pupil of fig. l a and the full a p e r t u r e of fig. lb. The pupil d i m e n s i o n s w e r e 2.8 × 20 m m 2. An opt i c a l s y s t e m with a m a g n i f i c a t i o n M = 12 was used. Th e r e s u l t i n g i m a g e i s shown in fig. 2a f o r the s y n t h e s i z i n g pupil and in fig. 2b for the full a p e r t u r e . Although the i m a g e in the f i r s t c a s e is of c o u r s e l e s s a t t r a c t i v e , no r e s o l u t i o n l o s s is apparent.

[lllll a)

7 September 1970

b)

Fig. 1. a) synthesizing pupil b) full aperture to be synthesized

a

b

Fig. 2. Photographs of a resolution bar target imaged through the synthesizing pupil (a) and the full aperture (b). t a nc e contained in the full a p e r t u r e . It follows that, through s u i t a b l e f i l t e r i n g o p e r a t i o n s , the pupils of fig. l a and l b can give the s a m e s p r e a d

Reference s [1] G. W. Stroke, Phys. Letters 28A (1968) 252. [2] G.W. Stroke, Phys. Letters 30A (1969) 485. [3] D. J. Cronin and G. O. Reynolds, J. Opt. Soe. Am. 59 (1969) 501A. [4] D. Yansen, G.O. Reynolds and D. J. Cronin, J. Opt. Soc. Am. 60 (1970) 737A. [5] F. Gori and G. Guattari, Phys. Letters, to be published. $ $ $ $ $

447