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References

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  1. F. T. S. Yu, E. Y. Wang, Appl. Opt. 12, 1656 (1973).
    [CrossRef] [PubMed]
  2. P. B. Mauer, 1973 Fall Meeting of the Optical Society of America.
  3. L. I. Goldfischer, J. Opt. Soc. Am. 55, 247 (1965).
    [CrossRef]
  4. L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).
  5. S. Lowenthal, H. Arsenault, J. Opt. Soc. Am. 60, 1478 (1970).
    [CrossRef]

1973 (1)

1970 (1)

1967 (1)

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

1965 (1)

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

L. H. Enloe, Bell Syst. Tech. J. 46, 1479 (1967).

J. Opt. Soc. Am. (2)

Other (1)

P. B. Mauer, 1973 Fall Meeting of the Optical Society of America.

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Figures (2)

Fig. 1
Fig. 1

The equivalent optical system.

Fig. 2
Fig. 2

The MTF of a mask of width a with random small apertures of width b.

Equations (18)

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f ( x ) = q ( x ) exp [ i ϕ ( x ) ] ,
< f ( x 1 ) f * ( x 2 ) > = δ ( x 1 - x 2 ) ,
< f ( x 1 ) f ( x 2 ) > = 0 ,
< f ( x 1 ) f * ( x 2 ) f ( x 3 ) f * ( x 4 ) > = δ ( x 1 - x 2 ) δ ( x 3 - x 4 ) + δ ( x 1 - x 4 ) δ ( x 2 - x 3 ) .
g i ( u ) = exp ( i k u 2 / 2 b ) f ( x ) t ( x 1 , u , ξ ) h i ( ξ ) d d ξ ,
t ( x 1 , u , ξ ) = exp { - i k [ ( x / a ) + ( u / b ) ] ξ } exp ( i k x 2 / 2 a ) ,
I ( u ) = i = 1 n g i ( u ) 2 ,
< I ( u ) > = { < f ( x 1 ) f * ( x 2 ) > t ( x 1 , u , ξ 1 ) t * ( x 2 , u , ξ 2 ) × [ 1 n h i ( ξ 1 ) h i * ( ξ 2 ) ] d x 1 d x 2 d ξ 1 d ξ 2 .
< I ( u ) > = δ ( ξ 1 - ξ 2 ) [ 1 n h i ( ξ 1 ) h i * ( ξ 2 ) ] d ξ 1 d ξ 2 = 1 n h i ( ξ ) 2 d ξ .
< I 2 ( u ) > = { < f ( x 1 ) f * ( x 2 ) f ( x 3 ) f * ( x 4 ) > × t ( x 1 , u , ξ 1 ) t * ( x 2 , u , ξ 2 ) t ( x 3 , u , ξ 3 ) t * ( x 4 , u , ξ 4 ) × [ 1 n h i ( ξ 1 ) h i * ( ξ 2 ) ] [ 1 n h i ( ξ 3 ) h i * ( ξ 4 ) ] } × d x 1 d x 2 d x 3 d x 4 d ξ 1 d ξ 2 d ξ 3 d ξ 4 .
< I 2 ( u ) > = [ < I ( u ) > ] 2 + i , j n h i ( ξ 1 ) h i * ( ξ 2 ) h j ( ξ 1 ) h j * ( ξ 2 ) d ξ 1 d ξ 2 .
h ( x ) = h * ( x ) = h 2 ( x )
< I ( u ) > = n α A .
h i 2 ( ξ 1 ) h i 2 ( ξ 2 ) d ξ 1 d ξ 2 = α 2 A 2 ,
h i ( ξ 1 ) h i ( ξ 2 ) h j ( ξ 1 ) h j ( ξ 2 ) d ξ 1 d ξ 2 = α 4 A 2 .
< I 2 ( u ) > = n 2 α 2 A 2 + n α 2 A 2 + n ( n - 1 ) α 4 A 2 .
Q n = [ α 2 + ( 1 - α 2 ) / n ] 1 / 2 .
r ( x ) = h ( x - ξ ) h ( ξ ) d ξ ,

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