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References

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  1. B. J. Pernick, S. Levinson, C. Bartolotta, Appl. Opt. 9, 1902 (1970).
    [CrossRef] [PubMed]
  2. H. Stark, W. R. Bennett, H. Arm, Appl. Opt. 8, 2165 (1969).
    [CrossRef] [PubMed]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

1970 (1)

1969 (1)

Appl. Opt. (2)

Other (1)

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), p. 86.

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Figures (4)

Fig. 1
Fig. 1

Mach-Zehnder interferometer used to subtract dc bias A2B(x,y) from the signal pulse bias A1T(x,y), followed by fourier transformation.

Fig. 2
Fig. 2

Transparency used to demonstrate method 2 experimentally.

Fig. 3
Fig. 3

Photodetector scans across region of f y = 0 when the input is (a) signal portion (y < 0) of the transparency represented in Fig. 2; (b) clear aperture portion (y < 0); and (c) entire transparency. Here f x = u/(1.25 × 10−2), where u is the spatial dimension.

Fig. 4
Fig. 4

Enlarged photograph of fourier transform plane when the transparency represented in Fig. 2 is the input.

Equations (6)

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rect ( x / w ) = { 1 x w / 2 0 elsewhere .
T ( x , y ) = [ B 1 + b 1 f ( x , y ) ] rect ( x / w ) rect ( y / h ) ,
B ( x , y ) = rect ( x , w ) rect ( y / h ) .
T ( x , y ) = rect ( x , w ) { [ B 1 + b 1 ( x , y ) ] rect [ ( y + h 1 / 2 ) / ( h 1 / 2 ) ] + rect [ ( y - h 2 / 2 ) / ( h 2 / 2 ) ] exp ( - j π ) } .
b 1 F ( f x , f y ) exp ( j π f y h 1 ) + w sinc ( w f x ) { B 1 h 1 / 2 sinc ( h 1 f y / 2 ) × exp ( j π f y h 1 ) + h 2 / 2 sinc ( h 2 f y / 2 ) exp ( - j π f y h 2 ) exp ( - j π ) } ,
b 1 F ( f x , 0 ) + 1 2 sinc ( w f x ) [ B 1 h 1 - h 2 ]

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