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  1. N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
    [CrossRef] [PubMed]
  2. P. M. Hirsch, J. A. Jordan, L. B. Lesem, U.S. Patent3,619,022 (9Nov.1971).
  3. R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).
  4. N. C. Gallagher, Ph.D. Dissertation, Princeton University, in preparation.
  5. B. Liu, N. C. Gallagher, “Optimum Fourier Transform Division Filters with Magnitude Constraint,” to appear in J. Opt. Soc. Am. (1974).
    [CrossRef]

1973 (1)

1972 (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Gallagher, N. C.

N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
[CrossRef] [PubMed]

N. C. Gallagher, Ph.D. Dissertation, Princeton University, in preparation.

B. Liu, N. C. Gallagher, “Optimum Fourier Transform Division Filters with Magnitude Constraint,” to appear in J. Opt. Soc. Am. (1974).
[CrossRef]

Gerchberg, R. W.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Hirsch, P. M.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, U.S. Patent3,619,022 (9Nov.1971).

Jordan, J. A.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, U.S. Patent3,619,022 (9Nov.1971).

Lesem, L. B.

P. M. Hirsch, J. A. Jordan, L. B. Lesem, U.S. Patent3,619,022 (9Nov.1971).

Liu, B.

N. C. Gallagher, B. Liu, Appl. Opt. 12, 2328 (1973).
[CrossRef] [PubMed]

B. Liu, N. C. Gallagher, “Optimum Fourier Transform Division Filters with Magnitude Constraint,” to appear in J. Opt. Soc. Am. (1974).
[CrossRef]

Saxton, W. O.

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Appl. Opt. (1)

Optik (1)

R. W. Gerchberg, W. O. Saxton, Optik 35, 237 (1972).

Other (3)

N. C. Gallagher, Ph.D. Dissertation, Princeton University, in preparation.

B. Liu, N. C. Gallagher, “Optimum Fourier Transform Division Filters with Magnitude Constraint,” to appear in J. Opt. Soc. Am. (1974).
[CrossRef]

P. M. Hirsch, J. A. Jordan, L. B. Lesem, U.S. Patent3,619,022 (9Nov.1971).

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Figures (1)

Fig. 1
Fig. 1

Left: (m,n)th point in the complex image plane at the rth iteration. Right: (p,q)th point in the transform plane at the rth iteration.

Equations (18)

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( τ mn ) m , n = 0 N 1
( ϕ mn ) m , n = 0 N 1
[ τ mn exp ( i ϕ mn ) ] m , n = 0 N 1 .
[ A pq exp ( i ψ pq ) ] p , q = 0 N 1 .
Φ 0 ( r ) = m , n = 0 N 1 [ A pq ( r ) α ( r ) A pq ] 2 .
{ [ ϕ mn ( j ) ] m , n = 0 N 1 , j = 1,2 } .
DFT { τ mn exp [ i ϕ mn ( r ) ] } = { A pq ( r ) exp [ i ψ pq ( r ) ] } .
α A pq = A pq ( r ) + c pq ( r ) ,
[ d mn ( r ) ] = IDFT { c pq ( r ) exp [ i ψ pq ( r ) ] } .
τ mn ( r ) exp [ i ϕ mn ( r + 1 ) ] = τ mn exp [ i ϕ mn ( r ) ] + d mn ( r ) .
e mn ( r ) = | τ mn τ mn ( r ) | .
e mn ( r ) | d mn ( r ) | .
Φ 0 ( r ) = ( 1 / N ) 2 m , n = 0 N 1 | d mn ( r ) | 2 ( 1 / N ) 2 m , n = 0 N 1 e mn 2 ( r ) .
( 1 / N ) 2 m , n = 0 N 1 e mn 2 ( r ) Φ 0 ( r + 1 )
DFT { τ mn ( r ) exp [ i ϕ mn ( r + 1 ) ] } = { α A pq exp [ i ψ pq ( r ) ] } and DFT { τ mn exp [ i ϕ mn ( r + 1 ) ] } = { A pq ( r + 1 ) exp [ i ψ pq ( r + 1 ) ] } .
( 1 / N ) 2 m , n = 0 N 1 | τ mn exp [ i ϕ mn ( r + 1 ) ] τ mn ( r ) exp [ i ϕ mn ( r + 1 ) ] | 2 = p , q = 0 N 1 | A pq ( r + 1 ) exp [ i ψ pq ( r + 1 ) ] α A pq exp [ i ψ pq ( r ) ] | 2 p , q = 0 N 1 | A pq ( r + 1 ) exp [ i ψ pq ( r + 1 ) ] α A pq exp [ i ψ pq ( r + 1 ) ] | 2 .
( 1 / N ) 2 m , n = 0 N 1 | e mn ( r ) | 2 p , q = 0 N 1 | c pq ( r + 1 ) | 2 = Φ 0 ( r + 1 ) .
Φ 0 ( r ) Φ 0 ( r + 1 ) .

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