Abstract

Based on the simple mathematical fact that the frequency spectrum of a constant is a δ function, and from the viewpoints of frequency spectrum analysis, two representative filters and the constant constraint criterion are analyzed. It is concluded that the constant constraint criterion is inconsistent.

© 1995 Optical Society of America

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References

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  1. A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
    [CrossRef]
  2. D. Casasent, A. Furman, Appl. Opt. 16, 1652 (1977).
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    [CrossRef]
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  11. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Chap. 7, p. 319.
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1988 (1)

1987 (2)

1986 (2)

1985 (1)

1984 (2)

D. Casasent, Appl. Opt. 23, 1620 (1984).
[CrossRef] [PubMed]

C. K. Tao, in ICO-13 Conference Digest (International Commission for Optics secretariat, Tokyo, 1984), p. 484.

1982 (2)

1980 (1)

1978 (1)

S. B. Gurevich, Transfer and Processing of Information for Holography (Soviet Radio, Moscow, 1978).

1977 (1)

1964 (1)

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

April, G.

Arsenault, H. H.

Arsennault, H. H.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Chap. 7, p. 319.

Casasent, D.

Furman, A.

Gianino, P. D.

Gurevich, S. B.

S. B. Gurevich, Transfer and Processing of Information for Holography (Soviet Radio, Moscow, 1978).

Hester, C. F.

Horner, J. L.

Hsu, Y.-N.

Kumar, B. V. K. V.

Mahalanobis, A.

Ochoa, E.

Schils, G.

Sweeney, D.

Tao, C. K.

C. K. Tao, in ICO-13 Conference Digest (International Commission for Optics secretariat, Tokyo, 1984), p. 484.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Inf. Theory IT-10, 139 (1964).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, London, 1980), Chap. 7, p. 319.

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Figures (3)

Fig. 1
Fig. 1

Frequency spectrum of (fi, h).

Fig. 2
Fig. 2

Typical rotation φ in plane. ɛ = π/2 and −πφπ.

Fig. 3
Fig. 3

Intersection set fintersection.

Equations (15)

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c ( 0 , 0 ) = ( f , h ) = f ( x , y ) h * ( x , y ) d x d y .
( f i , h ) = u i = const .
c f h ( P ) = u = const . ,
c f h ( P ) = c f h ( Δ φ ) = f ( φ + Δ φ , r ) h * ( φ , r ) r d r d φ .
C ( ω φ ) = F ( ω φ , r ) H * ( - ω φ , r ) = F ( ω φ , r ) H ( ω φ , r ) ,
h ( φ , r ) = [ F ( ω φ = 0 , r ) ] - 1 .
c f h ( Δ φ ) = f ( φ + Δ φ , r ) [ F ( ω φ = 0 , r ) ] - 1 r d r d φ .
C ( ω φ , ω r ) = F ( ω φ , ω r ) H ( ω φ , ω r ) ,
h ( x , y ) = e 1 f 1 ( x , y ) + + e N f N ( x , y ) = m e m f m ( x , y ) .
( f i , h ) = u i = 1 ;
m e m ( f i , f m ) = 1 .
Δ Ω x ~ 1 Δ X .
f intersection = f 1 ( x , y ) f 2 ( x , y ) f N ( x , y ) = i N f i ( x , y ) ,
H = { FT [ f 1 f 2 f N ] } * .
I = N DOF log 2 ( m + 1 ) ,

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