Abstract

Several noise suppression techniques in coherent imaging systems are described. For holographic imaging the diffuse wave, periodic phase modulation, and multiple wave techniques are compared and the implementation of the last is considered. For lens-type imaging systems the use of multiple incoherent waves results in excellent noise suppression.

© 1973 Optical Society of America

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References

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    [CrossRef] [PubMed]

1973 (1)

1972 (1)

A. H. Firester, E. C. Fox, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

1970 (1)

D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
[CrossRef]

1968 (2)

1967 (2)

W. Martienssen, S. Spiller, Phys. Lett. 24A, 126 (1967).

J. Upatnieks, Appl. Opt. 6, 1905 (1967).
[CrossRef] [PubMed]

1966 (1)

1964 (1)

1956 (1)

Altman, J. H.

Brand, G. B.

G. B. Brand, Appl. Opt. 12, 368 (1973).
[CrossRef]

G. B. Brand, U.S. Pat.3,620,598.

El-Sum, H. M. A.

Firester, A. H.

A. H. Firester, E. C. Fox, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Fox, E. C.

A. H. Firester, E. C. Fox, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Gabor, D.

D. Gabor, IBM J. Res. Dev. 14, 509 (1970).
[CrossRef]

Gerritsen, H. J.

Hannan, W. J.

A. H. Firester, E. C. Fox, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

H. J. Gerritsen, W. J. Hannan, E. G. Ramberg, Appl. Opt. 7, 2301 (1968).
[CrossRef] [PubMed]

Kirkpatrick, P.

Leith, E. N.

Lurie, M.

A. H. Firester, E. C. Fox, W. J. Hannan, M. Lurie, RCA Rev. 33, 131 (1972).

Martienssen, W.

W. Martienssen, S. Spiller, Phys. Lett. 24A, 126 (1967).

Ramberg, E. G.

Spiller, S.

W. Martienssen, S. Spiller, Phys. Lett. 24A, 126 (1967).

Upatnieks, J.

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Figures (6)

Fig. 1
Fig. 1

Source of noise and its suppression in an imaging system: (a) plane wave illumination, (b) phase modulation (could be periodic), and (c) multiple-wave illumination.

Fig. 2
Fig. 2

Intensity pattern from seven plane wave illumination of a field (a) as proposed by Gabor and (b) at a different plane that shows the basic period.

Fig. 3
Fig. 3

The MTF of hologram reconstruction (a) resulting from two incoherent additions and (b) resulting from incoherent integration obtained by using an extended source.

Fig. 4
Fig. 4

The MTF of a hologram reconstructed by a point source (solid horizontal line) and by an extended spatially incoherent source (curved line) that is the edge of the shaded region. The ratio of shaded area to the remaining area under the horizontal line is related to speckle contrast.

Fig. 5
Fig. 5

Image formed by a hologram of an object illuminated with a diffuse wavefront with bandwidth of ±40 lines/mm. Reconstructions are (a) point source, (b) ½ (ωo/ωm) = 1/3, S.C. = 1/9, (c) ½ (ωo/ωm) = 1/5, S.C. = 1/25, (d) ½ (ωo/ωm) = 1/9, S.C. = 1/81.

Fig. 6
Fig. 6

Images from a two-lens unit magnification telescope: (a) plane wave illumination, (b) multiple coherent-wave illumination, (c) multiple incoherent-wave illumination, (d) single extended spatially incoherent light source illumination corresponding to ±2.5 l/mm size at the Fourier transform plane, and (e) combination of (c) and (d) above.

Tables (1)

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Table I Characteristics of Illuminating Wavefronts

Equations (8)

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A ( x ) = a 0 + j a 1 cos ω 0 x + a 2 cos 2 ω 0 x + j a 3 cos 3 ω 0 x + a n cos n ω 0 x + j a n + 1 cos ( n + 1 ) ω 0 x + ,
A ( x ) 2 = a 0 2 + 2 a 1 2 + 2 a 2 2 + 2 a 3 2 + ( 2 a 1 2 + 4 a 0 a 2 + 4 a 1 a 3 ) cos ( 2 ω 0 x ) + ( 2 a 2 2 + 4 a 1 a 3 ) cos ( 4 ω 0 x ) + 2 a 3 2 cos ( 6 ω 0 x ) .
2 a 1 2 + 4 a 0 a 2 + 4 a 1 a 3 = 0 , 2 a 2 2 + 4 a 1 a 3 = 0.
exp ( j m cos ω 0 x ) = J 0 ( m ) + j 2 J 1 ( m ) cos ω 0 x - 2 J 2 ( m ) cos ( 2 ω 0 x ) - j 2 J 3 ( m ) cos ( 3 ω 0 x ) +
exp ( j m cos ω 0 x ) = n = - + ( j ) n J n ( m ) exp ( j n ω 0 x ) .
R n a n 2 / max a n 2 ,
R = f ( ω x , ω y ) 2 d ω x d ω y / max [ Δ ω x Δ ω y < f ( ω ) 2 > ] ,
V = ( I max - I min ) / ( I max + I min )

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