Abstract

Spatial phase modulation of wavefronts as used in holography and in spatial filtering is treated, and means of preventing or reducing noise and distortion are discussed. The phase index of modulation must be less than 0.2 rad to prevent intermodulation noise if a square-law detector is used. Phase holograms satisfy this requirement and, with care, so do spatial filters. In spatial filtering, however, an intolerable amount of distortion is introduced because the upper range of intensity levels of the fringe subcarrier exceeds the dynamic range of the recorder-modulator (photographic plates in this study). The impulse responses of spatial phase modulation filters show the effects of this distortion. Filters using spatial amplitude modulation have the same distortion but it is reduced because of the increasing opacity of the film in the overexposed regions. Simple blocking of the regions producing distortions effectively reduces the noise in the impulse response of the filter.

© 1966 Optical Society of America

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References

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  1. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962);J. Opt. Soc. Am. 53, 1377 (1963);J. Opt. Soc. Am. 54, 1295 (1964).
    [Crossref]
  2. A. VanderLugt, IEEE Trans. Information Theory IT-10, 139 (1964).
  3. W. T. Cathey, J. Opt. Soc. Am. 55, 457 (1965).
    [Crossref]
  4. A. K. Rigler, J. Opt. Soc. Am. 55, 1693 (1965).
    [Crossref]
  5. H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., Princeton, N. J., 1960), Ch. 12.
  6. M. Schwartz, Information Transmission, Modulation, and Noise (McGraw-Hill Book Co., Inc., New York, 1959), p. 116.

1965 (2)

1964 (1)

A. VanderLugt, IEEE Trans. Information Theory IT-10, 139 (1964).

1962 (1)

Black, H. S.

H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., Princeton, N. J., 1960), Ch. 12.

Cathey, W. T.

Leith, E. N.

Rigler, A. K.

Schwartz, M.

M. Schwartz, Information Transmission, Modulation, and Noise (McGraw-Hill Book Co., Inc., New York, 1959), p. 116.

Upatnieks, J.

VanderLugt, A.

A. VanderLugt, IEEE Trans. Information Theory IT-10, 139 (1964).

IEEE Trans. Information Theory (1)

A. VanderLugt, IEEE Trans. Information Theory IT-10, 139 (1964).

J. Opt. Soc. Am. (3)

Other (2)

H. S. Black, Modulation Theory (D. Van Nostrand Co., Inc., Princeton, N. J., 1960), Ch. 12.

M. Schwartz, Information Transmission, Modulation, and Noise (McGraw-Hill Book Co., Inc., New York, 1959), p. 116.

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Figures (6)

F. 1
F. 1

Surface variations of emulsion in which interference fringes are recorded. Horizontal scale: 10 μ. per division. Vertical scale: 240 Å per division. (a) low exposure, (b) medium exposure, (c) high exposure.

F. 2
F. 2

Surface variations of spatial-filter emulsion. Horizontal scale: 10 μ. per division. Vertical scale: 250 Å per division.

F. 3
F. 3

Image reconstructions using SPM bleached hologram.

F. 4
F. 4

Surface variations of spatial-niter emulsion near the focal point. (a) Effect of recorder saturation upon fringe recording. Horizontal scale: 10 μ per division. Vertical scale: 250 Å per division. (b) Surface variations showing saturation in region of focus. Horizontal scale: 127 μ per division. Vertical scale: 1270 Å per division.

F. 5
F. 5

Impulse responses of an SPM spatial filter; (a) with no block, (b) with 2.0-mm-diam block, (c) with 2.5-mm-diam block.

F. 6
F. 6

Impulse responses of an SAM spatial filter. (a) with no block, (b) with 0.5-mm-diam block, (c) with 1.0-mm-diam block.

Equations (5)

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| A ( x ) exp [ i ϕ ( x ) ] + A 0 exp [ i α x ] | 2 = A 0 2 + A 2 ( x ) + 2 A ( x ) A 0 cos [ α x ϕ ( x ) ] ,
B 0 exp { i γ [ A ( x ) 2 + A 0 2 + A ( x ) A 0 cos ( α x ϕ ) ] } ,
B 0 exp { i γ [ ] } = B 0 { 1 + i γ [ ] ( γ 2 [ ] / 2 ) + } .
B 0 ( 1 + i γ { A ( x ) 2 + A 0 2 + 2 A 0 A ( x ) cos [ α x ϕ ( x ) ] } ) = B 0 + i γ B 0 [ A ( x ) 2 + A 0 2 ] + i γ B 0 A 0 A ( x ) [ e i α x e i ϕ ( x ) + e i α x e i ϕ ( x ) ] .
C 0 γ { A ( x ) 2 + A 0 2 + A 0 A ( x ) cos [ α x ϕ ( x ) ] } = γ C 0 [ A ( x ) 2 + A 0 2 ] + γ C 0 A 0 A ( x ) [ e i α x e i ϕ ( x ) + e i α x e i ϕ ( x ) ] ,