Abstract

We describe a class of image-processing optical systems, based on a laser scanner, whose output is an electronic video signal from a simple photodetector. We show that certain image-processing properties of these systems are exactly equivalent to the properties of conventional, partially coherent, image-processing optical systems. These systems are of interest when we want to combine optical image processing with further electronic processing. Some applications, such as electronic read out of phase-encoded images, are discussed.

© 1975 Optical Society of America

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References

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  1. See, for example, W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), Ch. 7.
  2. H. H. Hopkins, Proc. R. Soc. (Lond.) A217, 408 (1953).
    [CrossRef]
  3. A. Vander Lugt, Opt. Acta 15, 1 (1968).
    [CrossRef]
  4. Robert E. Kinzly, J. Opt. Soc. Am. 56, 9 (1966).
    [CrossRef]
  5. See, for example, R. A. Sprague and Brian J. Thompson, Appl Opt. 11, 1469 (1972).
    [CrossRef] [PubMed]

1972 (1)

See, for example, R. A. Sprague and Brian J. Thompson, Appl Opt. 11, 1469 (1972).
[CrossRef] [PubMed]

1968 (1)

A. Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

1966 (1)

1953 (1)

H. H. Hopkins, Proc. R. Soc. (Lond.) A217, 408 (1953).
[CrossRef]

Goodman, W.

See, for example, W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), Ch. 7.

Hopkins, H. H.

H. H. Hopkins, Proc. R. Soc. (Lond.) A217, 408 (1953).
[CrossRef]

Kinzly, Robert E.

Sprague, R. A.

See, for example, R. A. Sprague and Brian J. Thompson, Appl Opt. 11, 1469 (1972).
[CrossRef] [PubMed]

Thompson, Brian J.

See, for example, R. A. Sprague and Brian J. Thompson, Appl Opt. 11, 1469 (1972).
[CrossRef] [PubMed]

Vander Lugt, A.

A. Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

Appl Opt. (1)

See, for example, R. A. Sprague and Brian J. Thompson, Appl Opt. 11, 1469 (1972).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Acta (1)

A. Vander Lugt, Opt. Acta 15, 1 (1968).
[CrossRef]

Proc. R. Soc. (Lond.) (1)

H. H. Hopkins, Proc. R. Soc. (Lond.) A217, 408 (1953).
[CrossRef]

Other (1)

See, for example, W. Goodman, Introduction to Fourier Optics (McGraw–Hill, New York, 1968), Ch. 7.

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Figures (5)

FIG. 1
FIG. 1

Conventional system for partially coherent optical system.

FIG. 2
FIG. 2

Schematic diagram of the laser scanning system.

FIG. 3
FIG. 3

Trace over a knife edge. (a) 6 lines/mm bandwidth, 1.0 × 1.0 mm detector, horizontal scale 87 μm/division; (b) 6 lines/mm bandwidth, 0.12 × 1.0 mm detector, horizontal scale 87 μm/division; (c) 30 lines/mm bandwidth, 1.0 × 1.0 mm detector, horizontal scale 17.5 μm/division.

FIG. 4
FIG. 4

Approximate profile of the phase object.

FIG. 5
FIG. 5

Trace over the phase image of Fig. 4, horizontal scale 178 μ m/division, (a) without differentiating wedge; (b) with differentiating wedge.

Equations (6)

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g ( x , u 1 ) = t ( x ) e - i u 1 x * h ( x ) ,
γ ( x ) = S t ( x ) e - i u x * h ( x ) 2 d u ,
g ( u , x 0 ) = - t ( x ) h ( x 0 - x ) e - i u x d x .
g ( u , x 0 ) = t ( x 0 ) e - i u x * h ( x 0 ) .
γ ( x 0 ) = S g ( u , x 0 ) 2 d u = S t ( x 0 ) e - i u x 0 * h ( x 0 ) 2 d u .
t ( x , y ) = exp [ i a ( x , y ) cos 2 π ϕ x ] ,