Abstract

When coherent light is used for imaging transparent objects, the images may be inferior because of Fresnel diffraction patterns from scattered light or may be degraded by granularity from diffuse illumination. This paper proposes a technique for improving image quality by using a spatially phase-modulated wavefront to illuminate the object. Analysis shows that the resulting image should be free from Fresnel diffraction patterns and should have a negligible amount of residual granularity. Experimental results verify these conclusions. Requirements of the imaging system and the wavefront are discussed. The technique is applicable to any nondiffuse, two-dimensional object and can be used in holography or with any other coherent imaging system.

© 1967 Optical Society of America

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References

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  1. P. Kirkpatrick, H. M. A. El-Sum, J. Opt. Soc. Am. 46, 825 (1956).
    [CrossRef]
  2. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 54, 1295 (1964).
    [CrossRef]
  3. T. J. Skinner, J. Opt. Soc. Am. 53, A1350 (1963).
  4. T. J. Skinner, thesis, Boston University (1965).
  5. W. Martienssen, E. Spiller, Naturwiss. 52, 53 (1965).
    [CrossRef]
  6. P. S. Consodine, J. Opt. Soc. Am. 56, 1001 (1966).
    [CrossRef]
  7. T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 814 (1966).
    [CrossRef]
  8. T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 807 (1967).
    [CrossRef]
  9. W. Martienssen, S. Spiller, Phys. Letters 24A, 126 (1967).
  10. E. N. Leith, J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [CrossRef]

1967

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 807 (1967).
[CrossRef]

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

1966

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 814 (1966).
[CrossRef]

P. S. Consodine, J. Opt. Soc. Am. 56, 1001 (1966).
[CrossRef]

1965

W. Martienssen, E. Spiller, Naturwiss. 52, 53 (1965).
[CrossRef]

1964

1963

T. J. Skinner, J. Opt. Soc. Am. 53, A1350 (1963).

1962

1956

Consodine, P. S.

El-Sum, H. M. A.

Hioki, R.

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 807 (1967).
[CrossRef]

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 814 (1966).
[CrossRef]

Kirkpatrick, P.

Leith, E. N.

Martienssen, W.

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

W. Martienssen, E. Spiller, Naturwiss. 52, 53 (1965).
[CrossRef]

Skinner, T. J.

T. J. Skinner, J. Opt. Soc. Am. 53, A1350 (1963).

T. J. Skinner, thesis, Boston University (1965).

Spiller, E.

W. Martienssen, E. Spiller, Naturwiss. 52, 53 (1965).
[CrossRef]

Spiller, S.

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

Suzuki, T.

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 807 (1967).
[CrossRef]

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 814 (1966).
[CrossRef]

Upatnieks, J.

J. Opt. Soc. Am.

Japan. J. Appl. Phys.

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 814 (1966).
[CrossRef]

T. Suzuki, R. Hioki, Japan. J. Appl. Phys. 5, 807 (1967).
[CrossRef]

Naturwiss.

W. Martienssen, E. Spiller, Naturwiss. 52, 53 (1965).
[CrossRef]

Phys. Letters

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

Other

T. J. Skinner, thesis, Boston University (1965).

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Figures (6)

Fig. 1
Fig. 1

Model of an imaging system used for the analysis. Input signal s0(x0,y0) at plane P0 is imaged to plane P2 and is designated si(x,y); the defects n(x1,y1) of the system are assumed to be in plane P1 at a distance z from the object plane, and are imaged to plane P3.

Fig. 2
Fig. 2

A block diagram showing the analogy of the imaging system in Fig. 1 to the transmission of information in communications systems. Signal dispersion takes place in optics by means of the free space between the object and the lenses. Signal compression is initiated by the lenses and is accomplished in the space between the lenses and the image plane. A conjugate phase plate can be placed in the image plane if recovery of phase is important.

Fig. 3
Fig. 3

A one-dimensional representation of the phase of incident wavefront ϕ(x0) at plane P0 and of the transfer function of the imaging system h(x0).

Fig. 4
Fig. 4

The imaging system used for experiments. Laser light is focused and filtered to obtain a uniform spherical illuminating wavefront that goes through the irregular glass surface in contact with the emulsion of the transparency. The irregular glass was removed to obtain a plane wavefront and was moved away from the transparency to obtain diffuse illumination.

Fig. 5
Fig. 5

Images of a transparency showing the effect of illuminating wavefront on the quality of the image. In (a) the plane wavefront was used, in (b) the irregular glass was placed 4 mm from the transparency to obtain diffuse illumination, and in (c) the irregular glass was in contact with the emulsion of the transparency to obtain a phase-modulated wavefront. The original transparency was 9 mm wide.

Fig. 6
Fig. 6

The effect of a defect in various types of illuminating wavefronts. The defect in this case is a 0.10-mm diam wire in front of the imaging lens. In (a) a plane wavefront shows a distinct diffraction pattern of the wire; in (b) ground glass provides diffuse illumination and the scattered light is almost completely lost in the granular background; in (c) a noticeable granular pattern appears but is less granular than that in (b) and is less distracting than that in (a). The images are of a clear field.

Equations (7)

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s 1 ( x 1 , y 1 ) = n ( x 1 , y 1 ) { s 0 ( x 1 , y 1 ) * exp [ - i k ( x 1 2 + y 1 2 ) ] } = n ( x 1 , y 1 ) d ( x 1 , y 1 ) exp [ i α ( x 1 , y 1 ) ] .
s 0 ( x 0 , y 0 ) = c 0 s ( x 0 , y 0 ) + { exp [ i k ( x 0 2 + y 0 2 ) } * { c ( x 0 , y 0 ) d ( x 0 , y 0 ) exp [ i α ( x 0 , y 0 ) ] } .
s 0 ( x 0 , y 0 ) = c 0 b 0 v ( x 0 , y 0 ) exp [ i ϕ ( x 0 , y 0 ) ] + d 0 exp [ i k ( x 0 2 + y 0 2 ) + ( α 0 / k ) ] .
s 0 ( x 0 , y 0 ) 2 = c 0 2 b 0 2 v 2 ( x 0 , y 0 ) + d 0 2 + 2 c 0 b 0 d 0 v ( x 0 , y 0 ) cos [ k ( x 0 2 + y 0 2 ) + α 0 - ϕ ( x 0 , y 0 ) ] .
S i = S 0 + U * V * { N exp [ - i k 1 ( p 2 + q 2 ) ] } .
s i ( x , y ) = b 0 h ( x - x 0 , y - y 0 ) exp [ i ϕ ( x 0 , y 0 ) ] d x 0 d y 0 .
0 b 0 | h ( x - x 0 , y - y 0 ) exp [ j ϕ ( x 0 , y 0 ) ] d x 0 d y 0 | b 0

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