Abstract

The effect of speckle in the imaging of diffusely illuminated gratings and continuous-tone objects was studied. It was found that when imaging diffuse gratings, the aperture of a coherently illuminated system must be 2.6 times as large as that of an incoherent system to obtain comparable resolution. This factor must be increased to five when imaging continuous-tone objects and to a factor of seven if the coherent image is subsequently low-pass filtered. A coherent system can achieve resolution which is comparable to an incoherent system of equal aperture if the coherent image is smoothed so that the mean to standard deviation ratio is ten or more.

© 1976 Optical Society of America

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References

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  1. Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York, 1975).
  2. J. Upatnieks and R. W. Lewis, Appl. Opt. 12, 2683 (1973).
    [Crossref]
  3. N. George and A. Jain, Appl. Opt. 12, 1202 (1973).
    [Crossref] [PubMed]
  4. R. W. Lewis, “Redundancy in Coherent Imaging Systems,” Ph. D. Thesis, University of Michigan (1973).
  5. J. C. Dainty, Opt. Acta 18, 327 (1971).
    [Crossref]
  6. M. Young, B. Faulkner, and J. Cole, J. Opt. Soc. Am. 60, 137 (1970).
    [Crossref]
  7. J. Johnson, Image Intensifier Symposium, Fort Belvoir, Va.October 6–7, 1958, AD-220160.

1973 (2)

1971 (1)

J. C. Dainty, Opt. Acta 18, 327 (1971).
[Crossref]

1970 (1)

Appl. Opt. (2)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

J. C. Dainty, Opt. Acta 18, 327 (1971).
[Crossref]

Other (3)

Laser Speckle and Related Phenomena, edited by J. C. Dainty (Springer-Verlag, New York, 1975).

R. W. Lewis, “Redundancy in Coherent Imaging Systems,” Ph. D. Thesis, University of Michigan (1973).

J. Johnson, Image Intensifier Symposium, Fort Belvoir, Va.October 6–7, 1958, AD-220160.

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Figures (5)

FIG. 1
FIG. 1

The optical system used in the experiments. (D) the opal glass diffuser, (O) the object plane, (T) the object transparency, (L1) and (L2) the lenses forming an afocal imaging system, (F) the filter plane containing the circular apertures, (I) the image plane and (f) the focal length of lenses L1 and L2.

FIG. 2
FIG. 2

Resolution as a function of optical system aperture for (1) incoherent imaging (2) coherent imaging with resolution judged by viewing the entire bar pattern and (3) coherent imaging with resolution judged by viewing the bar pattern through a slit of width equal to the grating period.

FIG. 3
FIG. 3

Bar targets imaged (a) incoherently with a 2.1 mm aperture and (b) coherently with a 4.1 mm aperture. The bar targets on the left have spatial frequencies, from top to bottom, of 3.16, 3.98, 5.01, 6.31, and 7.95 l/mm.

FIG. 4
FIG. 4

Increase in bar target resolution with the number, N, of superimposed coherent images with independent speckle patterns. The image marked N = ∞ was produced using incoherent illumination. The spatial frequencies of the complete bar targets on the left are, from top to bottom, 2.51, 3.16, and 3.98 l/mm.

FIG. 5
FIG. 5

Comparison of images made incoherently with coherent images and smoothed coherent images formed using larger apertures. (a) original image. (b) reference incoherent image formed through a 1.44 mm aperture. (c), (e), (g), and (i) coherent images formed with the aperture diameter increased by a factor of 8.6, 7.2, 5.8, and 4.3, respectively. (d), (f), (h), and (j) are (c), (e), (g), and (i), respectively, smoothed by incoherent filtering through a 1.44 mm aperture.