Abstract

Turbulence-degraded images have been processed to obtain an improvement of their visual image quality. The initial objects were photographed through laboratory-generated turbulence. The resulting transparencies of the degraded images were digitized by a photoelectric scanner and processed on a digital computer. The processing consisted of applying corrections to the amplitude and phase coefficients of the two-dimensional Fourier series representing the degraded images. The correction factors were obtained from the optical transfer function of the turbulence measured at the time the images were photographed. The experiment was done for 5-msec and 1-min exposure times. The processed data were used to generate photographs. The processed images were found to have significantly more visual detail than the original degraded images; the 5-msec-exposure restorations were superior to the 1-min-exposure restorations.

© 1967 Optical Society of America

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References

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  1. J. L. Harris, J. Opt. Soc. Am. 56, 569 (1966).
    [CrossRef]
  2. A nonlinearity, probably in the correction for the film H and D characteristics, caused the fundamental frequency of the optical transfer function for the time-variant case to have a value greater than unity. A partial correction was made by normalizing this frequency to unity. Therefore, the restoration factors for the time-variant case shown in Fig. 7 should be considered to be approximate values.

1966 (1)

J. Opt. Soc. Am. (1)

Other (1)

A nonlinearity, probably in the correction for the film H and D characteristics, caused the fundamental frequency of the optical transfer function for the time-variant case to have a value greater than unity. A partial correction was made by normalizing this frequency to unity. Therefore, the restoration factors for the time-variant case shown in Fig. 7 should be considered to be approximate values.

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Figures (9)

Fig. 1
Fig. 1

Block diagram of the system used in the restoration experiment.

Fig. 2
Fig. 2

Optical system used to obtain the turbulence-degraded images.

Fig. 3
Fig. 3

Paths of flux through the turbulence area.

Fig. 4
Fig. 4

Image-plane photographs. Top row: the known image; bottom row: the unknown image. (a) no turbulence; (b) with turbulence, 1-min exposure time (time-invariant image); (c) with turbulence, 5-msec exposure time (time-variant image).

Fig. 5
Fig. 5

The processed images. Top row: the time-invariant image of Fig. 4(b) after processing. Bottom row: the time-variant image of Fig. 4(c) after processing. The processing was done at spatial-frequency cutoffs of 2, 3, and 5 cycles/mm [(a), (b), and (c)].

Fig. 6
Fig. 6

Processed time-variant image of Fig. 5 (b) with the background removed by zeroing all values below a selected constant to increase contrast.

Fig. 7
Fig. 7

Restoration factors applied to the amplitudes of the horizontal frequencies of the degraded images.

Fig. 8
Fig. 8

Phase corrections applied to the phases of the horizontal frequencies of the degraded images.

Fig. 9
Fig. 9

Time-variant degraded image before and after processing. The experimental conditions were the same as for the time-variant image of Fig. 4(c) except that the angular size of the image in the turbulence area was one-half of that of Fig. 4(c).

Equations (4)

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F [ H I ( x , y ) ] = F [ H ( x , y ) ] F [ S I ( x , y ) ] ,
H ( x , y ) = F - 1 { F [ H ( x , y ) ] } = F - 1 { F [ H I ( x , y ) ] / F [ S I ( x , y ) ] } .
F [ S I ( x , y ) ] = F [ H I ( x , y ) ] K / F [ H ( x , y ) ] K .
[ H ( x , y ) ] U = F - 1 { F [ H I ( x , y ) ] U × F [ H ( x , y ) ] K / F [ H I ( x , y ) ] K } .