Abstract

The technique of measuring the velocity of a moving image by means of a parallel-slit spatial filter is treated as continuous optical correlation processing. This technique is compared with other approaches to measuring image velocity by correlation and is shown to be a special case where the image displacement necessary for the correlation measurement is held constant and the time interval required to traverse this fixed distance is measured. The time measurement is accomplished inherently in terms of the frequency of the periodic signal generated by the image motion. Based on a derived mathematical model of the process and the characteristics of spatial filters, some conclusions are drawn about the way various parameters affect signal quality and continuity.

© 1966 Optical Society of America

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References

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  1. J. T. Ator, J. Opt. Soc. Am. 53, 1416 (1963).
    [Crossref]
  2. C. E. Hendix, in Conference Proceedings of the National Institute of Radio Engineers Military Electronic Conference (Institute of Radio Engineers, New York, 1962), p. 140.
  3. P. A. Button, P. E. Mallory, S. B. Boor, in Proceedings of the National Specialists Meeting on Guidance of Aerospace Vehicles (Institute of Aeronautical Sciences, New York, 1960).
  4. B. Miller, Aviation Week Space Technol. 72, 81 (1960).
  5. R. C. Jennison, Fourier Transforms and Convolutions for the Experimentalist (Pergamon Press, Inc., New York, 1961), pp. 82–84.
  6. J. D. Finley, “Terrain Spectral Radiance Experiment,” USAF Tech. Report AFAL-TR-65-30 (April1965), p. 10.
  7. T. W. Miller, Phot. Eng. 31, 486 (1965).
  8. L. E. Watson, Aerospace Corporation (private communication, 1965).

1965 (1)

T. W. Miller, Phot. Eng. 31, 486 (1965).

1963 (1)

1960 (1)

B. Miller, Aviation Week Space Technol. 72, 81 (1960).

Ator, J. T.

Boor, S. B.

P. A. Button, P. E. Mallory, S. B. Boor, in Proceedings of the National Specialists Meeting on Guidance of Aerospace Vehicles (Institute of Aeronautical Sciences, New York, 1960).

Button, P. A.

P. A. Button, P. E. Mallory, S. B. Boor, in Proceedings of the National Specialists Meeting on Guidance of Aerospace Vehicles (Institute of Aeronautical Sciences, New York, 1960).

Finley, J. D.

J. D. Finley, “Terrain Spectral Radiance Experiment,” USAF Tech. Report AFAL-TR-65-30 (April1965), p. 10.

Hendix, C. E.

C. E. Hendix, in Conference Proceedings of the National Institute of Radio Engineers Military Electronic Conference (Institute of Radio Engineers, New York, 1962), p. 140.

Jennison, R. C.

R. C. Jennison, Fourier Transforms and Convolutions for the Experimentalist (Pergamon Press, Inc., New York, 1961), pp. 82–84.

Mallory, P. E.

P. A. Button, P. E. Mallory, S. B. Boor, in Proceedings of the National Specialists Meeting on Guidance of Aerospace Vehicles (Institute of Aeronautical Sciences, New York, 1960).

Miller, B.

B. Miller, Aviation Week Space Technol. 72, 81 (1960).

Miller, T. W.

T. W. Miller, Phot. Eng. 31, 486 (1965).

Watson, L. E.

L. E. Watson, Aerospace Corporation (private communication, 1965).

Aviation Week Space Technol. (1)

B. Miller, Aviation Week Space Technol. 72, 81 (1960).

J. Opt. Soc. Am. (1)

Phot. Eng. (1)

T. W. Miller, Phot. Eng. 31, 486 (1965).

Other (5)

L. E. Watson, Aerospace Corporation (private communication, 1965).

C. E. Hendix, in Conference Proceedings of the National Institute of Radio Engineers Military Electronic Conference (Institute of Radio Engineers, New York, 1962), p. 140.

P. A. Button, P. E. Mallory, S. B. Boor, in Proceedings of the National Specialists Meeting on Guidance of Aerospace Vehicles (Institute of Aeronautical Sciences, New York, 1960).

R. C. Jennison, Fourier Transforms and Convolutions for the Experimentalist (Pergamon Press, Inc., New York, 1961), pp. 82–84.

J. D. Finley, “Terrain Spectral Radiance Experiment,” USAF Tech. Report AFAL-TR-65-30 (April1965), p. 10.

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Figures (11)

Fig. 1
Fig. 1

Principal features of a parallel-slit image velocity sensor.

Fig. 2
Fig. 2

Typical implementation of two-slit correlator.

Fig. 3
Fig. 3

Time-displaced signals processed in the two-slit correlator.

Fig. 4
Fig. 4

Coplanar filter and intercepted image of area KL.

Fig. 5
Fig. 5

Partition of imagery into two periodic distributions.

Fig. 6
Fig. 6

Hypothetical image flux distribution reduced to a line distribution.

Fig. 7
Fig. 7

Graphical synthesis of correlation of image samples with a filter.

Fig. 8
Fig. 8

Result of superposition of image convolutions. (a) Resultant convolution of image and filter. (b) Smoothed convolution function.

Fig. 9
Fig. 9

Cyclic weighting function.

Fig. 10
Fig. 10

Autocorrelation function of a 5-cycle square-wave filter. Filter transmission characteristics.

Fig. 11
Fig. 11

Combination of out-of-phase square-wave filter autocorrelation functions. (a) Composite spatial filter (n = 5). (b) Composite filter autocorrelation function.

Equations (8)

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φ ( τ ) = lim T 1 T 0 T f ( t ) × f ( t + τ ) d t ,
R ( u , v ) = 1 K L x - K / 2 x + K / 2 y - L / 2 y + L / 2 f FIL ( x , y ) × f FIL ( x + u , y + v ) d x d y .
φ ( u , v ) = x - K / 2 x + K / 2 y - L / 2 y + L / 2 f FIL ( x , y ) f FIL ( x + u , y + v ) d x d y x - K / 2 x + K / 2 y - L / 2 y + L / 2 f FIL ( x , y ) 2 d x d y .
φ ( u , v ) = 1 K L x - K / 2 x + K / 2 y - L / 2 y + L / 2 f FIL ( x , y ) f IM ( x + u , y + v ) d x d y .
R ( x ) = { x - j d d / 2 , j d < x < ( j + 1 / 2 ) d 1 - x - ( j + 1 / 2 ) d d / 2 , ( j + 1 / 2 ) d < x < ( j + 1 ) d ,
φ ( x ) = 1 K x - K x [ R ( x ) ] [ f A ( x ) ] d x + 1 K x - K x [ R ( x + d / 2 ) ] [ f B ( x ) ] d x .
φ ( x ) = 1 K x - K x [ R ( x ) ] [ f A ( x ) ] d x + 1 K x - K x [ 1 - R ( x ) ] [ f B ( x ) ] d x ,
φ ( x ) = 1 K x - K x [ R ( x ) ] [ f A ( x ) - f B ( x ) ] d x + 1 K x - K x f B ( x ) d x .

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