Abstract

Ordinarily, in photographic recording, the shutter is opened for a finite time which can be described by a rectangular shutter function (= flux as a function of time). Such a shutter function, in connection with linear image motion, creates a degradation due to motion blur. If the shutter modulates the flux by a function cos2 (t2), a recording is obtained that has the properties of an incoherent one-dimensional hologram. Hence, compensation of motion blur is achieved by reconstructing a sharp image from the hologram. This method can be modified in order to cope with harmonic vibrational or random translational motion.

© 1969 Optical Society of America

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References

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  1. J. L. Harris, J. Opt. Soc. Am. 59, 497A (1969); J. Opt. Soc. Am. 56, 569 (1966).
  2. G. L. Rogers, Nature 166, 237 (1950); D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
    [Crossref]
  3. E. N. Leith and J. Upatnieks, J. Opt. Soc. Am. 52, 1123 (1962).
    [Crossref]
  4. L. Mertz, Transformations in Optics, (John Wiley & Sons, Inc., New York, 1965).
  5. O. Bryngdahl and A. Lohmann, J. Opt. Soc. Am. 58, 625 (1968).
    [Crossref]
  6. A. W. Lohmann, Appl. Opt. 5, 669 (1966).
    [Crossref] [PubMed]

1969 (1)

J. L. Harris, J. Opt. Soc. Am. 59, 497A (1969); J. Opt. Soc. Am. 56, 569 (1966).

1968 (1)

1966 (1)

1962 (1)

1950 (1)

G. L. Rogers, Nature 166, 237 (1950); D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
[Crossref]

Bryngdahl, O.

Harris, J. L.

J. L. Harris, J. Opt. Soc. Am. 59, 497A (1969); J. Opt. Soc. Am. 56, 569 (1966).

Leith, E. N.

Lohmann, A.

Lohmann, A. W.

Mertz, L.

L. Mertz, Transformations in Optics, (John Wiley & Sons, Inc., New York, 1965).

Rogers, G. L.

G. L. Rogers, Nature 166, 237 (1950); D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
[Crossref]

Upatnieks, J.

Appl. Opt. (1)

J. Opt. Soc. Am. (3)

Nature (1)

G. L. Rogers, Nature 166, 237 (1950); D. Gabor, Proc. Roy. Soc. (London) A197, 454 (1949).
[Crossref]

Other (1)

L. Mertz, Transformations in Optics, (John Wiley & Sons, Inc., New York, 1965).

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Figures (4)

Fig. 1
Fig. 1

Linear-motion blur. (a) object; (b) ordinary blur; (c) modulated blur.

Fig. 2
Fig. 2

Shutter functions. (a) ordinary shutter function; (b) shutter function suitable for holographic motion compensation.

Fig. 3
Fig. 3

The holographic compensation process. (a) the horizontal cylinder lens L1 images the blurred record into the output plane. (b) the linear Fresnel pattern focuses the light at a distance f, from where it is imaged by the vertical cylinder lens L2 into the output plane.

Fig. 4
Fig. 4

(a) The object; (b) the object with ordinary motion blur; (c) the recording where the motion blur is spatially modulated into one-dimensional Fresnel-zone pattern; (d) reconstructed image from (c). With the lenses used a larger horizontal than vertical magnification was obtained.

Equations (3)

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S ( t ) = cos 2 [ π ( v t / a ) 2 ] in 0 t 2 T ; 0 , otherwise .
0 2 T S ( t ) d t = T ; if ( 2 v t / a ) 2 is an integer .
S ( t ) δ ( x - v t - x ) d t = 1 / v cos 2 [ π ( x - x ) 2 / a 2 ] in x x x + 2 v T .