Abstract

This paper describes a new method offering relaxation of the traditional holographic restriction on the allowable velocity of a moving object, that is, that the change of path difference between the object and reference beams has to be negligible during exposure of a hologram. The proposed method depends on the frequency chirp of the laser pulse used for the hologram recording canceling the Doppler frequency shift due to the motion of the object. Experimental verification is also shown.

© 1978 Optical Society of America

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References

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  1. D. Pohl, Phys. Lett. A26, 357 (1968).
  2. H. H. Chau, G. W. Leppelmeier, J. Opt. Soc. Am. 61, 998 (1971).
    [CrossRef]
  3. L. D. Siebert, Appl. Opt. 10, 632 (1971).
    [CrossRef] [PubMed]
  4. D. B. Neumann, J. Opt. Soc. Am. 58, 447 (1968).
    [CrossRef]
  5. H. Fujiwara, M. Yasutake, K. Murata, Opt. Commun. 14, 21 (1975).
    [CrossRef]
  6. H. Fujiwara, A. Tomita, Opt. Commun. 20, 29 (1977).
    [CrossRef]
  7. S. Mallick, Appl. Opt. 14, 602 (1975).
    [CrossRef] [PubMed]
  8. R. L. Kurtz, H. Y. Loh, Appl. Opt. 9, 1040 (1970).
    [CrossRef] [PubMed]
  9. R. L. Kurtz, H. Y. Loh, Appl. Opt. 11, 1998 (1972).
    [CrossRef] [PubMed]

1977

H. Fujiwara, A. Tomita, Opt. Commun. 20, 29 (1977).
[CrossRef]

1975

H. Fujiwara, M. Yasutake, K. Murata, Opt. Commun. 14, 21 (1975).
[CrossRef]

S. Mallick, Appl. Opt. 14, 602 (1975).
[CrossRef] [PubMed]

1972

1971

1970

1968

D. Pohl, Phys. Lett. A26, 357 (1968).

D. B. Neumann, J. Opt. Soc. Am. 58, 447 (1968).
[CrossRef]

Chau, H. H.

Fujiwara, H.

H. Fujiwara, A. Tomita, Opt. Commun. 20, 29 (1977).
[CrossRef]

H. Fujiwara, M. Yasutake, K. Murata, Opt. Commun. 14, 21 (1975).
[CrossRef]

Kurtz, R. L.

Leppelmeier, G. W.

Loh, H. Y.

Mallick, S.

Murata, K.

H. Fujiwara, M. Yasutake, K. Murata, Opt. Commun. 14, 21 (1975).
[CrossRef]

Neumann, D. B.

Pohl, D.

D. Pohl, Phys. Lett. A26, 357 (1968).

Siebert, L. D.

Tomita, A.

H. Fujiwara, A. Tomita, Opt. Commun. 20, 29 (1977).
[CrossRef]

Yasutake, M.

H. Fujiwara, M. Yasutake, K. Murata, Opt. Commun. 14, 21 (1975).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Geometry used for the analysis of hologram recording of a moving object. S is the light source, P is a point of interest on the object, and H is a point on the hologram plate.

Fig. 2
Fig. 2

Three specific geometries of a hologram recording system. The direction of the object motion is (a) parallel, (b) perpendicular to the hologram plate, and (c) tangential to the ellipse whose focuses are located at S and H.

Fig. 3
Fig. 3

Geometry used in the analysis of the proposed method. āi+ and āi are symmetrical with ā, and these beams have time differences +τ and −τ compared with the reference beam.

Fig. 4
Fig. 4

Experimental setup for recording the hologram of a moving object.

Fig. 5
Fig. 5

Reconstructed images for (a) τ = 0, (b) τ = −1.3 nsec, (c) τ = ±1.3 nsec, and (d) an example of oscilloscope traces of laser output pulses. Vertical scales: 500 mV/div; horizontal scales: 50 nsec/div. The density of DDI is 1.0 × 10−6 mole/liter, and the pumping energy is 0.68 kJ.

Fig. 6
Fig. 6

Reconstructed images for (a) τ = 0, (b) τ = ±1.3 nsec, (c) τ = ±2.7 nsec, and (d) an example of oscilloscope traces of laser output pulses. Vertical scales: 200 mV/div; horizontal scales: 50 nsec/div. The density of DDI is 0.75 × 10−6 mole/liter, and the pumping energy is 0.61 kJ.

Equations (16)

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Δ ω = k υ ( a ¯ i a ¯ s ) · a ¯ ,
f ( t ) = E ( t ) exp [ i ( ω 0 t + 1 2 α t 2 ) ] ,
θ = ( a ¯ i a ¯ s ) · a ¯ .
f 0 ( t ) = r E ( t ) exp [ i ( ω 0 + 1 2 α t k υ θ ) t ] .
I H ( α , υ ) = | f ( t ) + f 0 ( t + τ ) | 2 d t = | E ( t ) exp [ i ( ω 0 t + 1 2 α t 2 ) ] + r E ( t + τ ) exp { i [ ω 0 + 1 2 α ( t + τ ) k υ θ ] ( t + τ ) } | 2 d t .
I H ( α , υ ) = r exp [ i ( ω 0 τ + α τ 2 2 k υ θ τ ) ] × E * ( t ) E ( t + τ ) exp [ i ( α τ k υ θ ) t ] d t .
I R ( α , υ ) = | r E * ( t ) E ( t + τ ) exp [ i ( α τ k υ θ ) t ] d t | 2 .
υ 0 = ( α τ ) / ( k θ ) ,
I R ( α , υ ) = exp ( 2 ln 2 τ 2 T 2 ) exp [ T 2 ( α τ k υ θ ) 2 8 ln 2 ] ,
( x 2 / A 2 ) + ( y 2 / B 2 ) = 1 ( A B ) ,
a ¯ i = { x + c [ ( x + c ) 2 + y 2 ] 1 / 2 , y [ ( x + c 2 ) + y 2 ] 1 / 2 } , a ¯ s = { c x [ ( x c ) 2 + y 2 ] 1 / 2 , y [ ( x c ) ] 2 + y 2 ] 1 / 2 } , a ¯ = [ A 2 y ( A 4 y 2 + B 4 x 2 ) 1 / 2 , B 2 x ( A 4 y 2 + B 4 x 2 ) 1 / 2 ] ,
θ = ( a ¯ i a ¯ s ) · a ¯ = 0.
I R ( α , υ ) = exp ( 2 ln 2 τ 2 / T 2 ) × | exp [ i ( ω 0 k υ θ 2 ) τ ] exp [ T ( α τ k υ θ 2 ) 16 ln 2 ] + exp [ + i ( ω 0 k υ θ 2 ) τ ] exp [ T 2 ( α τ k υ θ ) 2 16 ln 2 ] | 2 .
I R ( α , υ ) = exp ( 2 ln 2 τ 2 T 2 ) { exp [ T 2 ( α τ k υ θ ) 2 8 ln 2 ] + exp [ T 2 ( α τ + k υ θ ) 2 8 ln 2 ] } .
V max = [ 16 ( ln 2 ) 2 + α 2 T 4 2 T 2 k 2 θ 2 ] 1 / 2 .
P ( ω ) = a 2 [ T 4 16 ( ln 2 ) 2 + α 2 T 4 ] 1 / 2 × exp [ 4 ln 2 16 ( ln 2 ) 2 + α 2 T 4 ( ω ω 0 ) 2 ] .

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