Abstract

This paper reports on a newly developed algorithm for improving the previously reported basic theory of computer-generated polarization holography. An application of the algorithm to the basic theory shortens the hologram making time, which uses a limited quantity energy of an illuminating uv spot light. A relation between a polarization angle of the illuminating uv beam and an effective amplitude transmittance Tp of a crystal-analyzer pair is derived. Furthermore, a method for correcting an effect of the pre-existing unbalance of the degree of the density balance of M-centers in a binary state is proposed. Also, the theory of the method is theoretically discussed in detail together with a derivation of the θ vs Tp curves characteristic of this case.

© 1978 Optical Society of America

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References

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  1. M. Nakajima, H. Komatsu, Y. Mitsuhashi, T. Morikawa, Appl. Opt. 15, 1030 (1976).
    [CrossRef] [PubMed]
  2. Y. Mitsuhashi, M. Sahara, N. Okada, M. Nakajima, T. Morikawa, Appl. Opt. 16, 1138 (1977).
    [CrossRef]

1977

1976

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Figures (7)

Fig. 1
Fig. 1

Conceptional illustration of an orientational relation between N+ and N for one sampling cell.

Fig. 2
Fig. 2

Schematic representation of an orientational relation among I+, I, and I.

Fig. 3
Fig. 3

Optical arrangement for hologram reading.

Fig. 4
Fig. 4

Plot of the calculated and measured amplitude transmittance Tp of the NaF-analyzer pair for a linearly polarized reading beam as a function of the polarization angle θ of a writing beam. The solid lines show the calculated value, and the plotted marks show the measured values.

Fig. 5
Fig. 5

Relation between the calculated amplitude transmittance Tp and the polarization angle θ of the writing beam in the case when the equilibrium of the initial orientational state is destroyed to a considerable degree where N+0/N−0 = 60/40.

Fig. 6
Fig. 6

Conceptional illustration of an analyzer angle correction.

Fig. 7
Fig. 7

An effect of an analyzer angle correction. Solid lines show characteristic curves after correction and dotted ones before correction.

Equations (13)

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N T = N + + N .
d N + ( t ) / d t = k [ N ( t ) I + N + ( t ) I ] ,
d N ( t ) / d t = k [ N + ( t ) I N ( t ) I + ] ,
I + = I sin 2 ( θ + π 4 ) ,
I = I cos 2 ( θ + π 4 ) ,
N + ( t ) = N T sin 2 ( θ + π 4 ) + [ N + 0 N T sin 2 ( θ + π 4 ) ] exp ( k I t ) ,
N ( t ) = N T cos 2 ( θ + π 4 ) + [ N 0 N T cos 2 ( θ + π 4 ) ] exp ( k I t ) ,
φ = tan 1 exp [ α ( N + 0 N 0 ) ] ( π / 4 ) .
T p = T 0 2 { cos ( π 4 + φ ) exp [ α N T sin 2 ( θ + π 4 ) + [ N + 0 N T sin 2 ( θ + π 4 ) ] exp ( k I t ) ] cos ( π 4 φ ) exp [ α N T cos 2 ( θ + π 4 ) + [ N 0 N T cos 2 ( θ + π 4 ) ] exp ( k I t ) ] } .
T + = 1 2 T 0 exp ( α N + )
T = 1 2 T 0 exp ( α N ) ,
T p = 1 2 ( T + T ) .
T p = T 0 2 ( exp { α N T sin 2 ( θ + π 4 ) + [ N + 0 N T sin 2 ( θ + π 4 ) ] exp ( k I t ) } exp { α N T cos 2 ( θ + π 4 ) + [ N 0 N T cos 2 ( θ + π 4 ) ] exp ( k I t ) } .

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