Abstract

When normal laser holographic technique is applied to subjects in strong incoherent illumination, an additional darkening of the photographic plate due to the incoherent light is introduced. Effects of the darkening on the signal-to-noise ratio of the reconstructed image are analyzed using a simplified model for photographic plate characteristics. Optimum values of the fraction of laser light used as reference, plate exposure, and S/N are obtained. Reconstructed images of reasonable contrast and pictorial quality have been obtained for 3-D subjects illuminated with substantial incoherent light intensity in addition to the laser light.

© 1968 Optical Society of America

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  1. From an internal Bell Telephone Laboratories memorandum by I. Kogelnik.
  2. C. B. Burckhardt, Appl. Opt. 6, 1359 (1967).
    [CrossRef] [PubMed]

1967 (1)

Appl. Opt. (1)

Other (1)

From an internal Bell Telephone Laboratories memorandum by I. Kogelnik.

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Figures (14)

Fig. 1
Fig. 1

Arrangement for hologram formation with the subject illuminated in strong incoherent light as well as laser light.

Fig. 2
Fig. 2

First factor of Eq. (11) vs B02/C2. Solid line: case where available laser power is limited; broken line: a preset optics arrangement case.

Fig. 3
Fig. 3

F(X,B02/C2) vs X for various values of B02/C2. X is the fraction of available laser power used for a reference wave.

Fig. 4
Fig. 4

G(τ02,m) vs τ02 for various values of m. τ02 is the average intensity transmission of the plate.

Fig. 5
Fig. 5

Optimum transmission coefficient τ M vs m.

Fig. 6
Fig. 6

(2/n)2g0M vs m. M is figure of merit.

Fig. 7
Fig. 7

Hologram formation arrangement with a transparency illuminated by incoherent as well as coherent light.

Fig. 8
Fig. 8

Intensity transmission τ02 vs wavelength λ for the red glass filter.

Fig. 9
Fig. 9

Photographs of reconstructed images from holograms (see Table 1). (a) Without incoherent illumination, (b) with the incoherent wave 31 dB higher in intensity than the subject wave.

Fig. 10
Fig. 10

Photographs of reconstructed images from holograms with different reference wave intensities (Table I). Reference wave of (a) is 10 dB stronger than that of (b).

Fig. 11
Fig. 11

Arrangement for hologram formation with a three-dimensional subject in strong incoherent illumination.

Fig. 12
Fig. 12

Photographs of reconstructed images from holograms (see Table II): (a) Without incoherent wave, (b) with an incoherent wave 16 dB higher in intensity than the subject wave.

Fig. 13
Fig. 13

Transmission coefficient τ vs , the exposure, for Kodak 649F plates (by Kogelhik).

Fig. 14
Fig. 14

Noise intensity g, on an arbitrary scale, vs intensity transmission τ02 for Kodak 649F plates. (Clear plate loss of 1 dB subtracted to obtain abscissa values.)

Tables (2)

Tables Icon

Table I Hologram Formation Illumination Conditions for Transmission Subjects

Tables Icon

Table II Hologram Formation Illumination Conditions for Three-Dimensional Subjects

Equations (23)

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= ( A 2 + B 2 + C 2 + A B * + A * B ) T ,
0 + 1 + 1 ,
0 = ( B 2 + C 2 ) T ,
1 = A B * T , 1 = A * B T ,
τ τ 0 + τ 1 + τ 1 ,
τ 0 = f ( 0 ) ,
τ 1 = f ( 0 ) 1 , τ 1 = f ( 0 ) 1 ,
B τ 1 = f ( 0 ) A B 2 T ,
S = [ f ( 0 ) ] 2 A 2 B 4 T 2 = [ A 2 B 4 / ( B 2 + C 2 ) 2 ] [ f ( 0 ) ] 2 0 2 .
N = g ( τ 0 2 ) B 2 .
S N = { 4 A 2 B 2 ( B 2 + C 2 ) 2 } { [ f ( 0 ) ] 2 0 2 4 g ( τ 0 2 ) } .
4 A 2 B 2 ( B 2 + C 2 ) 2 = A 0 2 B 0 2 C 4 4 X ( 1 - X ) ( 1 + X B 0 2 / C 2 ) 2 = ( A 0 2 / C 2 ) ( B 0 2 / C 2 ) ( 1 + B 0 2 / C 2 ) F ( X , B 0 2 / C 2 ) ,
F ( X , B 0 2 / C 2 ) = 4 ( 1 + B 0 2 / C 2 ) X ( 1 - X ) ( 1 + X B 0 2 / C 2 ) 2 ,
X opt = 1 2 + B 0 2 / C 2 ,
τ = f ( ) = 1 1 + k n ,
g ( τ 0 2 ) = g 0 ( 1 + m ) 1 + m m m τ 0 2 m ( 1 - τ 0 2 ) ,
[ f ( 0 ) ] 2 0 2 / 4 g ( τ 0 2 ) = M G ( τ 0 2 , m ) ,
M = ( n 2 ) 2 1 g 0 m m ( 1 + m ) 1 + m τ M 2 ( 1 - m ) ( 1 - τ M ) ( 1 + τ M ) ,
τ M = [ 1 + 4 ( 1 - m ) 2 ] 1 2 - 1 2 ( 1 - m ) ,
G ( τ 0 2 , m ) = 1 + τ M τ M 2 ( 1 - m ) ( 1 - τ M ) τ 0 2 ( 1 - m ) ( 1 - τ 0 ) ( 1 + τ 0 ) .
τ = 0.96 / ( 1 + 0.122 2.53 ) ,
g 0 = 2 × 10 - 9 per ( lines / mm ) 2 × ( 220 lines / mm ) 2 10 - 4 , n = 2.53 ,             m = 0.75.
g 0 = 2 × 10 - 9 per ( lines / mm ) 2 × ( 70 lines / mm ) 2 10 - 5 , n = 2.53 ,             m = 0.75 ,             τ M = 0.24.

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