Effects of Photographic Gamma on Hologram Reconstructions*†

James C. Wyant; M. Parker Givens

doi:10.1364/JOSA.59.001650

Effects of Photographic Gamma on Hologram Reconstructions

James C. Wyant and M. Parker Givens

Journal of the Optical Society of America
Vol. 59,
Issue 12,
pp. 1650-1658
(1969)
•https://doi.org/10.1364/JOSA.59.001650

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James C. Wyant and M. Parker Givens, "Effects of Photographic Gamma on Hologram Reconstructions*†," J. Opt. Soc. Am. 59, 1650-1658 (1969)

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History
- Original Manuscript: December 26, 1968
- Published: December 1, 1969

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Abstract

An expression derived for hologram exposures made along the straight-line portion of an H–D curve of a photographic plate gives the first-order transmittance of a hologram made of several object points exposed simultaneously (conventional holograms). This expression is compared with a similar expression derived previously for holograms made of several object points exposed sequentially (synthetic holograms). Theory and experiments show the effect of the nonlinearity of the photographic process on the contrast of the reconstruction of conventional holograms. Synthetic and conventional holograms are studied theoretically and experimentally to determine how the total amount of light in the reconstruction image depends upon the number of object points when the total amount of light in the object is constant. It is shown that the reconstructed image formed by a conventional hologram contains more light than the image formed by a synthetic hologram of the same number of object points. Both synthetic and conventional holograms are also studied to determine the ratio of reference-beam illuminance to object-beam illuminance that maximizes the amount of light in the reconstructed image.

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Object illuminance ratio	Reconstructed-image luminance ratio			Beam-balance ratio	Average hologram density
Object illuminance ratio	Measured	Calculated using measured value of gamma	Calculated if γ = −2	Beam-balance ratio	Average hologram density
1.5	1.6	1.6	1.5	4.0	0.88
3.3	3.7	3.6	3.3	6.0	0.90
1200	1440	1440	1200	6.5	1.24
10 000	11 300	12 200	10 000	5.3	1.10
17.5	17	17.6	17.5	120	1.10
175	175	176	175	120	1.10
88	100	99	88	8.0	0.92
8.8	9.3	9.8	8.8	7.5	0.95

Hologram exposure ratio	Number of object points for hologram	Reconstructed luminance ratio
Hologram exposure ratio	Number of object points for hologram	Measured	Calculated using measured value of gamma	Calculated if γ = −2
Plate 1
2	2	3.6	3.73	4
2	6	3.9	3.98	4
2	11	4.0	3.99	4
Plate 2
3	2	7.8	8.16	9
3	6	8.7	8.97	9
3	11	8.8	8.99	9
Plate 3
3	2	7.7	7.80	9
3	6	9.0	8.94	9
3	11	9.0	8.99	9
Plate 4
3	2	8.1	8.02	9
3	6	8.9	8.96	9
3	11	8.9	8.99	9
Plate 5
2	2	3.6	3.60	4
2	6	3.9	3.97	4
2	11	3.9	3.99	4

Object illuminance ratio	Number of object points for hologram	Reconstructed luminance ratio
Object illuminance ratio	Number of object points for hologram	Measured	Calculated using measured value of gamma	Calculated if γ = −2
Plate 1
9.5	2	11.2	10.9	9.5
9.5	6	10.5	9.9	9.5
9.5	11	10.3	9.7	9.5
Plate 2
74	2	86	86.5	74
74	6	77	76.9	74
74	11	74	75.4	74
Plate 3
13.2	2	14.4	14.8	13.2
13.2	6	13.8	13.6	13.2
13.2	11	13.2	13.4	13.2
Plate 4
97	2	112	108.8	97
97	6	97	99.7	97
97	11	93	98.3	97
Plate 5
10	2	12.0	12.3	10
10	6	10.4	10.6	10
10	11	10.0	10.3	10
Plate 6
49	2	56	60.7	49
49	6	51	52.0	49
49	11	50	50.5	49

N, number of exposures	Total-light ratio			Average density of hologram
N, number of exposures	Measured	Calculated using measured value of gamma	Calculated if γ = −2	Average density of hologram
2	1/1.94	1/2	1/2	0.26
5	1/5.1	1/5	1/5	0.26
8	1/8.7	1/8.7	1/8	0.7
4	1/4.95	1/5.95	1/4	0.7
8	1/8.33	1/8.1	1/8	0.5

N, number of object points	Total-light ratio			Beam-balance ratio	Average density of hologram
N, number of object points	Measured	Calculated using measured value of gamma	Calculated if γ = −2	Beam-balance ratio	Average density of hologram
2	0.91	0.88	1	4.5	0.8
2	1.0	0.99	1	31.0	0.8
3	0.92	0.90	1	6.0	0.7
5	0.86	0.89	1	8.0	0.9
5	0.75	0.76	1	4.5	0.9
4	0.80	0.77	1	4.0	0.75
8	0.71	0.71	1	4.0	0.75
12	0.70	0.69	1	4.0	0.75

Humber of object points	Beam-balance ratio	Average measured relative luminance of hologram reconstruction	% standard deviation of average measured relative luminance	Calculated relative luminance for given values of E₀ and γ			% deviation from measurement
Humber of object points	Beam-balance ratio		% standard deviation of average measured relative luminance	Luminance	E₀	γ	% deviation from measurement
1	2.9	0.921	2.1%	0.9335	10	4.80	1.36%
				0.9193	10	4.90	−0.185
				0.9553	10	4.65	3.58
				0.9347	11	5.30	1.60
				0.9090	9	4.45	−1.30
4	1.45	1.2028	1.38	1.2031	11.5	3.25	0.26
				1.2010	11.5	3.30	0.083
				1.2072	11.5	3.15	0.60
				1.2048	12.5	3.55	0.40
				1.1944	10.5	3.10	−0.30
8	2.0	1.1096	1.77	1.1161	11	5.35	−0.55
				1.1074	11	5.45	−0.30
				1.1248	11	5.25	1.33
				1.0704	10	5.0	−3.60
				1.0859	9	5.7	−2.20
12	1.45	1.1503	0.94	1.1556	10	3.75	0.46
				1.1444	10	4.00	−0.55
				1.1647	10	3.55	1.25
				1.1636	11	3.95	1.16
				1.1452	9	3.60	−0.434

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