Information Capacity of Photographic Films

R. Clark Jones

doi:10.1364/JOSA.51.001159

Journal of the Optical Society of America
Vol. 51,
Issue 11,
pp. 1159-1171
(1961)
•https://doi.org/10.1364/JOSA.51.001159

Information Capacity of Photographic Films

R. Clark Jones

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R. Clark Jones, "Information Capacity of Photographic Films," J. Opt. Soc. Am. 51, 1159-1171 (1961)

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Abstract

The information capacity of four Kodak films is computed. The results lie in the range from one to six million bits per square centimeter—the Panatomic-X film having the largest information capacity, and the Royal-X film the least. The basic formula for the information capacity of a photographic film involves the Wiener spectrum of the granularity and the sine-wave response; data adequate for the calculation of these functions were published in 1958. The results obtained hold only if messages recorded on the film are coded in an optimal way. No optimal methods of coding are known, but methods that are close to optimal have been developed. It is known that when optimal coding is employed, nearly every message looks just like a grainy film. After the problem is formulated in mathematical terms, the chief mathematical problem is that of selecting the optimum set of messages; this is done with the help of the calculus of variations.

A photographic film is a peak-limited recording channel: the density is limited in both directions. The theory of information capacity is not yet adequately developed for such channels; the calculation is actually based on the existing formulas for mean-square-limited channels; at the end of the calculation an ad hoc correction is made to take account of the peak limiting.

Photographic films are nonlinear in at least two different ways: the noise (granularity) depends on the signal, and the output (density) is a nonlinear function of the input (exposure). It is shown that the first nonlinearity may be unloaded on the second, so that only the input–output nonlinearity remains.

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I	Kodak Royal-X Pan film, code 6128
II	Eastman Tri-X Panchromatic negative film, type 5233
III	Eastman Plus-X Panchromatic negative film, type 4231
IV	Kodak Panatomic-X film, code 5240

Material	Abbreviation	Time	Developer	Gamma
I	Royal-X	5 min	DK-50	0.65
II	Tri-X	6.5 min	SD-28	0.54
III	Plus-X	6.5 min	SD-28	0.79
IV	Pan-X	6 min	D-76	0.67

Film	$D$	$W G$ cm²
Royal-X	0.10	78.5×10⁻¹⁰
	0.34	201×10⁻¹⁰
	0.80	311×10⁻¹⁰
	1.18	366×10⁻¹⁰
Tri-X	0.06	33.2×10⁻¹⁰
	0.36	88.2×10⁻¹⁰
	0.74	88.2×10⁻¹⁰
	1.14	131×10⁻¹⁰
Plus-X	0.06	7.07×10⁻¹⁰
	0.30	28.3×10⁻¹⁰
	0.80	43.0×10⁻¹⁰
	1.40	34.2×10⁻¹⁰
Pan-X	0.04	8.04×10⁻¹⁰
	0.26	20.4×10⁻¹⁰
	0.66	28.3×10⁻¹⁰
	1.10	39.6×0⁻¹⁰

	W_G cm²	b cycle/cm	ΔE	ℰ_av ergs/cm² at 430mμ
Royal-X	314×10⁻¹⁰	248	0.995	0.0188
Tri-X	123×10⁻¹⁰	252	1.04	0.1148
Plus-X	38.5×10⁻¹⁰	270	1.25	0.288
Pan-X	38.5×10⁻¹⁰	470	1.05	0.384

Film	$D_{min}$	$D_{max}$	D_min	D_max	ΔE	D_av	$D_{av}$	ℰ_avergs/cm²
Royal-X	0.105	2.0	0.229	2.22	0.995	1.22	0.923	0.0188
Tri-X	0.055	2.0	0.139	2.22	1.04	1.18	0.880	0.1148
Plus-X	0.051	2.5	0.131	2.63	1.25	1.38	1.082	0.288
Pan-X	0.009	1.9	0.034	2.13	1.05	1.08	0.788	0.384

x Microns	Pan-X A(x)	x Microns	Plus-X A(x)	Tri-X A(x)	Royal-X A(x)
0.0	1.000	0	1.000	1.000	1.000
0.5	0.970	1	0.938	0.955	0.950
1.0	0.900	2	0.810	0.860	0.880
1.5	0 800	3	0.640	0.735	0.785
2.0	0.670	4	0.470	0.600	0.655
2.5	0.535	5	0.360	0.475	0.480
3.0	0.420	6	0.305	0.360	0.360
3.5	0.320	7	0.267	0.274	0.290
4.0	0.245	8	0.235	0.228	0.243
4.5	0.207	9	0.208	0.202	0.215
5	0.182	10	0.182	0.182	0.192
6	0.145	12	0.142	0.150	0.157
7	0.116	14	0.107	0.122	0.127
8	0.092	16	0.078	0.101	0.101
9	0.0825	18	0.051	0.083	0.079
10	0.0540	20	0.029	0.068	0.062

R	f
0	1.000
0.4	0.900
0.5	0.739
0.6	0.574
0.7	0.436
0.8	0.332
0.9	0.255
1	0.199

Film	(ΔE)²/(πW_Gb²)	πb² log₂e cm⁻²	Z_1,max	C₁ bits/cm²
Royal-X	163.2	0.279×10⁶	1.79	0.499×10⁶
Tri-X	440.8	0.288×10⁶	2.93	0.845×10⁶
Plus-X	1772	0.330×10⁶	5.63	1.86×10⁶
Pan-X	412.6	1.001×10⁶	2.85	2.85×10⁶

X	Y	Z₀	P	Q
1	$1 \frac{2}{3}$	0.3068	1.330	0.194
1.5	$4 \frac{1}{2}$	0.5837	1.149	0.185
2	$9 \frac{1}{3}$	0.9014	1.072	0.171
2.5	$16 \frac{2}{3}$	1.247	1.035	0.154
3	27	1.614	1.018	0.138
4	$58 \frac{2}{3}$	2.391	1.013	0.108
5	$108 \frac{1}{3}$	3.208	1.026	0.0823
6	180	4.054	1.047	0.0615
7	$277 \frac{2}{3}$	4.921	1.071	0.0453
8	$405 \frac{1}{3}$	5.803	1.097	0.0336
9	567	6.697	1.124	0 0259
10	$767 \frac{2}{3}$	7.602	1.153	0.0221
11	$1008 \frac{1}{3}$	8.515	1.179	0.0217
12	1296	9.435	1.207	0.0246
13	$1633 \frac{2}{3}$	10.361	1.234	0.0308
14	$2025 \frac{1}{3}$	11.292	1.260	0.0397

Film	R=0.4	0.5	0.6	0.7	0.8	0.9	1.0
Royal-X	2.96	3.50	4.00	4.48	4.94	5.37	5.79
Tri-X	4.28	5.03	5.73	6.40	7.04	7.65	8.24
Plus-X	7.11	8.25	9.38	10.44	11.46	12.43	13.37
Pan-X	4.18	4.91	5.60	6.25	6.88	7.48	8.05

Film	R=0.4	0.5	0.6	0.7	0.8	0.9	1.0
Royal-X	1.59	2.00	2.40	2.79	3.14	3.51	3.88
Tri-X	2.63	3.24	3.83	4.40	4.96	5.51	6.04
Plus-X	4.98	6.05	7.04	8.00	8.95	9.82	10.7
Pan-X	2.54	3.15	3.71	4.28	4.82	5.33	5.87

Film	R=0.4	0.5	0.6	0.7	0.8	0.9	1.0
Royal-X	1.50	1.70	1.78	1.77	1.71	1.64	1.55
Tri-X	2.50	2.80	2.92	2.93	2.87	2.76	2.63
Plus-X	4.76	5.33	5.57	5.63	5.57	5.40	5.20
Pan-X	2.41	2.71	2.82	2.84	2.78	2.66	2.54

Film	C₁ bits/cm²	$A$ =C₁⁻¹ microns²/bit	$r = {(A / π)}^{\frac{1}{2}}$ microns	C₁/ℰ_av bits/erg	ℰ_av/hνC₁ photons/bit	T_HF sec/cm²	$A_{TVF}$ cm²/frame
Royal-X	0.449×10⁶	200	7.98	26.5×10⁶	8180	3.01	2.98
Tri-X	0.845×10⁶	118.4	6.14	7.35×10⁶	29 400	5.1	1.76
Plus-X	1.86×10⁶	53.8	4.14	6.45×10⁶	33 600	11.2	0.80
Pan-X	2.85×10⁶	35.0	3.34	7.45×10⁶	29 200	17.2	0.52

Abstract

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Figures (5)

Tables (13)

Equations (64)

Journal of the Optical Society of America