Light Absorption in Heterogeneous Systems with Application to Photographic Dye Images*

R. J. Gledhill; D. B. Julian

doi:10.1364/JOSA.53.000239

Journal of the Optical Society of America
Vol. 53,
Issue 2,
pp. 239-246
(1963)
•https://doi.org/10.1364/JOSA.53.000239

Light Absorption in Heterogeneous Systems with Application to Photographic Dye Images

R. J. Gledhill and D. B. Julian

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R. J. Gledhill and D. B. Julian, "Light Absorption in Heterogeneous Systems with Application to Photographic Dye Images*," J. Opt. Soc. Am. 53, 239-246 (1963)

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Abstract

A quantitative theory for the absorption of light by colloidal suspensions of spherical particles has been developed and extended to polydispersed systems. It has been applied to photographic dye images. The density, covering power, and efficiency of light absorption in a particulate image are defined in terms of the particle-size distribution, the molar absorbance of the dye, and the composition of the image. Well-substantiated by the experimental evidence, the theory quantitatively explains the loss in absorption efficiency and the broadening of spectral absorption bands in a particulate dye image.

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			Dye		λ(mμ)	∊		c
			Cyan		647	3.04×10⁴		0.780
			Magenta		548	4.90×10⁴		0.200
Dye	Size distribution		C/∊				Av sizes
Dye	Size distribution		V	Obs	Calcd	Δ%	d_e	d_h	d_g
Cyan		1	0.270	0.897	0.895	0.2	0.081	0.052	0.077
			0.156	0.880	0.865	1.7	0.080	0.053	0.077
		2	0.270	0.870	0.873	0.3	0.105	0.070	0.101
			0.156	0.848	0.838	1.2	0.103	0.074	0.101
		3	0.270	0.684	0.695	1.6	0.289	0.164	0.284
			0.156	0.642	0.638	0.6	0.288	0.174	0.284
Magenta		4	0.345	0.533	0.517	3.0	1.34	1.36	1.51
Magenta		5	0.354	0.324	0.323	0.3	2.70	2.62	3.09

		∊=4.90×10⁴			c=0.200	V=0.345
i	f_i	d_i(μ)	β_i	T_pi	a_i	d_i/d_i₊₁	a_iT_pi	T_i
1	0.1	2.01	1.97	0.091	0.0518	1.058	0.0047	0.4451
2	0.1	1.90	1.86	0.101	0.0546	1.068	0.0055	0.4843
3	0.2	1.78	1.75	0.113	0.1155	1.092	0.0130	0.5288
4	0.2	1.63	1.60	0.130	0.1305	1.140	0.0170	0.6102
5	0.2	1.43	1.40	0.160	0.1501	1.212	0.0240	0.7149
6	0.1	1.18	1.16	0.210	0.0883	1.527	0.0185	0.8429
7	0.1	0.773	0.758	0.342	0.0969	—	0.0331	0.9362
(C/∊)=−(1/β₁V) logT₁=0.517

Size distribution	V	t(μ)	C×10⁻⁴ (calcd)	Density		Δ%
Size distribution	V	t(μ)	C×10⁻⁴ (calcd)	Calcd	Obs	Δ%
1	0.270	2.39	2.720	1.37	1.39	1.4
	0.156	2.19	2.630	0.70	0.67	4.5
	0.156	12.53	2.630	4.00	3.86	3.6
2	0.270	5.81	2.653	3.25	3.40	4.4
3	0.270	7.34	2.113	3.27	3.35	2.4
4	0.345	8.90	2.533	1.56	1.60	2.5
5	0.354	8.75	1.585	0.98	0.98	0.0

			Dye		λ(mμ)	∊		c
			Cyan		647	3.04×10⁴		0.780
			Magenta		548	4.90×10⁴		0.200
Dye	Size distribution		C/∊				Av sizes
Dye	Size distribution		V	Obs	Calcd	Δ%	d_e	d_h	d_g
Cyan		1	0.270	0.897	0.895	0.2	0.081	0.052	0.077
			0.156	0.880	0.865	1.7	0.080	0.053	0.077
		2	0.270	0.870	0.873	0.3	0.105	0.070	0.101
			0.156	0.848	0.838	1.2	0.103	0.074	0.101
		3	0.270	0.684	0.695	1.6	0.289	0.164	0.284
			0.156	0.642	0.638	0.6	0.288	0.174	0.284
Magenta		4	0.345	0.533	0.517	3.0	1.34	1.36	1.51
Magenta		5	0.354	0.324	0.323	0.3	2.70	2.62	3.09

		∊=4.90×10⁴			c=0.200	V=0.345
i	f_i	d_i(μ)	β_i	T_pi	a_i	d_i/d_i₊₁	a_iT_pi	T_i
1	0.1	2.01	1.97	0.091	0.0518	1.058	0.0047	0.4451
2	0.1	1.90	1.86	0.101	0.0546	1.068	0.0055	0.4843
3	0.2	1.78	1.75	0.113	0.1155	1.092	0.0130	0.5288
4	0.2	1.63	1.60	0.130	0.1305	1.140	0.0170	0.6102
5	0.2	1.43	1.40	0.160	0.1501	1.212	0.0240	0.7149
6	0.1	1.18	1.16	0.210	0.0883	1.527	0.0185	0.8429
7	0.1	0.773	0.758	0.342	0.0969	—	0.0331	0.9362
(C/∊)=−(1/β₁V) logT₁=0.517

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Journal of the Optical Society of America