Visual-Perception Models

G. H. Kornfeld; W. R. Lawson

doi:10.1364/JOSA.61.000811

Visual-Perception Models

G. H. Kornfeld and W. R. Lawson

Journal of the Optical Society of America
Vol. 61,
Issue 6,
pp. 811-820
(1971)
•https://doi.org/10.1364/JOSA.61.000811

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G. H. Kornfeld and W. R. Lawson, "Visual-Perception Models," J. Opt. Soc. Am. 61, 811-820 (1971)

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- Original Manuscript: May 21, 1970
- Published: June 1, 1971

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Abstract

Several theoretical models for the prediction of liminal contrast are studied. One model that employs the known excitation and inhibition spread functions of the eye accurately predicts, at 10 mL, thresholds for circular targets, sine waves, and rectangles, including the line as a special case. Semiempirically, this model is extended to include thresholds at low light levels.

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Equations (33)

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Model	Expression for

	Large area	Small area	Line
Point radiance	1	$a / {(π Γ)}^{2}$	a/(πΓ)
Area radiance	$a^{\frac{1}{2}}$	$a / (2 π Γ)$	$(a \sqrt b) / {(2 π Γ)}^{\frac{1}{2}}$
Excitation–inhibition	$[{(\frac{1}{2} c)}^{\frac{1}{2}} {(σ^{2} - Γ^{2})}^{\frac{1}{2}}] G_{B}$	$[a / (2 π Γ)] G_{S}$	$[(a \sqrt b) / {(2 π Γ)}^{\frac{1}{2}}] G_{L}$

Background luminance(mL)	Retinal illuminance(td)	N [photons per (min)² reaching rod or cone]^a	Γ (′) (min of arc)	σ (min of arc)	t_g (s)	Frequency of Maximal Sensitivity (cycles/min)			r_c (′) (min of arc)	D for forced choice	G_B	G_L	G_S

						Theor.	Schade	V−M^b
10³	1.2 ×10⁴	1.95×10⁶	0.89	8	0.3	⋯	⋯	⋯	30	2.7	0.37	0.95	0.91
10²	2.05×10³	3.05×10⁵	1.05	8	0.3	⋯	0.082	⋯	30	2.7	0.32	0.95	0.91
10	3.5 ×10³	4.4 ×10⁴	1.2	8	0.3	0.048	0.064	0.050	30	2.7	0.30	0.95	0.91
1	51	8.12×10³	1.6	11	0.32	0.035	0.050	0.036	51	2.7	0.26	0.96	0.92
10⁻¹	7	1.22×10³	2.0	16	0.35	0.025	0.033	0.023	72	2.7	0.23	0.97	0.94
10⁻²	0.87	177	2.5	23	0.4	0.018	0.024	0.008	96	3.5	0.20	0.97	0.95
10⁻³	0.11	24	3.9	41	0.5	0.010	0.017	⋯	120	7.1	0.16	0.98	0.97
10⁻⁴	1.21×10⁻²	3.1	5.5	66	0.8	0.006	⋯	⋯	120	7.1	0.13	.099	0.98
10⁻⁵	1.3 ×10⁻³	0.32	6.5	110	1.6	0.005	⋯	⋯	120	7.1	0.11	0.99	0.98

Model	Expression for

	Large area	Small area	Line
Point radiance	1	$a / {(π Γ)}^{2}$	a/(πΓ)
Area radiance	$a^{\frac{1}{2}}$	$a / (2 π Γ)$	$(a \sqrt b) / {(2 π Γ)}^{\frac{1}{2}}$
Excitation–inhibition	$[{(\frac{1}{2} c)}^{\frac{1}{2}} {(σ^{2} - Γ^{2})}^{\frac{1}{2}}] G_{B}$	$[a / (2 π Γ)] G_{S}$	$[(a \sqrt b) / {(2 π Γ)}^{\frac{1}{2}}] G_{L}$

Background luminance(mL)	Retinal illuminance(td)	N [photons per (min)² reaching rod or cone]^a	Γ (′) (min of arc)	σ (min of arc)	t_g (s)	Frequency of Maximal Sensitivity (cycles/min)			r_c (′) (min of arc)	D for forced choice	G_B	G_L	G_S

						Theor.	Schade	V−M^b
10³	1.2 ×10⁴	1.95×10⁶	0.89	8	0.3	⋯	⋯	⋯	30	2.7	0.37	0.95	0.91
10²	2.05×10³	3.05×10⁵	1.05	8	0.3	⋯	0.082	⋯	30	2.7	0.32	0.95	0.91
10	3.5 ×10³	4.4 ×10⁴	1.2	8	0.3	0.048	0.064	0.050	30	2.7	0.30	0.95	0.91
1	51	8.12×10³	1.6	11	0.32	0.035	0.050	0.036	51	2.7	0.26	0.96	0.92
10⁻¹	7	1.22×10³	2.0	16	0.35	0.025	0.033	0.023	72	2.7	0.23	0.97	0.94
10⁻²	0.87	177	2.5	23	0.4	0.018	0.024	0.008	96	3.5	0.20	0.97	0.95
10⁻³	0.11	24	3.9	41	0.5	0.010	0.017	⋯	120	7.1	0.16	0.98	0.97
10⁻⁴	1.21×10⁻²	3.1	5.5	66	0.8	0.006	⋯	⋯	120	7.1	0.13	.099	0.98
10⁻⁵	1.3 ×10⁻³	0.32	6.5	110	1.6	0.005	⋯	⋯	120	7.1	0.11	0.99	0.98

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