Role of geodesics in Schrödinger’s theory of color vision

Anil K. Jain

doi:10.1364/JOSA.63.000934

Journal of the Optical Society of America
Vol. 63,
Issue 8,
pp. 934-939
(1973)
•https://doi.org/10.1364/JOSA.63.000934

Role of geodesics in Schrödinger’s theory of color vision

Anil K. Jain

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Anil K. Jain, "Role of geodesics in Schrödinger’s theory of color vision," J. Opt. Soc. Am. 63, 934-939 (1973)

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Abstract

Relation between geodesics in color space and Schrödinger’s theory of color vision is discussed. The FMC1 formula is used to test this theory by examining intersection of geodesics on the constant-brightness surface. Validity of the FMC1 formula in numerical verification of Schrödinger’s concept is indicated.

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Number of geodesic	End point	Y
1	(0.7, 0.25)	33.0
2	(0.6, 0.21)	35.0
3	(0.5, 0.15)	33.6
4	(0.33, 0.08)	32.4
5	(0.26, 0.05)	33.0
6	(0.19, 0.02)	23.5
7	400 nm	7.0
8	440 nm	15.5
9	447 nm	19.5
10	455 nm	25.0
11	473 nm	37.0
12	478 nm	39.0
13	481 nm	39.5
14	485 nm	40.0
15	490 nm	40.0
16	496 nm	40.0
17	503 nm	39.0
18	540 nm	45.3
19	563 nm	48.7
20	572 nm	49.0
21	577 nm	48.6
22	583 nm	48.1
23	590 nm	46.4
24	600 nm	43.0

	x	y	Y
1	0.700	0.250	33.0
2	0.661	0.274	36.7
3	0.629	0.291	39.4
4	0.602	0.304	41.4
5	0.577	0.313	43.0
6	0.555	0.321	44.3
7	0.535	0.326	45.3
8	0.517	0.331	46.1
9	0.500	0.334	46.8
10	0.483	0.336	47.4
11	0.468	0.337	47.9
12	0.454	0.338	48.3
13	0.440	0.338	48.7
14	0.428	0.338	49.0
15	0.415	0.337	49.2
16	0.404	0.337	49.4
17	0.392	0.335	49.6
18	0.382	0.334	49.7
19	0.371	0.332	49.8
20	0.362	0.330	49.9
21	0.352	0.330	49.9
22	0.343	0.327	50.0
23	0.334	0.324	50.0
24	0.326	0.321	50.0
25	0.317	0.319	50.0
26	0.310	0.316	50.0

	Cross-spectrum geodesic				Intersecting geodesic				d = \|x₁ − x₂\| + \|y₁ − y₂\|	∊ = \|Y₁ − Y₂\|
	Number	x₁	y₁	Y₁	Number	x₂	y₂	Y₂	d = \|x₁ − x₂\| + \|y₁ − y₂\|	∊ = \|Y₁ − Y₂\|
1	40	0.335	0.205	48.6	4	0.336	0.204	47.3	0.002	1.3
2	40	0.308	0.207	49.6	5	0.310	0.205	49.1	0.003	0.5
3	40	0.281	0.207	50.3	6	0.282	0.209	49.6	0.004	0.7
4	40	0.275	0.206	50.4	7	0.275	0.207	48.1	0.001	2.3
5	40	0.260	0.205	50.6	8	0.260	0.206	49.3	0.001	1.3
6	40	0.252	0.204	50.7	9	0.251	0.206	49.2	0.003	1.4
7	40	0.236	0.201	50.7	10	0.234	0.200	49.2	0.004	1.5
8	40	0.176	0.182	49.0	11	0.175	0.183	47.8	0.001	1.2
9	40	0.130	0.161	44.8	12	0.130	0.162	44.6	0.001	0.2
10	41	0.335	0.223	41.4	4	0.334	0.221	48.1	0.002	6.7
11	41	0.290	0.241	42.8	6	0.290	0.236	49.9	0.005	7.0
12	41	0.281	0.244	43.1	8	0.281	0.251	49.8	0.007	6.7
13	41	0.264	0.250	43.5	10	0.263	0.247	49.8	0.005	6.3
14	41	0.221	0.257	42.8	12	0.221	0.257	49.4	0.001	6.6
15	41	0.174	0.266	41.9	14	0.174	0.266	47.4	0.001	5.6
16	42	0.309	0.376	46.3	18	0.309	0.377	49.7	0.001	3.4
17	42	0.326	0.360	46.6	19	0.325	0.360	49.9	0.001	3.3
18	42	0.338	0.349	46.7	21	0.337	0.350	50.0	0.002	3.3
19	42	0.348	0.339	46.8	24	0.349	0.337	50.0	0.003	3.2
20	42	0.358	0.329	46.8	1	0.357	0.329	49.9	0.001	3.1
21	42	0.376	0.310	46.6	2	0.376	0.310	49.5	0.001	3.0
22	43	0.425	0.492	48.9	20	0.425	0.493	49.3	0.002	0.4
23	43	0.435	0.453	48.8	21	0.435	0.454	49.2	0.002	0.4
24	43	0.444	0.420	48.6	22	0.443	0.420	49.3	0.001	0.7
25	43	0.450	0.395	48.3	23	0.450	0.394	49.1	0.001	0.7
26	43	0.456	0.373	48.0	24	0.456	0.373	48.6	0.001	0.6
27	43	0.465	0.337	47.2	1	0.465	0.337	47.9	0.000	0.7
28	43	0.479	0.279	45.1	2	0.480	0.280	45.7	0.001	0.6
29	44	0.494	0.447	48.2	22	0.494	0.449	48.7	0.002	0.5
30	44	0.496	0.407	47.7	23	0.495	0.408	47.9	0.002	0.2
31	44	0.498	0.381	47.3	24	0.497	0.379	47.7	0.003	0.4
32	44	0.500	0.339	46.3	1	0.500	0.334	46.8	0.006	0.5
33	44	0.505	0.268	43.6	2	0.506	0.268	44.1	0.001	0.5

	Cross-spectrum geodesic				Intersecting geodesic				d = \|x₁ − x₂\| + \|y₁ − y₂\|	∊ = \|Y₁ − Y₂\|
	Number	x₁	y₁	Y₁	Number	x₂	y₂	Y₂	d = \|x₁ − x₂\| + \|y₁ − y₂\|	∊ = \|Y₁ − Y₂\|
1	50	0.246	0.119	47.6	6	0.247	0.120	46.7	0.001	1.0
2	50	0.243	0.127	48.3	7	0.242	0.127	44.6	0.001	3.7
3	50	0.233	0.148	49.3	8	0.233	0.148	47.8	0.001	1.5
4	50	0.227	0.159	49.5	9	0.227	0.159	48.1	0.001	1.5
5	50	0.219	0.171	49.6	10	0.218	0.171	48.5	0.001	1.0
6	50	0.190	0.203	48.5	11	0.190	0.203	48.6	0.001	0.0
7	50	0.178	0.214	47.9	12	0.175	0.214	47.9	0.003	0.0
8	50	0.163	0.226	47.0	13	0.166	0.228	47.2	0.005	0.2
9	50	0.139	0.243	45.5	14	0.138	0.247	45.6	0.004	0.1
10	51	0.277	0.193	49.1	6	0.277	0.194	49.4	0.001	0.3
11	51	0.275	0.206	49.3	7	0.275	0.207	48.1	0.001	1.2
12	51	0.272	0.224	49.4	8	0.269	0.225	49.6	0.004	0.2
13	51	0.268	0.242	49.4	9	0.271	0.244	49.7	0.005	0.3
14	51	0.265	0.254	49.4	10	0.268	0.255	49.9	0.005	0.5
15	51	0.257	0.277	49.1	11	0.260	0.276	50.0	0.004	0.9
16	51	0.254	0.285	49.0	12	0.256	0.282	49.9	0.004	0.9
17	51	0.254	0.285	49.0	13	0.252	0.287	49.7	0.005	0.7
18	51	0.251	0.292	48.9	14	0.250	0.298	49.5	0.007	0.6
19	51	0.241	0.314	48.4	15	0.241	0.317	49.0	0.004	0.7
20	51	0.213	0.362	47.0	16	0.216	0.365	47.8	0.005	0.8
21	52	0.391	0.444	49.6	20	0.391	0.444	49.6	0.001	0.0
22	52	0.390	0.427	49.6	21	0.406	0.426	49.5	0.002	0.1
23	52	0.385	0.373	49.8	22	0.384	0.381	49.9	0.008	0.1
24	52	0.383	0.356	49.8	23	0.383	0.364	49.8	0.009	0.0
25	52	0.383	0.356	49.8	24	0.383	0.352	49.7	0.004	0.1
26	52	0.380	0.332	49.7	1	0.380	0.333	49.7	0.001	0.0
27	52	0.376	0.309	49.6	2	0.376	0.311	49.5	0.002	0.1
28	52	0.368	0.273	49.4	3	0.368	0.277	49.1	0.004	0.3
29	52	0.339	0.184	47.5	4	0.338	0.183	46.0	0.002	1.5

Number of geodesic	End point	Y
1	(0.7, 0.25)	33.0
2	(0.6, 0.21)	35.0
3	(0.5, 0.15)	33.6
4	(0.33, 0.08)	32.4
5	(0.26, 0.05)	33.0
6	(0.19, 0.02)	23.5
7	400 nm	7.0
8	440 nm	15.5
9	447 nm	19.5
10	455 nm	25.0
11	473 nm	37.0
12	478 nm	39.0
13	481 nm	39.5
14	485 nm	40.0
15	490 nm	40.0
16	496 nm	40.0
17	503 nm	39.0
18	540 nm	45.3
19	563 nm	48.7
20	572 nm	49.0
21	577 nm	48.6
22	583 nm	48.1
23	590 nm	46.4
24	600 nm	43.0

Abstract

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Figures (7)

Tables (4)

Equations (5)

Journal of the Optical Society of America