Theory of the Concave Grating. II. Application of the Theory to the Off-Plane Eagle Mounting in a Vacuum Spectrograph*†

T. Namioka

doi:10.1364/JOSA.49.000460

Journal of the Optical Society of America
Vol. 49,
Issue 5,
pp. 460-465
(1959)
•https://doi.org/10.1364/JOSA.49.000460

Theory of the Concave Grating. II. Application of the Theory to the Off-Plane Eagle Mounting in a Vacuum Spectrograph

T. Namioka

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
T. Namioka, "Theory of the Concave Grating. II. Application of the Theory to the Off-Plane Eagle Mounting in a Vacuum Spectrograph*†," J. Opt. Soc. Am. 49, 460-465 (1959)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A recent treatment of concave grating theory is applied to an off-plane Eagle vacuum spectrograph, especially to that employing a grating of 21-foot radius and 30 000 lines/inch. Three tables and two graphs summarize the numerical calculations on the following factors: (1) change in wavelength from that calculated by the ordinary grating equation; (2) angle of slit rotation with respect to the grating rulings as a function of the angle of incidence; (3) optimum grating size as a function of the angle of incidence and spectral order; (4) resolving power in the 1250 to 2000-A region as affected by emulsion grain size, length of slit illumination, spectral order, and slit width. The calculations are found to be in reasonable agreement with experiment.

Full Article | PDF Article

More Like This

Design of High-Resolution Monochromator for the Vacuum Ultraviolet. An Application of Off-Plane Eagle Mounting*†

T. Namioka
J. Opt. Soc. Am. 49(10) 961-965 (1959)

Theory of the Ellipsoidal Concave Grating. II. Application of the Theory to the Specific Grating Mountings*,†

Takeshi Namioka
J. Opt. Soc. Am. 51(1) 13-16 (1961)

Theory of the Concave Grating. III. Seya-Namioka Monochromator*†‡

T. Namioka
J. Opt. Soc. Am. 49(10) 951-961 (1959)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (2)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (3)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (17)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

α₀	λ₀ (A)	Δλ = λ₀−λ (A)
α₀	λ₀ (A)	z₀/R = 0.014	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
1°	295.53	0.03	0.06	0.13	0.24	0.37	0.53	0.72	0.94	1.19
2	590.96	0.06	0.12	0.27	0.47	0.74	1.06	1.44	1.88	2.38
3	886.22	0.09	0.18	0.40	0.71	1.11	1.60	2.17	2.83	3.58
4	1181.21	0.12	0.24	0.53	0.95	1.48	2.13	2.90	3.78	4.78
5	1475.84	0.15	0.30	0.67	1.19	1.86	2.67	3.63	4.74	5.99
6	1770.02	0.18	0.36	0.81	1.43	2.23	3.21	4.37	5.70	7.20
7	2063.65	0.21	0.42	0.94	1.67	2.61	3.76	5.11	6.67	8.43
8	2356.66	0.24	0.48	1.08	1.92	3.00	4.31	5.87	7.65	9.67
9	2648.96	0.27	0.54	1.22	2.17	3.39	4.87	6.63	8.65	10.93
10	2940.44	0.30	0.61	1.36	2.42	3.78	5.44	7.40	9.65	12.20
11	3231.03	0.33	0.67	1.51	2.68	4.18	6.02	8.18	10.68	13.50
12	3520.64	0.36	0.74	1.66	2.94	4.59	6.61	8.98	11.72	14.81
13	3809.17	0.39	0.80	1.80	3.21	5.01	7.20	9.79	12.78	16.15
14	4096.54	0.43	0.87	1.96	3.48	5.43	7.81	10.62	13.85	17.51
15	4382.67	0.46	0.94	2.11	3.75	5.86	8.43	11.46	14.96	18.90
16	4667.46	0.50	1.01	2.27	4.04	6.30	9.07	12.33	16.08	20.32
17	4950.83	0.53	1.08	2.43	4.33	6.75	9.72	13.21	17.23	21.78
18	5232.69	0.57	1.16	2.60	4.62	7.22	10.38	14.12	18.42	23.27
19	5512.95	0.60	1.23	2.77	4.93	7.69	11.07	15.05	19.63	24.81
20	5791.54	0.64	1.31	2.95	5.24	8.18	11.77	16.00	20.88	26.38
21	6068.36	0.68	1.39	3.13	5.56	8.68	12.49	16.99	22.16	28.00
22	6343.34	0.72	1.48	3.32	5.90	9.20	13.24	18.00	23.48	29.68
23	6616.38	0.77	1.56	3.51	6.24	9.74	14.01	19.05	24.85	31.40
24	6887.41	0.81	1.65	3.71	6.59	10.29	14.81	20.13	26.26	33.18
25	7156.34	0.85	1.74	3.92	6.96	10.87	15.63	21.25	27.72	35.03
26	7423.08	0.90	1.84	4.13	7.34	11.46	16.49	22.41	29.23	36.94
27	7687.57	0.95	1.94	4.35	7.74	12.08	17.37	23.62	30.80	38.92
28	7949.72	1.00	2.04	4.59	8.15	12.72	18.29	24.87	32.43	40.98
29	8209.44	1.05	2.15	4.83	8.57	13.38	19.25	26.17	34.13	43.12
30	8466.67	1.10	2.26	5.08	9.02	14.08	20.25	27.52	35.90	45.35
31	8721.31	1.16	2.37	5.34	9.48	14.80	21.29	28.94	37.74	47.68
32	8973.30	1.22	2.49	5.61	9.97	15.56	22.38	30.41	39.66	50.11
33	9222.55	1.29	2.62	5.90	10.47	16.35	23.51	31.96	41.67	52.65
34	9469.00	1.35	2.75	6.19	11.00	17.17	24.70	33.57	43.78	55.31
35	9712.56	1.42	2.89	6.51	11.56	18.04	25.95	35.27	45.99	58.10
36	9953.16	1.49	3.04	6.84	12.14	18.96	27.26	37.05	48.31	61.02
37	10 190.73	1.57	3.19	7.18	12.76	19.91	28.64	38.92	50.75	64.10
38	10 425.20	1.65	3.36	7.55	13.41	20.92	30.09	40.89	53.31	67.34
39	10 656.49	1.73	3.53	7.93	14.09	21.99	31.62	42.97	56.02	70.75
40	10 884.54	1.82	3.71	8.34	14.81	23.11	33.23	45.16	58.87	74.35
41	11 109.27	1.91	3.90	8.77	15.57	24.30	34.94	47.48	61.89	78.16
42	11 330.61	2.01	4.10	9.22	16.38	25.56	36.75	49.93	65.09	82.19
43	11 548.51	2.12	4.32	9.70	17.23	26.89	38.67	52.54	68.48	86.46
44	11 762.88	2.23	4.54	10.22	18.14	28.31	40.71	55.30	72.08	91.00
45	11 973.68	2.35	4.79	10.76	19.11	29.82	42.87	58.24	75.90	95.82

α₀	W_opt (cm)
α₀	m = 1	m = 2	m = 3	m = 4	m = 5	m = 6	m = 7	m = 8	m = 9	m = 10
5°	45.66	35.42	30.21	26.86	24.45	22.61	21.14	19.92	18.90	18.02
6	42.75	32.96	28.01	24.84	22.57	20.84	19.46	18.33	17.37	16.55
7	40.37	30.96	26.23	23.21	21.06	19.42	18.12	17.05	16.15	15.38
8	38.36	29.28	24.74	21.85	19.80	18.24	17.00	15.99	15.14	14.41
9	36.63	27.83	23.46	20.69	18.72	17.24	16.06	15.09	14.28	13.59
10	35.10	26.57	22.34	19.68	17.79	16.37	15.24	14.32	13.55	12.89
11	33.74	25.45	21.36	18.79	16.97	15.60	14.52	13.64	12.90	12.27
12	32.51	24.44	20.47	17.99	16.24	14.92	13.88	13.03	12.32	11.72
13	31.38	23.52	19.67	17.27	15.58	14.31	13.30	12.49	11.80	11.22
14	30.35	22.68	18.94	16.61	14.98	13.75	12.78	11.99	11.33	10.77
15	29.39	21.90	18.26	16.00	14.42	13.23	12.30	11.54	10.90	10.36
16	28.49	21.17	17.64	15.44	13.91	12.76	11.85	11.12	10.50	9.98
17	27.65	20.50	17.05	14.92	13.43	12.32	11.44	10.73	10.13	9.63
18	26.86	19.86	16.50	14.43	12.98	11.90	11.05	10.36	9.79	9.30
19	26.10	19.25	15.99	13.97	12.56	11.51	10.69	10.02	9.46	8.99
20	25.38	18.68	15.49	13.53	12.17	11.15	10.35	9.70	9.16	8.70
21	24.69	18.14	15.03	13.12	11.79	10.80	10.02	9.39	8.87	8.42
22	24.03	17.61	14.58	12.72	11.43	10.47	9.71	9.10	8.59	8.16
23	23.39	17.11	14.15	12.34	11.09	10.15	9.42	8.82	8.33	7.91
24	22.77	16.63	13.74	11.98	10.76	9.85	9.13	8.56	8.08	7.67
25	22.17	16.16	13.35	11.63	10.44	9.55	8.86	8.30	7.83	7.44
26	21.59	15.71	12.97	11.29	10.14	9.27	8.60	8.06	7.60	7.22
27	21.03	15.28	12.60	10.97	9.84	9.00	8.35	7.82	7.38	7.00
28	20.48	14.85	12.24	10.65	9.56	8.74	8.10	7.59	7.16	6.80
29	19.94	14.44	11.89	10.35	9.28	8.49	7.87	7.37	6.95	6.60
30	19.41	14.04	11.55	10.05	9.01	8.24	7.64	7.15	6.75	6.40
35	⋯	12.16	9.98	8.67	7.77	7.10	6.58	6.16	5.81	5.51
40	⋯	10.45	8.56	7.43	6.65	6.08	5.63	5.27	4.97	4.71
45	⋯	8.87	7.26	6.29	5.63	5.15	4.77	4.46	4.20	3.99

α₀	W_opt (cm)
α₀	m = 1	m = 2	m = 3	m = 4	m = 5	m = 6	m = 7	m = 8	m = 9	m = 10
5°	71.74	56.94	49.31	44.32	40.69	37.89	35.62	33.73	32.13	30.74
6	67.56	53.36	46.05	41.29	37.83	35.16	33.01	31.23	29.71	28.40
7	64.14	50.43	43.39	38.81	35.50	32.95	30.90	29.20	27.76	26.52
8	61.25	47.95	41.14	36.73	33.55	31.10	29.13	27.51	26.13	24.95
9	58.74	45.81	39.21	34.94	31.87	29.51	27.62	26.06	24.74	23.61
10	56.54	43.93	37.51	33.38	30.40	28.13	26.30	24.80	23.53	22.44
11	54.56	42.25	36.00	31.98	29.10	26.90	25.14	23.69	22.47	21.42
12	52.78	40.73	34.64	30.73	27.93	25.80	24.09	22.69	21.51	20.50
13	51.14	39.35	33.39	29.59	26.87	24.80	23.15	21.79	20.65	19.67
14	49.63	38.07	32.25	28.54	25.90	23.88	22.28	20.97	19.86	18.92
15	48.23	36.88	31.19	27.57	25.00	23.04	21.48	20.21	19.14	18.22
16	46.92	35.77	30.21	26.67	24.16	22.26	20.74	19.50	18.47	17.58
17	45.68	34.73	29.28	25.83	23.38	21.52	20.05	18.85	17.84	16.98
18	44.50	33.75	28.41	25.03	22.64	20.84	19.40	18.23	17.25	16.42
19	43.38	32.81	27.58	24.28	21.95	20.19	18.79	17.65	16.70	15.89
20	42.31	31.92	26.79	23.56	21.29	19.57	18.21	17.11	16.18	15.39
21	41.29	31.06	26.04	22.88	20.66	18.99	17.66	16.58	15.68	14.91
22	40.30	30.24	25.31	22.23	20.06	18.43	17.14	16.09	15.21	14.46
23	39.34	29.45	24.62	21.60	19.48.	17.89	16.63	15.61	14.76	14.03
24	38.41	28.68	23.95	21.00	18.93	17.38	16.15	15.15	14.32	13.61
25	37.50	27.94	23.30	20.42	18.40	16.88	15.69	14.71	13.90	13.21
26	36.62	27.21	22.67	19.85	17.88	16.40	15.24	14.29	13.50	12.83
27	35.76	26.51	22.06	19.30	17.38	15.93	14.80	13.88	13.11	12.46
28	34.91	25.82	21.47	18.77	16.89	15.48	14.38	13.48	12.73	12.10
29	34.08	25.15	20.89	18.25	16.42	15.05	13.97	13.10	12.37	11.75
30	33.26	24.49	20.32	17.75	15.96	14.62	13.57	12.72	12.01	11.41
35	⋯	21.38	17.66	15.38	13.81	12.64	11.72	10.98	10.36	9.84
40	⋯	18.49	15.22	13.23	11.86	10.85	10.05	9.41	8.88	8.43
45	⋯	15.78	12.95	11.24	10.07	9.20	8.52	7.98	7.53	7.14

α₀	λ₀ (A)	Δλ = λ₀−λ (A)
α₀	λ₀ (A)	z₀/R = 0.014	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
1°	295.53	0.03	0.06	0.13	0.24	0.37	0.53	0.72	0.94	1.19
2	590.96	0.06	0.12	0.27	0.47	0.74	1.06	1.44	1.88	2.38
3	886.22	0.09	0.18	0.40	0.71	1.11	1.60	2.17	2.83	3.58
4	1181.21	0.12	0.24	0.53	0.95	1.48	2.13	2.90	3.78	4.78
5	1475.84	0.15	0.30	0.67	1.19	1.86	2.67	3.63	4.74	5.99
6	1770.02	0.18	0.36	0.81	1.43	2.23	3.21	4.37	5.70	7.20
7	2063.65	0.21	0.42	0.94	1.67	2.61	3.76	5.11	6.67	8.43
8	2356.66	0.24	0.48	1.08	1.92	3.00	4.31	5.87	7.65	9.67
9	2648.96	0.27	0.54	1.22	2.17	3.39	4.87	6.63	8.65	10.93
10	2940.44	0.30	0.61	1.36	2.42	3.78	5.44	7.40	9.65	12.20
11	3231.03	0.33	0.67	1.51	2.68	4.18	6.02	8.18	10.68	13.50
12	3520.64	0.36	0.74	1.66	2.94	4.59	6.61	8.98	11.72	14.81
13	3809.17	0.39	0.80	1.80	3.21	5.01	7.20	9.79	12.78	16.15
14	4096.54	0.43	0.87	1.96	3.48	5.43	7.81	10.62	13.85	17.51
15	4382.67	0.46	0.94	2.11	3.75	5.86	8.43	11.46	14.96	18.90
16	4667.46	0.50	1.01	2.27	4.04	6.30	9.07	12.33	16.08	20.32
17	4950.83	0.53	1.08	2.43	4.33	6.75	9.72	13.21	17.23	21.78
18	5232.69	0.57	1.16	2.60	4.62	7.22	10.38	14.12	18.42	23.27
19	5512.95	0.60	1.23	2.77	4.93	7.69	11.07	15.05	19.63	24.81
20	5791.54	0.64	1.31	2.95	5.24	8.18	11.77	16.00	20.88	26.38
21	6068.36	0.68	1.39	3.13	5.56	8.68	12.49	16.99	22.16	28.00
22	6343.34	0.72	1.48	3.32	5.90	9.20	13.24	18.00	23.48	29.68
23	6616.38	0.77	1.56	3.51	6.24	9.74	14.01	19.05	24.85	31.40
24	6887.41	0.81	1.65	3.71	6.59	10.29	14.81	20.13	26.26	33.18
25	7156.34	0.85	1.74	3.92	6.96	10.87	15.63	21.25	27.72	35.03
26	7423.08	0.90	1.84	4.13	7.34	11.46	16.49	22.41	29.23	36.94
27	7687.57	0.95	1.94	4.35	7.74	12.08	17.37	23.62	30.80	38.92
28	7949.72	1.00	2.04	4.59	8.15	12.72	18.29	24.87	32.43	40.98
29	8209.44	1.05	2.15	4.83	8.57	13.38	19.25	26.17	34.13	43.12
30	8466.67	1.10	2.26	5.08	9.02	14.08	20.25	27.52	35.90	45.35
31	8721.31	1.16	2.37	5.34	9.48	14.80	21.29	28.94	37.74	47.68
32	8973.30	1.22	2.49	5.61	9.97	15.56	22.38	30.41	39.66	50.11
33	9222.55	1.29	2.62	5.90	10.47	16.35	23.51	31.96	41.67	52.65
34	9469.00	1.35	2.75	6.19	11.00	17.17	24.70	33.57	43.78	55.31
35	9712.56	1.42	2.89	6.51	11.56	18.04	25.95	35.27	45.99	58.10
36	9953.16	1.49	3.04	6.84	12.14	18.96	27.26	37.05	48.31	61.02
37	10 190.73	1.57	3.19	7.18	12.76	19.91	28.64	38.92	50.75	64.10
38	10 425.20	1.65	3.36	7.55	13.41	20.92	30.09	40.89	53.31	67.34
39	10 656.49	1.73	3.53	7.93	14.09	21.99	31.62	42.97	56.02	70.75
40	10 884.54	1.82	3.71	8.34	14.81	23.11	33.23	45.16	58.87	74.35
41	11 109.27	1.91	3.90	8.77	15.57	24.30	34.94	47.48	61.89	78.16
42	11 330.61	2.01	4.10	9.22	16.38	25.56	36.75	49.93	65.09	82.19
43	11 548.51	2.12	4.32	9.70	17.23	26.89	38.67	52.54	68.48	86.46
44	11 762.88	2.23	4.54	10.22	18.14	28.31	40.71	55.30	72.08	91.00
45	11 973.68	2.35	4.79	10.76	19.11	29.82	42.87	58.24	75.90	95.82

α₀	W_opt (cm)
α₀	m = 1	m = 2	m = 3	m = 4	m = 5	m = 6	m = 7	m = 8	m = 9	m = 10
5°	45.66	35.42	30.21	26.86	24.45	22.61	21.14	19.92	18.90	18.02
6	42.75	32.96	28.01	24.84	22.57	20.84	19.46	18.33	17.37	16.55
7	40.37	30.96	26.23	23.21	21.06	19.42	18.12	17.05	16.15	15.38
8	38.36	29.28	24.74	21.85	19.80	18.24	17.00	15.99	15.14	14.41
9	36.63	27.83	23.46	20.69	18.72	17.24	16.06	15.09	14.28	13.59
10	35.10	26.57	22.34	19.68	17.79	16.37	15.24	14.32	13.55	12.89
11	33.74	25.45	21.36	18.79	16.97	15.60	14.52	13.64	12.90	12.27
12	32.51	24.44	20.47	17.99	16.24	14.92	13.88	13.03	12.32	11.72
13	31.38	23.52	19.67	17.27	15.58	14.31	13.30	12.49	11.80	11.22
14	30.35	22.68	18.94	16.61	14.98	13.75	12.78	11.99	11.33	10.77
15	29.39	21.90	18.26	16.00	14.42	13.23	12.30	11.54	10.90	10.36
16	28.49	21.17	17.64	15.44	13.91	12.76	11.85	11.12	10.50	9.98
17	27.65	20.50	17.05	14.92	13.43	12.32	11.44	10.73	10.13	9.63
18	26.86	19.86	16.50	14.43	12.98	11.90	11.05	10.36	9.79	9.30
19	26.10	19.25	15.99	13.97	12.56	11.51	10.69	10.02	9.46	8.99
20	25.38	18.68	15.49	13.53	12.17	11.15	10.35	9.70	9.16	8.70
21	24.69	18.14	15.03	13.12	11.79	10.80	10.02	9.39	8.87	8.42
22	24.03	17.61	14.58	12.72	11.43	10.47	9.71	9.10	8.59	8.16
23	23.39	17.11	14.15	12.34	11.09	10.15	9.42	8.82	8.33	7.91
24	22.77	16.63	13.74	11.98	10.76	9.85	9.13	8.56	8.08	7.67
25	22.17	16.16	13.35	11.63	10.44	9.55	8.86	8.30	7.83	7.44
26	21.59	15.71	12.97	11.29	10.14	9.27	8.60	8.06	7.60	7.22
27	21.03	15.28	12.60	10.97	9.84	9.00	8.35	7.82	7.38	7.00
28	20.48	14.85	12.24	10.65	9.56	8.74	8.10	7.59	7.16	6.80
29	19.94	14.44	11.89	10.35	9.28	8.49	7.87	7.37	6.95	6.60
30	19.41	14.04	11.55	10.05	9.01	8.24	7.64	7.15	6.75	6.40
35	⋯	12.16	9.98	8.67	7.77	7.10	6.58	6.16	5.81	5.51
40	⋯	10.45	8.56	7.43	6.65	6.08	5.63	5.27	4.97	4.71
45	⋯	8.87	7.26	6.29	5.63	5.15	4.77	4.46	4.20	3.99

Abstract

Cited By

Figures (2)

Tables (3)

Equations (17)

Journal of the Optical Society of America