Table I
The deviation from the ordinary grating equation. λ0 and λ are the wavelengths calculated from the ordinary grating equation and the modified grating equation, respectively. α0 is the angle of incidence for the ray originated from the center of the slit.
α0 | λ0 (A) | Δλ = λ0−λ (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 |
Table II
The optimum grating width, Wopt, for R = 21 ft, z0 = 12.5 cm, σ = 2.54/30000 cm, and m = 1 to 10. R, z0, σ, and m are the radius of curvature of the grating, the distance between the center of the grating and the Rowland plane, the grating constant, and the spectral order.
α0 | Wopt (cm) |
---|
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 |
Table III
The optimum grating width, Wopt, for R = 35 ft, z0 = 15 cm, α = 2.54/30000 cm, and m = 1 to 10. R, z0, σ, and m are the radius of curvature of the grating, the distance between the center of the grating and the Rowland plane, the grating constant, and the spectral order.
α0 | Wopt (cm) |
---|
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 |