Table I
N 3 2 1 0 −1 −2 −3 ψ 57°52′ 34°22′ 16°24′ 0 −16°24′ −34°22′ −57°52′ A 0.29358 11.0977 31.7755 12.2763 0.0000 1.4733 0.10083 B 0.10083 1.4733 0.0000 12.2763 31.7755 11.0977 0.29358 C −0.13325 3.9513 0.0005 −12.2496 0.0005 3.9513 −0.13325 %* 0.24 15.10 29.04 11.24 29.04 15.10 0.24
* As was mentioned in the test, the “%” in each order is given by 100
D i /Σ
D i . Thus, symmetrical grooves yield symmetrical spectra at normal incidence.
Table II
N 3 2 1 0 −1 −2 −3 ψ 57°52′ 34°22′ 16°24′ 0 −16°24′ −34°22′ −57°52′ A 5.827 15.515 11.450 2.683 0.000 0.622 0.656 B 0.890 0.092 2.189 9.152 34.338 7.363 2.546 C 2.254 −1.047 −1.834 −2.431 −0.001 0.666 1.236 % 9.73 15.80 12.81 10.20 37.26 9.39 4.82
Table III
N 3 2 1 0 −1 −2 −3 ψ 57°52′ 34°22′ 16°24′ 0 −16°24′ −34°22′ −57°52′ A 19.591 4.538 0.064 0.936 0.326 0.000 0.074 B 0.025 0.744 0.050 2.746 5.207 57.941 1.318 C 0.641 −1.346 0.052 −1.470 0.006 −0.005 −0.208 % 22.20 4.31 0.18 2.42 6.07 63.50 1.30
Table IV
N 3 2 1 0 −1 −2 −3 ψ 57°52′ 34°22′ 16°24′ 0 −16°24′ −34°22′ −57°52′ A 0.328 0.051 0.004 0.000 0.004 0.051 0.328 B 0.572 0.227 0.051 0.042 120.382 0.238 0.696 C −0.121 0.075 0.015 0.000 −0.727 −0.058 −0.048 % 0.63 0.29 0.06 0.03 97.99 0.19 0.80
Table V
N 5 4 3 2 1 0 −1 ψ
4358 48°9′ 29°34′
13
°
18
1
2
′
−
1
°
33
1
2
′ −16°32′ −32°49′ −53°4′ 4780 57°52′ 34°22′ 16°24′ 0 −16°24′ −34°22′ −57°52′ 5200 71°33′ 39°54′ 19°32′ 1°34′ −16°15′ −35°56′ −63°23′ A
4358 0.127 1.901 12.359 120.265 0.437 0.904 2.215 4780 0.406 0.000 0.268 113.725 2.313 3.330 1.249 5200 0.771 0.698 1.156 87.597 11.621 4.363 0.104 B
4358 0.023 0.115 0.131 0.089 0.011 0.087 0.591 4780 0.124 0.000 0.005 0.000 0.048 0.319 0.381 5200 0.424 0.100 0.040 0.066 0.193 0.417 0.037 C
4358 0.037 0.231 0.456 −2.782 −0.065 0.098 −0.759 4780 0.061 0.000 −0.037 0.008 −0.231 0.549 0.690 5200 0.563 −0.079 −0.150 −1.248 −0.337 −1.346 0.056 %
4358 0.14 1.65 9.49 86.15 0.28 0.80 1.50 4780 0.48 0.00 0.19 92.26 1.73 3.41 1.88 5200 1.67 0.68 1.00 82.26 10.93 3.27 0.19
Table VI
N 4 3 2 1 0 −1 −2 ψ
4358 51°5′ 30°59′ 14°55′ 0 −14°55′ −30°59′
−
50
°
32
1
2
′ 4780 57°52′
34
°
22
1
2
′ 16°24′ 0 −16°24′
−
34
°
22
1
2
′ −57°52′ 5200 67°7′
37
°
53
1
2
′ 17°53′ 0 −17°53′
−
37
°
53
1
2
′ −67°7′ A
4358 0.001 4.443 121.112 2.135 0.037 0.404 1.110 4780 1.144 0.245 89.240 0.204 0.792 1.572 0.612 5200 1.563 2.754 88.173 5.224 2.485 1.587 0.005 B
4358 0.000 0.059 0.082 0.053 0.003 0.083 0.513 4780 0.164 0.006 0.000 0.004 0.068 0.314 0.343 5200 0.375 0.113 0.059 0.089 0.215 0.393 0.004 C
4358 0.000 −0.279 3.145 0.200 0.011 0.098 −0.745 4780 0.001 −0.037 0.000 0.028 0.125 −0.472 −0.061 5200 0.766 −0.086 −1.201 0.215 −0.316 −0.759 0.005 %
4358 0.00 3.15 92.82 1.78 0.04 0.44 1.77 4780 1.39 0.23 94.64 0.25 1.04 1.50 0.95 5200 2.64 2.72 85.08 5.40 2.95 1.19 0.00
Table VII(a)
l
\
N 4 3 2 1 0 −1 −2 −3 ψ
3* 82°47′ 45°7′ 25°10′ 8°9′ −8°9′ −25°10′ −45°8′ −82°49′ 3† 58°17′ 34°32′ 16°28′ 0 −16°28′ −34°32′ 58°17′ 6† −58°17′ 16°28′ −16°28′ −58°17′ A
3* 0.899 0.266 0.054 70.061 0.049 0.215 0.542 1.000 3† 0.360 0.092 0.012 120.514 0.337 0.615 1.123 6† 1.104 11.945 13.443 1.323 B
3* 0.522 0.030 0.001 0.000 0.001 0.019 0.136 1.034 3† 0.113 0.009 0.000 0.000 0.007 0.059 0.346 6† 0.345 0.255 0.276 0.408 C
3* 0.465 −0072 −0.008 0.002 0.008 0.056 0.259 −1.015 3† −0.081 −0.027 −0.002 −0.175 0.046 0.124 −0.211 6† −0.027 0.309 −1.474 0.624 %
3* 2.53 0.30 0.06 94.01 0.08 0.39 1.26 1.37 3† 0.32 0.06 0.01 97.63 0.32 0.65 1.02 6† 4.98 43.84 42.92 8.25
* Grating set with first-order 3
μ on exit slit.
† Grating set with first-order 6
μ on exit slit.
Table VII(b)
N 4 3 2 1 0 −1 −2 −3 %
3* 2.23 1.11 94.23 0.05 0.35 0.82 0.59 0.62 3† 1.14 0.18 95.86 0.20 0.84 1.03 0.75 6† 0.99 94.93 0.98 3.10
* Grating set with first-order 3
μ on exit slit.
† Grating set with first-order 6
μ on exit slit.
Table VIII(a)
l
\
N 3 2 1 0 −1 ψ
3* 39°38′ 12°16½′ −12°16½′ −39°38′ 3† 58°15′ 25°10′ 0°0′ −25°10′ −58°15′ 6† 25°10′ −25°10′ A
3* 0.151 55.316 0.122 0.523 3† 0.280 0.035 51.952 0.871 1.518 6† 5.004 6.544 B
3* 0.009 0.000 0.066 0.124 3† 0.089 0.002 0.002 0.041 0.459 6† 0.263 0.309 C
3* −0.034 −0.017 0.025 0.090 3† −0.079 −0.008 −0.289 0.141 −0.375 6† 1.142 −1.327 %
3* 0.22 98.19 0.27 1.31 3† 0.53 0.05 94.56 1.93 2.93 6† 53.70 46.30
* Grating set with first-order 3
μ on exit slit.
† Grating set with first-order 6
μ on exit slit.
Table VIII(b)
l
\
N 3 2 1 0 −1 %
3* 96.33 0.31 1.80 1.56 3† 1.56 93.86 1.23 2.68 0.65 6† 94.19 5.81
* Grating set with first-order 3
μ on exit slit.
† Grating set with first-order 6
μ on exit slit.
Table IX
N 18μ 21.5μ 25μ Blaze at l = ψ % ψ % ψ % 1 25°10′ 90.95 30°31′ 82.55 36°12′ 72.47 18μ 0 −25°10′ 9.05 −30°31′ 17.45 −36°12′ 27.53 1 same 98.92 same 92.61 same 79.97 21.5μ 0 same 1.06 same 7.39 same 20.03 1 same 99.92 same 91.96 same 75.20 25μ 0 same 0.08 same 8.04 same 24.80
Table X
N 18μ 21.5μ 25μ Blaze at l = ψ % ψ % ψ % 2
39
°
37
1
2
′ 0.06
49
°
37
1
2
′ 3.48 62°21′ 6.95 18μ 1
12
°
16
1
2
′ 99.57
14
°
42
1
2
′ 86.68
17
°
10
1
2
′ 72.91 0
−
12
°
16
1
2
′ 0.06
−
14
°
42
1
2
′ 6.18
−
17
°
10
1
2
′ 14.43 −1
−
39
°
37
1
2
′ 0.31
−
49
°
37
1
2
′ 3.66 −62°21′ 5.07 2 same 2.33 same 0.54 same 4.52 21.5μ 1 same 95.87 same 96.34 same 85.87 0 same 1.64 same 0.60 same 6.24 −1 same 0.15 same 2.52 same 3.37 2 same 23.70 same 0.51 same 0.16 25μ 1 same 71.11 same 97.02 same 99.30 0 same 4.91 same 0.68 same 0.13 −1 same 0.28 same 1.79 same 0.41
Table XI
ψ * = − ϕ + 2β with blaze at l/a =
[ψ − ψ *] with blaze at l/a =
% of light in various orders (term A alone) with blaze at l/a =
% of light in various orders (term D ) with blaze at l/a =
l/a N ϕ ψ 0.5 0.6 0.8 1.0 1.2 0.5 0.6 0.8 1.0 1.2 0.5 0.6 0.8 1.0 1.2 0.5 0.6 0.8 1.0 1.2 0.5 2 14°29′ 48°35′ 14°29′ 20°25′ 32°41′ 45°31′ 59°15′ 34°6′ 28°10′ 15°54′ 3°4′ 10°40′ 0.59 1.72 56.66 96.34 94.90 0.49 1.46 63.14 95.02 91.50 1 14°29′ 14°29′ 0 5°56′ 18°12′ 31°2′ 34°46′ 97.11 96.53 37.13 0.59 3.49 96.53 96.41 31.93 0.80 4.19 0 14°29′ −14°29′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 0.42 1.02 6.20 2.56 0.67 0.55 1.34 4.83 2.79 1.34 −1 14°29′ −48°35′ 63°4′ 69°0′ 81°16′ 94°6′ 107°50′ 1.88 0.74 0.00 0.51 0.94 2.42 0.79 0.10 1.39 2.98 0.6 2 17°27′ 64°9′ 11°31′ 17°27′ 29°43′ 42°33′ 56°17′ 52°38′ 46°42′ 24°26′ 21°36′ 7°52′ 3.81 1.59 4.86 59.36 92.36 5.50 1.51 5.99 63.95 87.77 1 17°27′ 17°27′ 5°56′ 0 12°16′ 25°6′ 38°50′ 85.00 93.73 89.63 31.67 1.60 83.30 93.74 85.28 24.87 2.18 0 17°27′ −17°27′ 28°58′ 34°54′ 47°10° 60°0′ 73°44′ 6.97 0.90 2.38 6.64 4.38 7.71 1.21 3.32 5.36 3.53 0 17°27′ −17°27′ 75°40′ 81°36′ 93°52′ 106°42′ 120°26′ 4.21 3.78 3.14 2.34 1.65 3.49 3.54 5.41 5.82 6.52 2/3 2 19°28′ 90°0′ 9°30′ 15°26′ 27°42′ 40°32′ 54°16′ 80°30′ 74°34′ 62°18′ 49°28′ 35°44′ 9.47 8.58 1.71 2.10 27.70 1 19°28′ 19°28′ 9°58′ 4°2′ 8°14′ 21°4′ 36°38′ 70.90 76.79 87.02 60.58 15.91 0 19°28′ −19°28′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 12.69 6.12 0.19 6.46 6.33 1 19°28′ −90°0′ 99°30′ 105°26′ 117°42′ 130°32′ 144°16′ 6.95 8.50 11.09 30.86 50.06 0.7 1 20°30′ 20°30′ 8°28′ † 14°43′ 26°40′ 39°30′ 53°14′ 12°2′ † 5°28′ 6°10′ 19°0′ 33°44′ 81.60 † 92.0399.94 94.03 77.38 0 20°30′ −20°30′ 28°58′ † 34°54′ 47°10′ 60°0′ 73°44′ 18.40 † 7.970.06 5.97 22.62 0.8 1 23°35′ 23°35′ 5°23′ 11°19′ 23°35′ 36°25′ 50°9′ 18°12′ 12°16′ 0 12°50′ 26°34′ 65.30 81.41 96.73 99.99 98.33 72.34 82.80 95.41 99.93 95.75 0 23°35′ −23°35′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 34.70 18.59 3.27 0.01 1.67 27.66 17.20 4.59 0.07 4.25 1.0 1 30°0′ 30°0′ −1°2′ 4°54′ 17°10′ 30°0′ 43°44′ 31°2′ 25°6′ 12°50′ 0 13°44′ 41.05 57.09 83.34 91.77 95.95 52.83 67.78 84.69 89.33 92.83 0 30°0′ −30°0′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 58.95 42.91 13.66 8.23 4.05 47.17 32.22 15.31 10.67 7.17 1.2 1 36°52′ 36°52′ −7°54′ −1°58′ 10°18′ 23°8′ 36°52′ 44°46′ 38°50′ 26°34′ 13°44′ 0 25.10 37.34 60.73 75.97 83.09 34.22 50.26 71.02 78.63 81.92 0 36°52′ −36°52′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 74.90 62.66 39.27 24.03 16.91 65.78 49.74 28.98 21.37 18.08 1.4 1 44°26′ 44°26′ −15°28′ −9°32′ 2°44′ 15°34′ 29°18′ 59°54′ 53°58′ 41°42′ 28°42′ 15°8′ 15.12 23.52 42.80 59.05 68.74 20.40 33.06 56.22 67.77 71.75 0 44°26′ −44°26′ 28°58′ 34°54′ 47°10′ 60°0′ 73°44′ 84.88 76.48 57.20 40.95 31.26 79.60 66.94 43.78 32.23 28.25