Table I
Calculated line widths at the image as a function of distance of the entrance slit from the tangential focal point of the collimator (Δt).
| Calculated line width (microns) position alone focal curve (cm) |
---|
Δt (cm) | 0 | 12 | 25 | 37 | 50 |
---|
|
|
|
|
|
---|
w | U | w | U | w | U | w | U | w | U |
---|
θ = 52.8508° |
2.00 | 6.2 | 13 | 3.6 | 10 | 8.6 | 21 | 12.6 | 29 | 15.2 | 34 |
1.00 | 6.4 | 13 | 3.6 | 10 | 8.8 | 21 | 12.6 | 29 | 15.4 | 34 |
0.00 | 6.4 | 13 | 3.6 | 10 | 8.8 | 21 | 13.0 | 29 | 15.8 | 35 |
−1.00 | 6.2 | 13 | 3.8 | 11 | 9.2 | 22 | 13.2 | 30 | 16.0 | 36 |
−2.00 | 6.2 | 13 | 4.0 | 12 | 9.4 | 22 | 13.6 | 31 | 16.6 | 37 |
θ = 61.2732° |
2.00 | 5.2 | 11 | 2.6 | 5 | 4.2 | 9 | 6.0 | 12 | 7.8 | 14 |
1.00 | 5.2 | 11 | 2.8 | 6 | 4.2 | 9 | 6.2 | 14 | 8.2 | 16 |
0.00 | 5.2 | 11 | 3.0 | 6 | 4.6 | 10 | 6.6 | 13 | 8.6 | 16 |
−1.00 | 5.2 | 10 | 3.0 | 6 | 4.8 | 11 | 7.0 | 14 | 9.0 | 16 |
−2.00 | 5.2 | 10 | 3.0 | 6 | 4.8 | 11 | 7.2 | 14 | 9.4 | 17 |
θ = 67.8078° |
2.00 | 4.2 | 8 | 3.2 | 6 | 4.4 | 9 | 6.2 | 12 | 8.8 | 18 |
1.00 | 4.4 | 8 | 3.4 | 7 | 4.6 | 10 | 6.6 | 14 | 9.4 | 19 |
0.00 | 4.2 | 9 | 3.4 | 6 | 4.8 | 9 | 6.8 | 13 | 9.8 | 19 |
−1.00 | 4.4 | 9 | 3.4 | 7 | 4.8 | 10 | 7.0 | 15 | 10.0 | 21 |
−2.00 | 4.2 | 9 | 3.4 | 7 | 5.0 | 10 | 7.2 | 15 | 10.2 | 21 |
Table II
Values of the grating angle, θ, required to bring the tenth order of the given wavelength to the center of the plate.
λm(Å) | θ(°) |
---|
5448 | 52.8508 |
5948 | 61.2732 |
6248 | 67.8078 |
Table III
Calculated line widths at the image as a function of ΔZ, the displacement of the grating from the position required by the Fastie–Rosendahl equation. Positive ΔZ corresponds to displacement away from the entrance slit. Calculations are for a wavelength of 5948 Å in the tenth order at the center of the focal curve.
| Calculated line widths (microns) position along focal curve (cm). |
---|
ΔZ (cm) | 0 | 12 | 25 | 37 | 50 |
---|
|
|
|
|
|
---|
w | U | w | U | w | U | w | U | w | U |
---|
0.0 | 5.8 | 12 | 3.0 | 6 | 4.4 | 9 | 6.4 | 12 | 8.4 | 15 |
2.0 | 8.6 | 17 | 5.0 | 9 | 4.2 | 8 | 5.8 | 11 | 8.0 | 15 |
4.0 | 11.2 | 22 | 7.4 | 14 | 5.8 | 11 | 6.6 | 13 | 8.8 | 18 |
6.0 | 14.0 | 27 | 10.2 | 19 | 8.2 | 13 | 8.2 | 15 | 10.2 | 19 |
8.0 | 16.8 | 32 | 12.8 | 23 | 10.6 | 18 | 10.4 | 17 | 12.2 | 22 |
10.0 | 19.6 | 37 | 15.6 | 28 | 13.4 | 23 | 13.0 | 21 | 14.6 | 24 |
12.0 | 22.2 | 42 | 18.4 | 34 | 16.0 | 28 | 15.6 | 25 | 17.2 | 27 |
Table IV
Calculated line image widths at the plate center as a function of ΔZ, the displacement of the grating from the position required by the Fastie–Rosendahl equation. Calculation is based on tracing rays lying in the central plane of the spectrograph. The wavelength is 5948 Å and the order is the tenth.
| Width (microns) |
---|
ΔZ (cm) | w | W |
---|
0.0 | 1.2 | 2 |
2.0 | 2.4 | 5 |
4.0 | 4.8 | 8 |
6.0 | 7.4 | 11 |
8.0 | 10.2 | 15 |
10.0 | 13.0 | 19 |
12.0 | 15.2 | 23 |
Table V
The sagitta of the focal curve as a function of Δt, the displacement of the entrance slit from the tangential focal point of the collimator. Sagitta is negative if the curve is concave toward the camera mirror. (R − g) is the longitudinal distance of the grating from the vertices of the spherical mirrors.
| Sagitta of the focal curve |
---|
|
|
---|
| R − g = 328 cm | R − g = 335 cm |
---|
Δt (cm) | θ = 61.2739° | θ = 61.3441° |
---|
2.00 | −0.278 | −0.247 |
1.00 | −0.151 | −0.123 |
0.40 | −0.074 | −0.049 |
0.20 | −0.049 | −0.024 |
0.00 | −0.022 | 0.001 |
−0.20 | 0.003 | 0.026 |
−0.40 | 0.027 | 0.050 |
−1.00 | 0.106 | 0.125 |
−2.00 | 0.235 | 0.250 |
Table VI
Change of focus with change of grating angle for various positions of entrance slit. When Δt = 0.0 the slit is at the tangential focal point of the collimator. (R − g) = 335 cm.
Δt (cm) | Grating angle (deg) | Longitudinal distance of image from vertex of camera mirror (cm) |
---|
|
---|
Position along focal curve (cm) |
---|
|
---|
0 | 12 | 25 | 37 | 50 |
---|
1.00 | 52.925 | 398.72 | 398.58 | 398.40 | 398.21 | 397.98 |
| 61.344 | 398.64 | 398.43 | 398.16 | 397.86 | 397.44 |
| 67.875 | 398.51 | 398.21 | 397.77 | 397.24 | 396.39 |
0.40 | 52.925 | 399.45 | 399.37 | 399.28 | 399.19 | 399.08 |
| 61.344 | 399.42 | 399.32 | 399.19 | 399.05 | 398.86 |
| 67.875 | 399.37 | 399.23 | 399.04 | 398.80 | 398.44 |
0.20 | 52.925 | 399.69 | 399.64 | 399.58 | 399.51 | 399.44 |
| 61.344 | 399.68 | 399.62 | 399.53 | 399.45 | 399.34 |
| 67.875 | 399.66 | 399.57 | 399.46 | 399.32 | 399.13 |
0.00 | 52.925 | 399.93 | 399.90 | 399.87 | 399.84 | 399.81 |
| 61.344 | 399.94 | 399.91 | 399.88 | 399.84 | 399.81 |
| 67.875 | 399.95 | 399.92 | 399.88 | 399.85 | 399.81 |
−0.20 | 52.925 | 400.18 | 400.17 | 400.16 | 400.16 | 400.17 |
| 61.344 | 400.20 | 400.21 | 400.22 | 400.24 | 400.29 |
| 67.875 | 400.23 | 400.26 | 400.30 | 400.37 | 400.50 |
−0.40 | 52.925 | 400.42 | 400.44 | 400.46 | 400.49 | 400.54 |
| 61.344 | 400.47 | 400.51 | 400.56 | 400.64 | 400.76 |
| 67.875 | 400.52 | 400.60 | 400.72 | 400.89 | 401.18 |
−1.00 | 52.925 | 401.15 | 401.23 | 401.34 | 401.47 | 401.64 |
| 61.344 | 401.25 | 401.40 | 401.60 | 401.84 | 402.19 |
| 67.875 | 401.39 | 401.63 | 401.99 | 402.46 | 403.24 |