Optimal F-Number of Ritchey–Chrétien Telescope Based on Tolerance Analysis of Mirror Components
Abstract
:1. Introduction
2. Allowable Range of F-Numbers and Design Cases of the Telescope
3. Tolerance of Mirror Elements Versus the F-Number
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
Appendix A
Design Case | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
Pupil Diameter/fn | 800/7.5 | 770/7.8 | 740/8.1 | 710/8.5 | 680/8.8 | 650/9.2 | 620/9.7 | 590/10.2 | 560/10.7 | |||||||||||
Surface | Type | Material | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness | Radius | Thickness |
M1 | Conic | ZERODUR | –2770.622 | –998.50 | –2772.368 | –999.27 | –2771.799 | –998.60 | –2771.040 | –998.23 | –2773.306 | –999.32 | –2772.677 | –999.11 | –2772.403 | –997.62 | –2772.582 | –997.58 | –2772.672 | –997.57 |
Conic Constants | –1.158236204 | –1.158495625 | –1.161542256 | –1.162045757 | –1.1626831 | –1.165604029 | –1.165797514 | –1.169222324 | –1.17032774 | |||||||||||
M2 | Conic | ZERODUR | –1067.075 | 1079.22 | –1067.331 | 1079.07 | –1068.899 | 1079.08 | –1068.980 | 1077.18 | –1069.105 | 1079.67 | –1068.500 | 1080.70 | –1074.296 | 1080.41 | –1074.880 | 1080.72 | –1075.137 | 1081.14 |
Conic Constants | –4.662679579 | –4.665672011 | –4.70237211 | –4.709208378 | –4.716077121 | –4.742799171 | –4.766289194 | –4.802887116 | –4.815626274 | |||||||||||
L1 | Sphere | SILICA | 173.075 | 35.60 | 172.000 | 35.19 | 169.666 | 34.88 | 169.204 | 34.18 | 168.708 | 33.90 | 166.027 | 33.77 | 166.276 | 32.90 | 164.703 | 32.58 | 163.660 | 32.22 |
Sphere | –362.650 | 6.27 | –363.669 | 5.92 | –359.746 | 5.63 | –363.209 | 5.92 | –359.505 | 6.28 | –345.696 | 5.11 | –358.561 | 6.57 | –353.486 | 6.49 | –349.625 | 6.39 | ||
L2 | Sphere | SILICA | –396.301 | 20.00 | –402.299 | 20.00 | –403.298 | 20.00 | –408.167 | 20.00 | –400.460 | 20.00 | –385.414 | 20.00 | –403.308 | 20.00 | –400.979 | 20.00 | –396.968 | 20.00 |
Sphere | 214.798 | 26.42 | 216.256 | 26.97 | 215.456 | 26.41 | 219.428 | 25.24 | 218.517 | 23.58 | 214.096 | 26.50 | 216.042 | 22.06 | 216.187 | 21.00 | 215.816 | 20.80 | ||
L3 | Sphere | SILICA | –235.739 | 6.00 | –236.312 | 6.00 | –231.928 | 6.00 | –236.334 | 6.00 | –235.304 | 6.00 | –228.056 | 6.00 | –230.529 | 6.00 | –226.726 | 6.00 | –224.828 | 6.00 |
Sphere | 223.899 | 97.16 | 219.778 | 97.62 | 218.980 | 98.99 | 216.485 | 102.71 | 219.462 | 102.05 | 219.213 | 99.30 | 218.780 | 103.78 | 220.203 | 105.14 | 220.580 | 105.40 | ||
L4 | Sphere | SILICA | 302.732 | 23.82 | 300.210 | 23.72 | 306.828 | 23.50 | 307.639 | 23.21 | 315.745 | 23.01 | 320.653 | 23.11 | 322.406 | 22.77 | 336.094 | 22.56 | 343.035 | 22.44 |
Sphere | –1788.857 | 150.00 | –1947.817 | 150.00 | –1790.501 | 150.00 | –2144.501 | 150.00 | –1917.467 | 150.00 | –1473.205 | 150.00 | –1751.763 | 150.00 | –1531.474 | 150.00 | –1419.355 | 150.00 | ||
Filter | Sphere | SILICA | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 | Infinity | 1.10 |
Sphere | Infinity | 2.96 | Infinity | 2.96 | Infinity | 2.96 | Infinity | 3.01 | Infinity | 2.96 | Infinity | 2.96 | Infinity | 2.96 | Infinity | 2.96 | Infinity | 2.97 | ||
Cover | Sphere | D 263® T | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 | Infinity | 0.70 |
Sphere | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | Infinity | 0.75 | ||
Image | FPA | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– | Infinity | –– |
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Parameters | Description |
---|---|
Spectral Range | 400–900 nm |
Filter Bands | 2 Panchromatic + 6 Multi-Spectral |
Sensor Pixel Pitch/Resolution | Pan.: 7 μm/12,000 pixel, M.S.: 28 μm/3000 pixel |
Ground Sampling Distance | 0.7 m/pixel @ 600 km of Altitude; Sun-Synchronous Orbit |
Field of View | >1° (Diagonal) |
Swath Width | >8.4 km |
Optical MTF | As–Built ≥ 0.25 @ 71.429 lp/mm, Panchromatic; 18 lp/mm, Multi-Spectral |
ξ/ξc | ξc = 1/(λ⋅ fn) | fn |
---|---|---|
0.35 | 204.1 | 7.7 |
0.36 | 198.4 | 8.0 |
0.37 | 193.1 | 8.2 |
0.38 | 188.0 | 8.4 |
0.39 | 183.2 | 8.6 |
0.40 | 178.6 | 8.8 |
0.41 | 174.2 | 9.1 |
0.42 | 170.1 | 9.3 |
0.43 | 166.1 | 9.5 |
0.44 | 162.3 | 9.7 |
0.45 | 158.7 | 10.0 |
Design Case | (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) |
---|---|---|---|---|---|---|---|---|---|
Pupil Diameter/fn | 800/7.5 | 770/7.8 | 740/8.1 | 710/8.5 | 680/8.8 | 650/9.2 | 620/9.7 | 590/10.2 | 560/10.7 |
min. MTF | 0.39 | 0.37 | 0.36 | 0.36 | 0.34 | 0.33 | 0.32 | 0.31 | 0.30 |
Distortion (%) | 0.149 | 0.149 | 0.149 | 0.148 | 0.149 | 0.149 | 0.149 | 0.149 | 0.150 |
Chief Ray Angle (°) | 2.63 | 2.63 | 2.63 | 2.60 | 2.63 | 2.63 | 2.63 | 2.62 | 2.62 |
Obstruction Ratio | 0.325 | 0.338 | 0.341 | 0.344 | 0.347 | 0.348 | 0.355 | 0.356 | 0.357 |
fn | M1 & M2 RMS Surface WFE (nm) | Primary Mirror, M1 Surface | Secondary Mirror, M2 Surface | ||
---|---|---|---|---|---|
Tilt Error Δα, Δβ (arcmin) ** | De-Center Δx, Δy (μm) * | Tilt Error Δα, Δβ (arcmin) ** | De-Center Δx, Δy (μm) * | ||
7.5 | 27 | 0.16 | 58 | 0.67 | 55 |
7.8 | 27 | 0.18 | 64 | 0.71 | 62 |
8. | 25 | 0.19 | 68 | 0.74 | 65 |
8.5 | 25 | 0.21 | 77 | 0.81 | 74 |
8.8 | 24 | 0.23 | 84 | 0.85 | 80 |
9.2 | 23 | 0.26 | 93 | 0.90 | 90 |
9.7 | 22 | 0.27 | 101 | 0.90 | 98 |
10.2 | 21 | 0.31 | 114 | 0.98 | 108 |
10.7 | 20 | 0.34 | 126 | 1.04 | 119 |
Tolerance Type | Primary Mirror, M1 Surface | Secondary Mirror, M2 Surface |
---|---|---|
RMS Surface WFE (nm) | 22 | 22 |
De-center Δx, Δy (μm) | 98 | 98 |
Tilt error Δα, Δβ (arcmin) | 0.26 | 0.90 |
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Lin, S.-F.; Chen, C.-H.; Huang, Y.-K. Optimal F-Number of Ritchey–Chrétien Telescope Based on Tolerance Analysis of Mirror Components. Appl. Sci. 2020, 10, 5038. https://doi.org/10.3390/app10155038
Lin S-F, Chen C-H, Huang Y-K. Optimal F-Number of Ritchey–Chrétien Telescope Based on Tolerance Analysis of Mirror Components. Applied Sciences. 2020; 10(15):5038. https://doi.org/10.3390/app10155038
Chicago/Turabian StyleLin, Sheng-Feng, Cheng-Huan Chen, and Yi-Kai Huang. 2020. "Optimal F-Number of Ritchey–Chrétien Telescope Based on Tolerance Analysis of Mirror Components" Applied Sciences 10, no. 15: 5038. https://doi.org/10.3390/app10155038
APA StyleLin, S.-F., Chen, C.-H., & Huang, Y.-K. (2020). Optimal F-Number of Ritchey–Chrétien Telescope Based on Tolerance Analysis of Mirror Components. Applied Sciences, 10(15), 5038. https://doi.org/10.3390/app10155038