The Opto-Mechanical–Thermal Coupling Analysis and Verification of an All-Aluminum Freeform Imaging Telescope
<p>The final design of three-mirror freeform optical system. M1–M3 represent the three freeform mirrors.</p> "> Figure 2
<p>(<b>a</b>) The MTF and (<b>b</b>) the spot diagram of the final FIT.</p> "> Figure 3
<p>Three-dimensional model of all-aluminum freeform imaging telescope.</p> "> Figure 4
<p>The flow chart of opto-mechanical–thermal coupling analysis. Firstly, the optical design and structural design was carried out. Secondly, the 3D model of the FIT was imported into finite-element software for structural and thermal integration analysis. Thirdly, data processing software (Matlab, Mathmatica, etc.) was used to convert the deformation data into the coefficients of XY polynomial. Finally, the coefficients of XY polynomial were imported into ZEMAX software for optical analysis of the FIT.</p> "> Figure 5
<p>The process of <math display="inline"><semantics> <mrow> <msub> <mi>z</mi> <mn>0</mn> </msub> </mrow> </semantics></math> correction.</p> "> Figure 6
<p>Node coordinate distribution (<b>a</b>) before correction (<b>b</b>) after correction.</p> "> Figure 7
<p>The schematic diagram of the global coordinates and the local coordinates for a node.</p> "> Figure 8
<p>(<b>a</b>) The finite-element model of the all-aluminum FIT and (<b>b</b>) the thermal deformation of M1 in the global coordinate system.</p> "> Figure 9
<p>Fitted surface profile of M1 (<b>a</b>) with and (<b>b</b>) without the rigid displacement.</p> "> Figure 10
<p>(<b>a</b>) Geometric diffuse spots after fitting and (<b>b</b>) the MTF of the optical system according to the fitting results.</p> "> Figure 11
<p>(<b>a</b>) The three freeform mirrors. (<b>b</b>) The prototype of the FIT.</p> "> Figure 12
<p>Thermo-optical test setup of the all-aluminum FIT.</p> "> Figure 13
<p>(<b>a</b>) The target images taken at 20 °C. (<b>b</b>) The target images taken at −20 °C.</p> ">
Abstract
:1. Introduction
2. Design of All-Aluminum Freeform Imaging Telescope
2.1. Optical Design
2.2. Structural Design
3. Opto-Mechanical–Thermal Coupling Analysis
3.1. Principles of Opto-Mechanical–Thermal Coupling Analysis
3.2. Data Correction
3.3. Coordinate Transformation
3.4. Opto-Mechanical–Thermal Coupling Analysis
4. Thermal and Optical Testing
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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F# | Field of View | Entrance Pupil Diameter (mm) | Wavelength (nm) | Pixel Size (μm2) |
---|---|---|---|---|
4 | 4° × 4° | 40 | 400–700 | 5.5 × 5.5 |
Density (kg/m3) | Thermal Expansion Coefficient (K−1) | Elastic Modulus (N/m2) | Poisson’s Ratio | Thermal Conductivity (W/(m·K)) |
---|---|---|---|---|
2710 | 2.4 × 10−5 | 6.9 × 1010 | 0.33 | 154 |
Term | M1 | M2 | M3 | Term | M1 | M2 | M3 | Term | M1 | M2 | M3 |
---|---|---|---|---|---|---|---|---|---|---|---|
X1Y0 | −3.46 × 10−5 | −8.14 × 10−5 | −1.53 × 10−3 | X1Y3 | −6.34 × 10−11 | 3.15 × 10−11 | 9.04 × 10−6 | X2Y4 | −1.86 × 10−12 | −7.60 × 10−12 | −7.45 × 10−4 |
X0Y1 | 1.70 × 10−4 | 1.46 × 10−4 | −1.72 × 10−3 | X0Y4 | 2.51 × 10−9 | −1.22 × 10−7 | −1.02 × 10−2 | X1Y5 | 1.29 × 10−13 | 5.60 × 10−14 | −8.28 × 10−6 |
X2Y0 | −1.99 × 10−4 | −7.69 × 10−4 | −8.37 × 10−2 | X5Y0 | 1.01 × 10−11 | 5.39 × 10−14 | 7.87 × 10−6 | X0Y6 | −2.29 × 10−13 | −9.92 × 10−12 | −3.58 × 10−4 |
X1Y1 | −3.5 × 10−8 | 1.84 × 10−8 | 1.09 × 10−5 | X4Y1 | 2.70 × 10−11 | 1.58 × 10−9 | 1.00 × 10−3 | X7Y0 | 5.62 × 10−15 | 1.23 × 10−16 | 1.87 × 10−5 |
X0Y2 | −2.80 × 10−4 | −2.11 × 10−3 | −3.17 × 10−1 | X3Y2 | −2.12 × 10−11 | 4.12 × 10−13 | −4.65 × 10−5 | X6Y1 | −1.34 × 10−14 | −2.05 × 10−12 | −7.75 × 10−4 |
X3Y0 | −4.11 × 10−9 | −1.44 × 10−11 | −3.90 × 10−5 | X2Y3 | 1.40 × 10−11 | 1.83 × 10−9 | 1.88 × 10−4 | X5Y2 | −5.11 × 10−15 | −1.15 × 10−16 | −1.07 × 10−5 |
X2Y1 | −1.79 × 10−6 | 2.73 × 10−7 | 7.67 × 10−3 | X1Y4 | −3.12 × 10−11 | −2.86 × 10−13 | −5.29 × 10−5 | X4Y3 | 1.12 × 10−14 | 2.25 × 10−12 | 7.54 × 10−4 |
X1Y2 | 1.26 × 10−8 | −2.30 × 10−9 | 4.06 × 10−5 | X0Y5 | 3.95 × 10−12 | 5.58 × 10−10 | −2.41 × 10−4 | X3Y4 | −2.48 × 10−14 | −2.00 × 10−15 | −7.52 × 10−5 |
X0Y3 | −2.21 × 10−6 | −8.57 × 10−6 | −2.20 × 10−2 | X6Y0 | −3.29 × 10−13 | 3.54 × 10−13 | −1.34 × 10−4 | X2Y5 | 1.79 × 10−14 | 2.29 × 10−12 | 3.42 × 10−4 |
X4Y0 | 8.39 × 10−9 | 4.85 × 10−8 | −2.67 × 10−3 | X5Y1 | −1.92 × 10−14 | −1.12 × 10−13 | 6.05 × 10−6 | X1Y6 | −1.64 × 10−14 | 9.19 × 10−16 | −4.55 × 10−5 |
X3Y1 | −3.23 × 10−12 | 5.80 × 10−11 | −6.95 × 10−6 | X4Y2 | 5.80 × 10−13 | 9.22 × 10−12 | −3.64 × 10−4 | X0Y7 | 2.78 × 10−15 | −3.78 × 10−13 | −1.27 × 10−4 |
X2Y2 | 1.03 × 10−8 | −3.73 × 10−8 | −1.07 × 10−2 | X3Y3 | 1.90 × 10−13 | 9.70 × 10−14 | −1.13 × 10−5 |
Temperature | −55°C | 0°C |
MTF | ||
Temperature | 20°C | 70°C |
MTF |
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Gao, R.; Li, J.; Wang, P.; Yu, J.; Xie, Y.; Mao, X. The Opto-Mechanical–Thermal Coupling Analysis and Verification of an All-Aluminum Freeform Imaging Telescope. Symmetry 2022, 14, 2391. https://doi.org/10.3390/sym14112391
Gao R, Li J, Wang P, Yu J, Xie Y, Mao X. The Opto-Mechanical–Thermal Coupling Analysis and Verification of an All-Aluminum Freeform Imaging Telescope. Symmetry. 2022; 14(11):2391. https://doi.org/10.3390/sym14112391
Chicago/Turabian StyleGao, Rong, Jinpeng Li, Peng Wang, Jiadong Yu, Yongjun Xie, and Xianglong Mao. 2022. "The Opto-Mechanical–Thermal Coupling Analysis and Verification of an All-Aluminum Freeform Imaging Telescope" Symmetry 14, no. 11: 2391. https://doi.org/10.3390/sym14112391