Method for retrieving thermal deformation of scanning mirror of remote sensing camera via the neural network algorithm

Fig. 9. (a), (d), (g), (j), (m) Theoretical surface deformation of the scanning mirror calculated by the finite element analysis; (b), (e), (h), (k), (n) Surface deformation calculated via BP network algorithm; (c), (f), (i), (l), (o) Residual errors

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Table 1. Parameters of the optical system
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Table 1. Parameters of the optical system
No. Parameter Value
1 Field of view/(°) 1.0×4.0
2 Aperture/nm φ120
3 Wavelength/µm 0.55-0.90
4 Focal length 350

Table 2. The key parameters of SiC

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Table 2. The key parameters of SiC

No.	Parameter	Value
1	Density/kg·m⁻³	3.1
2	Young’s modulus/GPa	403
3	Poisson’s ratio	0.168
4	Isotropic instantaneous coefficient of thermal expansion/×10⁻⁶K	2.24
5	Isotropic thermal conductivity λ/W·m·K⁻¹	140

Table 3. The meaning of the first 11 terms of Zernike polynomial

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Table 3. The meaning of the first 11 terms of Zernike polynomial

n	m	Term	Polynomial	Meaning
0	0	0	1	Piston
1	+1	1	$ \rho \mathrm{cos}\theta $	Tilt X
1	−1	2	$ \rho \mathrm{sin}\theta $	Tilt Y
1	0	3	$ 2\;{\rho }^{2}-1 $	Power
2	+2	4	$ \;{\rho }^{2}\mathrm{cos}2\theta $	Astigmatism X
2	−2	5	$ \;{\rho }^{2}\mathrm{sin}2\theta $	Astigmatism Y
2	+1	6	$ \left(3\;{\rho }^{2}-2\right)\rho \mathrm{cos}\theta $	Coma X
2	−1	7	$ \left(3\;{\rho }^{2}-2\right)\rho \mathrm{sin}\theta $	Coma Y
2	0	8	$ 6\;{\rho }^{4}-6\;{\rho }^{2}+1 $	Primary spherical
3	+3	9	$ \;{\rho }^{3}\mathrm{cos}3\theta $	Trefoil X
3	−3	10	$ \;{\rho }^{3}\mathrm{sin}3\theta $	Trefoil Y

Table 4. Temperature values of 8 temperature measurement points on the back of scanning mirror (Unit: ℃)

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Table 4. Temperature values of 8 temperature measurement points on the back of scanning mirror (Unit: ℃)

No.	T1	T2	T3	T4	T5	T6	T7	T8	Ave temp
1	7.49	9.12	10.41	11.26	4.91	3.17	7.95	6.82	7.64
2	16.98	21.08	−0.2	5.14	19.66	17.05	8.26	5.58	11.69
3	22.90	20.87	2.6	1.44	21.12	22.82	7.49	9.24	13.56
4	18.87	14.05	9.62	5.58	16.93	19.89	10.75	13.88	13.70
5	24.29	21.38	17.12	14.63	24.39	26.38	19.45	21.33	21.12

Table 5. Aberration coefficients of scanning mirror via Zernike polynomials

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Table 5. Aberration coefficients of scanning mirror via Zernike polynomials

No.	Power/λ	Ast ρ/λ	Ast θ/(°)	Com ρ/λ	Comθ/(°)	Tref ρ/λ	Tref θ/(°)	Sph/λ
1	0.0330	0.0569	81.912	0.0603	68.336	0.0926	29.651	0.0379
2	0.0012	0.0326	40.045	0.0353	106.58	0.0801	28.686	0.0255
3	−5e-4	0.01395	32.6296	0.02962	59.6132	0.06413	37.1308	0.01664
4	−0.0024	−0.0036	93.065	0.0346	90.018	0.0503	39.795	0.0189
5	−0.018	0.0163	3.5802	0.00142	33.143	0.01940	9.2916	0.00100

Table 6. The difference between the surface deformation calculated by neural network and the theoretical surface deformation, λ=0.632 8 µm

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Table 6. The difference between the surface deformation calculated by neural network and the theoretical surface deformation, λ=0.632 8 µm

No.	Theoretical surface deformation (RMS, λ)	BP network algorithm (RMS, λ)	Residual errors (RMS, λ)
1	0.049559	0.049555	0.0160
2	0.029358	0.035631	0.0195
3	0.022354	0.026707	0.0119
4	0.031312	0.024892	0.0133
5	0.012395	0.013173	0.0077

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Zhengda Li, Shengli Sun, Xiaojin Sun, Yifan Chen, Yixiao Han, Xiaohao Ma, Xiaotian Shen. Method for retrieving thermal deformation of scanning mirror of remote sensing camera via the neural network algorithm[J]. Infrared and Laser Engineering, 2023, 52(10): 20230065

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