Neural-network-based wavefront solution algorithm for a wide field survey telescope

Xincheng Tan; Xincheng Tan; Zheng Lou; Yingxi Zuo; Xiaoling Zhang

doi:10.1364/AO.490065

Applied Optics
Vol. 62,
Issue 18,
pp. 4987-5002
(2023)
•https://doi.org/10.1364/AO.490065

Neural-network-based wavefront solution algorithm for a wide field survey telescope

Xincheng Tan, Zheng Lou, Yingxi Zuo, and Xiaoling Zhang

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Xincheng Tan, Zheng Lou, Yingxi Zuo, and Xiaoling Zhang, "Neural-network-based wavefront solution algorithm for a wide field survey telescope," Appl. Opt. 62, 4987-5002 (2023)

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Abstract

The wide field survey telescope (WFST) is a 2.5 m optical survey telescope currently under construction in China. The telescope employs a primary-focus optical design to achieve a wide field of view of 3 deg, and its focal plane is equipped with four pairs of curvature sensors to perform wavefront sensing and active optics. Currently, there are several wavefront solution algorithms available for curvature sensors, including the iterative fast Fourier transform method, orthogonal series expansion method, Green’s function method, and sensitivity matrix method. However, each of these methods has limitations in practical use. This study proposes a solution method based on a convolutional neural network model with a U-Net structure for the curvature wavefront sensing of the WFST. Numerical simulations show that the model, when properly trained, has a high accuracy and performs a curvature wavefront solution effectively. Upon a comparison with the sensitivity matrix method, this new method demonstrates its superiority. Finally, the study is summarized, and the drawbacks of the proposed method are discussed, which leads to direction for future optimizations.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Name	Value	Name	Value
Pfa1	0.0015 mm	Zp3	1.7230 nm
Pfa2	0.0014 mm	Zp4	1.6487 nm
Pfa3	6.8192 E-04 mm	Zp5	0.8760 nm
Pfa4	1.0638 E-04°	Zp6	0.7707 nm
Pfa5	1.0041 E-04°	Zp7	0.7726 nm
Zp1	1.7272 nm	Zp8	1.2840 nm
Zp2	1.6355 nm	Zp9	1.2075 nm

Waveband	Magnitude of Sky Background Nsoise
U	21.8
G	21.3
R	20.8
I	19.7
Z	17.5
W	20.8

Name	Value	Name	Value
Pfa1	0.0328 mm	Zp3	31.5109 nm
Pfa2	0.0345 mm	Zp4	31.0295 nm
Pfa3	0.0045 mm	Zp5	9.0306 nm
Pfa4	0.0023°	Zp6	14.0537 nm
Pfa5	0.0022°	Zp7	14.6482 nm
Zp1	57.7496 nm	Zp8	20.5822 nm
Zp2	56.4284 nm	Zp9	20.2100 nm

Wavefront Aberration Vector $\vec{x}$ ( $L e n g t h = 14$ )	Wavefront Measurement Vector $\vec{b}$ ( $L e n g t h = 168$ )
PFA axial offset	Zernike expansion coefficients (Z1–Z21) of the intra-focus image on sensor W1
	Zernike expansion coefficients (Z1–Z21) of the extra-focus image on sensor W1
PFA decenter along x-direction	Zernike expansion coefficients (Z1–Z21) of the intra-focus image on sensor W2
PFA decenter along y-direction	Zernike expansion coefficients (Z1–Z21) of the extra-focus image on sensor W2
PFA tilted around x axis	Zernike expansion coefficients (Z1–Z21) of the intra-focus image on sensor W3
PFA tilted around y axis	Zernike expansion coefficients (Z1–Z21) of the extra-focus image on sensor W3
Zernike coefficients of Primary mirror surface shape error (Z5, Z6, Z9-Z15)	Zernike expansion coefficients (Z1–Z21) of the intra-focus image on sensor W4 (Z1–Z21)
	Zernike expansion coefficients (Z1–Z21) of the extra-focus image on sensor W4

Name	Value	Name	Value
Pfa1	0.0778 mm	Zp3	87.6443 nm
Pfa2	0.0790 mm	Zp4	85.9125 nm
Pfa3	0.0150 mm	Zp5	17.7245 nm
Pfa4	0.0038°	Zp6	46.0397 nm
Pfa5	0.0037°	Zp7	45.4560 nm
Zp1	161.8439 nm	Zp8	159.8797 nm
Zp2	154.3401 nm	Zp9	153.7159 nm

Waveband	Wavelength Range	Magnitude of the Observation Source
U	322–391 nm	10	11	12	13	14	15	16	17	18
G	400–550 nm	9	10	11	12	13	14	15	16	17
R	549–690 nm	9	10	11	12	13	14	15	16	17
I	688–820 nm	8	9	10	11	12	13	14	15	16
Z	819–922 nm	6	7	8	9	10	11	12	13	14
W	400–820 nm	9	10	11	12	13	14	15	16	17

Name	Value	Name	Value
Pfa1	0.0324 mm	Zp3	33.1450 nm
Pfa2	0.0357 mm	Zp4	31.2587 nm
Pfa3	0.0047 mm	Zp5	9.4426 nm
Pfa4	0.0022°	Zp6	14.7921 nm
Pfa5	0.0024°	Zp7	14.6323 nm
Zp1	57.7576 nm	Zp8	21.6310 nm
Zp2	58.4584 nm	Zp9	21.9949 nm

Abstract

Data availability

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Figures (16)

Tables (8)

Equations (8)

Applied Optics