Simulation Technology for Assembly of Off-Axis Three-Mirror Optical Systems Based on KAN-Transformer

Lei Sheng; Lijuan Li; Xihong Fu; Xuezhu Lin; Lili Guo

doi:10.3788/AOS241722

Acta Optica Sinica, Volume. 45, Issue 5, 0522002(2025)

Simulation Technology for Assembly of Off-Axis Three-Mirror Optical Systems Based on KAN-Transformer

Lei Sheng¹, Lijuan Li^1,2、*, Xihong Fu^3,4、**, Xuezhu Lin^1,2, and Lili Guo^1,2

¹Key Laboratory of Photoelectric Measurement and Optical Information Transmission Technology of Ministry of Education, School of Optoelectronic Engineering, Changchun University of Science and Technology, Changchun 130022, Jilin , China

²Zhongshan Institute of Changchun University of Science and Technology, Zhongshan 528437, Guangdong , China

³Xi’an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, Xi’an 710119, Shaanxi , China

⁴University of Chinese Academy of Sciences, Beijing 100049, China

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Figures & Tables(22)

Fig. 1. Diagram of initial installation and adjustment

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Fig. 2. Flowchart of model construction

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Fig. 3. Structure diagram of shallow MLP and KAN. (a) Shallow structure of MLP; (b) shallow structure of KAN

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Fig. 4. Structure diagram of KAN-Transformer

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Fig. 5. Optical path diagram of a certain off-axis three-mirror optical system

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Fig. 6. Production process of dataset

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Fig. 7. MSE and MAE of different network structures under training dataset. (a) MSE; (b) MAE

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Fig. 8. Linear distribution diagrams of small-scale predicted values and preset values based on Transformer. (a) X-decenter predicted values and preset values; (b) Y-decenter predicted values and preset values; (c) Z-decenter predicted values and preset values; (d) X-tilt predicted values and preset values; (e) Y-tilt predicted values and preset values; (f) Z-tilt predicted values and preset values

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Fig. 9. Linear distribution diagram of small-scale predicted values and preset values based on KAN-Transformer. (a) X-decenter predicted values and preset values; (b) Y-decenter predicted values and preset values; (c) Z-decenter predicted values and preset values; (d) X-tilt predicted values and preset values; (e) Y-tilt predicted values and preset values; (f) Z-tilt predicted values and preset values

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Fig. 10. Design residual wavefront aberration for F(0°, 0°), F(2°, -2°), and F(2°, 2°) fields of view. (a) F(0°, 0°); (b) F(2°, -2°); (c) F(2°, 2°)

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Fig. 11. Simulating wavefront aberration in the fields of F(0°, 0°), F(2°, -2°), and F(2°, 2°) after misalignment. (a) F(0°, 0°); (b) F(2°, -2°); (c) F(2°, 2°)

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Fig. 12. Wavefront aberration in the fields of F(0°, 0°), F(2°, -2°), and F(2°, 2°) after Simulated assembly. (a) F(0°, 0°); (b) F(2°, -2°); (c) F(2°, 2°)

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Fig. 13. Prediction errors of different network structures

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Fig. 14. Field of F(0°, 0°), F(0°, 2°), and F(2°, 2°) of PV error value and RMS error value of the system. (a) F(0°, 0°) PV error; (b) F(0°,2°) PV error; (c) F(2°, 2°) PV error; (d) F(0°, 0°) RMS error; (e) F(0°, 2°) RMS error; (f) F(2°, 2°) RMS error

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Fig. 15. Training process of neural network with added noise

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Table 1. Design parameters of three-mirror optical system
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Table 1. Design parameters of three-mirror optical system
Surface Radius /mm Semi-diameter /mm Thickness /mm Conic
Primary-mirror -1058.989 175.286 -276.007 -1.315
Second-mirror -324.065 30.615 319.161 0.889
Third-mirror -543.965 176.171 -321.621 0.226

Table 2. Comparison between sensitivity matrix method calculation results and preset values

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Table 2. Comparison between sensitivity matrix method calculation results and preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	-0.0517	-0.0014	-0.2249	-0.1421	-0.2766	0.1407
Y-decenter	0.4648	0.0129	0.0086	-0.0118	0.4562	0.0247
Z-decenter	-0.2801	0.3903	0.7927	2.0239	-1.0728	-1.6336
X-tilt	-0.3423	0.4725	-0.0212	-0.0347	-0.3211	0.5072
Y-tilt	-0.0021	-0.0310	-0.1456	0.0868	0.1435	-0.1178
Z-tiit	—	0.0126	—	-0.0022	—	0.0148

Table 3. Comparison between neural network calculation results and preset values

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Table 3. Comparison between neural network calculation results and preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	-0.0517	-0.0014	-0.0573	0.0022	0.0056	-0.0036
Y-decenter	0.4648	0.0129	0.4737	0.0076	-0.0089	0.0053
Z-decenter	-0.2801	0.3903	-0.2848	0.3966	0.0047	-0.0063
X-tilt	-0.3423	0.4725	-0.3488	0.4799	0.0062	-0.0074
Y-tilt	-0.0021	-0.0310	-0.0115	-0.0201	0.0094	-0.0109
Z-tiit	—	0.0126	—	0.0051	—	0.0075

Table 4. Comparison between the second round sensitivity matrix method calculation results and preset values

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Table 4. Comparison between the second round sensitivity matrix method calculation results and preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	-0.2766	0.1407	-0.0745	0.0862	-0.3511	0.0545
Y-decenter	0.4562	0.0247	0.5236	0.0194	0.0674	0.0053
Z-decenter	-1.0728	-1.6336	0.2036	-0.2051	-1.2764	-1.4285
X-tilt	-0.3211	0.5072	-0.4234	0.6873	0.1023	-0.1801
Y-tilt	0.1435	-0.1178	0.0828	-0.1932	0.0607	0.0754
Z-tiit	—	0.0148	—	0.0239	—	-0.0091

Table 5. Comparison between the results of the second round of neural network calculations and the preset values

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Table 5. Comparison between the results of the second round of neural network calculations and the preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	0.0056	-0.0036	0.0060	-0.0032	-0.0004	-0.0004
Y-decenter	-0.0089	0.0053	-0.0087	0.0044	-0.0002	0.0009
Z-decenter	0.0047	-0.0063	0.0053	-0.0075	-0.0006	0.0012
X-tilt	0.0062	-0.0074	0.0055	-0.0072	0.0007	-0.0002
Y-tilt	0.0094	-0.0109	0.0091	-0.0108	0.0003	-0.0001
Z-tiit	—	0.0075	—	0.0067	—	0.0008

Table 6. Comparison between simulated noise training neural network of the first round of calculation results and preset values

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Table 6. Comparison between simulated noise training neural network of the first round of calculation results and preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	-0.1185	0.2083	-0.1332	0.1992	0.0147	0.0091
Y-decenter	0.1893	-0.0274	0.1989	-0.0352	-0.0096	0.0105
Z-decenter	0.2306	-0.0872	-0.2219	-0.0924	0.0087	0.0052
X-tilt	-0.0067	0.3725	0.0059	0.3814	-0.0126	-0.0089
Y-tilt	-0.4027	0.0181	-0.3837	-0.0063	-0.0190	0.0118
Z-tiit	—	0.4126	—	0.4208	—	-0.0082

Table 7. Comparison between simulated noise training neural network of the second round of calculation results and preset values

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Table 7. Comparison between simulated noise training neural network of the second round of calculation results and preset values

Parameter	Reference /mm		Output /mm		Error /mm
Parameter	Second-mirror	Third-mirror	Second-mirror	Third-mirror	Second-mirror	Third-mirror
X-decenter	0.0147	0.0091	0.0111	0.0074	0.0036	0.0017
Y-decenter	-0.0096	0.0105	-0.0112	0.0112	0.0016	-0.0007
Z-decenter	0.0087	0.0052	0.0068	0.0066	0.0019	-0.0014
X-tilt	-0.0119	-0.0089	-0.0152	-0.0097	0.0033	0.0008
Y-tilt	-0.0190	0.0118	-0.0163	0.0144	-0.0027	-0.0026
Z-tiit	—	-0.0082	—	-0.0094	—	0.0012

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Lei Sheng, Lijuan Li, Xihong Fu, Xuezhu Lin, Lili Guo. Simulation Technology for Assembly of Off-Axis Three-Mirror Optical Systems Based on KAN-Transformer[J]. Acta Optica Sinica, 2025, 45(5): 0522002

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Paper Information

Category: Optical Design and Fabrication

Received: Nov. 6, 2024

Accepted: Jan. 3, 2025

Published Online: Mar. 21, 2025

The Author Email: Lijuan Li (custjuan@163.com), Xihong Fu (fuxh@opt.ac.cn)

DOI:10.3788/AOS241722

CSTR:32393.14.AOS241722

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Design parameters of three-mirror optical system

Table 1. Design parameters of three-mirror optical system

Table 2. Comparison between sensitivity matrix method calculation results and preset values

Table 2. Comparison between sensitivity matrix method calculation results and preset values

Table 3. Comparison between neural network calculation results and preset values

Table 3. Comparison between neural network calculation results and preset values

Table 4. Comparison between the second round sensitivity matrix method calculation results and preset values

Table 4. Comparison between the second round sensitivity matrix method calculation results and preset values

Table 5. Comparison between the results of the second round of neural network calculations and the preset values

Table 5. Comparison between the results of the second round of neural network calculations and the preset values

Table 6. Comparison between simulated noise training neural network of the first round of calculation results and preset values

Table 6. Comparison between simulated noise training neural network of the first round of calculation results and preset values

Table 7. Comparison between simulated noise training neural network of the second round of calculation results and preset values

Table 7. Comparison between simulated noise training neural network of the second round of calculation results and preset values