Opto-thermal deformation fitting method based on a neural network and a transfer learning

The thermal deformation fitting result of an optical surface is an important factor that affects the reliability of optical–mechanical–thermal integrated analysis. The traditional numerical methods are challenging to balance fitting accuracy and efficiency, especially the insufficient ability to deal with high-order Zernike polynomials. In this Letter, we innovatively proposed an opto-thermal deformation fitting method based on a neural network and a transfer learning to overcome shortcomings of numerical methods. The one-dimensional convolutional neural network (1D-CNN) model, which can represent deformation of the optical surface, is trained with Zernike polynomials as the input and the optical surface sag change as the output, and the corresponding Zernike coefficients are predicted by the identity matrix. Meanwhile, the trained 1D-CNN is further combined with the transfer learning to efficiently fit all thermal deformations of the same optical surface at different temperature conditions and avoids repeated training of the network. We performed thermal analysis on the main mirror of an aerial camera to verify the proposed method. The regression analysis of 1D-CNN training results showed that the determination coefficient is greater than 99.9%. The distributions of Zernike coefficients predicted by 1D-CNN and transfer learning are consistent. We conducted an error analysis on the fitting results, and the average values of the peak-valley, root mean square, and mean relative errors of the proposed method are 51.56%, 60.51, and 45.14% of the least square method, respectively. The results indicate that the proposed method significantly improves the fitting accuracy and efficiency of thermal deformations, making the optical–mechanical–thermal integrated analysis more reliable.