A Review on Zernike Coefficient-Solving Algorithms (CSAs) Used for Integrated Optomechanical Analysis (IOA)

An integrated optomechanical analysis (IOA) can predict the response of an optomechanical system to temperature, gravity, vibrations, and other local loadings; thus, the normal operation of instruments under special conditions is guaranteed. Zernike polynomials are the most popular for fitting the IOA-derived mechanical deformation data. By solving the Zernike coefficients of all deformed optical surfaces, the relationship between aberrations and deformations can be further revealed. The process of IOA is summarized in this article. The principles of four primary Zernike coefficient-solving algorithms (CSAs) were expounded, and the corresponding applications are reviewed in detail, including the least squares method, the Gram-Schmidt orthogonalized method, the Householder transformation, and singular value decomposition (SVD). Artificial neural networks (ANNs) trained for solving a similar overdetermined set of equations are also discussed; an innovative Zernike CSA based on a one-dimensional convolutional neural network (1D-CNN) was proposed, emphasizing its potential for Zernike CSA. The feasibility of the neural network method was verified by conducting experiments on the primary mirror of the front reflection system of a space camera. This review can provide references for the precise optimization of IOA.