Enhanced calibration for freeform surface misalignments in non-null interferometers by convolutional neural network.

Most tested surface calibration methods in interferometers, such as the direct coefficients removing method, the sensitive matrix (SM) method, and deep neural network (DNN) calibration method, rely on Zernike coefficients. However, due to the inherent rotationally non-symmetric aberrations in a non-null freeform surface interferometer, the interferograms are usually non-circular even if the surface apertures are circular. The Zernike coefficients based methods are inaccurate due to the non-orthogonality of Zernike polynomials in the non-circular area. A convolutional neural network (CNN)-based misalignment calibration method is proposed. Instead of Zernike coefficients, the well-trained CNN treats the interferogram directly to estimate the specific misalignments. Simulations and experiments are carried out to validate the high accuracy.