ZernikeNet: a deep learning-based approach for accurate Zernike coefficients calculation in aspheric optical components

This paper presents a new method called ZernikeNet for accurately calculating Zernike coefficients in aspheric optical components. Surface figure error (SFE) measurements obtained using interferometer often include alignment errors and low-order aberrations, such as piston, tip, tilt, and defocus, which need to be removed to effectively analyze high-order aberrations. The traditional method for removing low-order aberrations involves Zernike polynomial fitting to the SFE, but this assumes that the optical component is circular and can be decomposed into an orthogonal basis set of Zernike polynomials. However, for aspheric optical components, the orthogonality of Zernike polynomials may not hold, making it challenging to accurately represent the SFE. To address this challenge, ZernikeNet employs a deep learning-based approach, where interferometer map of the optical component is fed into a multi-layer neural network structure to output a set of 36 Zernike coefficients. The proposed deep learning network is trained using a single-shot metrology approach, where a single input interferometer map is used to generate high-accuracy Zernike coefficients through intentional overfitting. Experimental results using data from aspheric mirror show that ZernikeNet can effectively remove low-order aberrations, leaving only high-order aberrations, resulting in a low residual SFE RMS value. This method offers a significant advantage over traditional Zernike polynomial fitting approaches for optical components with complex shapes, making it a promising tool for the design and analysis of advanced optical systems.