High-order Reduced Radial Zernike Polynomials for Modal Reconstruction of Wavefront Aberrations in Radial Shearing Interferometers

We present a method for improving the accuracy of the modal wavefront reconstruction in the radial shearing interferometers (RSIs). Our approach involves expanding the reduced radial terms of Zernike polynomials to high-order, which enables more precise reconstruction of the wavefront aberrations with high-spatial frequency. We expanded the reduced polynomials up to infinite order with symbolic variables of the radius, shearing amount, and transformation matrix elements. For the simulation of the modal wavefront reconstruction, we generated a target wavefront subsequently, magnified and measured wavefronts were generated. To validate the effectiveness of the high-order Zernike polynomials, we ap-plied both low-and high-order polynomials to the wavefront reconstruction process. Consequently, the peak-to-valley (PV) and RMS errors notably decreased with values of 0.011λ and 0.001λ, respectively, as the order of the radial Zernike polynomial increased.