Analysis of design for Hartmann-Shack measurements under usage of Fourier-iteration and Zernike approximation wavefront reconstruction methods

摘要

The measurement of a wavefront is a powerful tool for characterizing optical systems. The most commonly used wavefront measurement technique is the method of local-light aberrometry. The conventional version of this kind of measurement principle is the Hartmann-Shack wavefront sensor. This method returns the result of the matrix of spatially-resolved gradients of the wavefront. However, the last and crucial step of the wavefront analysis is the reconstruction of the wavefront from the measured data packets. The issues of the measurement preparation and design are interesting in the same volume. The work presented here describes the comparison between a Fourier-Iteration algorithm and the Zernike approximation method for the wavefront reconstruction in relation to the measurement design. In the context of this work, the term "design of the measurement" refers to the issue of the number and relative positions of the measurement points. In this work, the behavior of the wavefront reconstruction method using Monte-Carlo simulations was analyzed. The optimum point distribution was found and a validation parameter to describe the impact of measurement errors on the analysis results was determined. Based on this parameter, a Monte-Carlo based simulation to make the design of the experiment with the highest accuracy was realized. The technique of white noise injection was implemented in the reconstruction routine and the propagation of errors was analyzed. The presented comparison technique was applied to determine the optimum measurement positions over the beam's surface.