Abstract

The traditional multiposition method of the ${M^2}$ factor measurement system is a good method, but it is relatively time consuming, so it cannot meet the requirements of the transient test of a Gaussian beam. To solve this problem, a quadriwave lateral shearing interferometer and a wavefront construction method based on a difference Zernike polynomial are analyzed. This interferometer uses a special grating to select four replicas of the wavefront, and the interferogram generated by four replicas includes difference wavefront information. Then the difference Zernike polynomial method is used to analyze quadriwave lateral shearing interferograms. The characteristic parameters are obtained after finding the optimal terms of the Zernike polynomials. As a result, the errors of F-number, beam radius, and radius of curvature are 3.7%, 3.8%, and 0.6%, respectively, which verifies this method to calculate parameters of Gaussian beam. In addition, we also find that the shear amount has influence on the reconstructed wavefront. It is showed that as the amount of shear increases from 20 pixels to 90 pixels, the peak-to-valley (P-V) values and RMS values both gradually decrease with a nonlinear relationship, which could be used to decrease the error of wavefront reconstruction further.

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