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Wavefront reconstruction from two lateral shearing interferograms with Hilbert–Huang transform in monitoring of high power laser beam quality

The quality of an optical system forming a laser beam can be characterized through the measurement of aberrations in a deformed wavefront. The wavefront can be evaluated interferometrically in lateral shearing interferometer in which a coherent wavefront under test interferes with a laterally sheared wavefront copy. The resulted fringe pattern contain information on the first derivative of wavefront shape, according to direction of the shear. In this contribution we discuss the challenge related to wavefront shape reconstruction based on two lateral shearing interferograms from orthogonal shear directions. In case of not complicated wavefront the directional phase integration can be applied. Proposed method of reconstruction entirely omits this complicated process. It is based on calculations of the coefficients of Zernike polynomials from derivatives of wavefront shape and they are used for wavefront shape reconstruction. The utility of the proposed approach is tested numerically and demonstrated with characterization of aberrated wavefronts. Moreover, the simple configuration of lateral shear interferometer with two separated lateral shearing direction is introduced with context of monitoring of high power laser beam. At the end of the data analysis we apply an method for extracting the Zernike coefficients. The accuracy of implemented method is verified by characterization of generated spherical and highly aberrated wavefront. An error analysis indicates optimal conditions of measurements and proves high accuracy of developed method.