Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting

Tong Ling; Dong Liu; Lei Sun; Yongying Yang; Zhongtao Cheng

doi:10.1117/12.2023621

7 September 2013 Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting

Tong Ling, Dong Liu, Lei Sun, Yongying Yang, Zhongtao Cheng

Author Affiliations +

Proceedings Volume 8838, Optical Manufacturing and Testing X; 88380J (2013) https://doi.org/10.1117/12.2023621
Event: SPIE Optical Engineering + Applications, 2013, San Diego, California, United States

Abstract

In experiments of inertial confinement fusion (ICF), the thickness uniformity of capsule and the density uniformity of deuterium-tritium (DT) ice are both key to successful ignition, while the cross-grating lateral shearing interferometer (CGLSI), which is accurate and insensitive to disturbance, can be employed to test the density distribution of DT ice precisely. In this paper, a wavefront retrieval method for CGLSI based on differential Zernike polynomial fitting is presented. Fast Fourier Transform technique (FFT) is employed to get the frequency spectrum of the interferogram obtained by CGLSI. By performing Inverse Fast Fourier Transform (IFFT) of the +1 order spectrum in both X and Y directions, it is possible to extract shearing wavefronts from the interferogram in both two orthogonal directions. Utilizing differential Zernike polynomial fitting method, we are capable of integrating two shearing wavefronts in both X and Y directions together and retrieving the wavefront under testing. In the process of solving Zernike coefficients, the characteristics of differential Zernike orthogonal polynomials should be taken fully into account in mathematical modeling. To avoid the retrieval error introduced due to matrix mutation, the determination of discrete grid number and aperture shape must be in line with the theory that Zernike polynomials are orthogonal over a unit circle as well. The result of simulation analysis shows that the wavefront retrieval method for CGLSI based on differential Zernike polynomial fitting is correct and accurate, and the root-mean-square error of this method is less than λ/15.

Citation Download Citation

Tong Ling, Dong Liu, Lei Sun, Yongying Yang, and Zhongtao Cheng "Wavefront retrieval for cross-grating lateral shearing interferometer based on differential Zernike polynomial fitting", Proc. SPIE 8838, Optical Manufacturing and Testing X, 88380J (7 September 2013); https://doi.org/10.1117/12.2023621

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