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.