Two new iterative algorithms to be used to reconstruct a tested wavefront from its cyclic radial shearing (CRS) fringe pattern are
proposed. First, the phase difference (PHD) in the common area of the contracted and expanded tested wavefront are determined directly from
the CRS fringe pattern of the tested wavefront by the Fourier transform method. Then, according to the PHD, the tested wavefront is reconstructed
precisely by the two iterative algorithms. The numerical simulation of the reconstruction of a tested wavefront with distortion is implemented,
showing that the wavefront reconstruction can be performed precisely by these algorithms with root mean square (rms)??/20. A CRS
interferometer is constructed with a radial shearing ratio of s51:1.4 and is used to test a distorted wavefront with a one-step phase jump successfully.
The results of numerical simulation and optical testing show that with these algorithms, the CRS interferometric technique can be
easily used to make the evaluation of the optical component quality as well as testing of the wavefront distortion of a high-power laser. Finally,
the convergence of two algorithms is also analyzed.