The wavefront reconstruction of the preconditioned conjugate-gradient method and the Fourier transform method in the lateral shearing interferometry are discussed for their feasibility and accuracy in this paper. The numerical simulation study on the accuracy of both the wavefront reconstruction method under ideal situation and under the simulated noisy situation is also introduced. Simulation experiments show that the preconditioned conjugate-gradient method has better anti-noise performance, and provides higher precision for discontinuous phase wavefront reconstruction. The two-grating lateral shearing interference experiment is carried out to verify the simulated results based on both the preconditioned conjugate-gradient method and the Fourier transform method.
The two-dimensional wavefront reconstruction method based on double-shearing and least squares fitting is proposed in this paper. Four one-dimensional phase estimates of the measured wavefront, which correspond to the two shears and the two orthogonal directions, could be calculated from the differential phase, which solves the problem of the missing spectrum, and then by using the least squares method the two-dimensional wavefront reconstruction could be done. The numerical simulations of the proposed algorithm are carried out to verify the feasibility of this method. The influence of noise generated from different shear amount and different intensity on the accuracy of the reconstruction is studied and compared with the results from the algorithm based on single-shearing and least squares fitting. Finally, a two-grating lateral shearing interference experiment is carried out to verify the wavefront reconstruction algorithm based on doubleshearing and least squares fitting.
This paper introduces a new way of two-dimensional wavefront reconstruction based on the Fourier modal method. Expending the target wavefront by using Fourier series, calculating the expansion coefficient based on the differential phase measured from the experiment, and fitting the coefficients at the missing points by averaging adjacent values, the target wavefront could be reconstructed eventually by using inverse Fourier transform on the expansion coefficients. The paper also introduces our numerical simulation study on the precisions of both the wavefront reconstruction under ideal situation and under the situation with simulated noise respectively. Corresponding verification experiment for the two-dimensional wavefront reconstruction based on the Fourier modal method is also done by using a two-grating lateral shearing interferometry system, with the 3D profile of the sample obtained.