We numerically and experimentally demonstrate an iterative method to simultaneously reconstruct two unknown interfering wavefronts. A three-dimensional interference pattern is analyzed and then Zernike polynomials and the stochastic parallel gradient descent algorithm are used to expand and calculate wavefronts.

We investigate the determination of nonlinear refractive index n(2), based on solving the transport of intensity equation (TIE) in conjunction with a pump-probe technique. As the pump and probe beams propagate through a sample, the pump-induced refractive index variations in the sample change the phase distribution of the probe beam. Using two recorded probe intensities in TIE, this phase change is derived, and so the nonlinear refractive index n(2) is obtained. The influence of some characteristics of the pump beam and noise on the accuracy of determining n(2) is also investigated. The simulation results show that the proposed method has a good capability for determining the nonlinear refractive index of materials.

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