Application of optical diffraction method in designing phase plates

Continuous phase plate（CPP）,which has a function of beam shaping in laser systems,is one kind of important diffractive optics.Based on the Fourier transform of the Gerchberg-Saxton（G-S） algorithm for designing CPP,we proposed an optical diffraction method according to the real system conditions.A thin lens can complete the Fourier transform of the input signal and the inverse propagation of light can be implemented in a program.Using both of the two functions can realize the iteration process to calculate the near-field distribution of light and the far-field repeatedly,which is similar to the G-S algorithm.The results show that using the optical diffraction method can design a CPP for a complicated laser system,and make the CPP have abilities of beam shaping and phase compensation for the phase aberration of the system.The method can improve the adaptation of the phase plate in systems with phase aberrations.

Centroids analysis for circle of confusion in reverse Hartmann test

The point spread function（PSF） is investigated in order to study the centroids algorithm in a reverse Hartmann test（RHT） system. Instead of the diffractive Airy disk in previous researches, the intensity of PSF behaves as a circle of confusion（CoC） and is evaluated in terms of the Lommel function in this paper. The fitting of a single spot with the Gaussian profile to identify its centroid forms the basis of the proposed centroid algorithm. In the implementation process, gray compensation is performed to obtain an intensity distribution in the form of a two-dimensional（2D） Gauss function while the center of the peak is derived as a centroid value. The segmental fringe is also fitted row by row with the one-dimensional（1D） Gauss function and reconstituted by averaged parameter values. The condition used for the proposed method is determined by the strength of linear dependence evaluated by Pearson＇s correlation coefficient between profiles of Airy disk and CoC. The accuracies of CoC fitting and centroid computation are theoretically and experimentally demonstrated by simulation and RHTs. The simulation results show that when the correlation coefficient value is more than 0.9999, the proposed centroid algorithm reduces the root-mean-square error（RMSE） by nearly one order of magnitude, thus achieving an accuracy of - 0.01 pixel or better performance in experiment. In addition, the 2D and 1D Gaussian fittings for the segmental fringe achieve almost the same centroid results, which further confirm the feasibility and advantage of the theory and method.