Improved wavefront reconstruction algorithm from slope measurements

In this paper, we propose a wavefront reconstruction algorithm from slope measurements based on a zonal method. In this algorithm, the slope measurement sampling geometry used is the Southwell geometry, in which the phase values and the slope data are measured at the same nodes. The proposed algorithm estimates the phase value at a node point using the slope measurements of eight points around the node, as doing so is believed to result in better accuracy with regard to the wavefront. For optimization of the processing time, a successive over-relaxation method is applied to iteration loops. We use a trial-and-error method to determine the best relaxation factor for each type of wavefront in order to optimize the iteration time and, thus, the processing time of the algorithm. Specifically, for a circularly symmetric wavefront, the convergence rate of the algorithm can be improved by using the result of a Fourier Transform as an initial value for the iteration. Various simulations are presented to demonstrate the improvements realized when using the proposed algorithm. Several experimental measurements of deflectometry are also processed by using the proposed algorithm.