Study on the algorithm for improving the FFT calculation accuracy of the Richards-Wolf focusing field in the xz plane

Aiming at the error problems in the computation of the fast Fourier transform (FFT) of the traditional Richards-Wolf focusing field in the xy-plane and xz-plane, this study proposes an improved FFT integration method, which aims to improve the computational accuracy through the integration boundary correction. The method is achieved by finely adjusting the integration boundary grid sampling point and integration area, specifically adjusting the integration boundary grid sampling point to the grid centre in Algorithm 1 and to the centre of the boundary polygon in Algorithm 2. In Algorithm 3, the boundary polygon is divided into triangles and the centres of the triangles are taken as the sampling points, and the product of the function value and the corresponding area at these points is calculated as the contribution to the FFT integration. Simulation results show that compared with the traditional FFT algorithm, the improved FFT algorithm significantly improves the computational accuracy while reducing the number of sampling points required, effectively reducing the computation time and improving the computational efficiency. This result fully confirms the effectiveness of the FFT algorithm based on the integral boundary correction in optimising the computational accuracy of the RichardsWolf focusing field FFT, which provides new powerful tools and methods for the research in the fields of holographic optical tweezers and the analysis of the optical field distribution near the focusing plane, and it is expected to push forward the technological advancement and the application development of these fields.