Scalar far-field diffraction modelling using nonuniform fast Fourier transform for diffractive optical phase elements design

Due to their advantages of compact geometries and lightweight, diffractive optical elements (DOEs) are attractive in various applications such as sensing, imaging and holographic display. When designing DOEs based on algorithms, a diffraction model is required to trace the diffracted light propagation and to predict the performance. To have more precise diffraction field tracing and optical performance simulation, different diffraction models have been proposed and developed. However, they are limited in diffraction angles or still suffer from serious aberrations within the nonparaxial region in the far-field, which are not desired for the aforementioned applications. In this work, we developed an optimized diffraction modelling method using a nonuniform fast Fourier transform (NUFFT) to minimize the aberrations in the nonparaxial diffraction area in the far field for DOE design. The simulation result shows that the imaging distortion of DOE designed using iterative Fourier transform algorithm (IFTA) with integration of our proposed diffraction modelling method was effectively optimized. Moreover, the designed DOE has a diffraction efficiency of 90.73% and a root mean square error (RMSE) of 0.4817. It exhibits 7.17% higher in diffraction efficiency and 8.59% smaller in RMSE (0.0453), respectively, compared to DOE designed with a diffraction modelling method by directly taking nonuniform diffraction sampling points that are mapped from the diffracted wavefronts surface on the output plane, which has a diffraction efficiency of 83.56% and a RMSE of 0.5270. Furthermore, a compensation matrix was introduced into the developed diffraction model to further improve the imaging quality of designed DOE. A further increase of diffraction efficiency by 0.18% and a decrease of RMSE by 12.43% (0.0599) were achieved. In addition, we also utilized the proposed approach for DOE design in the case of off-axis diffraction, and diffraction fields with an incident illumination angle up to 30° can be reconstructed and simulated.