Modeling off-axis diffraction with the least-sampling angular spectrum method

Accurately yet efficiently simulating off-axis diffraction is vital to design large-scale computational optics, but existing rigid sampling and modeling schemes fail to address this. Herein, we establish a universal least-sampling angular spectrum method that enables efficient off-axis diffraction modeling with high accuracy. Specifically, by employing the Fourier transform’s shifting property to convert off-axis diffraction to quasi-on-axis, and by linking the angular spectrum to the transfer function, essential sampling requirements can be thoroughly optimized and adaptively determined across computation. Leveraging a flexible matrix-based Fourier transform, we demonstrate the off-axis point spread function of exemplary coded-aperture imaging systems. For the first time, to our knowledge, a significant speed boost of around 36× over the state of the art at 20° is demonstrated, and so is the viability of computing ultra-large angles such as 35° within seconds on a commercial computer. The applicability to high-frequency modulation is further investigated.