Retained accuracy with reduced precision in wave propagation modeling

Wave propagation modeling is fundamental to optics, facilitating diverse applications including lens design, computational imaging, and optical computing. However, existing approaches encounter a critical trade-off between computational accuracy and efficiency, primarily limited by numerical precision constraints. In this study, we establish the explicit numerical limits in wave propagation modeling and demonstrate that accurate simulations are achievable with reduced precision. Our analysis reveals that the limited significant decimal digits and dynamic range of floating-point arithmetic compromise phase and amplitude representation accuracy, thereby constraining the dimensions and space-bandwidth product of optical systems that can be reliably modeled. To address this challenge, we introduce a differentiable modeling scheme that maintains accurate phase representation through wrapping from double precision and appropriately prescales the amplitude to ensure the integral result remains within the representable dynamic range. We validate our approach by simulating point spread functions of optical systems, solving phase retrieval problems, and synthesizing holograms for light shaping. Our method achieves, on average, ∼20× acceleration in diffraction modeling while retaining accuracy comparable to double-precision implementations. Optical experiments further demonstrate our approach’s effectiveness. Specifically, our method successfully reconstructs complex amplitudes of laser beams from coded measurements and designs phase-only holograms for desired diffraction patterns. We envision that this technique will advance research in computational optics with enhanced computational efficiency.