Improved theoretical model for differential wavefront sensing based on complex Gaussian decomposition with hard-edge apertures

In differential wavefront sensing (DWS), increasing the size of quadrant photodiodes (QPDs) effectively enhances angular measurement sensitivity and accuracy. However, existing erf-based models introduce significant theoretical deviations due to integral approximations, especially when simulating larger QPD sizes. We propose an improved model based on complex Gaussian decomposition of hard-edge apertures. This model replaces the erf-based integration with a window function constructed from complex Gaussian functions, thereby reducing approximation deviations. By optimizing the complex Gaussian function parameters, the model further improves integration accuracy and phase calculation precision. Simulations and experiments show a two-order-of-magnitude improvement in phase accuracy, confirming its effectiveness for larger QPDs and providing more precise guidance for DWS system design.