Wave-function reconstruction for large phase gradients based on optical differentiation

The wave function is the cornerstone of quantum theory, and various techniques have been proposed for its direct measurement. The reconstruction of the wave function can be achieved by utilizing the real and imaginary components of momentum weak value, which correspond to amplitude and phase differentiation, respectively. However, these methods are limited in their applicability to wave functions with large phase gradients due to the weak coupling condition, which is a fundamental constraint. In this paper, we propose a method for reconstructing wave functions with large phase gradients based on optical differentiation through weak measurement. We have developed a more generalized theory of phase differentiation and implemented a common optical path and fast measurement for wave functions with large phase gradients. The experimental detection of wave functions with varying phase gradients has validated the reliability of our method. This work expands the range of applications for weak measurement while retaining its high resolution and sensitivity advantages, particularly in the field of wavefront sensing.