This article simulates a study on a phase recovery technique that combines triangular aperture illumination as a supporting constraint and partially overlapped random binary amplitude modulation. Inspired by the concept of ptychography, a random binary amplitude mask is designed with partially transparent regions that overlap each other randomly. The overlapping regions of the amplitude modulation mask impose a strong constraint on the coherence of the light field, similar to the overlap constraint in ptychography. Moreover, the redundant information brought by the overlapping binary masks can improve the reconstruction accuracy, and the triangular aperture constraint enables faster convergence in the method. Compared with the original binary amplitude modulation method, this constraint leads to higher convergence accuracy and speed in the iterative algorithm.