Single-pixel phase imaging via a complex-valued Zernike basis

Single-pixel phase imaging (SPPI) utilizes a single-pixel detector combined with interferometry to capture phase information of an unknown field. However, to reconstruct an M × N image, normally M × N modulations and detections are required, leading to a long imaging time for SPPI. Here, a complex-valued Zernike basis SPPI (Zernike-SPPI) is proposed to achieve phase reconstruction at as high quality as possible with a very low sampling ratio. Simulations and experiments demonstrate that Zernike-SPPI achieves better imaging quality at a sampling ratio of less than 10% compared to the state-of-the-art SPPI techniques based on Hadamard basis. This means Zernike-SPPI can obtain a high-quality phase image with less imaging time. This work offers a solution to achieve fast SPPI while guaranteeing quality phase reconstruction as high as possible.