Fourier Single-pixel Imaging Based On Arbitrary N-step Phase-shifting Structured Light

Single-pixel imaging is a new imaging technique that uses a bucket detector(single-pixel detector)without spatial resolution to measure the intensity information of the target object,and then reconstructs the image of the object through correlation measurement or phase-shifting differential measurement.In recent years,Fourier single-pixel imaging has revealed potential applications in the fields of non-visible band imaging and three-dimensional imaging,and has attracted the attention of researchers.Four-step phase-shifting structured light has been mainly utilized in previous studies.To promote the universality and application of this imaging technique,this paper expands the implementation of Fourier single-pixel imaging from four-step phase-shifting to arbitrary n-step phase-shifting,and investigates Fourier single-pixel amplitude and phase imaging with n-step phase-shifting structured light.The specific results are as follows:According to the essence of Fourier transform,four strategies for realizing Fourier single-pixel amplitude imaging based on arbitrary n-step phase-shifting structured light are proposed,and the general theoretical expressions are obtained.Numerical simulations and optical experimental verification are carried out with binary and grayscaled pictures acting as amplitude objects,respectively.The results show that Fourier single-pixel amplitude imaging can be realized with arbitrary n-step phaseshifting structured light.The peak signal-to-noise ratios of reconstructed images are different in different phase-shifting strategies due to the different abilities in these strategies to balance noise.In particular,it should be noted that in the fourth strategy,the higher-step phase shifting Fourier single-pixel imaging can be performed with lower-step phase-shifting differential measurement.These results could provide a path for solving the contradiction between the quality and speed of the image,and expand the universality and application of Fourier single-pixel imaging.Based on interference and holography,the strategy and general theoretical expression of Fourier single-pixel phase imaging with n-step phase-shifting structured light are presented,and the numerical simulation experiments are carried out with epidermal cells and cameraman as phase object.The results show that Fourier singlepixel phase imaging can be achieved with n-step phase-shifting structured light.On this basis,this paper further studies the Fourier single-pixel phase imaging of the fusion watermark,and gives two methods to fuse the watermark.Moreover,the results are verified by numerical simulation with onion epidermal cells as the host phase object and local onion epidermal cells as the watermark,which show that the local calibrated cells can be quickly distinguished form the reconstructed image.The results could be helpful to the application of Fourier single-pixel imaging in biomedical imaging.