Single-pixel non-imaging object authentication using Fourier spectrum coefficients

Single-pixel imaging (SPI) techniques acquire one-dimensional (1-D) intensities from different projections of the object. Applying SPI to object authentication with optical encryption has the advantages of high security and easy transmission. However, previous image-based schemes have the problem of taking long time to reconstruct image from a large number of measurements. What's more, perfect reconstruction is not necessary for object authentication. We propose an imageless object authentication strategy using single-pixel detection and sub-Nyquist sampling of Fourier spectrum coefficients. The method consists of three steps: encoding, four-step phase-shifting and authentication. First, we conduct SPI to encode image to 1-D intensities with Fourier basis patterns. Second, we use four-step phase-shifting method to get the Fourier transform of the object (i.e., Fourier spectrum) instead of image reconstruction. Third, calculate the correlation extent between the object and the reference image and then visualize it as a map. If there is only one area that is much higher than other places in the map, the similarity between the image and the reference is high. We have verified the effectiveness of this method by adding noise in simulation. When adding noise or performing at low sampling rate, our scheme still realizes accurate authentication.