Fourier single-pixel imaging using fewer illumination patterns

Single-pixel imaging (SPI), which is generally based on computational imaging, has the advantages of a wide bandwidth and the ability to image objects beyond the visual field. However, the major challenge in developing SPI is the large number of illumination patterns that are required. Unlike traditional SPI that relies on random measurement patterns, the SPI method proposed in this letter involves a two-step phase shift that reduces greatly the required number of illumination patterns. Theoretical analysis shows that 6724 illumination patterns are required to reconstruct a 128 × 128-pixel image whose peak signal-to-noise ratio exceeds 30, and these can be projected in 0.3362 s with a digital micromirror device working at full speed. Compared to SPI with a four-step phase shift, half the number of illumination patterns are required. Verification experiments show that the reconstructed images can be obtained even at a sampling ratio of 20%. The proposed SPI with a two-step phase shift is an effective means of requiring fewer illumination patterns and has great potential in dynamic detection.