Theoretical analysis of spectrum reconstruction imaging using single-pixel detection

As a novel imaging method, single-pixel imaging based on spectrum reconstruction is interesting. To date, however, there has not yet been a theory that can analyze the method in detail. In order to obtain a comprehensive understanding of the single-pixel imaging technique, a detailed theoretical analysis is proposed. Firstly, in the presented imaging theory, we analyze the effects of several factors involved in the imaging process on imaging reconstruction, including the direct detection, namely, the back scattering light from the imaged object is received by a detector; indirect detection, namely, the back scattering light is received after undergoing the diffuse reflections by multiple diffusing surfaces in proper sequence; multi-channel detection, namely, the scattering light is together detected after experiencing multiple diffuse reflections in proper sequence along multiple different paths; the size and location of the single-pixel detector. The theoretical results show that whether it is direct detection or indirect detection and whether it is single-channel detection or multi-channel detection, the above imaging method is valid as long as the scattering light can be received by the detector, and the obtained results are also in accord with the existing experimental results. Since the single-pixel detector is treated as a component of many point detectors due to its practical size, the effect of the single-pixel detector size on image reconstruction is equivalent to the integration of reconstructed images from multiple point detectors at different locations. Secondly, the spectrum reconstruction based on a three-step phase shift technique is also derived to increase the image reconstruction speed. Finally, the experimental results of the imaging reconstruction of an object, whose surface reflectivity is uniform, are demonstrated.