2023/03/06 by Youfa Li, Li, Youfa, Shengli Fan +3
Computer Science · Physics and Astronomy · #42C40 #94A12 #Advanced X-ray Imaging Techniques #Digital Holography and Microscopy #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Optical measurement and interference techniques
paper · pdf · doi:10.48550/arxiv.2303.02839
openalex publication_date 2023/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The phase-shifting digital holography (PSDH) is a widely used approach for recovering signals by their interference (with reference waves) intensity measurements. Such measurements are traditionally from multiple shots (corresponding to multiple reference waves). However, the imaging of dynamic signals requires a single-shot PSDH approach, namely, such an approach depends only on the intensity measurements from the interference with a single reference wave. In this paper, based on the uniform admissibility of plane (or spherical) reference wave and the interference intensity-based approximation to quasi-interference intensity, the nonnegative refinable function is applied to establish the single-shot PSDH in Sobolev space. Our approach is conducted by the intensity measurements from the interference of the signal with a single reference wave. The main results imply that the approximation version from such a single-shot approach converges exponentially to the signal as the level increases. Moreover, like the transport of intensity equation (TIE), our results can be interpreted from the perspective of intensity difference.