Image Formation and Resolution in Spatially Variant Coherent Imaging Systems.

Since the invention of lasers, coherent imaging has been widely employed in digital holographic microscopy. Improving the resolution of the image field remains a key challenge for achieving high-precision measurements. However, due to the high coherence of the laser, the resolution of the wavefront at the image plane depends not only on the radius of curvature of the illumination wavefront, but also on the observation position and direction. Existing theoretical approaches, which provide only approximate calculations of the amplitude distribution of the image field, are insufficient for practical applications. In this study, a theoretical framework for calculating the complex wavefield at the image plane is established, and analytical expressions describing the spectral distribution as functions of observation position and direction are derived. The proposed theory is experimentally validated using digital holographic microscopy. The results show good agreement between theory and experiment, demonstrating that the proposed approach accurately characterizes the spectral and resolution variations in the image field. These findings provide a solid theoretical foundation for the optimal design of digital holographic microscopy systems and illumination wavefields.