Since the advent of lasers, coherent optical imaging has found significant applications in optical precision measurement. Among these, digital holography is a key research area. In detection studies, accurately obtaining the amplitude and phase of the object being measured through digital holographic image reconstruction is a critical research task. However, current coherent optical imaging formulas can only calculate the amplitude distribution of the image light field when the object size is smaller than one-quarter of the diameter of the optical system’s entrance pupil, making it difficult to meet the needs of applied research. This paper derives formulas that are not restricted by the size of the incident pupil and can calculate the amplitude and phase distributions of the image light field. Based on the mathematical analysis of the formulas, this paper introduces a technique for obtaining the amplitude and phase distribution of detected objects and provides experimental evidence.

In the field of digital holographic microscopy (DHM), the microscope objective and the optical path of the system invariably introduce additional phase distortions. These distortions obscure the true phase information of the sample, thus compromising the accuracy of quantitative measurements. To address this issue, this paper proposes an accurate phase compensation method based on the generalized transfer function. By integrating the theory of image-plane diffraction-limited coherent imaging, our method precisely extracts the generalized transfer function of the imaging system through a single holographic recording of the “object-free field” and numerical reconstruction of the ideal wavefront, thereby achieving deterministic elimination of the wavefront aberrations to be measured. The experimental results demonstrate that the proposed method achieves significantly higher accuracy in three-dimensional topography detection compared with the conventional double-exposure technique. The nominal relative deviations from the corresponding bright-field optical microscopy measurements for 50 µm silica microspheres, 20 µm polystyrene microspheres, and mouse red blood cells were reduced to 0.67%, 1.4%, and 1.7%, respectively; compared with the double-exposure technique, these deviations were reduced by 70.61%, 30%, and 43.3%, respectively. Requiring only a single sample hologram after a one-time object-free calibration for high-fidelity wavefield reconstruction, this method effectively circumvents complex iterative computations and residual higher-order aberrations, thereby providing an efficient approach for high-precision dynamic phase compensation in digital holographic microscopy. Consequently, it holds significant application potential in fields such as real-time monitoring of living cells and quantitative characterization of micro- and nanostructures.