With the development of digital holography, the accuracy requirements for the reconstruction phase are becoming increasingly high. The transfer function of the double fast transform (D-FFT) algorithm is distorted when the diffraction distance is larger than the criterion distance ${\mathrm{d}}_{\mathrm{t}}$, which reduces the accuracy of solving the phase. In this paper, the Fresnel diffraction integration algorithm is improved by using the low-pass Tukey window to obtain more accurate reconstructed phases. The improved algorithm is called the D-FFT (Tukey) algorithm. The D-FFT (Tukey) algorithm adjusts the degree of edge smoothing of the Tukey window, using the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) to remove the ringing effect and obtain a more accurate reconstructed phase. In a simulation of USAF1951, the longitudinal resolution of the reconstructed phase obtained by D-FFT (Tukey) reached 1.5 $\mathsf{\mu }\mathrm{m}$, which was lower than the 3 $\mathsf{\mu }\mathrm{m}$ obtained by the T-FFT algorithm. The results of Fresnel holography experiments on lung cancer cell slices also demonstrated that the phase quality obtained by the D-FFT (Tukey) algorithm was superior to that of the T-FFT algorithm. D-FFT (Tukey) algorithm has potential applications in phase correction, structured illumination digital holographic microscopy, and microscopic digital holography.

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.