In this paper, a layered method based on focal depth is proposed for the fast generation of computational holograms. The method layers objects with focal depth as spacing and approximates triangles on the object as projections on the layers based on the physical properties of the focal depth to simplify the computation. Finally, the diffraction distributions of all layers are calculated via angular spectral diffraction and superimposed to obtain the hologram. The proposed method has been proven to be about 20 times faster on a CPU than the analytical polygon-based method. A hologram containing tens of thousands of triangles can be computed on a GPU in a fraction of a second. In addition, this method makes it easy to attach complex textures, which is difficult with polygon-based analysis methods. Finally, holograms of objects with complex textures were generated, and the three-dimensionality of these holograms was confirmed by numerical and optical reconstruction.

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 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.

Weld stability is directly related to the safety and reliability of engineering, and continuous improvement of its detection technology has great research significance. This paper presents a novel method for weld stability detection based on color digital holography. A color digital holography optical path was designed to capture the holograms of welds under varying loads. Several common denoising algorithms were used to deal with speckle noise in the wrapped phase, among which the 4-f optical simulation integrated cycle-consistent generative adversarial network (4f-CycleGAN) denoising algorithm based on deep learning was more suitable for the color digital holographic detection system. The three-dimensional deformation fields of three samples (lap-jointed, butt-jointed, and defective butt-jointed aluminum alloy plates) under different loads were calculated. The center profile of the deformation field in the direction of load and holographic reconstruction images are used to determine the position of the weld. The coefficient of variation near the weld was used to evaluate the weld stability. The coefficient of variation for lap-jointed, butt-jointed and defective butt-jointed plates are 0.0335 (<0.36, good stability), 0.1240 (0.36, poor stability), respectively. The research results of this paper provide a new strategy for detecting weld stability.

In holographic three-dimensional (3D) display, phase-only spatial light modulators (SLMs) can only accept pure phase modulation signals, often leading to amplitude distortion in the reconstructed image and inaccurate object reconstruction. This paper presents a new modulating phase encoding method with amplitude compensation. Based on the imaging characteristics of phase digital holograms, the object light amplitude variation is extended to the nonlinear region of the first-order Bessel function to maximize the intensity of the reconstructed 3D image. The amplitude distortion of the reconstructed image is effectively eliminated by pre-distortion treatment of the light amplitude. Numerical simulations and optical experiments validate the presented method.