We propose a technique in which intensity images are reconstructed from a digital hologram to provide inputs for the transport-of-intensity equation for unwrapped phase recovery. By doing this, we avoid shifting of the sample or the camera in the experiment, a method commonly employed while using the method of transport-of-intensity equation for phase retrieval. Computer simulations as well as experimental results have been demonstrated to verify the effectiveness of the proposed idea. The underlying numerical technique can also be viewed as an alternative to existing phase-unwrapping algorithms.

A finite difference method is proposed for solving the transport of intensity equation. Simulation results show that although slower than fast Fourier transform (FFT)-based methods, finite difference methods are able to reconstruct the phase with better accuracy due to relaxed assumptions for solving the transport of intensity equation relative to FFT methods. Finite difference methods are also more flexible than FFT methods in dealing with different boundary conditions.

Digital holographic tomography by a few projections is developed. A section of fiber with symmetrical structure and a plaster head model with nonsymmetrical structure are used as test samples. Both simulation analysis and experimental results are analyzed. Simulation analysis shows that the weighted coefficientwij and the relaxation factor λ affect evidently the quality of the reconstructed image, in addition, the relaxation factor λ also influences the computer speed. Thus the weighted coefficient wij is evaluated by using a nonlinear method and the relaxation factor λ is selected appropriately by comparing several simulation reconstructions. Experimental results reveal the feasibility and the availability of digital holographic tomography by a few projections for symmetrical samples and nonsymmetrical one. In the next work, the real time digital holographic tomography based on three projections and single hologram will be developed to reconstruct the multi-refractive index of biological samples.

With this study, we propose a method to image the tip crack on transparent materials by using digital holographic microscopy. More specifically, an optical system based on Mach–Zehnder interference along with an inverted microscopy (Olympus CKX53) was used to image the tip crack of Dammar Varnish transparent material under thermal excitation. A series of holograms were captured and reconstructed for the observation of the changes of the tip crack. The reconstructed holograms were also compared temporally to compute the temporal changes, showing the crack propagation phenomena. Results show that the Dammar Varnish is sensitive to the ambient temperature. Our research demonstrates that digital holographic microscopy is a promising technique for the detection of the fine tip crack and propagation in transparent materials.