Junchang Li

Digital holographic reconstruction of large objects using a convolution approach and adjustable magnification

We present a numerical method for reconstructing large objects using a convolution method with an adjustable magnification. The method is based on the image locations and magnification relations of holography when the illuminating beam is a spherical wavefront. A modified version of the angular spectrum transfer function is proposed that allows the filtering in the spatial frequency spectrum. Experimental results confirm the suitability of the proposed method.

Real-time three-sensitivity measurements based on three-color digital Fresnel holographic interferometry

This Letter presents a method for real-time 3D measurements based on three-color digital holographic interferometry. The optical setup is considerably simplified, since the reference beams are combined into a unique beam. A convolution algorithm allows the three monochrome images to be superposed to provide simultaneous full-field 3D measurements. Experimental results confirm the suitability of the proposed method.

Method of digital holographic recording and reconstruction using a stacked color image sensor

We discuss a method to record and reconstruct color holograms by using a stack of photodiode sensors associated to a one-way reference beam. The reconstruction algorithm follows a convolution strategy in which a transverse magnification leads to the full reconstruction of the object in the reconstructed horizon. The transverse magnification of the object depends on the curvature of the reference wave. Analysis of the spatial resolution indicates that it is linked to the transversal magnification but that no extra information is gained or lost in the process. Experimental results confirm the validity of the proposed approach for two-color digital holography. The error due to spectral mixing is investigated and found to be quite irrelevant compared to the range of the phase measurement.

Spatial bandwidth extended reconstruction for digital color Fresnel holograms

This paper presents a reconstruction algorithm based on the convolution formula of diffraction which uses the Fresnel impulse response of free space propagation. The bandwidth of the reconstructing convolution kernel is extended to the one of the object in order to allow the direct reconstruction of objects with size quite larger than the recording area. The spatial bandwidth extension is made possible by the use of a numerical spherical wave as a virtual reconstructing wave, thus modifying the virtual reconstruction distance and increasing the kernel bandwidth. Experimental results confirm the suitability of the proposed method in the case of the simultaneous recording of two-color digital holograms by using a spatial color multiplexing scheme.

Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method

The axicon-based-Bessel-Gauss resonator (ABGR) has been proposed for the production of Bessel-Gauss beams. To analyze eigenfields of the ABGR with a plane or spherical output coupler, we present and demonstrate the transfer-matrix method. Since the method is slow to converge to eigenmodes of the ABGR by use of the Fox and Li iterative algorithm, in this paper the Huygens-Fresnel diffraction integral equations associated with ray matrices are converted into finite-sum matrix equations, and mode-fields and corresponding losses are described as eigenvectors and eigenvalues of a transfer matrix according to the self-reproducing principle of the laser field. By solving the transfer matrix for eigenvectors and eigenvalues, we obtain field distributions and losses of the dominant eigenmodes. Moreover, eigenfields across arbitrary interfaces between the axicon and the output coupler, and the propagation of output beams, are simulated by using the fast-Fourier transform (FFT). The calculation results reveal that because of the ABGRs poor transverse mode discrimination the ABGR should be improved to produce good-quality Bessel-Gauss beams.

Digital holographic reconstruction of a local object field using an adjustable magnification

In the research of digital holography, this paper presents a numerical method using an adjustable magnification for local object field reconstruction together with experiment verification. The method first designs a spherical wave according to the given magnification to illuminate the digital hologram, then through a Fourier transform of diffraction, it calculates the reconstructed image plane. Afterward, a filtering window is set in the image plane to extract the image of the local object field, and then the object field reached hologram plane is formed using diffractions inverse operation. Finally, the object field is reconstructed through diffractions angular spectrum theory.

Phase calibration unwrapping algorithm for phase data corrupted by strong decorrelation speckle noise

Robust phase unwrapping in the presence of high noise remains an open issue. Especially, when both noise and fringe densities are high, pre-filtering may lead to phase dislocations and smoothing that complicate even more unwrapping. In this paper an approach to deal with high noise and to unwrap successfully phase data is proposed. Taking into account influence of noise in wrapped data, a calibration method of the 1st order spatial phase derivative is proposed and an iterative approach is presented. We demonstrate that the proposed method is able to process holographic phase data corrupted by non-Gaussian speckle decorrelation noise. The algorithm is validated by realistic numerical simulations in which the fringe density and noise standard deviation is progressively increased. Comparison with other established algorithms shows that the proposed algorithm exhibits better accuracy and shorter computation time, whereas others may fail to unwrap. The proposed algorithm is applied to phase data from digital holographic metrology and the unwrapped results demonstrate its practical effectiveness. The realistic simulations and experiments demonstrate that the proposed unwrapping algorithm is robust and fast in the presence of strong speckle decorrelation noise.

Calculation of diffraction patterns on a spatial surface

An approximated formulation of the Fresnel function is put forward and is used in the approximate evaluation of the Fresnel diffraction integral. By comparing the approximate formulation with the experimental measurements and calculations in the fast Fourier transform (FFT) method of the diffraction integral, we demonstrate that the proposed method is sufficiently accurate for calculating the Fresnel diffraction. For the diffraction field calculation on a spatial surface, the calculation speed of this method is usually higher than that of the FFT method.

Robust processing of phase dislocations based on combined unwrapping and inpainting approaches

This Letter proposes a robust processing of phase dislocations to recover continuous phase maps. The approach is based on combined unwrapping and inpainting methods. Phase dislocations are determined using an estimator based on the second order phase gradient. The algorithm is validated using a realistic simulation of phase dislocations, and the phase restoration exhibits only weak errors. A comparison with other inpainting algorithms is also provided, demonstrating the suitability of the approach. The approach is applied to experimental data from off-axis digital holographic interferometry. The phase dislocation from phase data from a wake flow at Mach 0.73 are identified and processed. Excellent phase restoration can be appreciated.

Research on the recording hologram with Foveon in digital color holography

This letter presents a method for real-time three-color digital holographic interferometry based on Foveon CCD. The control mode of CCD is optimized and color aliasing is limited consumedly. The influence on color hologram becomes very little. On the whole, color aliasing is eliminated especially in the phase difference detecting. Moreover, the optical setup is considerably simplified, since the reference beams are combined into a unique beam. Experimental results confirm the suitability of the proposed method.