Removal of residual images in parallel phase-shifting digital holography

Parallel phase-shifting digital holography (PPSDH) is a technique of single-shot phase-shifting digital holography. We found that there are two problems with this technique. (1) Some extraneous noises caused by the intensity unevenness of the reference wave become slightly superimposed on the object image. (2) The conjugate image cannot be completely removed. This is because the object wave causes the phase-shift error by illuminating an image sensor with a large incident angle. To solve these problems, we propose an algorithm for removing residual 0th-order diffraction and conjugate images in PPSDH. In the proposed algorithm, we modified phase-shifting interferometry in order to work through the unevenness of the intensity distribution and applied the Fourier transform technique to PPSDH to remove the residual conjugate image. The effectiveness of the proposed algorithm was experimentally verified.     

High-speed phase imaging by parallel phase-shifting digital holography

Parallel phase-shifting digital holography can obtain three-dimensional information of a dynamically moving object with high accuracy by using space-division multiplexing of multiple holograms required for phase-shifting interferometry. We demonstrated high-speed parallel phase-shifting digital holography and obtained images of the phase variation of air caused by a compressed gas flow sprayed from a nozzle. In particular, we found the interesting phenomenon of periodic phase distributions. Reconstructed images were obtained at frame rates of 20,000 and 180,000 frames per second.     

相移数字全息子图拼接研究

 将全息图拼接技术应用到相移数字全息术中,改善再现像的质量。用全息图强度相关原理进行全息图拼接,再通过标准四步算法对拼接后的全息图进行运算,恢复原始物光。作为对比,对没有拼接的全息图进行了同样的操作。计算机模拟实验证明该全息图拼接技术可明显提高再现像的质量。同时,通过对光学实验获得的全息图进行零填充和拼接对比研究证明,前者只能提高系统成像的细节显示能力,后者能够提高再现像的分辨率和视场大小。     

Surface contouring by phase-shifting digital holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed object phases due to the tilt of object illumination. Surface height from a reference plane is directly obtained from the phase change. Its sensitivity depends on the tilt angle as well as on the initial incident angle. By proper selection of the angles we can derive surface height without phase unwrapping. The sensitivity can be enhanced by increasing the tilt angle. Then we need phase unwrapping that is sensitive to noise due to laser speckles in the reconstructed images. This noise could be suppressed by selecting phase values at points of the maximum product of amplitudes before and after the illumination change in the course of data reduction from 1024×1024 to 512×512 and by selecting paths for phase unwrapping by looking for the intensity maximum. The observed height resolution is 20 μm. Effects of numerical focusing have also been investigated. The present method has the same sensitivity as the fringe projection method, but it has larger measurement depth and is also applicable to the deformation measurement with the same arrangement.     

Three-dimensional microscopy with phase-shifting digital holography

We applied phase-shifting digital holography to microscopy by deriving the complex amplitude of light scattered from microscopic three-dimensional objects through a microscope objective by video camera recording, phase-shifting analysis, and computer reconstruction. This method requires no mechanical movement and provides a flexible display and quantitative evaluation of the reconstructed images. A theory of image formation and experimental verification with specimens are described.     

One-shot in-line digital holography based Hilbert phase-shifting

A novel one-shot in-line digital holography based on Hilbert phase-shifting is proposed. By weakening the ratio of object wave to reference wave and applying natural logarithmized operation on the in-line digital hologram, the real part of object wave can be well extracted. Then utilizing Hilbert transform to digitally realize 7r/2-phase shift, which would make it possible to reconstruct the object wavefront from a single-exposure in-line digital hologram. Preliminary experimental results are presented to confirm the proposed method. This technique can be used for real time imaging or monitoring moving objects.     

Quantitative detection and compensation of phase-shifting error in two-step phase-shifting digital holography

Phase-shifting digital holographic technique is a powerful tool for the measurement of various physical parameters, such as object deformation and liquid or cell’s refractive index change. However, for an accurate measurement, phase-shifting error in the reference wave path is still a major issue. In this paper, three novel and simple algorithms are proposed to quantitatively detect and correct phase-shifting error for a pure phase object in two-step phase-shifting digital holography. Influence of phase-shifting error is illustrated, and the effectiveness of the proposed algorithms is demonstrated by numerical simulation results.     

Parallel two-step phase-shifting digital holography using polarization

We propose an optical implementation of a parallel two-step phase-shifting digital holography that utilizes a polarization technique. The implementation uses a phase-shifting array device consisting of a retarder array attached to an image sensor, and does not require the optical system to image the phase-shifting array device onto the image sensor required for the previously reported optical implementation of the parallel two-step phase-shifting digital holography. Then, the proposed implementation is essentially simple to align and compose. A preliminary experiment showed that the parallel two-step phase-shifting digital holography based on the proposed implementation can remove the conjugate image clinging to the image reconstructed by Fresnel transform alone with DC term suppression. Also, when the reconstruction distance was changed, the qualities of the reconstructed images were quantitatively evaluated by using normalized root-mean-square error. It was clarified that the proposed implementation was superior to other parallel phase-shifting digital holographies and Fresnel transform alone. Thus, the validity of the proposed implementation was confirmed.     

四步相移数字全息中随机误差的抑制方法

提出一种在四步相移数字全息中消除随机相移误差及CCD噪声的方法。通过多次重复四步相移数字全息的实验过程,使得每一步的相移都有多幅全息图像与之对应,把每一步对应的多幅全息图像进行数学平均就会得到4幅全息均值图像。理论分析表明,使用这4幅全息均值图像进行数字全息的重建,可以得到精确的物光波的分布,有效地消除随机相移误差及CCD噪声的影响。计算机模拟结果表明:该方法有助于提高数字全息重建光场质量。     

Wave-front curvature compensation of polarization phase-shifting digital holography

An on-axis polarization phase-shifting digital holographic microscope, based on a normal upright optical microscope, is constructed to quantitatively measure both the amplitude and phase distributions of specimen. The condenser lens and microscope objective employed in the object beam path enhance the illumination and magnification of the image, however, they induce additional phase aberration of the object wave. The physical formation of the phase aberration is theoretically analyzed, and a formula for the object wave front involving the phase aberration in the CCD plane is derived. The phase aberration can be eliminated in the reconstruction procedure by measuring a specimen-free hologram and then fitting the aberration phase with a least square ellipsoidal model to determine the parameters of the system. This phase aberration compensation procedure also reduces some of noises in the reconstructed phase of the specimen. The practicability of this method is demonstrated by a test experiment on microlenses.     

A novel phase-recovering algorithm for the intensity quantization error in the digital grating phase-shifting profilometry

In this paper, a novel phase-recovering algorithm is proposed to overcome the phase error cause by the image quantization procedure. As the quantization error level is different in one period of the sinusoidal fringe pattern, the intensity errors in the wave crest and wave valley area are much lager than that of other areas. By increasing the phase-shifting steps, the phase value in each point can be extracted without the intensity data from the wave crest and wave valley area. The phase-recovering algorithm is deduced in the whole period. Finally, the validity of the proposed algorithm is proved by data simulation method.     

Image encryption with two-step-only quadrature phase-shifting digital holography

An image encryption method with two-step-only quadrature phase-shifting digital holography, based on the calculated intensity of reference wave is proposed. Compared with the presented image encryption method based on phase-shifting technique, the technique need only to record two quadrature-phase holograms on CCD camera, without reference-wave intensity or object-wave intensity measurement, and the encryption keys to perform image encryption on Mach-Zehnder interferometer. When the reference-wave intensity is acquired from 2D correlation coefficient method our presented, the clear retrieved image can be obtained at high speed by certain algorithm. Its feasibility and validity were verified by a series of computer simulations.     

Single-shot phase-shifting digital holography with a photon-sieve-filtering telescope

A method of single-shot phase-shifting digital holography with a photon-sieve-filtering telescope is proposed. Three copy images with different phases are first generated by use of a monofocal photon-sieve filter in Kepler telescope, and then interfere with the reference plane wave by a beam combiner. The hologram is captured by a charge-coupled device(CCD)in one single exposure. The complex-valued amplitude of the test object can be reconstructed by three-step phase-shifting interferometry through three frames of extracted sub-interferograms from the single-exposure hologram. The principle and simulation experiments are carried out and verified the validity of our proposed method. This method can be applied for snapshot imaging and three-dimensional object construction.     

Study on digital holography with single phase-shifting operation

The digital holography with single phase-shifting operation has been studied. Experimental results and computer-simulated work are presented. The phase-shifting error makes the intensity of primary image decrease and the conjugate image appear in reconstruction. The explicit equation for explaining these effects is given. The calculation of the normalized intercorrelation peak between the input and the reconstruction for different algorithms shows that, when the phase-shifting operation is the main error source, the quality of the image reconstructed from the digital holography with single phase-shifting operation is favorable.     

Phase-shifting error and its elimination in phase-shifting digital holography

We investigate the influence of phase-shifting error on the quality of the reconstructed image in digital holography and propose a method of error elimination for a perfect image. In this method the summation of the intensity bit errors of the reconstructed image is taken as an evaluation function for an iterative algorithm to find the exact phase-shifting value. The feasibility of this method is demonstrated by computer simulation.     

Object recognition by use of polarimetric phase-shifting digital holography

Pattern recognition by use of polarimetric phase-shifting digital holography is presented. Using holography, the amplitude distribution and phase difference distribution between two orthogonal polarizations of three-dimensional (3D) or two-dimensional phase objects are obtained. This information contains both complex amplitude and polarimetric characteristics of the object, and it can be used for improving the discrimination capability of object recognition. Experimental results are presented to demonstrate the idea. To the best of our knowledge, this is the first report on 3D polarimetric recognition of objects using digital holography.     

Performance comparison of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography

To improve the quality of reconstructed images, we apply bicubic interpolation and B-spline interpolation to parallel phase-shifting digital holography for the first time. The effectiveness of bilinear interpolation, bicubic interpolation, and B-spline interpolation in parallel phase-shifting digital holography is shown by a numerical simulation. In the simulation result, the application of bicubic interpolation and B-spline interpolation succeeded in decreasing the rootmean- square error of the reconstructed image by 12.6 and 11.9%, respectively.     

Single-shot polarization-imaging digital holography based on simultaneous phase-shifting interferometry

We propose single-shot digital holography which is capable of simultaneously capturing both the information of multiple phase-shifted holograms and the distribution of the polarization. In this technique, a single image sensor records both the information required for phase-shifting interferometry and that of the polarization states of objects using an array of polarizers. The essence of the technique is the capability of imaging the distribution of the polarization of three-dimensional objects with a single-shot exposure by using the space-division multiplexing of holograms. The validity of the proposed technique was confirmed by the preliminary experiments.     

Digital microscopy using phase-shifting digital holography with two reference waves

A lensless, coherent optical microscope is described that uses a version of phase-shifting digital holography (PSDH) in conjunction with a field backpropagation algorithm to form coherent images of transmission-type objects. The PSDH is implemented by use of only two reference waves, in contrast with the usual implementation that requires four quadrature phase-shifting reference waves. Therefore only two digital holograms need to be recorded, and the complexity of the microscopic system is reduced. Experimental results are presented that compare images generated from conventional Gabor digital holography, two-reference-wave PSDH, and conventional white-light microscopy.     

Holography and speckle in phase-shifting digital holography（Invited Paper）

The correlation properties of the optical field diffusely reflected from a rough surface under coherent illumination are analyzed numerically. The cross-correlations of the complex amplitudes and the intensities before and after translation and/or tilt of the surface are calculated at an arbitrary observation plane in three-dimensional （3D） space. The results provide us with the 3D distributions of phase changes and speckle displacement that lead to the distributions measured by holographic interferometry and speckle relationships and physical interpretation of them are and signal-to-noise ratio of the displacement to be correlation technique. Comparisons with analytical also discussed.