Phase-error correction in digital holography

The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with >15 speckle realizations and high SNR, phase corrections better than lambda/50 root-mean-square (RMS) were obtained. Corrections better than lambda/10 RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.     

Efficient fringe image enhancement based on dual-tree complex wavelet transform

In optical phase shift profilometry (PSP), parallel fringe patterns are projected onto an object and the deformed fringes are captured using a digital camera. It is of particular interest in real time three-dimensional (3D) modeling applications because it enables 3D reconstruction using just a few image captures. When using this approach in a real life environment, however, the noise in the captured images can greatly affect the quality of the reconstructed 3D model. In this paper, a new image enhancement algorithm based on the oriented two-dimenional dual-tree complex wavelet transform (DT-CWT) is proposed for denoising the captured fringe images. The proposed algorithm makes use of the special analytic property of DT-CWT to obtain a sparse representation of the fringe image. Based on the sparse representation, a new iterative regularization procedure is applied for enhancing the noisy fringe image. The new approach introduces an additional preprocessing step to improve the initial guess of the iterative algorithm. Compared with the traditional image enhancement techniques, the proposed algorithm achieves a further improvement of 7.2 dB on average in the signal-to-noise ratio (SNR). When applying the proposed algorithm to optical PSP, the new approach enables the reconstruction of 3D models with improved accuracy from 6 to 20 dB in the SNR over the traditional approaches if the fringe images are noisy.     

Comparison of two-, three-, and four-exposure quadrature phase-shifting holography

In standard (four-exposure) quadrature phase-shifting holography (QPSH), two holograms and two intensity maps are acquired for zero-order-free and twin-image-free reconstruction. The measurement of the intensity map of the object light can be omitted in three-exposure QPSH. Furthermore, the measurements of the two intensity maps can be omitted in two-exposure QPSH, and the acquisition time of the overall holographic recording process is reduced. In this paper we examine the quality of the reconstructed images in two-, three-, and four-exposure QPSH, in simulations as well as in optical experiments. Various intensity ratios of the object light and the reference light are taken into account. Simulations show that two- and three-exposure QPSH can provide reconstructed images with quality comparable to that of four-exposure QPSH at a low intensity ratio. In practice the intensity ratio is limited by visibility, and thus four-exposure QPSH exhibits the best quality of the reconstructed image. The uniformity and the phase error of the reference light are also discussed. We found in most cases there is no significant difference between the reconstructed images in two- and three-exposure QPSH, and the quality of the reconstructed images is acceptable for visual applications such as the acquisition of three-dimensional scene for display or particle tracking.     

Effects of quantization in phase-shifting digital holography

We discuss quantization effects of hologram recording on the quality of reconstructed images in phase-shifting digital holography. We vary bit depths of phase-shifted holograms in both numerical simulation and experiments and then derived the complex amplitude, which is subjected to Fresnel transformation for the image reconstruction. The influence of bit-depth limitation in quantization has been demonstrated in a numerical simulation for spot-array patterns with linearly varying intensities and a continuous intensity object. The objects are provided with uniform and random phase modulation. In experiments, digital holograms are originally recorded at 8 bits and the bit depths are changed to deliver holograms at bit depths of 1 to 8 bits for the image reconstruction. The quality of the reconstructed images has been evaluated for the different quantization levels.     

In-line digital holographic interferometry

An optical system based on in-line digital holography for the evaluation of deformations is described. In-line holograms are recorded on a CCD chip. The problem of overlapping twin images typical for the in-line arrangement is solved by digital reconstruction and filtering of the unwanted wave fronts. Two separate interferograms of an object under test in its undeformed and deformed states are recorded each on a CCD chip. The phases of the two wave fronts are obtained from the complex amplitudes of the digital reconstructed wave fronts, and the deformation is calculated from the phase differences. Experimental results are presented.     

Discrete reconstruction of real phase objects: a comparison with computer-simulated phase objects

The Gerchberg-Saxton algorithm for iterative phase retrieval is applied in reconstructing an optical wave arriving from a coherently illuminated phase object. Computer simulations show that the algorithm converges to the correct solution when magnitude information for both image and Fourier domains is provided. Phase retrieval from measured intensities in an experimental optical system is compared with the simulations. Charge-coupled-device sensors, in which the output voltage is a nonlinear function of the light intensity, are used to perform measurements of the quasi magnitude information. Because of the accuracy of the measured data, phase retrieval for real simple objects is possible, and schlieren images can be generated on the computer screen.     

Polarization imaging by use of digital holography

We present what we believe to be a new digital holographic imaging method that is able to determine simultaneously the distributions of intensity, phase, and polarization state at the surface of a specimen on the basis of a single image acquisition. Two reference waves with orthogonal polarization states interfere with the object wave to create a hologram that is recorded on a CCD camera. Two wave fronts, one for each perpendicular polarization state, are numerically reconstructed in intensity and phase. Combining the intensity and the phase distributions of these two wave fronts permits the determination of all the components of the Jones vector of the object-wave front. We show that this method can be used to image and measure the distribution of the polarization state at the surface of a specimen, and the obtained results indicate that precise quantitative measurements of the polarization state can be achieved. An application of the method to image the birefringence of a stressed polymethyl methacrylate sample is presented.     

Correction of wave-front errors caused by the slight tilt of a reference beam in phase-shifting interferometry

In standard phase-shifting interferometry the reference beam is supposed to be a plane wave exactly normal to the recording plane. A slight tilt of the reference beam, however, may occur in practice, and it will introduce phase distortion for the reconstructed object wave front. The effects of reference wave tilt on the wave reconstruction are analyzed, and a novel method is proposed to correct the errors caused by this tilt. This method is simple and convenient without the need of any additional optical devices and measurements, and it can be used for both the smooth and the diffuse object surfaces. The effectiveness of this method is verified by a series of computer simulations.     

Remote metrology by comparative digital holography

A method for the remote comparison of objects with regard to their shape or response to a load is presented. The method allows interferometric sensitivity for comparing objects with different microstructure. In contrast to the well-known incoherent techniques based on inverse fringe projection this new approach uses the coherent optical wave field of the master object as a mask for the illumination of the sample object. The coherent mask is created by digital holography to allow instant access to the complete optical information of the master object at any place desired. The mask is reconstructed by a spatial light modulator (SLM). The optical reconstruction of digital holograms with SLM technology allows modification of reconstructed wavefronts with respect to improvement of image quality, the skilled introduction of additional information about the object (augmented reality), and the alignment of the master and test object.     

全息图再现象研究

通过分析全息图记录的干涉条纹图样，指出对于二维全息图，一束再现光将产生两个对称于全息图面的物象，两束对称于全息图面的再现光将产生位形相同的物象；三维全息图的再现，象的对称性不变，但原物象的对称再现象有一定的弥散，对称光再现时，等亮度再现象出现在全息图转动一个角度之后，实验上制作了具有清晰透射彩虹全息象的象面反射全息图。     

Quantization noise and its reduction in lensless Fourier digital holography

Digital holography is an imaging technique that enables recovery of topographic 3D information about an object under investigation. In digital holography, an interference pattern is recorded on a digital camera. Therefore, quantization of the recorded hologram is an integral part of the imaging process. We study the influence of quantization error in the recorded holograms on the fidelity of both the intensity and phase of the reconstructed image. We limit our analysis to the case of lensless Fourier off-axis digital holograms. We derive a theoretical model to predict the effect of quantization noise and we validate this model using experimental results. Based on this, we also show how the resultant noise in the reconstructed image, as well as the speckle that is inherent in digital holography, can be conveniently suppressed by standard speckle reduction techniques. We show that high-quality images can be obtained from binary holograms when speckle reduction is performed.     

Intrinsic aberrations due to Mie scattering in particle holography

Holography of small particles is a newly revived topic because of its importance in holographic particle image velocimetry (HPIV). However, the property of particle images formed through holography remains largely unexplored. This fact undermines the measurement reliability of HPIV techniques and has become one of the obstacles in the full deployment of HPIV. We study the intrinsic aberrations in the holographic particle image introduced by particle light scattering and investigate how accurately holography can deliver information about the particles that are being imaged. Consistent with our experimental observations, simulations based on Mie scattering theory show that even with a perfect hologram the reconstructed particle images demonstrate complex three-dimensional morphologies and bodily shifts. These characteristics, manifested as image aberrations, result from uneven scattering amplitude and phase distributions across the finite aperture of the hologram. Such aberrations degrade the signal-to-noise ratio in the reconstructed image as well as introducing systematic errors in detected particle image positions. We examine the effect of these aberrations on HPIV measurements.     

Secure three-dimensional data transmission and display

An optical three-dimensional (3D) display system interfaced with digital data transmission is proposed. In this system, an original 3D object is encrypted by use of a random phase mask and then the encrypted pattern is recorded as a digital hologram. The digital hologram key is also recorded for optical decryption. Both the encrypted digital hologram and the digital hologram key are transmitted to a receiver through a conventional communication data channel. At the receiver, the 3D scene is reconstructed and displayed optically in a retrieval system based on a joint-transform correlation. Experimental results are presented. We investigate the influence of quantization of the joint power spectrum in the optical correlator on the quality of the reconstructed image.     

Purely numerical compensation for microscope objective phase curvature in digital holographic microscopy: influence of digital phase mask position

Introducing a microscope objective in an interferometric setup induces a phase curvature on the resulting wavefront. In digital holography, the compensation of this curvature is often done by introducing an identical curvature in the reference arm and the hologram is then processed using a plane wave in the reconstruction. This physical compensation can be avoided, and several numerical methods exist to retrieve phase contrast images in which the microscope curvature is compensated. Usually, a digital array of complex numbers is introduced in the reconstruction process to perform this curvature correction. Different corrections are discussed in terms of their influence on the reconstructed image size and location in space. The results are presented according to two different expressions of the Fresnel transform, the single Fourier transform and convolution approaches, used to propagate the reconstructed wavefront from the hologram plane to the final image plane.     

一种去除离焦粒子像的简便方法

记录着不同深度位置的粒子全息图在数值重构过程中由于直透光、孪生像的影响以及离焦粒子像的存在,导致了聚焦粒子再现像质量的下降.针对这一问题,本文提出一种数值处理方法来减小上述三因素对聚焦粒子再现像的影响.该方法通过对数值重构出的两个聚焦与非聚焦面上粒子复振幅相减,将直透光、孪生像和离焦粒子像对聚焦粒子的影响同时减小,因此提高和改善了聚焦粒子再现像的对比度.在同轴数字全息层析再现粒子场过程中,该方法适用于在某一聚焦面仅显示聚焦粒子.此外,该过程仅需要一张全息图,而且不需要对全息图做预前和后期处理.给出了简要理论以及仿真、实验结果.     

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 diffraction's inverse operation. Finally, the object field is reconstructed through diffraction's angular spectrum theory.     

Image reconstruction algorithm based on the extended regularised total least squares method for electrical capacitance tomography

Electrical capacitance tomography (ECT) is a non-invasive imaging technology that aims at the visualisation of the cross-sectional permittivity distribution of a dielectric object based on the measured capacitance data. Successful applications of ECT depend greatly on the precision and speed of the image reconstruction algorithms. ECT image reconstruction is a typical ill-posed problem, and its solution is unstable, that is, the solution is sensitive to noises in the input data. Methods that ensure the stability of a solution while enhancing the quality of the reconstructed images should be used to obtain a meaningful reconstruction result. An image reconstruction algorithm based on the regularised total least squares (TLS) method that considers the errors in both the sensitivity field matrix and the capacitance data for ECT is presented. The regularised TLS method is extended using a combination robust estimation technique and an extended stabilising functional according to the ill-posed characteristics of ECT, which transforms the image reconstruction problem into an optimisation problem. In addition, the Newton algorithm is employed to solve the objective functional. Numerical simulations indicate that the algorithm is feasible and overcomes the numerical instability of ECT image reconstruction; for the cases of the reconstructed objects considered here, the spatial resolution of the reconstructed images obtained using the algorithm is enhanced; as a result, an efficient method for ECT image reconstruction is introduced.     

Phase-shifting digital holography with a low-coherence light source for reconstruction of a digital relief object hidden behind a light-scattering medium

Hiding image data with a light-scattering medium is effective as a basic data protection technique. The hidden image data can be observed only by using a low-coherence interference technique and is thus protected from unauthorized access. Unlike an intensity-distributed object, a digital relief object has no intensity distribution, making it possible to hide its existence by using a dilute light-scattering medium. To reconstruct the digital relief object through the light-scattering medium, we developed phase-shifting digital holography with a low-coherence light source. The experimental performance, including the spatial resolution and phase error of the reconstructed image, is estimated.     

Method for reduction of background artifacts of images in scanning holography with a Fresnel-zone-plate coded aperture

Near-infrared scanning holography with a Fresnel zone plate (FZP) coded aperture has potential applications in imaging through turbid media. However, the nonnegative intensity-distribution function of the FZP coded aperture introduces the background artifacts into the reconstructed images, reducing the contrast and the signal-to-noise ratio (SNR) of the images. A novel method termed as the composite hologram is proposed to reduce the artifacts. The computer simulations showed that the contrast and the SNR of the reconstructed images had improvements of at least 50.2% and 5.58-dB, respectively, compared with the conventional method. The composite hologram of a metal ring with a 6.0-mm diameter made by a wire with a 0.4-mm diameter immersing in 1% intralipid solution was recorded, and the reconstruction was performed numerically. The experimental results demonstrated that the contrast and the SNR of the reconstructed image had improvements of at least 32.3% and 2.51-dB, respectively.     

Iterative reconstruction method in phase-diversity imaging

An object is iteratively reconstructed from two atmospherically degraded images, one of which is detected by shifting of a known amount of phase with respect to the other. The iterative reconstruction scheme is based on the ideas of the blind-deconvolution method and the error-reduction algorithm. An optical system to do phase shifting is proposed in which a deformable mirror is employed. Several computer simulations are conducted to exemplify the usefulness of our method.