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.     

数字同轴和数字离轴全息系统分析

利用最高空间频率分析法,通过逐点分析记录在 CCD 上的空间频率信息,研究了物体可允许记录的最大横向尺寸、最小记录距离、全息图的信息量、空间分辨力、再现像的横向分辨力、轴向分辨力及散斑大小,并得到了数学表达式。理论分析和实验结果表明,数字同轴全息系统放宽了对 CCD 分辨力的要求,有较高的分辨力,较低的散斑噪声、灵活、简单的系统结构及较高的 CCD 空间带宽利用率,在增强系统性能方面要优于数字离轴全息系统。这一研究为数字全息系统的设计和操作提供了一定的理论和实验指导。     

Intrinsic speckle noise in off-axis particle holography

In holographic imaging of particle fields, the interference among coherent wave fronts associated with particle scattering gives rise to intrinsic speckle noise, which sets a fundamental limit on the amount of information that particle holography can deliver. It has been established that the intrinsic speckle noise is especially severe in in-line holography because of superposition of virtual image waves, the direct transmitted wave, and the real image. However, at sufficiently high particle number densities, such as those typical in holographic particle image velocimetry (HPIV) applications, intrinsic speckle noise also arises in off-axis particle holography from self-interference among wave fronts that form the real image of particles. To overcome the latter problem we have constructed a mathematical model that relates the first- and second-order statistical properties of the intrinsic speckle noise to relevant holographic system parameters. Consistent with our experimental data, the model provides a direct estimate of the information capacity of particle holography. We show that the noise-limited information capacity can be expressed as the product of particle number density and the extent of the particle field along the optical axis. A large angular aperture of the hologram contributes directly to achievement of high information capacity. We also show that filtering in either digital or optical form is generally ineffective in removing the intrinsic speckle noise from the particle image as a result of the similar spectral properties of the two. These findings emphasize the importance of angular aperture in designing holographic particle imaging systems.     

Optimal noise suppression in Fresnel incoherent correlation holography (FINCH) configured for maximum imaging resolution

An optimal setup in the sense of imaging resolution for the Fresnel incoherent correlation holography (FINCH) system is proposed and analyzed. Experimental results of the proposed setup in reflection mode suffer from low signal-to-noise ratio (SNR) due to a granular noise. SNR improvement is achieved by two methods that rely on increasing the initial amount of phase-shifted recorded holograms. In the first method, we average over several independent complex-valued digital holograms obtained by recording different sets of three digital phase-shifted holograms. In the second method, the least-squares solution for solving a system of an overdetermined set of linear equations is approximated by utilizing the Moore-Penrose pseudoinverse. These methods improve the resolution of the reconstructed image due to their ability to reveal fine and weak details of the observed object.     

Reduction of speckle in digital holography by discrete Fourier filtering

We present a digital signal processing technique that reduces the speckle content in reconstructed digital holograms. The method is based on sequential sampling of the discrete Fourier transform of the reconstructed image field. Speckle reduction is achieved at the expense of a reduced intensity and resolution, but this trade-off is shown to be greatly superior to that imposed by the traditional mean and median filtering techniques. In particular, we show that the speckle can be reduced by half with no loss of resolution (according to standard definitions of both metrics).     

单次相移数字全息中相移值的提取

为了消除相移误差对数字全息中再现像的像质的影响,本文时单次相移数字全息进行了研究.基于相位统计特性,提出了一种有效消除相移误差的新方法,该方法能够对任意未知相移量进行提取,并利用数字全息图所有抽样点的强度偏差之和作为评价标准,通过逐步改变计算得到的初始相移值来寻找正确的实际相移角.计算机模拟得到了很好的再现结果,证明了该方法的可行性和有效性.     

Compression of digital holograms for three-dimensional object reconstruction and recognition

We present the results of applying lossless and lossy data compression to a three-dimensional object reconstruction and recognition technique based on phase-shift digital holography. We find that the best lossless (Lempel-Ziv, Lempel-Ziv-Welch, Huffman, Burrows-Wheeler) compression rates can be expected when the digital hologram is stored in an intermediate coding of separate data streams for real and imaginary components. The lossy techniques are based on subsampling, quantization, and discrete Fourier transformation. For various degrees of speckle reduction, we quantify the number of Fourier coefficients that can be removed from the hologram domain, and the lowest level of quantization achievable, without incurring significant loss in correlation performance or significant error in the reconstructed object domain.     

Hybrid digital holographic imaging system for three-dimensional dense particle field measurement

To apply digital holography to the measurement of three-dimensional dense particle fields in large facilities, we have developed a hybrid digital holographic particle-imaging system. The technique combines the advantages of off-axis (side) scattering in suppressing speckle noise and on-axis (in-line) recording in lowering the digital sensor resolution requirement. A camera lens is attached to the digital sensor to compensate for the weak object wave from side scattering over a large recording distance. A simple numerical reconstruction algorithm is developed for holograms recorded with a lens without requiring complex and impractical mathematical corrections. We analyze the effect of image sensor resolution and off-axis angle on system performance and quantify the particle positioning accuracy of the system. The holographic system is successfully applied to the study of inertial particle clustering in isotropic turbulence.     

Contouring of Diffused Objects by Using Lensless Fourier Transform Digital Holography and Dual‐Index Immersion Method

Abstract: A simple method for contouring of diffused objects by using lensless Fourier transform digital holography and dual‐index immersion method is presented. It is noticed that to get more accurate results speckle noise should be eliminated/reduced from the reconstructed phase map from digital holograms. Speckle noise is handled by 5 × 5 median filtering. Depth contour interval up to a maximum of 0.12 mm could be achieved without making the interference phase fringes overcrowded.     

Underwater digital holography for studies of marine plankton

Conventional and digital holographies are proving to be increasingly important for studies of marine zooplankton and other underwater biological applications. This paper reports on the use of a subsea digital holographic camera (eHoloCam) for the analysis and identification of marine organisms and other subsea particles. Unlike recording on a photographic film, a digital hologram (e-hologram) is recorded on an electronic sensor and reconstructed numerically in a computer by simulating the propagation of the optical field in space. By comparison with other imaging techniques, an e-hologram has several advantages such as three-dimensional spatial reconstruction, non-intrusive and non-destructive interrogation of the recording sampling volume and the ability to record holographic videos. The basis of much work in optics lies in Maxwell's electromagnetic theory and holography is no exception: we report here on two of the numerical reconstruction algorithms we have used to reconstruct holograms obtained using eHoloCam and how their starting point lies in Maxwell's equations. Derivation of the angular spectrum algorithm for plane waves is provided as an exact method for the in-line numerical reconstruction of digital holograms. The Fresnel numerical reconstruction algorithm is derived from the angular spectrum method. In-line holograms are numerically processed before and after reconstruction to remove periodic noise from captured images and to increase image contrast. The ability of the Fresnel integration reconstruction algorithm to extend the reconstructed volume beyond the recording sensor dimensions is also shown with a 50% extension of the reconstruction area. Finally, we present some images obtained from recent deployments of eHoloCam in the North Sea and Faeroes Channel.     

Digital holography of particle fields: reconstruction by use of complex amplitude

Digital holography appears to be a strong contender as the next-generation technology for holographic diagnostics of particle fields and holographic particle image velocimetry for flow field measurement. With the digital holographic approach, holograms are directly recorded by a digital camera and reconstructed numerically. This not only eliminates wet chemical processing and mechanical scanning, but also enables the use of complex amplitude information inaccessible by optical reconstruction, thereby allowing flexible reconstruction algorithms to achieve optimization of specific information. However, owing to the inherently low pixel resolution of solid-state imaging sensors, digital holography gives poor depth resolution for images, a problem that severely impairs the usefulness of digital holography especially in densely populated particle fields. This paper describes a technique that significantly improves particle axial-location accuracy by exploring the reconstructed complex amplitude information, compared with other numerical reconstruction schemes that merely mimic traditional optical reconstruction. This novel method allows accurate extraction of particle locations from forward-scattering particle holograms even at high particle loadings.     

Improvement of color reproduction in color digital holography by using spectral estimation technique

We propose a color digital holography by using spectral estimation technique to improve the color reproduction of objects. In conventional color digital holography, there is insufficient spectral information in holograms, and the color of the reconstructed images depend on only reflectances at three discrete wavelengths used in the recording of holograms. Therefore the color-composite image of the three reconstructed images is not accurate in color reproduction. However, in our proposed method, the spectral estimation technique was applied, which has been reported in multispectral imaging. According to the spectral estimation technique, the continuous spectrum of object can be estimated and the color reproduction is improved. The effectiveness of the proposed method was confirmed by a numerical simulation and an experiment, and, in the results, the average color differences are decreased from 35.81 to 7.88 and from 43.60 to 25.28, respectively.     

Improvement of accuracy in digital holography by use of multiple holograms

Speckle pattern decorrelation reduces the accuracy of interferometric shape and deformation measurements. We introduce a technique for the reduction of speckle noise in digital holography. The method is not based on classical filtering techniques such as median filters. Instead it utilizes the shift theorem of the Fourier transform. For this method several holograms of the same object under test are recorded. The reconstruction leads to a set of object wave fields with different speckle patterns. A proper averaging procedure, taking into account the properties of the wrapped phases, leads to an improvement of the accuracy in the resulting phase difference. The theory of the applied method is described and our first results for technical components with an improvement of accuracy up to 1/57 of the wavelength are presented.     

Optimally tuned spatial light modulators for digital holography

Digital holography and comparative digital holography are applications that require computer-addressable modulators for the optical reconstruction of digital holograms. The quality of the reconstructed holograms depends on the modulator's properties. Therefore a characterization of the modulators is required. We show the result of a modulator characterization and the modulator's influence on the quality of the reconstructed hologram. We then compare qualitatively and quantitatively the optical reconstruction of phase and amplitude holograms by considering their level of detail and their diffraction efficiency.     

Scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography

We propose a scheme to improve the reconstructed image in parallel quasi-phase-shifting digital holography. Parallel quasi-phase-shifting digital holography is a technique capable of noiseless instantaneous measurement of three-dimensional objects, and it implements four kinds of phase shifting at a time with an array of 2 x 2 phase-shifting devices located in the reference wave. In the phase-shifting calculation in the reconstruction process of the technique, the scheme assigns the 2 x 2 cell configuration for each pixel in the vertical direction and for each 1-pixel interval in the horizontal direction of the hologram recorded by the image sensor. We conduct both a numerical simulation and a preliminary experiment. The results show that the proposed scheme can improve the quality of the reconstructed image calculated by the conventional scheme of parallel quasi-phase-shifting digital holography we previously proposed, and then the effectiveness of the proposed scheme is verified.     

High topographical accuracy by optical shot noise reduction in digital holographic microscopy

In this work, we present a new method to reduce the shot noise in phase imaging of digital holograms. A spatial averaging process of phase images reconstructed at different reconstruction distances is performed, with the reconstruction distance range being specified by the numerical focus depth of the optical system. An improved phase image is attained with a 50% shot noise reduction. We use the integral of the angular spectrum as a reconstruction method to obtain a single-object complex amplitude that is needed to perform our proposal. We also show the corresponding simulations and experimental results. The topography of a homemade TiO2 stepwise of 100 nm high was measured and compared with the atomic force microscope results.     

Inverse-problem approach for particle digital holography: accurate location based on local optimization

We propose a microparticle localization scheme in digital holography. Most conventional digital holography methods are based on Fresnel transform and present several problems such as twin-image noise, border effects, and other effects. To avoid these difficulties, we propose an inverse-problem approach, which yields the optimal particle set that best models the observed hologram image. We resolve this global optimization problem by conventional particle detection followed by a local refinement for each particle. Results for both simulated and real digital holograms show strong improvement in the localization of the particles, particularly along the depth dimension. In our simulations, the position precision is > or =1 microm rms. Our results also show that the localization precision does not deteriorate for particles near the edge of the field of view.     

Multi-plane imaging for arbitrary reconstruction positions in digital holography

A novel method for multi-plane imaging in digital holography is proposed: holograms of objects located at various places are recorded and then reconstructed simultaneously through one-step Fresnel diffraction using the quadratic distorted phase factor (QDPF). The theory of one-step Fresnel diffraction with the QDPF is deduced and experimental results support the theoretical investigation.     

Theoretical analysis of three-dimensional imaging and recognition of micro-organisms with a single-exposure on-line holographic microscope

Single-exposure on-line (SEOL) digital holography is a recently proposed technique for monitoring, visualization, and recognition of three-dimensional (3D) objects. In contrast to traditional multi-exposure on-line digital holography, it uses only one exposure, which makes it particularly suitable for imaging and recognizing moving micro-organisms. However, the cost of using only one exposure is the superposition of a conjugate image on the desired reconstructed image. The influence of the conjugate image on the visualization and recognition performance is investigated. The conditions for which the cross-talk noise induced by the conjugate image is negligible are derived. It is demonstrated that with conditions common in imaging of microscopic 3D biological objects, SEOL digital holography is highly tolerant of cross-talk noise induced by the conjugate image.     

Speckle noise arising from coherently illuminated polydisperse and continuous size distributions of discs

Abstract

An existing model of the speckle noise affecting images in far-field in-line holographic imaging is extended to distributions of disc-shaped particles which are no longer of uniform diameter. In this model the signal-to-noise ratio in replayed images from ideal in-line holograms in the Fraunhofer regime is limited by the speckle field arising from the overlapping Airy patterns. The original study was motivated by holographic particle image velocimetry and assumed that all the particles were of uniform diameter. We extend this model to cover polydisperse, power-law, exponential and Gaussian distribution functions and include an explicit limit on our maximum particle diameter to ensure that the hologram is recorded in the far-field of all the particles.