An error detection and recovery algorithm for the transmission of digital holography over noisy channels

Digitalization enables and expertise storage and transmission of holographic data. However, the reconstructed object image is vulnerable to transmission errors over the noisy channel. We present a novel algorithm of what we believe is the first approach to reduction of noise effects on digital holograms corrupted by transmission errors. To accomplish this work, we exploit new interdependencies on the interference holograms and develop a detection-based algorithm to detect error points and to identify the corresponding interference holograms with the largest errors. In the reconstruction process, the conventional four-step algorithm is used for the recovery of error-free points. In contrast, a three-step algorithm is employed to reconstruct error points by removing the largest error holograms. With accurate detection, the proposed algorithm is capable of recovering the object image from digital holograms with severe transmission errors. It is shown that the proposed algorithm provides much better reconstruction performances than the conventional four-step reconstruction algorithm in an error-prone environment.     

Fast reconstruction of multiple off-axis holograms based on a combination of complex encoding and digital spatial multiplexing

An algorithm is proposed for the fast reconstruction of off-axis digital holograms based on a combination of complex encoding(CE) and spatial multiplexing(SM). In this algorithm, every two off-axis holograms recorded in sequence are first assembled into a CE hologram using the CE method, and then four of the CE holograms are again encoded into one complex spatial multiplexing(CSM) hologram based on the SM algorithm. It is demonstrated that the eight holograms encoded into such one CSM hologram can be quickly reconstructed by performing a two-dimensional(2D) Fourier transform(FT) on the CSM hologram. Using this method, the eight 2D FTs required for the reconstruction of the eight holograms in the conventional spatial filtering methods can be simplified to a process with only one 2D FT, which can largely improve the computation efficiency with the     

3D trapping and manipulation of micro-particles using holographic optical tweezers with optimized computer-generated holograms

A multi-plane adaptive-additive algorithm is developed for optimizing computer-generated holograms for the reconstruction of traps in three-dimensional(3D) spaces.This algorithm overcomes the converging stagnation problem of the traditional multi-plane Gerchberg-Saxton algorithm and improves the diffraction efficiency of the holograms effectively.The optimized holograms are applied in a holographic optical tweezers(HOT) platform.Additionally,a computer program is developed and integrated into the HOT platform for the purpose of achieving the interactive control of traps.Experiments demonstrate that the manipulation of micro-particles into the 3D structure with optimized holograms can be carried out effectively on the HOT platform.     

Automatic focusing in digital holography and its application to stretched holograms

The searching and recovering of the correct reconstruction distance in digital holography (DH) can be a cumbersome and subjective procedure. Here we report on an algorithm for automatically estimating the in-focus image and recovering the correct reconstruction distance for speckle holograms. We have tested the approach in determining the reconstruction distances of stretched digital holograms. Stretching a hologram with a variable elongation parameter makes it possible to change the in-focus distance of the reconstructed image. In this way, the proposed algorithm can be verified at different distances by dispensing the recording of different holograms. Experimental results are shown with the aim of demonstrating the usefulness of the proposed method, and a comparative analysis has been performed with respect to other existing algorithms developed for DH.     

利用反射全息实现计算全息三维显示

计算全息和光学全息都可应用于三维显示,但各有自己的优势和缺陷.将计算全息和光学反射全息相结合,可以突破光学全息对记录物体的限制,进行虚拟物体或自然场景的全息图的制作,同时可以实现白光再现.本文首先用三维扫描仪获得实际物体的三维数据,用"点云算法"模拟得到其菲涅耳全息图透射率数据,采用计算全息打印机将其输出于全息记录介质,得到可光学再现的菲涅耳计算全息图H1.然后将H1作为光学全息的记录物体进行反射全息记录,将平面全息转化为体全息,实现了计算全息白光再现.     

利用反射全息实现计算全息三维显示

计算全息和光学全息都可应用于三维显示,但各有自己的优势和缺陷.将计算全息和光学反射全息相结合,可以突破光学全息对记录物体的限制,进行虚拟物体或自然场景的全息图的制作,同时可以实现白光再现.本文首先用三维扫描仪获得实际物体的三维数据,用"点云算法"模拟得到其菲涅耳全息图透射率数据,采用计算全息打印机将其输出于全息记录介质,得到可光学再现的菲涅耳计算全息图H₁.然后将H₁作为光学全息的记录物体进行反射全息记录,将平面全息转化为体全息,实现了计算全息白光再现.     

A new wavelet-based reconstruction algorithm for twin image removal in digital in-line holography

Two original methods are proposed here for digital in-line hologram processing. Firstly, we propose an entropy-based method to retrieve the focus plane which is very useful for digital hologram reconstruction. Secondly, we introduce a new approach to remove the so-called twin images reconstructed by holograms. This is achieved owing to the Blind Source Separation (BSS) technique. The proposed method is made up of two steps: an Adaptive Quincunx Lifting Scheme (AQLS) and a statistical unmixing algorithm. The AQLS tool is based on wavelet packet transform, whose role is to maximize the sparseness of the input holograms. The unmixing algorithm uses the Independent Component Analysis (ICA) tool. Experimental results confirm the ability of convolutive blind source separation to discard the unwanted twin image from in-line digital holograms.     

Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength

A method for allowing direct perfect superimposition and comparison of Fresnel-transform reconstructions of digital holograms recorded of the same object at different distances and wavelengths is proposed and demonstrated. The method takes into account the dependence of the reconstruction pixel on the distance and the wavelength by the Fresnel-transform algorithm. The method avoids the need for image scaling at the end of the reconstruction process that usually is performed in multi-wavelength digital holography. Demonstration is given by superposing the numerical reconstructions of holograms recorded at different distances and wavelengths. The method can be potentially very useful for real-time monitoring in biological processes or for recognition and ranging by multiple wavelengths of a target with fast movements or finally for very fast investigation and study of very fast processes.     

Comment on "Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution"

We comment on a recent Letter by Zhang et al. [Opt. Lett. 31, 1633 (2006)] in which the authors proposed a reconstruction algorithm for high-numerical-aperture (NA) holograms. Such an algorithm has been available for in-line holography for more than a decade. The authors' "achievement" of high NA for digital in-line holography, NA=0.17, is below what was reported already several years ago (NA=0.30) and is considerably lower than what is routinely achieved now. We present reconstructions of holograms acquired with NAs above 0.4 in which we show maximal achievable resolution.     

粒子场数字全息诊断中的再现算法研究

 粒子场的数字全息诊断中,良好的再现算法能够在较短的时间内给出高质量的再现像。利用标准粒子板模拟单层面的粒子场,使用大面阵CCD实现同轴数字全息记录,得到了大尺寸的数字全息图。针对4种数字全息再现算法,本文从再现图像的质量、再现全息图的大小和计算速度3个主要方面进行了比较研究,结果表明角谱算法(FFT-AS)具有再现图像背景均匀,再现结果中无物理图像压缩,可以再现大尺寸的全息图且具有较快计算速度的优点,适合于粒子场同轴数字全息图的再现计算。     

Computer-Generated Image Holograms for 3D-Display

Computer-generated image holograms are particularly useful for 3D-display applications. We discuss the properties of the reconstructions obtained with this hologram type. Conditions are given which must be fulfilled to ensure a disturbance free reconstruction. A new efficient algorithm is presented which implements the hidden surface effect for synthetic image holograms.Presented at the International Commission for Optics Topical Meeting, Kyoto, 1994.     

Reconstruction algorithm for high-numerical-aperture holograms with diffraction-limited resolution

A fast algorithm is proposed for the reconstruction of digital holograms that are recorded at high numerical aperture. The method directly evaluates the Rayleigh-Sommerfeld diffraction integral by use of a fast convolution algorithm. A shift parameter that accounts for the coordinate system's transverse displacement of the object plane and the hologram plane is introduced in a discrete representation of the diffraction kernel. Combination of the samplings reconstructed with different shift values yields diffraction-limited resolution over the full field of view. The algorithm is suitable for various applications such as holographic microscopy and metrology. Simulation and experimental results are presented.     

Improved low energy electron projection in-line holograms reconstruction: application to the holograms of a tungsten tip

A modification of the classical calculation algorithm is presented which allows to minimize the effect of the long range oscillations created by the twin object in the reconstruction process of in-line holograms obtained by low energy electron projection microscopy. The reconstructed shapes of a tungsten tip, observed with different magnifications are shown.     

Holographic Subsurface Radar Technique for Nondestructive Testing of Dielectric Structures

Holographic subsurface radar method is compared with the conventional technology of impulse radars. Basic relationships needed for the reconstruction of complex microwave holograms are presented. Possible applications of the proposed technology are discussed. Diagnostics of polyurethane foam coatings of spacecrafts is used as an example of the efficiency of holographic subsurface radars. Results of reconstruction of complex and amplitude microwave holograms are compared. It is demonstrated that the image quality that results from reconstruction of complex microwave holograms is higher than the image quality obtained with the aid of amplitude holograms.     

Synthesis of Binary Computer－Generated Hologram by Optimal Recursive Direct Binary Search Algorithm

ＳｙｎｔｈｅｓｉｓｏｆＢｉｎａｒｙＣｏｍｐｕｔｅｒ－ＧｅｎｅｒａｔｅｄＨｏｌｏｇｒａｍｂｙＯｐｔｉｍａｌＲｅｃｕｒｓｉｖｅＤｉｒｅｃｔＢｉｎａｒｙＳｅａｒｃｈＡｌｇｏｒｉｔｈｍ￥ＺＨＡＩＪｉｎｈｕｉ；ＲＵＡＮＹＵ（Ｄｅｐｔ．ｏｆＯｐｔｏｅｌｅｃｔｒｏ...     

An algorithm for evaluating overlapping bubble images recorded by double pulsed laser holography

The present paper describes a method for evaluating images of a bubbly flow in stirred aerated tanks which are typical when pulsed laser holography is applied as the measuring technique. Features of the brightness histograms of reconstructed bubble images are discussed. A procedure is presented to evaluate the bubble images taken from a reconstructed hologram in order to determine the center of gravity of the bubble image. Double pulsed holograms were taken to measure bubble velocities and diameters simultaneously. In this case, overlapping bubble images are sometimes observed in the reconstruction. This significantly impedes the evaluation of the characteristics of the bubbles. Thus, an algorithm is presented in this work to distinguish between single and overlapping bubble images and to separate the overlapping bubble image in a two-dimensional image for a bubbly flow at low void fraction recorded from double pulse holograms. This algorithm was confirmed to be effective if the bubble images are extracted from the entire image.     

Averaging scheme for atomic resolution off-axis electron holograms

All micrographs are limited by shot-noise, which is intrinsic to the detection process of electrons. For beam insensitive specimen this limitation can in principle easily be circumvented by prolonged exposure times. However, in the high-resolution regime several instrumental instabilities limit the applicable exposure time. Particularly in the case of off-axis holography the holograms are highly sensitive to the position and voltage of the electron-optical biprism. We present a novel reconstruction algorithm to average series of off-axis holograms while compensating for specimen drift, biprism drift, drift of biprism voltage, and drift of defocus, which all might cause problematic changes from exposure to exposure. We show an application of the algorithm utilizing also the possibilities of double biprism holography, which results in a high quality exit-wave reconstruction with 75 pm resolution at a very high signal-to-noise ratio.     

Color lensless digital holographic microscopy with micrometer resolution

Color digital lensless holographic microscopy with micrometer resolution is presented. Multiwavelength illumination of a biological sample and a posteriori color composition of the amplitude images individually reconstructed are used to obtain full-color representation of the microscopic specimen. To match the sizes of the reconstructed holograms for each wavelength, a reconstruction algorithm that allows for choosing the pixel size at the reconstruction plane independently of the wavelength and the reconstruction distance is used. The method is illustrated with experimental results.     

基于位相变更的非相干数字全息自适应成像

菲涅耳非相干数字全息作为一种非扫描的三维成像技术具有其独特的优势,但其成像过程中会受到各种像差的影响,导致成像分辨率、再现像的质量降低.为了解决这一问题,可以结合适当的自适应光学技术对波前像差进行探测和校正.位相变更是一种基于两幅具有已知位相差的强度图像实现波前探测和像差校正的技术.本文发展了基于位相变更的非相干数字全息自适应成像技术,不需要引入引导星,利用全息记录过程中的两幅相移全息图,实现波前像差的探测.本文给出了所发展技术的数值仿真和实验结果,结合位相变更算法求解出系统像差的位相分布,将像差的共轭位相加载到光瞳面上,在全息图记录的同时校正像差,从而提高重建像的质量.     

Computer generated holograms using personal computers

Holography or the method of wave-front reconstruction to produce an image was introduced by D. Gabor in 1948. Normally a laser is necessary to produce holograms in the laboratory. This paper introduces the usage of the high resolution display of the IBM-PC and a graphics printer to generate holograms. The advantages of using this method are that holograms of real or fictitious objects can be made, since all objects can be represented by a collection of points and one does not need an elaborate set up to make the holograms. This method is also useful for making Fourier transform holograms, image plane holograms, spatial filters, optical elements, etc.^1,2