Extended ABCD matrix formalism for the description of femtosecond diffraction patterns; application to femtosecond digital in-line holography with anamorphic optical systems

We present a new model to predict diffraction patterns of femtosecond pulses through complex optical systems. The model is based on the extension of an ABCD matrix formalism combined with generalized Huygens-Fresnel transforms (already used in the CW regime) to the femtosecond regime. The model is tested to describe femtosecond digital in-line holography experiments realized in situ through a cylindrical Plexiglas pipe. The model allows us to establish analytical relations that link the holographic reconstruction process to the experimental parameters of the pipe and of the incident beam itself. Simulations and experimental results are in good concordance. Femtosecond digital in-line holography is shown to allow significant coherent noise reduction, and this model will be particularly efficient to describe a wide range of optical geometries. More generally, the model developed can be easily used in any experiment where the knowledge of the precise evolution of femtosecond transverse patterns is required.     

傅里叶变换同轴数字全息记录余弦变换谱系数

余弦变换广泛应用于图像和视频的压缩编码以及模式识别之中。余弦变换为实偶对称的傅里叶变换,把实偶对称物体传送到位于傅里叶变换透镜前焦面的空间光调制器上,采用单色均匀平面激光光波照射,则在后焦面上为光波复振幅分布为实偶对称物体的傅里叶变换,即为物体的余弦变换。由于余弦变换谱系数既有正实数又有负实数,提出了采用傅里叶变换同轴数字全息方法记录余弦变换谱系数,通过把数字全息图减去参考光光强和物光光强而得到余弦变换系数。理论推导和实验结果表明了该方法的可行性,该方法可应用于图像的快速余弦变换。     

Magnified reconstruction of digitally recorded holograms by Fresnel-Bluestein transform

A method for numerical reconstruction of digitally recorded holograms with variable magnification is presented. The proposed strategy allows for smaller, equal, or larger magnification than that achieved with Fresnel transform by introducing the Bluestein substitution into the Fresnel kernel. The magnification is obtained independent of distance, wavelength, and number of pixels, which enables the method to be applied in color digital holography and metrological applications. The approach is supported by experimental and simulation results in digital holography of objects of comparable dimensions with the recording device and in the reconstruction of holograms from digital in-line holographic microscopy.     

Accurate Linewidth Measurements in Aperture Limited In-line Fraunhofer Holography

Abstract

Methods for accurate width analysis of line objects in aperture limited in-line Fraunhofer holography are described. One approach involves size correction utilizing the nature of the error commonly introduced. The other technique used involves measuring the width at a certain normalized intensity and not at the apparent edge. The general background is discussed in detail using an opaque object model.     

Studies of digital microscopic holography with applications to microstructure testing

We propose an in-line digital microscopic holography system for testing of microstructures. With the incorporation of a long-distance microscope with digital holography, the system is capable of imaging test microstructures with high resolution at sufficient working distances to permit good illumination of samples. The system, which was developed in an in-line configuration, achieves high imaging capacity and exhibits properties that are favorable for micromeasurement. We demonstrate the performance of the system with experiments to determine the displacement of a silicon microcantilever and with investigations of the microscopic resolution capability.     

Time-averaged in-line digital holographic interferometry for vibration analysis

Time-averaged in-line digital holography is applied for vibration analysis. In particular, by use of a double-exposure approach, simultaneous determination of vibration mode shape and mean static state deformation during a vibration cycle are obtained. The subtraction of two numerically reconstructed digital holograms recorded at the same resonant frequency but with a small difference in amplitude shows the mixing of Bessel-type time-averaged fringes owing to vibration and of the double-exposure fringes owing to differences in the mean deformation of the object. It is shown that separation of these fringe patterns can be readily accomplished numerically. An experimental demonstration of this effect by use of in-line digital holography for relatively small membranes is demonstrated.     

Digital holographic microscope for measuring three-dimensional particle distributions and motions

Better understanding of particle-particle and particle-fluid interactions requires accurate 3D measurements of particle distributions and motions. We introduce the application of in-line digital holographic microscopy as a viable tool for measuring distributions of dense micrometer (3.2 microm) and submicrometer (0.75 microm) particles in a liquid solution with large depths of 1-10 mm. By recording a magnified hologram, we obtain a depth of field of approximately 1000 times the object diameter and a reduced depth of focus of approximately 10 particle diameters, both representing substantial improvements compared to a conventional microscope and in-line holography. Quantitative information on depth of field, depth of focus, and axial resolution is provided. We demonstrate that digital holographic microscopy can resolve the locations of several thousand particles and can measure their motions and trajectories using cinematographic holography. A sample trajectory and detailed morphological information of a free-swimming copepod nauplius are presented.     

Coal powder measurement by digital holography with expanded measurement area

The field of view of digital in-line holography for flow field diagnostics is restricted to a small volume due to the finite size and the low spatial resolution of the available CCD. Expansion of the measurement cross section of digital holographic particle image velocimetry was investigated with a lens-based holography configuration. By sampling the chirp signal in the center lobe completely and undersampling the chirp signal in the second- and higher-order lobes by a magnified virtual recording plane produced by an imaging camera lens, the field of view is expanded. Simulation results show that the three-dimensional (3D) location and size of the relatively large particle can be reconstructed with good accuracy. A digital holographic particle image velocimetry system was established for coal particle flow field diagnostics. Compared with the lensless configuration, the field of view of the digital holography system was enlarged 1.9 times, up to 2.78 cm × 2.78 cm × 3 cm. The 3D location, size distribution, and the 3D vector field of coal powder were obtained. The results show that the application of digital in-line holography to measure large particle flow field is feasible.     

Parallel three-step phase-shifting digital holography

We propose parallel three-step phase-shifting digital holography as a technique capable of noiseless instantaneous measurement of three-dimensional objects based on phase-shifting interferometry. The proposed digital holography carries out three-step phase shifting at the same time by using a phase-shifting array device located in the reference beam. The array device has a periodic three-step phase distribution, and its configuration is simplified compared with that required for conventional parallel phase-shifting digital holography. Therefore the optical system of the proposed parallel phase-shifting digital holography is more suitable for the realization of the proposed holography. We conduct both a numerical simulation and a preliminary experiment. The results of the simulation and experiment agree well with those of the conventional phase-shifting method and are superior to the results obtained by conventional digital holography by using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

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.     

In-line recording and off-axis viewing technique for holographic particle velocimetry

Prior approaches (e.g., off-axis holography) to overcoming the limitations of in-line holography for particle fields, namely, intrinsic speckle noise and depth resolution, involved an increased complexity of the optical system. The in-line recording and off-axis viewing (IROV) technique employs a single laser beam to record an in-line hologram, which is then viewed off axis during reconstruction. The signal-to-noise ratio and depth resolution of IROV are higher than conventional in-line holography by an order of magnitude and are comparable with off-axis holography. IROV is a much simpler approach than off-axis holography and is highly promising for holographic particle velocimetry. Measurements of the three dimensional flow velocity field of a vortex ring obtained by an IROV-based holographic particle velocimetry system are presented.     

Parallel two-step phase-shifting digital holography

We propose a parallel two-step phase-shifting digital holography technique capable of instantaneous measurement of three-dimensional objects, with a view toward measurement of dynamically moving objects. The technique is based on phase-shifting interferometry. The proposed technique carries out the two-step phase-shifting method at one time and can be optically implemented by using a phase-shifting array device located in the reference beam. The array device has a periodic two-step phase distribution, and its configuration is simplified compared with that required for three-step and four-step parallel phase-shifting digital holographies. Therefore the optical system of the proposed technique is more suitable for the realization of a parallel phase-shifting digital holography system. We conduct both a numerical simulation and a preliminary experiment in the proposed technique. The results of the simulation and the experiment agree well with those of sequential phase-shifting digital holography, and results are superior to those obtained by conventional digital holography using the Fresnel transform alone. Thus the effectiveness of the proposed technique is verified.     

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.     

Digital in-line holography of microspheres

We have used digital in-line holography (DIH) with numerical reconstruction to image micrometer-sized latex spheres as well as ferrimagnetic beads suspended in gelatin. We have examined in detail theoretically and experimentally the conditions necessary to achieve submicrometer resolution of holographic reconstructions. We found that both transparent and opaque particles could be imaged with a resolution that was limited only by the wavelength of the light used. Simple inspection of intensity profiles through a particle allowed an estimate to be made of the particle's three position coordinates within an accuracy of a few hundred nanometers. When the derivative of a second-order polynomial fitted to the intensity profiles was taken, the X, Y, Z position coordinates of particles could be determined within +/-50 nm. More-accurate positional resolution should be possible with the help of more-advanced computer averaging techniques. Because a single hologram can give information about a large collection of distributed particles, DIH offers the prospect of a powerful new tool for three-dimensional tracking of particles.     

Digital image decoding for in-line X-ray holography using two holograms

Abstract

A novel solution to twin-image disturbance in in-line X-ray holography is presented. By computer simulation, this two-hologram-based digital way is proved to be efficient, while conditions relating to experiments are taken into account.     

Digital holography using a digital photo-camera

The possibilities of running digital holography using commonly available digital zoom photo-cameras are studied. A new modified method of the holographic set-up exploiting the properties of a photo-camera is suggested. This method offers a straightforward and simple way of both digital hologram recording and reconstructing. In order to verify the feasibility of the method, the holograms acquired are digitally reconstructed using a computer code based on the fast Fourier transform algorithm. Experimental results obtained are presented and discussed.     

小波变换在数字全息中的应用

数字全息是通过数字重构来同时获取被测物强度与相位,但记录时的激光散斑效应和重构时的零级衍射斑成为了这种方法的瓶颈。将小波变换引入数字全息,可直接消除零级衍射像,无需相移,也不需要采集多幅图像;小波非线性滤波器还可消除散斑噪声。模拟和实验结果表明,小波分析的引入,可以消除零级衍射影响,改善图像质量,提高测试分辨率。     

Resolution analysis of a digital holography system

Although digital holography (DH) has many advantages compared to conventional holography, its resolution is limited due to CCDs or other recording devices. Three factors contribute to this limitation, namely, the pixel averaging effect within the finite detection size of one pixel, a finite CCD aperture size limitation, and the sampling effect due to a finite sampling interval. In this paper, interactions of the three factors on resolution are investigated and presented. The resolution of a DH system can be determined for given parameters of these three factors. The domains dominated by different factors are explained along with their accuracy. As a DH system is space variant, influences of object extent on resolution are also discussed. The resolution performance of in-line and off-axis systems is studied and examples of resolution determination for a practical system are provided.     

同轴数字全息用于粒径测量的影响因素分析

采用同轴数字全息技术测量研究粒子场,其高分辨力的再现像和粒径高精度测量受到诸多因素的影响.本文简要介绍了同轴数字全息的基本概念、原理、方法及其在粒子直径测量中的应用,主要通过计算机仿真研究了记录距离和粒子浓度这两个因素对粒径测量精度的影响,给出了记录距离的范围,同时提出了基于灰度梯度提取粒子边缘进行粒径测量的方法,并通过实验进行了验证.     

Integrated gray-level gradient method applied for the extraction of three-dimensional velocity fields of sprays in in-line digital holography

In this study, an integrated gray-level gradient method is applied to extract the three-dimensional (3D) velocity fields of sprays. This method consists of a conventional edge-sharpness method and a new method, namely, the overall-sharpness method, which is an efficient supplement of the former. And then the synchronization system is designed and assembled to record double-exposure spray holograms in a short time interval. Finally, using the integrated gray-level gradient method and some image processing techniques, the 3D coordinates of droplets are easily obtained, which can be used to evaluate the 3D velocity fields and the size features of spray droplets in different spray injection pressures. It proves that the integrated gray-level gradient method is well applied to measure the characteristics of sprays in in-line digital holography.