Spatial filtering of the diffractional field of a double-exposure hologram of a focused scatterer image. Part II

Analysis is made of the interferometer sensitivity to transverse or longitudinal displacements of a diffusively scattering surface under double-exposure recording of a focused image hologram, where the distribution of the complex field amplitude results from two Fourier transforms of the distribution in the object plane. It is shown that in the case of transverse displacement of the scatterer, the interference patterns are localized in two planes, with each plane characterized by different interferometer sensitivity. In the case of control of the longitudinal displacement, the interference pattern is localized in one plane, however, in order to record it, it is necessary to perform spatial filtering of the diffraction field in the hologram plane. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 78–85, October, 2007.     

Solution to the twin image problem in holography

While holography truly constitutes an ingenious concept, ever since its invention by Gabor it has been troubled by the so-called twin-image problem limiting the information that can be obtained from a holographic record. For symmetry reasons there are always two images appearing in the reconstruction of a hologram and the unwanted out of focus twin-image obscures the object. Here we show a universal method of reconstructing a hologram completely free of twin-image disturbances while no assumptions about absorbing or phase shifting properties of the object need to be imposed. Thus, truthful amplitude and phase distributions are retrieved.     

Stokes参量数字全息法实现相位物体成像

为实现对相位物体的无损检测和成像,克服数字同轴全息相位物体成像技术在消除零级像和孪生像的干扰时存在的系列问题,提出一种基于Stokes参量的新的数字同轴全息技术。该方法区别于传统的利用干涉光场来记录原始像项的数字全息方法,通过测量物参光合成光束的Stokes参量来分别得到这两束光的振幅和相位差,从而准确、唯一地获得原始像项;再利用数字再现即可重构物光的振幅和相位信息。实验中对弱吸收的相位样品进行了测量,得到样品清晰的振幅和相位分布。结果表明,采用该方法对相位物体进行数字全息再现,可以克服传统同轴全息图中零级像和共轭像对相位物体信息的严重干扰,对于提取相位物体的振幅和相位信息是可行和有效的。     

Alignment on moiré fringes of finite width during optical processing of images of a periodic amplitude grating which are distorted by the reconstructed wave front

A method of alignment on moiré fringes of finite width for visualization of the deflection angles of rays reconstructed by a hologram of a phase object is described. It is suggested that the resulting moiré pattern be obtained by superposing two distorted images of amplitude gratings with different period. The result of an experimental test of the method is presented. Zh. Tekh. Fiz. 69, 130–132 (February 1999)     

Application of the holographic carrier fringe and FFT technique for deformation measurement

This paper describes a holographic system based on the use of fibre optics and automatic spatial carrier fringe pattern analysis. Carrier fringes are generated by simply translating the object beam between two exposures. Single-mode optical fibres are used to transfer both the object and reference beams. The fast Fourier transform method is used to process the interferograms: it extracts phase from fringe patterns resulting from the interference of tilted wavefronts. The method is illustrated by measuring the deformation of an arbitrarily clamped, uniformly loaded circular plate. The results are given for the perspective plot of the out-of-plane deformation field, the maps of wrapped and unwrapped phase, and a contour map of the unwrapped phase.     

X-ray interferometric Fourier holography

An X-ray interferometric Fourier holography was proposed and theoretically investigated. X-ray Interferometric Young fringes and the reconstruction of an object image were investigated by the Fourier transform method. It was shown that on the output surface of the analyzer crystal (the third plate of the interferometer) the interference pattern of two slits gives X-ray interferometric Young fringes. An expression for the period of X-ray interferometric Young fringes was obtained. The subsequent reconstruction of the slit image as an object is conducted by means of the Fourier transform method of intensity distribution on the hologram. Three methods for reconstruction of the function of complex transmission of the object are presented: an analytical one–the approximate method, the iteration method and the step-by-step approach. As examples a recording of X-ray interferometric Fourier hologram and the reconstruction of the function of complex amplitude transmission of a beryllium circular cylinder are given.     

Common-path phase-shifting lensless holographic microscopy

We present an approach capable of high-NA imaging in a lensless digital in-line holographic microscopy layout even outside the Gabor's regime. The method is based on spatial multiplexing at the sample plane, allowing a common-path interferometric architecture, where two interferometric beams are generated by a spatial light modulator (SLM) prior to illuminating the sample. The SLM allows phase-shifting interferometry by phase modulation of the SLM diffracted beam. After proper digital processing, the complex amplitude distribution of the diffracted object wavefront is recovered and numerically propagated to image the sample. Experimental results are reported that validate the proposed method.     

Enhancement of fringe visibility in a fibre interferometer

A simple method for increasing fringe visibility of an interference pattern in a Mach-Zehnder type fibre interferometer is presented. In order to obtain high visibility, two elliptically polarized waves emitted from fibres with birefringence are transformed into two linearly polarized waves of equal amplitude and with parallel planes of polarization by using ordinary optical components. Instability of fringe patterns due to temperature fluctuation of the air surrounding the fibres is also discussed.     

共轭对称延拓傅里叶计算全息

提出一种计算全息算法,将物光波进行共轭对称延拓,经快速傅里叶变换直接生成实函数,其中包含物光波的幅度和相位信息,可编码得到灰度全息图.利用此全息图可清晰地再现原物光波.通过共轭延拓生成计算全息图的方法与以往基于干涉的计算全息不同之处在于,这里并不需要模拟物光和参考光的干涉,计算效率很高.利用生成的全息图在数字再现和光电再现实验中均获得了良好的效果.理论推导和实验结果都验证了算法的有效性. 关键词： 计算全息 共轭对称 数字再现 光电再现     

Digital holography of self-luminous objects by using a Mach-Zehnder setup

We describe a method where the wavefront emitted by a self-luminous object is superimposed to its filtered counterpart by using a Mach-Zehnder interferometer. The amplitude and phase of the resulting interference pattern is used for digital three-dimensional imaging. Experimental results are presented.     

One step hologram calculation for multi-plane objects based on nonuniform sampling (Invited Paper)

The nonuniform sampling method in hologram plane is proposed to reconstruct objects on multi-plane simultaneously. The hologram is nonuniformly sampled by decomposing it into several parts with various sampling rates. The hologram is calculated based on the nonuniform fast Fourier transform （NUFFT） algorithm. In the experiment, we load this nonuniformly sampled hologram on phases-only spatial light modulator （SLM）, and by illumination with collimated light objects with different sampling rates are reconstructed at different distant planes simultaneously. Both of the numerically simulation and optical experiments are performed to demonstrate the feasibility of our method. The experiment also shows that our proposed nonuniform sampled hologram for multi-plane objects is calculated by only one step, better than conventional method that needs several steps of calculation proportional to the numbers of object planes.     

计算机制彩虹全息图的新算法

提出利用查表方法进行数字彩虹全息的计算方法.根据彩虹全息的基元全息图为线全息图的特点,找出物点与其线全息图的一一对应关系,建立空间点阵物点的线全息物光分布数据表.在对实际物体进行计算时,根据物点的位置,在数据表中找到与之对应的物光分布,并将这些分布进行叠加,从而形成实际物体被狭缝限制的物光分布,最后引入参考光计算其彩虹全息图.本方法充分利用了线全息图的性质,使得计算量大大减小,同时提高了计算速度.     

Sequential hologram interferometry with diffusely illuminated objects

Two simple holographic multiplexing techniques for sequential hologram interferometry of a diffusely illuminated object are described. These techniques enable one to use the frozen-fringe hologram interferometry to study a quasi-continuous change in the object and so regain some of the advantages of real-time hologram interferometry. In the first method of multiplexing with a single reference beam, a small angle prism is used for varying the direction of the reference beam between successive exposures and a double-exposure hologram is recorded at each position of the prism. In the second method of multiplexing with multiple reference beams, a separate reference beam is used for recording each state of the object independently and the interference pattern between any two states is obtained by simultaneous reconstruction of two light fields. The advantage of this method over the previous one is that it is also suitable for dynamic studies. Some reconstructed interferograms of a diffusely illuminated transparent object under different stresses are presented as illustrations.     

Step index fibre using laser interferometer

A model is suggested to describe the fringe shift which occurs due to the phase variations of cladded glass fibre introduced between the two plates of the liquid wedge interferometer illuminated with a He–Ne laser. The fringe shift of the phase object which appears in the denominator of the Airy distribution formula of the multiple beam interference is represented in the harmonic term. An experiment is conducted using liquid wedge interferometer where the step index glass fibre of a nearly quadratic thickness variation is introduced between the two plates of the interferometer. The obtained fringe shift shows a good agreement with the proposed quadratic model. The Matlab code is written to plot the interferometer fringes comprising the shift of the step index fibre. Secondly, recognition of elliptical fibres is outlined using tomographic imaging. Finally, results and concluding remarks are given.     

Fresnel hologram reconstruction of complex three-dimensional object based on compressive sensing

Reconstruction the computer generated Fresnel hologram of complex 3D object based on compressive sensing （CS） is presented. The hologram is synthesized from a color image and the depth map of the 3D object. With the depth map, the intensity of the color image can be divided into multiple slices, which satisfy the condition of the sparsity of CS. Thus, the hologram can be reconstructed at different distances with corresponding scene focused using the CS method. The quality of the recovered images can be greatly improved compared with that from the back-propagation method. What＇s more, with the sub-sampled hologram, the image can be ideally reconstructed by the CS method, which can reduce the data-rate for transmission or storage.     

基于液晶空间光调制器的全息显示

在传统的纯相位全息显示系统中, 一般基于快速傅里叶变换(FFT)算法来计算相位全息图, 在FFT的计算中需要遵循Nyquist采样定理, 因此, 重建图像的尺寸往往受限于空间光调制器的固定采样率. 这个限制可以通过卷积算法或者两步菲涅耳衍射算法来解决, 但是需要使用多个FFT的计算, 导致计算量增大. 鉴于此, 提出了一种基于透镜的纯相位全息图计算方法. 在全息图的计算中, 通过透镜的成像原理建立一个采样率可变的虚拟全息面, 通过调节相应的距离参数使得在全息图的计算中可以任意调节原始图像的采样率, 摆脱了传统方法中液晶空间光调制器带宽积对重建图像尺寸的限制, 并且这种算法只需使用一次FFT就能达到变采样率的衍射计算, 大幅提高了全息图的计算速度. 数值模拟及光学实验结果证明了此方法可以在全息显示光学系统中清晰地重建不同尺寸的图像. 同时该系统可以有效地消除由空间光调制器的像素化结构带来的零级衍射.     

X-ray interferometric Fresnel holography

The X-ray interferometric Fresnel holography was proposed and theoretically investigated. It was shown that under definite conditions the recorded interference pattern formed at the output surface ofthe analyzer crystal (the third block of interferometer) is the X-ray interferometric hologram (generally the Fresnel one) of the object under investigation. Further reconstruction of an image is performed with the help of visible light or a numerical method. As an example the recording of a Fresnel hologram of the simplest case of one-dimensional object, a narrow slit, and the reconstruction of an image by means of visible light were considered. This method may be used in X-ray microscopy and realized using synchrotron sources ofX-ray radiation, as well as X-ray free electron lasers.     

Holographic determination of the amplitude of vibrations of a surface scattering light diffusely

Formation of a focused-image time-averaged hologram of a surface scattering light diffusely and undergoing harmonic vibrations in its own plane is considered as an example. The Fresnel approximation is used in an analysis of the formation of an interference pattern from which the amplitude of such vibrations can be determined. It is shown theoretically and experimentally that this interference pattern is localized in the plane of formation of the Fourier transform of the scatterer and that the sensitivity of monitoring of the vibration amplitude increases on reduction in the radius of curvature of the wavefront of the radiation used to illuminate this surface.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 74–79, January, 1992.     

Numerical reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram

A numerical method of reconstruction of an object image using an X‐ray dynamical diffraction Fraunhofer hologram is presented. Analytical approximation methods and numerical methods of iteration are discussed. An example of a reconstruction of an image of a cylindrical beryllium wire is considered. The results of analytical approximation and zero‐order iteration coincide with exact values of the amplitude complex transmission coefficient of the object as predicted by the resolution limit of the scheme, except near the edges of the object. Calculations of the first‐ and second‐order iterations improve the result at the edges of the object. This method can be applied for determination of the complex amplitude transmission coefficient of amplitude as well as phase objects. It can be used in X‐ray microscopy.     

多平面全息三维显示及其噪声消除研究

基于层析法和Gerchberg-Saxton迭代算法,计算得到了多个平面构成的三维物体的计算全息图,并将该计算全息图加载于空间光调制器上,获得了具备全视差的三维立体显示。基于以上方法,对灰度图像进行显示,获得了较高的像质。构建了由100个平面组成的立方体,获得了立方体的三维图像。另外,在计算全息图时附加了相位平移函数,消除了由空间光调制器的栅格结构引起的多重衍射像噪声,将能量利用效率提高到原来的379%。这样,可获得高衍射效率、高像质且具备全视差的三维全息显示。