电子学全息法再现三维物场

叙述了一种采用电子学全息法分析三维物场的定量方法，它包括：（１）三维物场全息图的数字记录，２）全息图面上复振幅分布的数字再现，（３）利用空间频域衍射公式计算其它平面上的复振幅分布，由此可以获得整个三维物场的信息。本文同时还给出这一数字再现方法的空间分辨率。最后通过计算机模拟展示了一个理想三维物场的再现过程及再现结果。     

Holographic image projection using fractional Fourier transformation

A new method of image projection based on fractional Fourier transformation is presented. This method can project an image at any distance after a lens plane. We use a modified Gerschberg–Saxton (GS) iteration algorithm to compute a phase-only hologram. The amplitude distributions both on the hologram plane and image plane are restricted while allowing their phase distributions to drift into an optimum value. The quality of the image projected by fractional Fourier hologram is close to the image projected by Fourier hologram. The RMS error between the projected image and the constrained image is computed in our experiment. A comparison in flexibility of the two projection methods is also discussed.     

Real-time seeing through moving fog

Holographic observations through moving fog yield better images than ordinary photography does. Previously, holography through fog suffered from a time delay caused by the photographic development process of the hologram plate. Now we use the cathode of a TV tube for recording temporarily an image plane hologram of the object. This hologram is reconstructed at TV speed by means of an electronic high pass filter. The reconstructed image on the monitor is far superior over an ordinary image taken through the same fog.     

Lateral-shear interferograms registered with double-exposure recording of a gabor lens hologram

An analysis is made of the results of a double-exposure recording based on superposing the subjective speckle fields of a Gabor hologram with a negative lens located in the plane of the amplitude scatterer. It is shown that when the hologram is reconstructed a lateral-shear interferogram is formed in this plane and on the optic axis if the diffraction field is spatially filtered, and an interference pattern having twice the interferometer sensitivity for a fixed lateral shear is localized in the plane of the hologram. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 47–54, March, 1998.     

Quantization noise in binary holograms

The signal-to-noise (S/N) ratio in the reconstructed image from a binary hologram has been quantitatively related to the amplitude and phase quantization levels. The S/N ratio increases monotonically with increasing number of quantization levels. This observation is further supported by experimental results.     

Conjugate Image Plane Correlator with Holographic Disk Memory

A conjugate image plane correlator with holographic disk memory is proposed. Optical correlation between conjugate images reconstructed from a holographic disk and an input image on liquid-crystal television is executed with the rotation of the disk. Regardless of Fourier hologram recording with the pseudorandom diffuser, it is found possible to take out the diffuser from the original hologram recording scheme using an image reconstruction process and to get correlation signals between input and reconstructed conjugate images in the output plane of a two-lens imaging system. Generation of conjugate replicas with high contrast causes exact matching with an input image which results in high recognition performance for autocorrelation signals. The transfer function of an optical system can be controlled by adjustment of either hologram size or hologram area illuminated with a laser beam. Hence, the output intensity distribution can be adjusted by selecting a proper pupil function and the size of an output pupil defined by the input pupil size and the optical system magnification factor. The real-time character recognition by optical parallel high-speed processing for two dimensional images with position normalization is demonstrated.     

Fast calculation of wave front amplitude propagation: a tool to analyze the 3D image on a hologram (Invited Paper)

A simple approach to calculate the amplitude component of a wave front propagating in space from a hologram is proposed. It is able to calculate the amplitude distribution on a plane at any distance rapidly using a standard GPU. This is useful for analyzing and reconstructing the 3D image encoded on a hologram.     

Formation of the holographic image of a diffuse object in second-harmonic radiation generated by a nonlinear medium

Results of experiments on recording three-dimensional holographic images of extended diffuse objects using an SHG hologram generating the second harmonic are presented. In this case, the object image is formed by the second-harmonic radiation whose wavelength is smaller than the wavelength of object and reference waves recorded on a hologram by a factor of two. Elements of the theory of an SHG hologram are considered. A holographic image of a transparency object illuminated with diffuse light is obtained. It is shown that the resolving power of this image is close to the limit determined by diffraction effects. An experiment on defocusing the reconstructed image showed that it was localized in one spatial plane and, therefore, was three-dimensional.     

Object image correction using an X‐ray dynamical diffraction Fraunhofer hologram

Taking into account background correction and using Fourier analysis, a numerical method of an object image correction using an X‐ray dynamical diffraction Fraunhofer hologram is presented. An example of the image correction of a cylindrical beryllium wire is considered. A background correction of second‐order iteration leads to an almost precise reconstruction of the real part of the amplitude transmission coefficient and improves the imaginary part compared with that without a background correction. Using Fourier analysis of the reconstructed transmission coefficient, non‐physical oscillations can be avoided. This method can be applied for the determination of the complex amplitude transmission coefficient of amplitude as well as phase objects, and can be used in X‐ray microscopy.     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

Synthesis of multifrequency optical holograms of rotating objects

A two-channel system for synthesizing two-dimensional complex multifrequency optical holograms of rotating objects was developed. In the object irradiation (longitudinal) direction, a hologram is synthesized due to multifrequency laser radiation, and in the transverse direction, the synthesis is provided by object rotation. The object image is reconstructed in the plane coinciding with the plane of its rotation. The resolution of the synthesized hologram in the longitudinal direction is determined by the frequency bandwidth of the laser radiation, and in the transverse direction, the resolution is determined by the initial laser-radiation frequency and the angle of object rotation during the time of hologram synthesis. Using a digital simulation, the degree of isoplanarity of the multifrequency system for synthesizing holograms of rotating objects and its noise immunity under conditions of phase noises were analyzed.     

Particle digital in-line holography with spherical wave recording

In this paper, we propose a method of digital in-line holography of particle. A diverging spherical beam is used for illumination in recording hologram, the complex amplitude distribution generated by particle field at a single plane located in the Fresnel diffraction region is recorded by CCD, and a plane beam for reconstructing hologram, then, the magnified image can be obtained by numerical reconstruction in computer. This procedure can be interpreted by Fourier optical theory and the theoretical analysis have been done in detail, the experimental results, the air freshener being subject, are also given.     

Off-axis phase-only holograms of 3D objects using accelerated point-based Fresnel diffraction algorithm

A method for calculating off-axis phase-only holograms of three-dimensional (3D) object using accelerated point-based Fresnel diffraction algorithm (PB-FDA) is proposed. The complex amplitude of the object points on the z-axis in hologram plane is calculated using Fresnel diffraction formula, called principal complex amplitudes (PCAs). The complex amplitudes of those off-axis object points of the same depth can be obtained by 2D shifting of PCAs. In order to improve the calculating speed of the PB-FDA, the convolution operation based on fast Fourier transform (FFT) is used to calculate the holograms rather than using the point-by-point spatial 2D shifting of the PCAs. The shortest recording distance of the PB-FDA is analyzed in order to remove the influence of multiple-order images in reconstructed images. The optimal recording distance of the PB-FDA is also analyzed to improve the quality of reconstructed images. Numerical reconstructions and optical reconstructions with a phase-only spatial light modulator (SLM) show that holographic 3D display is feasible with the proposed algorithm. The proposed PB-FDA can also avoid the influence of the zero-order image introduced by SLM in optical reconstructed images.     

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.     

A new method for producing point holograms

A new method is proposed for producing point holograms by utilising highly correlated, extended sources rather than point-like sources in the recording process. The theory of this method is presented. Its feasibility is demonstrated experimentally. A multiple imaging experiment is described which utilises this kind of hologram. Advantages and limitations of holograms of extended sources are discussed.List of Symbols R complex amplitude of the reference wavefront in the hologram plane - S complex amplitude of the signal wavefront in the hologram plane - D complex amplitude of the reconstructing wavefront in the hologram plane - T complex amplitude of the reconstructed wavefront in the hologram plane - r complex amplitude of the wavefront illuminating the reference transparency - s complex amplitude of the wavefront illuminating the reference transparency - d complex amplitude of the wavefront illuminating the reference transparency - t complex amplitude of the wavefront illuminating the reference transparency - p amplitude transmittance of the reference transparency - amplitude transmittance of the signal transparency - (-function) amplitude transmittance of the reconstructing transparency - amplitude transmittance of the reconstructed transparency - P _r ,P _s propagation functions at distancesz _r ,z _s , respectively (equation 3) - x, y co-ordinates in the source plane - , co-ordinates in the hologram plane - z _r ,z _s distances of the reference, signal source from the hologram plane - X _r ,y _r co-ordinates of the reconstructing source (-function) - a, h shift co-ordinates in the autocorrelation integral (equation 12) - f _r,f _s Fourier transform operator at distances z_r,z _s (equation 7a) wavelength - k=2/ wavenumber - * conjugate complex - (*) convolution     

数字全息波前重建中的像平面滤波技术研究

基于数字全息图的频谱平面滤波及像平面滤波技术,最近出现两种可变放大率的物光波前重建方法.为适应数字全息精细检测的要求,对两种滤波方法进行了研究,导出让局部重建图像布满重建平面的表达式.研究结果表明,像平面滤波技术优于频谱平面滤波技术,基于像平面滤波技术的重建方法能够按照需要的放大率高质量地重建局部物光场.给出彩色数字全...     

High efficient generation of holographic stereograms based on wavefront recording plane

A computer generated holographic stereogram based on the wavefront recording plane(WRP) is presented. A WRP closed to the parallax image plane is introduced to record the complex amplitude in a small region for each point in the parallax image. By using three times of fast Fourier transform(FFT) to execute the Fresnel diffraction calculation between the WRP and the holographic stereogram plane, the object wave contributing to the hologram pattern can be achieved. The computation complexity of the proposed approach is dramatically reduced. The results show that the calculation time can be decreased by more than one order of magnitude.     

单幅同轴全息图两步迭代收缩重建

利用压缩传感理论中的两步迭代收缩重建算法,开展单幅同轴全息图重建实验研究,实现单幅同轴全息图共轭重建像的消除并克服数字全息技术在轴向聚焦平面识别能力的不足。以数字图像和标准分辨率板为记录物体,比较分析了基于两步迭代收缩算法和菲涅尔近似衍射重建算法的重建质量;以两根裸光纤为实验样本,分析了两步迭代收缩重建算法对记录物体轴向不同焦平面的识别能力。实验结果表明两步迭代收缩重建算法可得到清晰度高于68.73%的重建信息,同时对直径为125 m的两根光纤在9 mm的轴向间距条件下,显示出了比全息菲涅尔近似算法更好的聚焦平面识别能力。这一轴向聚焦识别能力有助于数字全息技术应用于功能材料梯度参数或功能涂层光学器件涂层厚度检测。     

Effect of intensity quantization level in parallel phase-shifting digital holography

Parallel phase-shifting digital holography (PPSDH) enables the instantaneous recording of three-dimensional fields. The three-dimensional field can be reconstructed using a computer by numerical scalar wave propagation. In PPSDH, we record a space-division multiplexed hologram that includes the required phase retardation in the spatial distribution of the reference wave and then interpolate the data at blanked pixels for each phase retardation to obtain the complex amplitude distribution of an object wave. The recorded quality of the multiplexed hologram influences the reconstruction quality. In this study, we investigate the effect of the intensity quantization of a multiplexed hologram on the reconstruction quality. We compare the influence of intensity quantization in PPSDH with that in the conventional phase-shifting method. Random noise is also added to the multiplexed hologram. The required intensity quantization level is helpful for selecting a digital image sensor.     

On the applicability of the linear regression model for describing Fourier holography

The linear regression model is shown to describe adequately the 4-f scheme of Fourier holography with wave front reversal in the correlation plane and with the use of the hologram with the inverse transfer characteristic at the stage of passage of light in the reverse direction. If an image as a realization of a random field possesses the property of wide-sense stationarity, then the halo around the image of the reference reconstructed with this scheme is the best prediction. The possibility of realization of a function of selective attention highlighting the image area in which changes occurred is ascertained. An experimental illustration using an aerial image of a forestland as an example is given.