Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects.     

基于滤波成像的大视角数字全息技术

为提高数字全息再现像视角,提出一种基于滤波成像的数字全息技术来实现大视角的三维物体面型测量.利用离轴像面数字全息技术,通过在4F相干图像处理系统的空间频谱面处放置可移动的低通滤波器,使满足CCD分辨率的物光波与参考光波干涉形成全息图,并控制低通滤波及成像区域分别记录不同谱段的子全息图.再现时,首先对子全息图进行数字傅里叶变换,重构对应频谱段,并对频谱段进行拼接形成完整的物光频谱|而后通过数字再现获得大视角的数字全息再现像.利用该方法测量了圆柱形表面（光滑的缝纫针）的三维形貌,并取得了较好的实验结果.     

Optical circular sampling system for translation and rotation invariant pattern recognition

A simple but effective rotation invariant pattern recognition method based on optical circular sampling of the input pattern is described. The object is decomposed by a set of concentric rings. The distribution of energy between those rings is independent of the orientation of the object and characterizes it sufficiently to allow its classification. A computer generated hologram formed of concentric diffraction grating rings of suitable spatial frequencies may perform the sampling in parallel. In combination with a lens, each ring is then focused to a given position on a CCD detector where the intensity distribution may be found. Translation invariance is added to the system by sampling the intensity of the Fourier transform of the input object in combination with a liquid crystal light valve. A phototypesetter is used to write the hologram whose quality is demonstrated by optical experiments.     

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.     

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.     

Shifting selectivity of collinear volume holographic storage

A paraxial equation for calculating pixel-based 2-D shifting selectivity of collinear holographic storage system is proposed. The equation shows that the broader reference pattern makes high shifting selectivity. In addition, both amplitude and phase modulation make no obvious change in shifting selectivity so shifting selectivity is not affected through advanced design of reference pattern. Besides, a simplified formula based on a point signal is proposed, which shows a clear physical insight that the shifting selectivity is the square of Fourier transform of the intensity distribution of reference pattern and does not depend on thickness of the disc when a point signal is applied.     

Holographic digital data storage using phase-modulated pixels

We propose and demonstrate the use of phase images for holographic data storage. Use of phase images as input leads to uniform diffraction efficiency of multiplexed data pages. Use of binary phase-based data pages with 0 and π phase changes produces uniform spectral distribution at the Fourier plane. This in turn facilitates better recording of higher spatial frequencies. We experimentally demonstrate a phase-based holographic data storage system using shift multiplexing in a Fe:LiNbO₃ crystal, and use it for associative retrieval. Preliminary studies indicate high discrimination capabilities of phase-based holographic data storage system over the amplitude-based system in a content-addressable memory.     

Study of the parameters of a difference image in the presence of a linear phase shift

The spatial filtering in the localization range of the holographic lateral shearing interferograms of a solid object shows that the effect of the subtraction of the compared original data arrays is realized in the presence of a filtering aperture in the center of a dark fringe [1, 2]. Methods for the holographic subtraction of the images involving the detection and spatial filtering in the Fourier plane of the optical system are proposed and realized in [3–5]. Thus, the difference data can be reconstructed with a narrow (unexpanded) laser beam. However, a relatively high level of speckle noise in the difference image is caused by the spatial filtering with a small aperture (laser beam) in the minimum of the superposition field in the Fourier hologram plane. The detection of double-exposed Fourier holograms with a linear phase shift and the effect of the size of the filtering reconstructing beam on the resolution of the difference image are studied. In addition, the application of the multiple exposure for the broadening of the interference maxima is analyzed.     

Common-path interferometry with one-dimensional periodic filters

We discuss a spatial filtering interferometry setup that employs a periodic spatial filter with either cosine transmittance or binary phase modulation. The setup's input plane is formed by two separate windows, one of which supports a phase object and the other, a reference beam. Using the appropriate frequency and orientation of the filter produces an interference pattern of the two input fields at the output plane of the system. The main attributes and advantages of the setup are discussed and experimentally illustrated with the example of a binary phase periodic filter implemented with a spatial light modulator.     

Hoe/lensless matched spatial filter wavelength-scaling correlator

A scaling correlator optical pattern recognition system is described in which a lensless matched spatial filter (with the second Fourier transform lens and the matched spatial filter recorded on the same plate) is used with a first Fourier transform lens that is also an holographic optical element. The matched spatial filter is recorded at one wavelength and correlation is obtained at a second wavelength. Experimental demonstration and output correlation SNR data are reported, together with a comparison of the system's noise level using conventional optics and holographic elements.     

参考光波面质量对全息存储质量影响的数值模拟研究

采用数值模拟方法研究了不同种类参考光波面质量对再现图像质量的影响.针对全息实验实际情况,对二值图像建立了傅里叶变换全息图记录和读出的物理模型,分别考察采用一般平面波参考光、高斯光束球面波参考光和散斑参考光时的读出图像质量,并以信噪比损失作为衡量图像质量的定量工具.模拟结果表明,在理想平面波参考光和球面波参考光的情形,全息读出图像质量非常好,与输入图像相比信噪比损失在0.6dB以下.但是对于散斑参考光,尽管其极优的位移选择性提供了高密度存储的可能性,但再现图像质量明显变差,信噪比损失在5dB以上,实现有效的数据存储位密度将是十分困难的.为了兼顾存储密度和再现质量,应该考虑优化参考光的途径.     

基于自聚焦透镜的光纤数字全息系统实验研究

在光纤数字全息光路中引入自聚焦透镜，利用其特有的成像特性，作为物光波的中继传输器件，构成一套紧凑型光纤数字无透镜傅里叶变换全息记录系统，以实现对微小物体的全息记录与数值再现.研究结果表明，结合自聚焦透镜和光纤数字全息术的特点，不仅可使光学测试系统紧〖CM(42〗〖JP2〗凑、微型化，而且还可以对一些特殊环境、光线难以直接到达的隐藏区域或封闭系统内部进行测量.     

Parallel and time sequential optical multiplex systems for pattern recognition

Two optical multiplex arrangements for pattern recognition are compared. In the first system the Fourier spectrum of an object transparency is optically multiplied for parallel processing with a matrix of different holographic Fourier filters. In the other arrangement the spectrum of the object transparency is switched time sequentially by means of a light beam deflector onto different filters in the Fourier plane. In comparison the time sequential method appears better adapted for high information content.     

Comparison of the angular selectivity characteristics for an off-axis holographic storage system calculated by Born approximation and coupled-wave theory

The first Born approximation is applied to calculate the angular selectivity for different positions on the reconstructed image as a function of the object beam's optical axis angle theta(ob) and reference beam angle theta(rw) for a holographic data storage system that records the Fourier transform holograms in a medium with an infinite plane-wave reference beam. Results are compared with those calculated by the coupled-wave theory.     

Holographic contouring using double-source technique and Fourier transform analysis

This paper describes a double-exposure holographic contouring technique by the movement of the object beam through fibre optics. Single-mode optic fibres are used to transfer both object and reference beams. Between two exposures the object illumination beam is displaced. The contouring fringes can be visualised on the object surfaces. The fringe patterns are automatically processed by the fast Fourier transform (FFT) method, which produces a 3D perspective plot. Examples are given for different objects.     

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.     

像面滤波技术在无透镜傅里叶变换数字全息中的应用

无透镜傅里叶变换数字全息波前重建主要采用全息图的一次快速傅里叶变换方法,重建图像不能充分占有重建平面.本文基于像平面滤波技术,提出对物体局部区域光波场进行放大重建并让重建图像布满重建平面的方法,给出具有精细结构物体的数字全息波前重建实例.此外,将数字全息光波场重建视为具有方形出射光瞳的光学系统的相干光成像过程,导出了物体放大图像的分辨率与光学系统相关参量的关系,并通过实验给予证明.     

物光参考光同光轴的体全息存储光学系统设计

将两块漫射板分别置于输入面的两侧,使物光和参考光同光轴,可以使体全息存储傅里叶变换光学系统更为紧凑。然而,在这种全息存储光学系统中,物光和参考光的总数值孔径较物光数值孔径大很多。分析这种体全息存储光学系统物光和参考光光路的设计要求和光学参量的确定;采用多重结构方法对物光正向光路、逆向光路和参考光光路同时优化设计,实现对物光光路二对物像共扼位置控制像差,并满足参考光光路的要求;给出前后组焦距分别为33 mm和30 mm的物光和参考光同光轴,前工作距为30 mm,物光和参考光总数值孔径为0.53的全息存储光学系统的设计结果。系统的波像差小于0.071λ,达到衍射极限。     

像面滤波技术在无透镜傅里叶变换数字全息中的应用

无透镜傅里叶变换数字全息波前重建主要采用全息图的一次快速傅里叶变换方法,重建图像不能充分占有重建平面.本文基于像平面滤波技术,提出对物体局部区域光波场进行放大重建并让重建图像布满重建平面的方法,给出具有精细结构物体的数字全息波前重建实例.此外,将数字全息光波场重建视为具有方形出射光瞳的光学系统的相干光成像过程,导出了物体放大图像的分辨率与光学系统相关参量的关系,并通过实验给予证明.     

Design of the spatial filter window for digital holographic convolution reconstruction of object beam field

In the convolution reconstruction process of digital holographic object beam field, the object beam fields with different magnifications can be obtained when the reconstructing beams are spherical waves with different wave curvature radii. This paper presents a theoretical and experimental discussion on the useful spatial frequency spectrum of the hologram numerically illuminated by the spherical wave. The result shows that there would be an image in the spatial frequency spectrum of digital hologram, which is completely the same as the object, if the wave surface radius of the spherical wave is equal to the distance from the object to the CCD sensor. Taking this image as a reference and designing a filter, the position of the reconstructed images with different magnifications can be predicted correctly in the reconstructed plane. Additionally, since the spectrum distribution of zero-order diffraction can be forecasted accurately in theory, its contribution can be effectively eliminated through changing the spatial filter shape; then a reconstructed object field containing more high-frequency information can be obtained.