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     

结合线性回归的离轴数字全息去载波相位恢复算法

为实现仅用一幅离轴数字全息图便能直接恢复相位,提出一种利用空间载波相移技术(spatial carrier phase shift, SCPS)和线性回归相结合的离轴数字全息去载波相位恢复算法.首先,利用SCPS将一幅离轴数字全息图分为四幅含有载波相移的全息图,其中载波相移由沿行、列两个方向的正交载波所引入;然后,将四幅载波相移全息图作为输入,将所求物体相位和两个正交的载波作为未知量,结合最小二乘法和线性回归同时求出载波和相位信息.相较于已有的去载波技术,本算法无需背景全息图作为参考,便可准确地去除载波,实现高质量的相位重建.本文结合数值仿真和具体实验结果验证本算法的有效性和优越性.     

Multiple information encryption by user-image-based gyrator transform hologram

A novel multiple information encryption by user-image-based gyrator transform hologram is proposed. In encryption process, each channel of the user image is phase encoded, modulated by random phase function and then gyrator transformed to get the gyrator spectrum of user image. Subsequently, each channel of the secret image is normalized, phase encoded, multiplied by modulated user image, and then gyrator transformed to obtain the gyrator spectrum of secret image. The encrypted digital hologram is recorded by the interference between the gyrator spectrum of user image and the spherical wave function. Similarly, the digital hologram for decryption is recorded by the interference between the gyrator spectrum of secret image and the spherical wave function. The multiple encrypted digital holograms are multiplexed into a final encoded hologram and the corresponding digital holograms for decryption are multiplexed into a final hologram for decryption. The wavelength and radius of the spherical wave function, and angle of gyrator transform are all essential keys for decryption. The proposed system has two main features. First, the encrypted hologram has no information about secret image. Second, the hologram for decryption used as identification key. Consequently the two marked security layers of information protection are achieved. The proposal can be realized by optoelectronic system. Numerical simulation results demonstrate the feasibility and security of the proposed technique.     

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.     

Synthetic aperture fourier holographic optical microscopy

We report a new synthetic aperture optical microscopy in which high-resolution, wide-field amplitude and phase images are synthesized from a set of Fourier holograms. Each hologram records a region of the complex two-dimensional spatial frequency spectrum of an object, determined by the illumination field's spatial and spectral properties and the collection angle and solid angle. We demonstrate synthetic microscopic imaging in which spatial frequencies that are well outside the modulation transfer function of the collection optical system are recorded while maintaining the long working distance and wide field of view.     

Optical retrieval of encrypted digital holograms for secure real-time display

Secure data transmission by use of encrypted digital holograms and an optical retrieval system for secure real-time display are proposed. Original images are encrypted by a double-random phase encryption technique and then are recorded as digital holograms in a CCD, together with a reference plane wave. This digital hologram of the encrypted image can be transmitted to receivers via any conventional electronic or digital communication channels. The decryption key is also recorded as a digital hologram. At the receiver, the original image can be retrieved by an optical correlation-based reconstruction process. Both encryption and retrieval can be performed by all-optical means, and thus a real-time secure display can be implemented. We demonstrate the proposed system numerically and experimentally.     

Review of Fresnel incoherent correlation holography with linear and non-linear correlations

Fresnel incoherent correlation holography(FINCH) is a well-established incoherent imaging technique. In FINCH, three selfinterference holograms are recorded with calculated phase differences between the two interfering, differently modulated object waves and projected into a complex hologram. The object is reconstructed without the twin image and bias terms by a numerical Fresnel back propagation of the complex hologram. A modified approach to implement FINCH by a single camera shot by pre-calibrating the system involving recording of the point spread function library and reconstruction by a nonlinear cross correlation has been introduced recently. The expression of the imaging characteristics from the modulation functions in original FINCH and the modified approach by pre-calibration in spatial and polarization multiplexing schemes are reviewed. The study reveals that a reconstructing function completely independent of the function of the phase mask is required for the faithful expression of the characteristics of the modulating function in image reconstruction. In the polarization multiplexing method by non-linear cross correlation, a partial expression was observed, while in the spatial multiplexing method by non-linear cross correlation, the imaging characteristics converged towards a uniform behavior.     

Digital off-axis holography without zero-order diffraction via phase manipulation

By means of manipulating the phase information of the object beam in an off-axis digital holographic setup, we show that it is possible to fully eliminate the zero-order diffraction (ZOD) from numerically reconstructed holograms. Two different approaches are presented. In the first method, we introduce a ground glass on the object path beam to provide a random phase illumination. The subtraction between two holograms recorded with different positions of the ground glass yields a ZOD free hologram. In the second approach, a piece of window glass inserted on the path of the object beam produces a constant phase shift. The subtraction of two holograms, one recorded with and one without window glass generates a new hologram whose numerical reconstruction is ZOD free. Theoretical models and experimental results are shown to validate our proposals. They show that the proposed methods totally remove the ZOD without ruining the object information.     

Performances of an all-optical subtracted joint transform correlator that uses a photorefractive crystal

An all-optical subtracted joint transform correlator (JTC) was proposed and it was experimentally shown that the correlator successfully performs the pattern recognition with the number of reference patterns. In the correlator, an optical interferometer was introduced to remove the additional correlation signals between the reference patterns themselves from the output plane and a photorefractive crystal was also introduced to record the joint power spectra as volume holograms. The processing for removing the additional correlation signals was performed by the parallel computations in the interferometer in real time. In this study it has been found that the correlator yields significantly better correlation results than the classical joint transform correlator does and the recording of the volume hologram corresponds to a nonlinear processing of the joint power spectrum in the fringe-adjusted joint transform correlator. However the volume hologram has angular selectivity for matching the Bragg condition. It would restrict the shift-invariant area of the input image plane. This restriction has been investigated experimentally.     

Multi-wavelengths digital holography: reconstruction, synthesis and display of holograms using adaptive transformation

A method based on spatial transformations of multiwavelength digital holograms and the correlation matching of their numerical reconstructions is proposed, with the aim to improve superimposition of different color reconstructed images. This method is based on an adaptive affine transform of the hologram that permits management of the physical parameters of numerical reconstruction. In addition, we present a procedure to synthesize a single digital hologram in which three different colors are multiplexed. The optical reconstruction of the synthetic hologram by a spatial light modulator at one wavelength allows us to display all color features of the object, avoiding loss of details.     

基于空间光调制器的非相干数字全息单次曝光研究

菲涅耳非相干相关全息术(Fresnel incoherent correlation holography,FINCH)利用在空间光调制器(spatial light modulator,SLM)上加载双透镜模式对同一物点光分束自相干,并通过改变加载的相位因子得到不同的相移全息图.本系统利用SLM可分区编码调制特性,将FINCH成像中SLM上分三次加载的0°,120°,240°相位双透镜掩模各提取1/3组成一幅复合相移模式加载,并研究了三种相位分布方式对FINCH成像质量的影响.结果表明:三个相位在SLM上分布间隔越大,再现像越清晰.在此基础上,提出了一种新的掩模加载方式,在SLM加载透镜阵列,每一个相位因子对应一个双透镜,具有一个光轴.实验表明,通过这种加载方式,通过SLM后形成的三个相移图能够一次在电荷耦合器上记录,并且三个相移图不重叠,然后通过MATLAB编程计算将不同相移角度的全息图分别提取出来,通过三步相移计算合成一幅包含有物光波的复值全息图,最后通过数值再现算法重建待测样品.此系统可用于对光源相干性较低的实时成像系统,也为微小形变测量、动态物体的观测提供了新方法,为非相干数字全息术的发展提供了新思路.     

A comparison of iterative Fourier transform algorithms for image quality estimation

A comparison was established between two iterative Fourier transform algorithms (IFTAs), such as the original Gerchberg–Saxton (GS) and the mixed-region amplitude freedom (MRAF) algorithms, for the hologram reconstruction of different target images through the full reference image quality estimation (IQE) and pixel homogeneity in the Fourier plane presented theoretically and experimentally. The comparison was applied depending upon both algorithms based on a computer-generated hologram (CGH) implemented utilizing a reflective phase-modulated liquid-crystal spatial light modulator (LC-SLM) to obtain the digital kinoform holograms of the desired intensity distributions. These digital holograms were applied to reconstruct the intensity patterns for 852 nm, which represents a laser beam source. The theoretical and experimental results of the reconstructed patterns obtained using the MRAF algorithm were found to be smoother and better than the patterns obtained using the GS algorithm. Unmodulated light beam (dc term) is removed from the reconstructed patterns attributed to digital kinoform holograms of MRAF algorithm as an alternative to the theoretical and experimental results without using any additional optic equipment at the light path. Moreover, this paper discussed the full reference objective quality estimations, such as mean square error (MSE), peak signal-to-noise ratio (PSNR), structural content (SC), normalized absolute error (NAE), normalized cross correlation (NK), and homogeneity of pixels, through the contrast (Cont) and inverse difference moment (IDM) for numerical and experimental results. According to the two desired intensity distributions processed theoretically and experimentally, the results of MRAF algorithm were found to be in the highly accurate recovered phase, the quality of image was enhanced, and the dc term was decreased. Image quality estimation of full reference objective relay on the feedback algorithms experimental attestation has not been implemented yet.     

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.     

Twin-image elimination experiments for three-dimensional images in optical scanning holography

Twin-image elimination in the context of optical scanning holography has recently been proposed. The proposed technique involves simultaneously acquiring sine and cosine Fresnel holograms. A complex hologram is then formed by complex addition of the holograms, and twin-image rejection is predicted by computer simulations. An experimental verification of the technique by optical acquisition of the two holograms and subsequent reconstruction of the complex hologram digitally is reported. Three-dimensional image reconstruction without twin-image noise is demonstrated.     

Holographic three-dimensional display synthesized from three-dimensional fourier spectra of real existing objects

A method of synthesizing computer-generated holograms of real existing objects is proposed that is based on a series of projection images of an incoherently illuminated object recorded from different perspectives. In accordance with the principles of computer tomography, the three-dimensional Fourier spectrum of the object is calculated by use of several projection images. A method of calculating a Fresnel hologram from the three-dimensional Fourier spectrum is proposed. Experimental results in the form of a computer simulation and optical reconstruction are presented.     

Transient vibration measurements using multi-pulse digital holography

An optical system for the evaluation of transient deformations will be described. In order to increase the temporal resolution, a ruby laser producing four pulses has been used. Four separate digital holograms (one hologram for each pulse) of the test object are recorded in a few microseconds on three CCD sensors. The Fourier method is used for the quantitative evaluation of the digital holograms. The phases are obtained from the complex amplitudes, and the deformation at different times is calculated from phase subtraction. Experimental results are presented.     

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.     

An Iterative Fourier Transform Algorithm for digital hologram generation using phase-only information and its implementation in a fixed-point digital signal processor

An Iterative Fourier Transform Algorithm (IFTA) for digital hologram generation from a digital image using phase-only information is described in this paper. The algorithm is implemented in a Texas Instruments TMS320C64x fixed point digital signal processor (DSP). The holograms are reconstructed in real time using a liquid crystal display system and a He–Ne laser. The ideas described in this paper can be extended to digital hologram generation of three-dimensional objects and their reconstruction in real time using liquid crystal spatial light modulators, which could be a way for 3D-display systems.     

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     

Symmetry dependence of holograms for optical trapping

No iterative algorithm is necessary to calculate holograms for most holographic optical trapping patterns. Instead, holograms may be produced by a simple extension of the prisms-and-lenses method. This formulaic approach yields the same diffraction efficiency as iterative algorithms for any asymmetric or symmetric but nonperiodic pattern of points while requiring less calculation time. A slight spatial disordering of periodic patterns significantly reduces intensity variations between the different traps without extra calculation costs. Eliminating laborious hologram calculations should greatly facilitate interactive holographic trapping.