一种有效解决离轴数字全息相图倾斜畸变的数字参考平面方法

离轴数字全息中使用倾斜的平面参考波以消除成像中的零级衍射和共轭像是一种简捷和常用的方法,然而该方法遇到的一个困扰是,由于倾斜参考波引入了附加的载波频率并很难通过实验测量准确地获得附加的载波频率值或倾角,因此会导致重建的相图出现一定的倾斜畸变而无法完全修正.本文提出了一种数字参考平面算法以解决这一问题.该算法利用重建相图的平坦区域选点构建一个能准确表征相图倾斜的数字参考平面,并建立该平面参量与参考波载波频率的数学关系和作为随后相图畸变修正迭代计算的判据.该算法简单有效,不仅能实现对倾斜相位畸变的准确修正,而且能准确地获得倾斜平面参考波的附加载波频率.由于在相位解包裹重建中结合了抑噪处理,因此该方法在环境和系统噪声的影响下仍然有效,实验结果验证了理论设计的有效性.     

基于希尔伯特变换的干涉条纹相位解调新算法

提出了一种新的应用希尔伯特变换解调干涉条纹相位的算法,可以从单幅干涉条纹图中解调出全场相位分布.在实际应用中,常借助傅里叶变换实现希尔伯特变换算法,但是会忽略负频率成分,造成相位信息的丢失.对于相位分布非单调变化的干涉条纹,提出了一种判断函数,用来计算相位信息零频率点的分布.利用相位的零频率点分布构造了一个二元模板,使用该模板对本文提出的两次希尔伯特变换法产生的包裹相位图进行修正.对修正后的包裹相位图进行解包裹处理,可以得到连续的全场相位分布.对该方法用计算机模拟进行了验证.     

基于Hilbert变换实现数字全息高精度相位重建

为了提高数字全息相位重建精度,研究了基于Hilbert变换重建相位的理论和方法,并通过像面数字全息实验对该方法的有效性进行了验证,同时与数字全息常规重建方法得到的结果进行了比较.结果表明:Hilbert变换本身具有消除直流项的作用,对利用频域滤波滤除零级谱后的全息图进行Hilbert变换,能够彻底消除零级衍射项的干扰,从而提高相位重建精度.与常规重建结果相比,基于Hilbert变换的相位重建结果的标准偏差降低了14.0%.本文结果对提高数字全息相位重建精度具有重要的指导意义.     

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.     

Correction of wave-front retrieval errors caused by the imperfect collimation of reference beam in phase-shifting interferometry

In phase-shifting interferometry (PSI) the standard wave retrieval formulae are usually derived based on the condition of a plane reference beam normal to the recording plane. In practice, however, the reference wave may be a spherical wave of large radius or even have a slight inclination at the same time due to the imperfect collimation and coaxality of the optical system, and this fact will introduce phase distortion for the reconstructed object wave-front. A simple digital processing algorithm without any additional measurements is proposed to determine the unknown parameters of the spherical reference wave and then correct the object wave errors reconstructed with standard wave retrieval formulae. The effectiveness of this method is verified by a series of computer simulations, and its limitation is also discussed.     

Speckle reduction by a rotating aperture at the fourier transform plane

Statistical properties of the time-averaged speckle-reduced pattern at the image plane of a coherently illuminated uniform diffuse object are theoretically and experimentally studied. The diffuse object is assumed to be approximated by a deep random phase screen and zero-mean circular complex Gaussian statistics is also assumed to hold for the formation of speckles. The time-averaging process is performed by using a rotating aperture at the Fourier transform plane of the object. A theoretical study of the speckle reduction is conducted for a rotating Gaussian soft aperture at the Fourier transform plane. Expressions are analytically derived for the mean, autocorrelation function, power spectrum, and contrast of the time-averaged speckle pattern at the image plane. In particular, the contrast of the time-averaged speckle pattern is theoretically evaluated and its characteristics are discussed in detail. The theoretical results for the contrast are experimentally confirmed using a TV/film recording system. Excellent agreement between theoretical and experimental results is obtained.     

数字无透镜傅里叶变换全息术中非傍轴及离焦像差的校正

对数字无透镜傅里叶变换全息图直接采用逆傅里叶变换进行物场的数值重建时.需要满足两个条件:第一,全息图的记录过程必须满足傍轴近似条件,否则再现过程中会产生非傍轴像差;第二,记录全息图时物平面与参考点光源到全息图记录平面的距离必须相等,否则再现过程中会产生离焦像差.理论分析了非傍轴及离焦记录条件下数字无透镜傅里叶变换全息图的灰度分布特点,并提出了相应的非傍轴及离焦像差的数值校正方法.根据实际的非傍轴或离焦记录情况.分别给所记录的数字全息图灰度分布矩阵乘以适当的非傍轴或离焦校正因子,以消除灰度矩阵中非傍轴或离焦因素的影响.然后再对校正后的伞息图灰度矩阵做逆傅里叶变换处理.即可得到准确的数字再现像.实验结果表明.该数值重建方法能够有效地消除无透镜傅里叶变换全息术中数字再现像的非傍轴像差及离焦像差,提高再现像的质量.     

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 image encryption using fractional Fourier transform and chaos

We propose a new method for image encryption using fractional Fourier transform and chaos theory. Random phase masks are generated using iterative chaos functions. The input image is combined with the first random phase mask at the object plane and is then transformed using the fractional Fourier transform. After the first fractional Fourier transform, the second random phase mask, again generated by using the chaos functions, is used at the fractional plane. The second fractional Fourier transform operation is then carried out to obtain the encrypted image. Three types of chaos functions have been used: the logistic map, the tent map and the Kaplan–Yorke map. The mean square error and the signal-to-noise ratio between the decrypted image and the input image for the correct order and the incorrect order of the fractional Fourier transform have been calculated. The computer simulations are presented to verify the validity of the proposed technique.     

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.     

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.     

通过保留相位进行全息图信息压缩的方法

从全息图的特点出发,研究了全息图的记录和再现原理,提出了一种对离轴菲涅耳全息图信息压缩的方法。对全息图进行傅里叶变换,滤除零级噪声及物光波的共轭波前,仅仅保留物光波的相位信息,而后以采用较低的采样频率对全息图重新抽样,从而大大减少了数字全息图的信息冗余。压缩后的全息图也可以获得良好像质的再现像。理论和实验均证明了该方法的可行性,为全息图的信息存贮与传输提供一条新的途径。     

Application of acoustic reflection tomography to sonar imaging

Computer-aided tomography is a technique for providing a two-dimensional cross-sectional view of a three-dimensional object through the digital processing of many one-dimensional views (or projections) taken at different look directions. In acoustic reflection tomography, insonifying the object and then recording the backscattered signal provides the projection information for a given look direction (or aspect angle). Processing the projection information for all possible aspect angles enables an image to be reconstructed that represents the two-dimensional spatial distribution of the object's acoustic reflectivity function when projected on the imaging plane. The shape of an idealized object, which is an elliptical cylinder, is reconstructed by applying standard backprojection, Radon transform inversion (using both convolution and filtered backprojections), and direct Fourier inversion to simulated projection data. The relative merits of the various reconstruction algorithms are assessed and the resulting shape estimates compared. For bandpass sonar data, however, the wave number components of the acoustic reflectivity function that are outside the passband are absent. This leads to the consideration of image reconstruction for bandpass data. Tomographic image reconstruction is applied to real data collected with an ultra-wideband sonar transducer to form high-resolution acoustic images of various underwater objects when the sonar and object are widely separated.     

Quantitative damage imaging using Lamb wave diffraction tomography

In this paper, we investigate the diffraction tomography for quantitative imaging damages of partly through-thickness holes with various shapes in isotropic plates by using converted and non-converted scattered Lamb waves generated numerically. Finite element simulations are carried out to provide the scattered wave data. The validity of the finite element model is confirmed by the comparison of scattering directivity pattern(SDP) of circle blind hole damage between the finite element simulations and the analytical results. The imaging method is based on a theoretical relation between the one-dimensional(1D) Fourier transform of the scattered projection and two-dimensional(2D) spatial Fourier transform of the scattering object. A quantitative image of the damage is obtained by carrying out the 2D inverse Fourier transform of the scattering object. The proposed approach employs a circle transducer network containing forward and backward projections, which lead to so-called transmission mode(TMDT) and reflection mode diffraction tomography(RMDT),respectively. The reconstructed results of the two projections for a non-converted S0 scattered mode are investigated to illuminate the influence of the scattering field data. The results show that Lamb wave diffraction tomography using the combination of TMDT and RMDT improves the imaging effect compared with by using only the TMDT or RMDT. The scattered data of the converted A0 mode are also used to assess the performance of the diffraction tomography method. It is found that the circle and elliptical shaped damages can still be reasonably identified from the reconstructed images while the reconstructed results of other complex shaped damages like crisscross rectangles and racecourse are relatively poor.     

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.     

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.     

Image encryption using fractional Mellin transform,structured phase filters,and phase retrieval

An image encryption scheme has been presented by using two structured phase masks in the fractional Mellin transform (FrMT) plane of a system, employing a phase retrieval technique. Since FrMT is a non-linear integral transform, its use enhances the system security. We also add further security features by carrying out spatial filtering in the frequency domain by using a combination of two phase masks: a toroidal zone plate (TZP) and a radial Hilbert mask (RHM). These masks together increase the key space making the system more secure. The phase key used in decryption has been obtained by applying an iterative phase retrieval algorithm based on the fractional Fourier transform. The algorithm uses amplitude constraints of secret target image and the ciphertext (encrypted image) obtained from multiplication of fractional Mellin transformed arbitrary input image and the two phase masks (TZP and RHM). The proposed encryption scheme has been validated for a few grayscale images, by numerical simulations. The efficacy of the scheme has been evaluated by computing mean-squared-error (MSE) between the secret target image and the decrypted image. The sensitivity analysis of the decryption process to variations in various encryption parameters has also been carried out.     

基于变形分数傅里叶变换的六重密钥图像加密

提出一种利用变形分数傅里叶变换和双随机相位编码对图像加密的方法.对要加密的图像分别进行两次变形分数傅里叶变换和两次随机相位函数调制,使加密图像的密钥由原来两重增加到六重.利用全息元件,可以用光学系统实现这种加密和解密变换.计算机模拟结果表明,只有当六重密钥都完全正确时,才能准确地重建原图像,这种六重密钥加密方法提高了图像信息的安全保密性.     

利用相位模板实现数字全息超分辨成像

为了简化数字全息超分辨记录系统,分别在其物光和参考光部分引入一块相位模板,以获得垂直和倾斜方向照明物体的光束和具有不同载波频率的参考光束.当这些具有不同照射方向的光透过物体后,可以使CCD在位置固定的情况下记录到携带低频和高频信息的物体衍射场,不同载波频率的参考光则保证了高频和低频信息在复合全息图的频谱面上能够相互分离.实验结果证明,通过将记录到的物体高频和低频信息合成,可以获得超出系统衍射极限分辨率的再现像.     

Investigation of the phase velocities of guided acoustic waves in soft porous layers

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.