Color pattern recognition based on the joint fractional Fourier transform correlator

A new system of multi-channel single-output joint fractional Fourier transform correlator (JFRTC) for color pattern recognition is proposed based on the conventional system of multi-channel single-output joint transform correlator (JTC). The theoretical analysis and optical experiments are performed. With this method, one can obtain three correlation peaks at the output plane which show a pair of desired cross-correlation peaks and one auto-correlation peak. In comparison, the conventional system leads to more correlation peaks playing a noise role in color pattern recognition.     

联合分数变换相关器的分数相关特性分析

从分数傅里叶变换（FRFT）的定义出发，理论分析了联合分数变换相关器（JFRTC）的分数相关特性.从所得JFRTC的数学表达式中可以看出，将FRFT应用到联合变换相关器（JTC）中得到的JFRTC具有与传统JTC不同的性质.对于传统JTC，一旦输入平面上参考图像与目标图像之间的距离给定，相关输出峰的位置即确定，而JFRTC的相关输出峰的位置则可以由分数级次p₁和p₂来自由调节，这个特性在实际模式识别中非常有用.另一方面，JFRTC的相关输出峰值在大多数情况下低于传统JTC的相关峰值，却是JFRTC的一大缺点.最后，从FRFT的比例性质出发，给出了FRFT谱畸变不变的实现条件，并由此预言了JFRTC畸变不变模式识别的功能.     

A new kind of double image encryption by using a cutting spectrum in the 1-D fractional Fourier transform domains

Based on 1-D fractional Fourier transform, we proposed an image encryption algorithm in order to hide two images simultaneously. When the fractional order is closed to 1, most energy in frequency domain is centralized in the center part of spectrum. The image can be recovered acceptable by using a half of spectrum, which locates in the middle part at x-direction or y-direction. Cutting operation is employed in order to combine two spectra. Double random phase encoding is employed for image encryption. The corresponding numerical simulations are performed to demonstrate the validity and efficiency of the algorithm.     

Laser speckle movements related to platinum-electrolyte interface

Speckle movements are discovered in the investigation of a platinum-hydrogen system in 1N HClO₄. The speckle pattern of the light scattered off by a platinum-electrode surface is displaced laterally as a whole as a function of the electrode potential. The derivative of the photocurrent profile corresponding to the speckle displacement has four peaks in the so-called hydrogen region of the electrode potential. Three of these peaks have a certain correlation with the electrochemical aging effect which is attributed to hydrogen adsorbed on to the electrode surface. The feasibility of using this effect for in situ investigations of the metal-solution interface is pointed out.     

利用分数傅里叶变换相关实现散斑相关测量

提出了一种在匹配滤波相关中利用分数傅里叶变换代替傅里叶变换实现散斑相关测量的方法.利用分数傅里叶变换的指数性质,采用把移变后的散斑图像先进行相位调制,再进行分数傅里叶变换的方法,有效地解决了分数傅里叶变换的移变性带来的谱移问题.编程模拟和拉伸试件位移场测量的结果表明,只要选择合适的分数傅里叶变换级次和相位调制函数,可以得到优于傅里叶变换相关的理想输出.     

Phase imaging from a diffraction pattern in the presence of vortices

We investigate phase imaging from a diffraction pattern in the presence of vortices. In particular we demonstrate that a difference map method for phase retrieval which contains a support constraint does not necessarily conserve the net topological charge of the trial wave field. Hence, no a priori information regarding the charges of the vortices is required for a successful phase retrieval.     

Optical color image encryption with redefined fractional Hartley transform

We propose a new method for color image encryption by wavelength multiplexing on the basis of two-dimensional (2-D) generalization of 1-D fractional Hartley transform that has been redefined recently in search of its inverse transform. A color image can be considered as three monochromatic images and then divided into three components and each component is encrypted independently with different wavelength corresponding to red, green or blue light. The system parameters of fractional Hartley transform and random phase masks are keys in the color image encryption and decryption. Only when all of these keys are correct, can the image be well decrypted. The optical realization is then proposed and computer simulations are also performed to confirm the possibility of the proposed method.     

The use of a consumer grade photo camera in optical-digital correlator for pattern recognition and input scene restoration

In this work an optical-digital correlator for pattern recognition and input scene restoration is described. Main features of the described correlator are portability and ability of multi-element input scenes processing. The correlator consists of a consumer grade digital photo camera with a diffractive optical element (DOE) inserted as a correlation filter. Correlation of an input scene with a reference image recorded on the DOE are provided optically and registered by the digital photo camera for further processing. Using obtained correlation signals and DOE’s point spread function (PSF), one can restore the image of the input scene from the image of correlation signals by digital deconvolution algorithms.The construction of the correlator based on the consumer grade digital photo camera is presented. The software procedure that is necessary for images linearization of correlation signals is described. Experimental results on optical correlation are compared with numerical simulation. The results of images restoration from conventionally and specially processed correlation signals are reported. Quantitative estimations of accuracy of correlation signals as well as restored images of the input scene are presented.     

Image watermarking based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform domain

A novel digital image watermarking system based on an iterative phase retrieval algorithm and sine-cosine modulation in the discrete-cosine-transform (DCT) domain is proposed. The original hidden image is first encrypted into two phase masks. Then the cosine and sine functions of one of the phase masks are introduced as a watermark to be embedded into an enlarged host image in the DCT domain. By extracting the watermark of the enlarged superposed image and decryption we can retrieve the hidden image. The feasibility of this method and its robustness against some attacks, such as occlusion, noise attacks, quantization have been verified by computer simulations. This approach can avoid the cross-talk noise due to direct information superposition and enhance the imperceptibility of hidden data.     

Phase measurement improvement in temporal speckle pattern interferometry using empirical mode decomposition

When the Hilbert transform method is used to recover the phase distribution in temporal speckle pattern interferometry, the influence of the fluctuations of the bias and the modulation intensities on the calculated phase must be driven heuristically. In this paper we show that the Empirical Mode Decomposition method can overcome these drawbacks and consequently introduces an improvement in the evaluation of the phase distribution. An example is used to illustrate the phase measurement improvement that can be obtained by the application of the proposed approach.     

Multichanneled puzzle-like encryption

In order to increase data security transmission we propose a multichanneled puzzle-like encryption method. The basic principle relies on the input information decomposition, in the same way as the pieces of a puzzle. Each decomposed part of the input object is encrypted separately in a 4f double random phase mask architecture, by setting the optical parameters in a determined status. Each parameter set defines a channel. In order to retrieve the whole information it is necessary to properly decrypt and compose all channels. Computer simulations that confirm our proposal are presented.     

X-ray study of molecular oxygen adsorbed on graphite

We have performed a detailed X-ray diffraction study of O₂ adsorbed on UCAR-ZYX and Le Carbon Lorraine vermicular exfoliated graphite between 15 and 50 K. At least four phases of physisorbed oxygen are found. The monolayer δ phase consists of a centered parallelogram lattice, with the molecular axes parallel to the graphite surface. The data are consistent with a triple point at 26 K. The melting transition at a coverage of one monolayer appears to be first order. At higher coverages the molecules undergo a lying-down to standing-up transition; the higher coverage ζ phase froms an approximately triangular lattice with the molecular axes perpendicular to the graphite surface. Satellite peaks around the (1, 0) Bragg peak indicate, however, that this cannot be a simple triangular lattice; possible explanations include successively incommensurate layers or a sinusoidal density modulation. For coverages in the two-layer region the ζ phase modulation peaks disappear at 37 K, and at 40 K the adsorbed oxygen appears to undergo a first order melting transition into a fluid phase. With increasing coverage, the 2D X-ray diffraction profiles and phase boundaries do not connect smoothly onto those of the 3D α and β phases. At low temperatures (T < 30 K) the ζ phase always coexists with bulk crystallites; for temperatures near the 2D melting transition the 3D peaks are not observable. These data, taken together with the heat capacity results, suggest a wetting transition with only the bilayer lamellar phase or bulk O₂ being stable at low temperatures.     

Vibrational anisotropy of MnO6 octahedron and phase separation in La0.67−yPryCa0.33MnO3 manganites

The role of vibrational anisotropy of Mn³⁺O₆ octahedron in the phase separation behavior of La_0.67−yPr_yCa_0.33MnO₃ (x=0, 0.15, 0.25 and 0.30) has been investigated by means of magnetization M, internal friction Q⁻¹, Young's modulus E along with the X-ray powder diffraction measurements. For the samples with y=0 and 0.15, the Q⁻¹ exhibits three peaks in the ferromagnetic region, which are attributed to the intrinsic inhomogeneity of ferromagnetic phase, i.e. the electronic phase separation with the coexistence of insulating and conducting phases. However, both the samples with y=0.25 and 0.30 undergo a magnetic phase separation with the coexistence of the antiferromagnetic and ferromagnetic phases, and the Q⁻¹ peaks related to the electronic phase separation have not been observed. In addition, the Q⁻¹ exhibits a peak in the paramagnetic region for all samples, which may result from the formation of magnetic clusters. We observed that the evolution from electronic to magnetic phase separation is close related to the rapid increase in the ratio of two kinds of Jahn-Teller distortion modes Q₃ and Q₂, i.e. Q₃/Q₂. A schematic phase diagram is given in the text, and it is suggested that the enhancement of vibrational anisotropy of Mn³⁺O₆ octahedron plays a key role in the evolution from electronic to magnetic phase separation.     

Uncertainty analysis of temporal phase-stepping algorithms for interferometry

We have addressed the problem of the uncertainty evaluation of phase values rendered by two popular algorithms: the N-bucket and the (N + 1)-bucket, both used to exploit temporal phase-stepping techniques. These algorithms, are mainly affected by errors in the calibration of the piezoelectric transducers used to achieve the phase shift, external vibration and optical noise. We have characterized and compared the influences of these errors on the phase uncertainty. We applied a Monte Carlo-based technique of uncertainty propagation that allowed us to consider in the uncertainty evaluation the simultaneous contributions of different error sources. The uncertainty evaluation was performed for phase values in the range (0, 2π), with different values of N and assuming that the phase was calculated from fringe patterns generated by using either Moiré interferometry or electronic speckle-pattern interferometry. We found that the uncertainties associated with the phases rendered by both algorithms are similar and they can be significantly affected by the optical noise and the value of N.     

Phase transition, structural and electrical properties of Pb(Zn1/3Nb2/3)O3-doped Pb(Ni1/3Nb2/3)O3-PbTiO3 ceramics prepared by solid-state reaction method

Phase pure perovskite (1−x−y)Pb(Ni_1/3Nb_2/3)O₃-xPb(Zn_1/3Nb_2/3)O₃-yPbTiO₃ (PNN-PZN-PT) ferroelectric ceramics were prepared by conventional solid-state reaction method via a B-site oxide mixing route. The PNN-PZN-PT ceramics sintered at the optimized condition of 1185 °C for 2 h exhibit high relative density and rather homogenous microstructure. With the increase of PbTiO₃ (PT) content, crystal structure and electrical properties of the synthesized PNN-PZN-PT ceramics exhibit successive phase transformation. A morphotropic phase boundary (MPB) is supposed to form in (0.9−x)PNN-0.1PZN-xPT at a region of x=32-36 mol% confirmed by X-ray diffraction (XRD) measurement and dielectric measurement. The MPB composition can be pictured as providing a “bridge” connecting rhombohedral ferroelectric (FE) phase and tetragonal one since crystal structure of the MPB composition is similar to both the rhombohedral and tetragonal lattices. Dielectric response of the sintered PNN-PZN-PT ceramics also exhibits successive phase-transition character. 0.64PNN-0.1PZN-0.26PT exhibits broad, diffused and frequency dependent dielectric peaks indicating a character of diffused FE-paraelectric (PE) phase transition of relaxor ferroelectrics and 0.40PNN-0.1PZN-0.50PT exhibits narrow, sharp and frequency independent dielectric peaks indicating a character of first-order FE-PE phase transition of normal ferroelectrics. The FE-PE phase transition of 0.56PNN-0.1PZN-0.34PT is nearly first-order with some diffused character, which also exhibits the largest value of piezoelectric constant d₃₃ of 462pC/N.     

A discrete fractional angular transform

A new discrete fractional transform defined by two parameters (angle and fractional order) is presented. All eigenvectors of the transform are obtained by an angle using recursion method. This transform is named as discrete fractional angular transform (DFAT). The computational load of kernel matrix of the DFAT is minimum than all other transforms with fractional order. This characteristics has very important practical applications in signal and image processing. Numerical results and the mathematical properties of this transform are also given. As fractional Fourier transform, this transform can be applied in one and two dimensional signal processing.     

Fractional Fourier transform for off-axis elliptical Gaussian beams

The fractional Fourier transform (FRT) is applied to off-axis elliptical Gaussian beam (EGB). An analytical formula is derived for the FRT of off-axis EGB in terms of the tensor method. The corresponding tensor ABCD law for performing the FRT of off-axis EGB is also obtained. By using the derived formulae, numerical examples are given. The derived formulae provide a convenient way for analyzing and calculating the FRT of off-axis EGB.     

Neutron diffraction studies of Tb2Rh3Si5 compound

In this work neutron diffraction studies of Tb₂Rh₃Si₅ compound are reported. The compound crystallizes in the monoclinic crystal structure of Lu₂Co₃Si₅-type. At 1.5 K an antiferromagnetic ordering with a propagation vector k=(1/2;1/2;1/2) was observed. The Tb magnetic moments of 9.8(2) μ_B form a non-collinear magnetic structure. In the vicinity of Néel temperature of 8 K a change of the magnetic ordering is evidenced. The change seems to be connected with phase transition from commensurate to incommensurate sine-wave modulation of the Tb magnetic moments.     

Commensurability effects in a Josephson tunnel junction in the field of an array of magnetic particles

Commensurability effects have been theoretically studied in a hybrid system consisting of a Josephson junction located in a nonuniform field induced by an array of magnetic particles. A periodic phase-difference distribution in the junction that is caused by the formation of a regular lattice of Abrikosov vortices generated by the magnetic field of the particles in superconducting electrodes is calculated. The dependence of the critical current through the junction I _c on the applied magnetic field H is shown to differ strongly from the conventional Fraunhofer diffraction pattern because of the periodic modulation of the Josephson phase difference created by the vortices. More specifically, the I _c(H) pattern contains additional resonance peaks, whose positions and heights depend on the parameters and magnetic state of the particles in the array. These specific features of the I _c(H) dependence are observed when the period of the Josephson current modulation by the field of the magnetic particles and the characteristic scale of the change in the phase difference by the applied magnetic field are commensurable. The conditions that determine the positions of the commensurability peaks are obtained, and they are found to agree well with experimental results.