Statistical properties of the phase difference between two interfering speckle fields in speckle interferometry

The statistical properties of the phase difference between the two interfering partially correlated and partially developed speckle fields were studied experimentally as a function of the intensity correlation coefficient. The gaussian statistics are assumed for the formation of speckle fields in the diffraction region and the correlation coefficient between the two speckle intensities is used to evaluate the phase difference. The standard deviation of the phase difference can be uniquely determined in the fully developed speckle field from the correlation coefficient of the two speckle intensities. However, it was found in the partially developed speckle field that the standard deviation of the phase difference between the two speckle fields cannot be uniquely determined from the correlation coefficient of the two speckle intensities.     

Studies on the statistical properties of phase difference of speckle fields

According to the relations between the phase and the complex speckle amplitude, a phase angle is constructed to estimate the free standard deviation of phase difference of speckle fields. The relative accurate amending expression of evaluating the free standard deviation of phase difference is derived for the Gaussian speckle fields. The statistical properties of phase difference are studied for the Gaussian speckle fields of diffraction fields. The theoretical values of the free standard deviation of phase difference for the case of fully developed speckle fields are compared with the numerical values of the free standard deviation which are calculated from the Gaussian theory of the fully developed speckle fields.     

Real-time visualisation of deformation fields using speckle interferometry and temporal phase unwrapping

A real-time system for analysing data from speckle interferometers, and speckle shearing interferometers, has been developed. Interferograms are continuously recorded by a digital camera at a rate of 60 frames s⁻¹ with temporal phase shifting carried out at the same rate. The images are analysed using a pipeline image processor. With a standard 4-frame phase-shifting algorithm (phase steps of π/2), wrapped phase maps are calculated and displayed at 15 frames s⁻¹. These are unwrapped using a temporal phase unwrapping algorithm to provide a real-time colour-coded display of the relevant displacement component. Each camera pixel (or cluster of pixels) behaves in effect as an independent displacement sensor. The reference speckle interferogram is updated automatically at regular user-defined intervals, allowing arbitrarily large deformations to be measured and errors due to speckle decorrelation to be minimised. The system has been applied to the problem of detecting sub-surface delamination cracks in carbon fibre composite panels.     

A comparative study of phase-shifting algorithms in digital speckle pattern interferometry

Digital speckle pattern interferometry (DSPI) is a tool for making qualitative as well as quantitative measurements of deformation of objects. Phase-shifting algorithms in DSPI are useful for extracting quantitative deformation data from the system. Comparative studies of the different phase-shifting algorithms in DSPI for object deformation measurement are presented. Static and quasi-dynamic deformation of the object can be measured using these algorithms. Error compensating five-step phase-shifting method is used for the algorithms.     

Measurement of sub-surface delaminations in carbon fibre composites using high-speed phase-shifted speckle interferometry and temporal phase unwrapping

A high-speed phase-shifted speckle interferometer has been developed recently for studying dynamic events. Speckle interferograms are continuously recorded by a CCD camera operating at 1 kHz with temporal phase shifting carried out by a Pockels cell running at the same frequency. Temporal phase unwrapping through sequences of more than 1000 frames allows the determination of time-varying absolute displacement maps. This paper presents the application of this speckle interferometry system to the detection and measurement of sub-surface delamination defects in carbon fibre specimens. The influence of re-referencing the temporal phase unwrapping algorithm after different time intervals is analysed to reduce the random phase errors produced by speckle decorrelation and vibration. The performance of several phase-shifting algorithms to minimize the influence of the vibration noise caused by the vacuum pump used to load the specimen is also investigated.     

GaP相变及热力学性质的理论研究

利用基于密度泛函理论的第一性原理方法研究了闪锌矿和氯化钠结构的GaP的相变及热力学性质.对两种结构的能量体积曲线做公切线,得到了从闪锌矿到氯化钠结构的相变压力约为26.2GPa,与实验结果一致.通过准谐德拜模型得到了不同温度下体积和热膨胀系数与压强的关系,以及不同压强下热容与温度的关系.     

Comparison of phase recovery methods in spiral speckle pattern interferometry correlation fringes

Spiral interferometry can be used as a solution to the problem of sign ambiguity presented in the conventional speckle pattern interferometric technique when the optical phase needs to be reconstructed from a single closed fringe system. Depressions and elevations of the topography corresponding to the object deformation are distinguished by the direction of rotation of the local spiral fringe pattern. In this work, we implement and compare several methods for optical phase reconstruction by analyzing a single image composed of spiral speckle pattern interferometry correlation fringes. The implemented methods are based on contour line demodulation, center line demodulation, Spiral Phase Quadrature Transform and the 2D Riesz transform with multivector structure. Contour line and center line demodulation approaches are exclusively dedicated to images containing a fringe system with spiral structure. The others are based on the 2D Riesz transform, these being well known approaches in conventional interferometry. We examine simulated experiments and analyze some of the emerging drawbacks for solving the phase reconstruction problem by using different mean values of speckle size and background noise levels. We also discuss several numerical procedures that may well improve the efficiency and robustness of the presented numerical implementations. The performance of the implemented demodulation methods is evaluated by using a universal image quality index and therefore a quantitative comparison is also presented.     

A new method of studying the statistical properties of speckle phase

A new theoretical method with generality is proposed to study the statistical properties of the speckle phase. The general expression of the standard deviation of the speckle phase about the first-order statistics is derived according to the relation between the phase and the complex speckle amplitude. The statistical properties of the speckle phase have been studied in the diffraction fields with this new theoretical method.     

Characterization of phase transition in liquid crystals by voltaic potential difference

Our investigations show that the determination of voltaic potential differences is a useful method to characterize the phase transition N → I and I → N for a liquid-crystal (LC) mixture and for a phase transition from one liquid-crystalline phase into another. The ΔV/T curves show reversible as well as an irreversible behaviour. Moreover, the transition from the smectic into the nematic phase is demonstrated on liquid-crystalline polymers.     

一种确定光纤传感器中3×3耦合器输出信号相位差的新算法

本文提出了一种基于Bessel函数展开,在频域内精确确定光纤传感器3×3耦合器输出信号相位差的算法。在Mach-Zehnder干涉仪原理的基础上,通过建立3~3耦合器输出信号的数学模型和利用耦合器输出光功率的Bessel展开,完成了算法的理论推导,并且在实验室中进行了声学实验。数据处理结果表明,该算法能够较精确地确定3×3耦合器输出信号的相位差,且相位差与调制频率无关,与理论相符。     

粗糙表面对散斑统计特性的影响

为研究高速摄影中激光相干噪声的影响因素,降低激光照明中散斑噪声对高速摄影成像质量的影响,对激光照射表面的粗糙程度与形成的散斑场统计特性之间的关系进行了研究。基于菲涅尔-基尔霍夫衍射原理,分析了高斯光束入射在随机粗糙表面上经反射形成的散斑图样,通过对大量散斑图样的数据统计,得出了激光散斑的信噪比、自相关函数、概率密度函数与入射表面粗糙度之间的变化关系。计算结果表明：粗糙度的增大使散斑场信噪比降低、相干程度减小、概率密度降低,即表面越粗糙散斑噪声越严重。     

Theoretical analysis for surface tilt and translation detection based on speckle photography in the Fresnel domain

The theoretical and numerical analysis in this work show that both surface tilting and translational motion can be simultaneously calculated using the speckle photographic technique by recording consecutive speckle pattern images in two different Fresnel diffraction distances. A simulation example based on the proposed scheme is given to verify the method’s validity and high accuracy of the calculated motion detection. Compared with other previous works the results show that this method is efficient and easy to implement.     

Theoretical study on liquid crystal cyanobiphenyls: Phase stability and phase behavior

This article presents a theoretical study on liquid crystalline materials in homologous series of 4'-n-alkyl-4-cyanobiphenyl (nCB) with propyl (3CB), pentyl (5CB), and heptyl (7CB) groups. The atomic net charge and dipole moment components at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh–Schrodinger perturbation theory along with the multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. Further, these interaction energy values have been used as input to calculate the translational entropy, and free energy of nCB (n=3, 5, and 7) molecules during the stacking, and in-plane interactions. The observed results have been correlated with the mesogenic behavior and phase stability based on the thermodynamic parameters introduced in this article. Further, an attempt has been made to elucidate the flexibility of a configuration at a particular temperature, which has a direct relation with phase transition property of the molecules.     

Optimal phase difference reconstruction: comparison of two methods

The present study compares the performance of the weighted mean (WM) and sensitivity encoding (SENSE) methods for reconstructing phase difference images over a large range of signal-to-noise ratio (SNR). It is found that the WM algorithm is suboptimal, compared to the SENSE method at low SNR. Numerical simulations, phantom and in vivo results are presented.     

The gated integration technique for the accurate measurement of the autocorrelation function of speckle intensities scattered from random phase screens

A new approach based on the gated integration technique is proposed for the accurate measurement of the autocorrelation function of speckle intensities scattered from a random phase screen. The Boxcar used for this technique in the acquisition of the speckle intensity data integrates the photoelectric signal during its sampling gate open, and it repeats the sampling by a preset number, m. The average analog of the m samplings output by the Boxcar enhances the signal-to-noise ratio by , because the repeated sampling and the average make the useful speckle signals stable, while the randomly varied photoelectric noise is suppressed by . In the experiment, we use an analog-to-digital converter module to synchronize all the actions such as the stepped movement of the phase screen, the repeated sampling, the readout of the averaged output of the Boxcar, etc. The experimental results show that speckle signals are better recovered from contaminated signals, and the autocorrelation function with the secondary maximum is obtained, indicating that the accuracy of the measurement of the autocorrelation function is greatly improved by the gated integration technique.     

基于电流和相位差的超声换能器频率自动跟踪

为了提高超声换能器频率跟踪的稳定性,通过对最小电流法和相位差法的原理和应用范围进行分析,提出了基于最小电流和相位差法相结合的并联谐振频率跟踪策略,该策略主要思想是将最小电流法运用于换能器空载阶段,相位差法运用于带载阶段,并且带载时的起始驱动频率取为空载阶段跟踪到的并联谐振频率。由此对最小电流法和相位差法这两种跟踪方法进行取长补短。基于该跟踪策略对换能器在不同负载下进行了实验,结果表明该策略可以快速地跟踪到换能器的并联谐振频率,并且工作稳定。     

Effects of the induced birefringence in photorefractive crystals on speckle optical vortices

In this work, we show that it is possible to change the properties of an optical vortex formed in a speckle pattern by the control of an external electric field applied to a sillenite-type photorefractive material in a non-holographic configuration. To show it, a scheme that allows the recovering of both, the polarization state and the phase distribution of an optical field was implemented. Changes in the polarization state of the light in the neighborhood of the vortex were observed with the application of an external electric field. Likewise, changes in the phase structure around the vortex and displacements of the vortices themselves were measured. These displacements have a fairly linear dependence on the applied field to the photorefractive crystal. Experimental results are qualitatively explained with the theoretical treatment of non-holographic recording in photorefractive crystals.     

Relation between statistical properties of surface roughness and the averaged speckle intensity in the diffraction field

A theoretical and experimental investigation is made on the relation between the statistical properties of a rough surface and the averaged speckle intensity in the diffraction field. The theoretical analysis is performed in some detail over a wide range of the random phase variation for various illuminated objects. The result gives an interpretation for the behavior of the averaged speckle intensity obtained experimentally for various states of rough surfaces.     

Analysis on diffraction properties of the transmission phase grating

Diffraction properties of the transmission phase grating are analyzed in terms of the Fourier optics theory. The analysis results show that the diffraction intensity distribution of the transmission phase grating is closely related to the optical thickness of the grating and the wavelength of the incident light, and not only determined by the grating's period and slit width. For monochromatic incident light, more than 80% of the diffraction energy will concentrate to the first diffraction order under certain conditions. For white incident light, the energy of the first order of diffraction spectrum may be much higher than other orders. Based on these results, some possible applications of the transmission phase grating are discussed.     

Simultaneous multiphoton ionization by two radiation fields. Effects of the statistical properties of the radiation

Summary We report on calculations of differential and total ionization cross-sections of hydrogen atoms irradiated by two radiation fields with different properties. One of the fields is of low intensity and relatively high frequency, the other is of low frequency and high intensity. In particular, we show that the inclusion of the multimode structure of the low-frequency laser field modifies considerably the shape of the angular distribution of the photoelectrons and the rates of ionization into the different channels characterized by the number of low-frequency photons exchanged. Further, we find that the average energy exchanged between the photoelectrons and the low-frequency radiation field is independent of the statistical properties of the low-frequency laser field.