Anisotropic partial differential equation noise-reduction algorithm based on fringe feature for ESPI

Noise reduction is one of the most exciting problems in electronic speckle pattern interferometry. We present a new anisotropic partial differential equation noise-reduction algorithm based on fringe orientation for interferometric fringe patterns. The proposed equation performs diffusion along the two directions of fringe gradient and isophote line, which are extracted accurately according to fringe feature. By restriction of diffusion in the gradient direction of fringe patterns, this method can provide optimal results in denoising but does not destroy fringe edges. The experimental results show that this technique is more capable of significantly improving the quality of the fringe patterns than the classical anisotropic diffusion equation proposed by Perona and Malik. Based on our filtered fringe patterns, the phase map obtained by phase-shifting technique can be extracted more accurately. It is an effective pre-processing method for electronic speckle pattern interferometry.     

Uncertainty analysis of whole-field phase-differences retrieved from ESPI fringe patterns by using the Fourier transform method (FTM)

We have evaluated the uncertainty associated with the whole-field phase-differences retrieved by using the Fourier transform method (FTM), from a fringe pattern generated by electronic speckle pattern interferometry (ESPI). The phase-differences were induced by applying load to an elastic sample. The FTM involved the Fourier transform application to the fringe pattern, the isolation of the term carrying the phase information by applying a band-pass filter in the spatial frequency domain, and then the inverse Fourier transform application. Since the fringes in the analyzed pattern were adequately open, the FTM outcomes were presumed to be mainly affected by errors in the determination of both the width and the location of the applied filter mask. The influence of these error sources was assessed by using a Monte Carlo-based computer simulation. It implied evaluating the phase-differences a large number of times under the influence of the involved error sources. We found that the phase uncertainty depends strongly on the width of the applied filter mask; the influence of the other error sources considered into the uncertainty propagation was significantly smaller.     

Evaluation of dynamic speckle activity using the empirical mode decomposition method

The empirical mode decomposition (EMD) method is used to process sequences of dynamic speckle patterns to segment the differential activity that presents a sample as a function of the spatial coordinates and time. The application of the method is illustrated by segmenting bruised regions in fruits. A discussion of the obtained results and a comparison with the use of the filter bank technique are also presented.     

Multiple-aperture speckle method applied to local displacement measurements

The goal of this work is to analyze the measurement capability of the modified speckle photography technique that uses different multiple aperture pupils in a multiple exposure scheme. In particular, the rotation case is considered. A point-wise analysis procedure is utilized to obtain the fringes required to access to the local displacement measurements. The proposed arrangement allows simultaneous displaying in the Fourier plane several fringes system each one associated with different rotations. We experimentally verified that the local displacement measurements can be determined with a high precision and accuracy.     

Formulation of moiré fringes based on spatial averaging

The use of moiré technique in measurements often involves locating the position of moiré fringe and in some cases determining its profile. Due to intensity fluctuation in the fringe pattern, these measurements are accompanied by some errors. It is possible to define a smoothed version of the original fringe pattern and then formulate the related subject in accordance with the characteristics of this new pattern. This procedure reduces these types of errors and gives a well-defined profile of the fringes. In this paper a formulation of moiré phenomenon based on spatial averaging is presented which, without ignoring any of frequencies, leads to a smooth profile.     

A simple method to simulate diffraction and speckle patterns with a PC

A simple, intuitive and pedagogical method is proposed in order to simulate the phenomenon of light diffraction in simple cases. A diffracting plane obstacle is simulated by means of a model with a variable transmittance from one point to another. A numerical matrix is built with transmittance values at those points taken as samples. The matrix is handled with the Matlab program, and the Fraunhofer approximation is used. The method is applied to variable module and constant phase transmittance obstacles in single slit, double slit, square window and round window cases. The method is also applied to an obstacle with a constant reflectance module and random variable phase with Gaussian statistics, which gives rise to speckle phenomenon.     

Modified temporal-phase-unwrapping method for measuring in real time the out-of-plane displacements of the tympanic membrane of Mongolian Gerbil

A technique for measuring in real-time continuous out-of-plane displacements of delicate objects is proposed, and demonstrated on the tympanic membrane of Mongolian Gerbil. The technique is based on the combination of two methods: the spatial phase shifting (SPS) and the modified temporal phase unwrapping (TPU). The combination allows to obtain, in several steps, the phase values of the points that undergo out-of-plane displacement as the object is deformed. The technique reduces the frame acquisition time of the standard TPU used in moiré interferometry by a factor of 4, which is important to diminish post-mortem artifacts during in-vitro experiments and to reduce motion artifacts in in-vivo tests. The proposed technique is robust against problems associated with the temporal phase-shifting method, such as nonlinear phase shift and noise. The advantages and disadvantages are discussed.     

Refractive and geometric lens characterization through multi-wavelength digital speckle pattern interferometry

Physical parameters of different types of lenses were measured through digital speckle pattern interferometry (DSPI) using a multimode diode laser as light source. When such lasers emit two or more longitudinal modes simultaneously the speckle image of an object appears covered of contour fringes. By performing the quantitative fringe evaluation the radii of curvature as well as the refractive indexes of the lenses were determined. The fringe quantitative evaluation was carried out through the four- and the eight-stepping techniques and the branch-cut method was employed for phase unwrapping. With all these parameters the focal length was calculated. This whole-field multi-wavelength method does enable the characterization of spherical and aspherical lenses and of positive and negative ones as well.     

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.     

Eliminating the zero spectrum in Fourier transform profilometry using a two-dimensional continuous wavelet transform

In this paper, a filtering technique based upon two-dimensional continuous wavelet transform (2D-CWT) is used to eliminate the low frequency components of fringe patterns. The filtered fringe patterns are subsequently demodulated using a standard Fourier transform profilometry (FTP) algorithm. This image pre-filtering stage improves the noise performance of the FTP algorithm and enables the FTP method to demodulate fringe patterns with larger bandwidths. Also, the 2D-CWT technique reduces speckle noise significantly. Moreover, only a single fringe pattern is required in this technique. The 2D-CWT algorithm is capable of separating low frequency terms from the high frequency terms that contain phase-modulated fringe information, even when both interfere, greatly, in the frequency domain. The proposed algorithm is tested, both via computer simulation and using real fringe patterns. This revealed the robustness of this algorithm and also demonstrably enables the demodulation of a wider range of fringe patterns using the FTP technique.     

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 control algorithms for focusing light through turbid media

Light propagation in materials with microscopic inhomogeneities is affected by scattering. In scattering materials, such as powders, disordered metamaterials or biological tissue, multiple scattering on sub-wavelength particles makes light diffuse. Recently, we showed that it is possible to construct a wavefront that focuses through a solid, strongly scattering object. The focusing wavefront uniquely matches a certain configuration of the particles in the medium. To focus light through a turbid liquid or living tissue, it is necessary to dynamically adjust the wavefront as the particles in the medium move. Here we present three algorithms for constructing a wavefront that focuses through a scattering medium. We analyze the dynamic behavior of these algorithms and compare their sensitivity to measurement noise. The algorithms are compared both experimentally and using numerical simulations. The results are in good agreement with an intuitive model, which may be used to develop dynamic diffusion compensators with applications in, for example, light delivery in human tissue.     

Speckle noise attenuation in optical coherence tomography by compounding images acquired at different positions of the sample

This study demonstrates a simple method for attenuating the speckle noise generated by coherent multiple-scattered photons in optical-coherence tomography images. The method could be included among the space-diversity techniques used for speckle reduction. It relies on displacing the sample along a weakly focused beam in the sample arm of the interferometer, acquiring a coherent image for each sample position and adding the individual images to form a compounded image. It is proven that the compounded image displays a reduction in the speckle noise generated by multiple scattered photons and an enhancement in the intensity signal caused by single-backscattered photons. To evaluate its potential biomedical applications, the method is used to investigate in vitro a caries lesion affecting the enamel layer of a wisdom tooth. Because of the uncorrelated nature of the speckle noise the compounded image provides a better mapping of the lesion compared to a single (coherent) image.     

Correlator-aided alignment of phase key in encrypted holographic storage systems

An encrypted holographic scheme with a compact alignment system for a phase key is proposed. Alignment for a phase key is performed by a holographic correlator. A filter in the correlator system contains the phase information used for encryption. Thus, it can be used to check the authorization of the phase key. Owing to the shift-invariant property of the holographic correlator, the location of the correlation peak is highly related to the alignment of the phase key. Therefore, the phase key can be repositioned on the desired location by searching for the specific position of the correlation peak. With the help of the correlator, alignment of the phase key can be done in 1 min. Experimental results using a correlator system in support of our proposed idea are demonstrated as well.     

A half-blind color image hiding and encryption method in fractional Fourier domains

We have proposed a new technique for digital image encryption and hiding based on fractional Fourier transforms with double random phases. An original hidden image is encrypted two times and the keys are increased to strengthen information protection. Color image hiding and encryption with wavelength multiplexing is proposed by embedding and encryption in R, G and B three channels. The robustness against occlusion attacks and noise attacks are analyzed. And computer simulations are presented with the corresponding results.     

Window fringe pattern demodulation by multi-functional fitting using a genetic algorithm

We present a new way to demodulate complicated fringe patterns containing closed fringes using a genetic algorithm (GA). The entire fringe pattern is divided into a set of partially overlapping smaller sub-image windows. Each of these has a lower dimensionality and as a consequence is faster and can be demodulated more reliably. The demodulation process proceeds row-by-row way passing from one sub-image in a neighborhood until the whole interferogram is processed. The modulating phase of each sub-image is modeled as a parametric analytic function whose parameters are optimized using a GA. The technique is demonstrated demodulating some normalized fringe patterns that have two main difficulties: closed fringes within the interferogram and regions of under-sampled fringes. These fringe images cannot be demodulated by techniques such as the regularized phase tracker (RPT).     

Topological and morphological transformations of developing singular paraxial vector light fields

The paper is devoted to establishment of the real-time topological and morphological dynamics of generic developing paraxial elliptic speckle fields generated and driven by the system ‘laser beam + photorefractive crystal LiNbO₃:Fe’. Generic space-time development of full gamut of polarization ellipse parameters (ellipticity, azimuth, morphology of C points, optical diabolos and handedness) and their combination in fixed beam cross-section was measured in details by the elaborated quick-action real-time Stokes-polarimetry. Whole field irreversible evolution is fulfilled through totality of random space/time C point pair nucleation/annihilation. The ‘life-story’ of C point and optical diabolo pairs is realized through ‘local topological/morphological transition’ with fully reversible scenario. It starts from smooth fragment of speckle field by formation of pre-nucleation local structure and finishes by after-annihilation local structure which decays to another smooth structure. Scenarios of star-monstar pair nucleation/annihilation and monstar  ↔  lemon transformation were established. Measured statistics of C point and diabolo morphological forms was in excellent agreement with theory predictions. All allowed scenarios of diabolo pair ‘life-story’ started/finished as star-hyperbolic monstar-hyperbolic pair were measured. Evolution of polarization ellipses handedness is implemented through L contours movement and reconnection with a saddle as the catalyst. Reconnection of L contour peninsula leads to birth of closed L contour delimiting island of fixed handedness ellipses with/without C points. Elaborated approach and presented results start the dynamic singular optics of time-dependent vector light fields.     

Analysis of reflection speckle holograms in a BSO crystal

A theoretical and experimental study of speckle registering in photorefractive BSO crystals through reflection hologram geometry is implemented. The three-dimensional speckle nature is considered in the diffraction efficiency calculations. The interference process produces index-of-refraction gratings in the speckle volume via the photorefractive effect. It is demonstrated that the coupled-wave theory for reflection geometry allows explaining the diffraction efficiency behavior when the interaction length is properly taken into account. It means that the speckle depth is related with the interaction length. The speckle depth can be controlled by the imaging system pupil aperture diameter. Under this condition, the influence of the speckle depth on the diffraction efficiency is analyzed. An agreement between the numerical model based on the coupled-wave theory and the experimental results is obtained.     

Effect of angle of incidence on self-mixing laser Doppler velocimeter and optimization of the system

Based on the theory of speckle and self-mixing interference in laser-diode, three-facet cavity model is introduced to analyze laser Doppler effect based on self-mixing interference in the case of a rough surface, and numerical solution of the signal is obtained. Simulation results of speckle-modulated Doppler signal based on self-mixing effect and tracking accuracy at different incident angles are given using parameters employed in the experiment. Simulation results indicate incident angle of around 30° is most suitable when both tracking accuracy and signal amplitude are considered. Experimental waveforms agree well with simulation results, and similar conclusions as simulation predictions about changing trend of tracking accuracies of the system at different incident angles can be made. Combining with difference frequency analog phase-lock loop (PLL) technique and appropriate sampling time, a laser Doppler velocimeter with tracking accuracy better than 1.3% in the range of 10-470 mm/s is realized.