Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the microdisplacement measurement

To provide a theoretical background for the superiority of the signal-domain phase-only correlation (SDPOC) technique proposed here for microdisplacement measurement, we study the first- and the second-order statistical properties of the complex amplitude of an analytic signal of a white-light speckle pattern, under the assumption of a Gaussian random process, and give a formula for the autocorrelation function of the pseudophase associated with the complex analytic signal. Based on these results, we show mathematically that SDPOC has a performance advantage over conventional intensity-based correlation techniques.     

Pseudo-Stokes Vector Correlation From Complex Signal Representation of a Speckle Pattern and Its Applications to Micro-Displacement Measurement

Abstract:  As an improvement of the intensity correlation used widely in conventional electronic speckle photography, we propose a new technique for displacement measurement based on correlating Stokes-like parameters derivatives for transformed speckle patterns. The method is based on a Riesz transform of the intensity speckle pattern, which converts the original real-valued signal into a complex signal. In closest analogy to the polarisation of a vector wave, the Stokes-like vector constructed from the spatial derivative of the generated complex signal has been applied for correlation. Experimental results are presented that demonstrate the validity and advantage of the proposed pseudo-Stokes vector correlation technique over conventional intensity correlation technique.     

Image preprocessing for rotation-invariant pattern recognition in the presence of signal-dependent noise

I propose a new method that ensures efficient rotation-invariant pattern recognition in the presence of signal-dependent noise by combining the application of rotation-invariant correlation filters with preprocessing of the noisy input images. The preprocessing uses local suboptimal estimators derived from estimation theory and implies an a priori knowledge of a model describing the noise source. The image noise sources considered are speckle and film-grain noise. Pour different metrics are used to analyze the correlation performance of the circular-harmonic filter, the phase-only circular-harmonic filter, and the binary phase-only circular-harmonic filter, with and without a preprocessing. Computer simulations show that signal-dependent noise can seriously degrade the performance of the phase-only circular-harmonic filter and the binary phase-only circular-harmonic filter. The most severe indication of correlation-performance degradation is the occurrence of false alarms in 15% to 20% of noise realizations of the correlation. Preprocessing increases the correlation-peak signal-to-noise ratio significantly and reduces the false-alarm probability by one to two orders of magnitude.     

Adaptive correction to the speckle correlation fringes by using a twisted-nematic liquid-crystal display

An innovative technique for reducing speckle noise and improving the intensity profile of the speckle correlation fringes is presented. The method is based on reducing the range of the modulation intensity values of the speckle interference pattern. After the fringe pattern is corrected adaptively at each pixel, a simple morphological filtering of the fringes is sufficient to obtain smoothed fringes. The concept is presented both analytically and by simulation by using computer-generated speckle patterns. The experimental verification is performed by using an amplitude-only spatial light modulator (SLM) in a conventional electronic speckle pattern interferometry setup. The optical arrangement for tuning a commercially available LCD array for amplitude-only behavior is described. The method of feedback to the LCD SLM to modulate the intensity of the reference beam in order to reduce the modulation intensity values is explained, and the resulting fringe pattern and increase in the signal-to-noise ratio are discussed.     

Improving binary phase correlation filters using iterative techniques

An iterative technique has been used to improve the design and performance of the binary phase version of a tandem-component correlation filter. The results are compared to a regular matched filter, a phase-only filter (POF), and a binary phase POF, in terms of optical efficiency, SNR, and peak correlation intensity.     

The Extension of the Electronic Speckle Photography to the Measurement of In-Plane Displacement

In this paper, a modified speckle photography technique is demonstrated for the measurement of a variable range of the in-plane displacement. The modification focuses on coupling the diode pump solid state laser DPSS with the conventional speckle photography technique. The DPSS laser emerges different wavelengths to provide speckle patterns of suitable size to measure the desired range of the in-plane displacement. The second harmonic generation in a nonlinear crystal of wavelength 532 nm and the principle diode laser wavelength 808 nm are employed in identifying the object positions within a lateral displacement made by a standard linear stage in the range from few microns up to 1.2 mm. The sensitivity and the correlation of the speckles formed by both wavelengths suit both small and large movements. A continues measurement by the modified technique can be achieved by identifying a scale factor in the uniform area in which both wavelengths are effective, and high correlation between the results obtained by 532 and 808 nm is maintained. The uncertainty in measuring 1.2 mm lateral movement by the modified speckle photography is found to be 26.8 μm.     

Correlation measurements using clipped laser speckle

Clipped laser speckle is used to measure the correlation of time-varying laser speckle. As with standard intensity correlation, clipped speckle is correlated to determine the magnitude of the correlation coefficient. The simple nature of clipped speckle permits high-speed measurements of correlation and velocity. A closed form approximation to the clipped correlation function valid for arbitrary clipping thresholds is presented. The approximation is used to make correlation measurements on speckle from a rotating diffuser using a 2-D random access detector array.     

Optical Intensity Filters for Pattern Recognition

Abstract

All the shape information of an object is preserved in its quarter-spectrum (QS). Some new uses of optical filters for pattern recognition based on QS are introduced. These filters are intensity functions so that amplitude modulating spatial light modulators or photographic film can be used. Some of the new filters yield better correlation performances than the phase-only filter and the amplitude-encoded phase-only filter. Computer simulations and optical experiments show the results.     

High-speed dynamic speckle interferometry: phase errors due to intensity, velocity, and speckle decorrelation

The recently developed technique of high-speed phase-shifting speckle interferometry combined with temporal phase unwrapping allows dynamic displacement fields to be measured, even for objects containing global discontinuities such as cracks or boundaries. However, when local speckle averaging is included, small phase errors introduced at each time step are accumulated along the time axis, yielding total phase values that depend strongly on the speckle rereference rate. We present an analysis of the errors introduced in the phase evaluation by three sources: intensity errors, velocity errors, and speckle decorrelation. These errors are analyzed when they act both independently and together, for the most commonly used phase-shifting algorithms, with computer-generated speckle patterns. It is shown that, in a controlled out-of-plane geometry, errors in the unwrapped phase map that are due to speckle decorrelation rise as the time between rereferencing events is increased, whereas those due to intensity and velocity errors are reduced. It is also shown that speckle decorrelation errors are typically more important than the intensity and velocity errors. These results provide guidance as to the optimal speckle rereferencing rate in practical applications of the technique.     

Correlation distance of dynamic speckles

The translational and boiling motions of dynamic speckles produced in the Fresnel diffraction field under illumination of a Gaussian beam are investigated in detail. The speckle motion is analyzed from the space-time cross-correlation function of speckle intensity fluctuations detected at the two points in the receiving plane. The correlation distance of time-varying speckles is compared with the translation distance of the spatial speckle pattern. The optical conditions for the translational and boiling motions of dynamic speckles are examined and expressed in a diagram. The characteristics for the correlation distance of time-varying speckle intensity fluctuations are finally verified by several experiments.     

Grinding surface roughness measurement based on the co-occurrence matrix of speckle pattern texture

Surface speckle pattern intensity distribution resulting from laser light scattering from a rough surface contains various information about the surface geometrical and physical properties. A surface roughness measurement technique based on the texture analysis of surface speckle pattern texture images is put forward. In the surface roughness measurement technique, the speckle pattern texture images are taken by a simple setup configuration consisting of a laser and a CCD camera. Our experimental results show that the surface roughness contained in the surface speckle pattern texture images has a good monotonic relationship with their energy feature of the gray-level co-occurrence matrices. After the measurement system is calibrated by a standard surface roughness specimen, the surface roughness of the object surface composed of the same material and machined by the same method as the standard specimen surface can be evaluated from a single speckle pattern texture image. The robustness of the characterization of speckle pattern texture for surface roughness is also discussed. Thus the surface roughness measurement technique can be used for an in-process surface measurement.     

Discrete Fourier preprocessing transforms for the binary phase-only filter

Two useful discrete Fourier preprocessing transforms (DFPTs), say, class 1 and class 2, are applied to the binary phase-only filter. The class-1 DFPT is very close to the discrete Fourier transform (DFT); therefore it preserves the properties similar to those for the DFT. The Class-2 DFPT's are location sensitive and are able to recognize the partial-shape-like input pattern that is the partial set of the pattern in the filter. The Class-2 DFPT's generate a delta-function-like correlation peak whose intensity is larger than that obtained by the DFT. These are different from the DFT-based binary phase-only filter. The elements of the DFPT's are very simple, containing only ±1 and 0; some even contain sparse ±1 values and plenty of zeros. Therefore the DFPT's are suitable for either optical or electrical implementation.     

Three-dimensional matching by use of phase-only holographic information and the Wigner distribution

Matching of three-dimensional (3-D) objects is achieved by Wigner analysis of the correlation pattern between the phase-only holographic information of a reference object and that of a target object. First, holographic information on the reference object and on the target object is extracted by use of optical scanning holography as a form of electrical signal. This electrical information is then stored in a computer for digital processing. In the digital computer, the correlation between the phase-only information of the hologram of the reference object and that of the target object is calculated and analyzed by use of a Wigner distribution. The Wigner distribution yields a space-frequency map of the correlation pattern that indicates whether the 3-D image of the target object matches that of the reference object. When the 3-D image of the target object matches that of the reference object, the Wigner distribution gives a well-defined line that directly indicates the 3-D location of the matched target object. Optical experiments with digital processing are described to demonstrate the proposed matching technique.     

Incoherent pattern detection using a liquid-crystal active lens

Incoherent pattern detection by a simple imaging system using a liquid-crystal active lens is proposed. The imaging system works as a spatial filtering system with a rewritable phase-only filter. We found that, in the incoherent matched filtering system, a conventional phase-only filter has a higher optical efficiency but a lower pattern discrimination than a complex filter. To improve the pattern discrimination ability, we optimized the phase-only filter by using simulated annealing and a genetic algorithm. We designed phase-only filters that have discrimination ability comparable with that in a complex filter. The performance of optimized phase-only filters is experimentally demonstrated.     

Accuracy in electronic speckle photography

Electronic speckle photography is an accurate, easy-to-use, video-based technique for the analysis of two- and three-dimensional deformation fields and in-plane strain fields, based on numerical cross correlation. Through the use of statistical optics, simulated speckle patterns, and experiments the accuracy in electronic speckle photography was found to depend on correlation, speckle size, window size, and correlation filter. The estimated correlation was found to be the combined effect of three mutually competing factors because of classical speckle correlation, subimage overlap, and displacement gradients. In many applications white-light speckle patterns provide a more accurate estimate of the displacement field than do laser speckle patterns.     

Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter

A phase-only filter based on logarithmic harmonics for projection-invariant pattern recognition is presented. This logarithmic-harmonic-derived filter is directly calculated in the Fourier plane. With respect to normal logarithmic-harmonic filters it provides a smaller variation of the correlation intensity with the projection factor of the target. Computer and optical experiments are presented.     

Improved speckle projection profilometry for out-of-plane shape measurement

An improved speckle projection profilometry that combines the projection of computer generated random speckle patterns using an ordinary LCD projector and the two-dimensional digital image correlation technique for in-plane displacements measurement is proposed for accurate out-of-plane shape and displacement measurements. The improved technique employs a simple yet effective calibration technique to determine the linear relationship between the out-of-plane height and the measured in-plane displacements. In addition, the iterative spatial domain cross-correlation algorithm, i.e., the improved Newton-Raphson algorithm using the zero-normalized sum of squared differences correlation criterion and the second-order shape function was employed in image correlation analysis for in-plane displacement determination of the projected speckle patterns, which provides more reliable and accurate matching with a higher correlation coefficient. Experimental results of both a regular cylinder and a human hand demonstrate that the proposed technique is easy to implement and can be applied to a practical out-of-plane shape and displacement measurement with high accuracy.     

Dynamic Properties of Laser Speckles on Images Transmitted Through an Image Fibre-bundle

Abstract

The statistical properties of time-varying laser speckles appearing on an image transmitted through an image fibre-bundle are studied experimentally and theoretically. The effect of defocusing on a stage of observation is investigated in relation to the stationarity of the detected speckle intensity. It is shown that a large amount of defocusing produces a stationary speckle field for which the correlation function of the speckle intensity variation is obtained in a stable form. This allows a system for monitoring the velocity of moving objects using an image fibre-bundle to be developed.     

Bandwidth estimation for multimode optical fibers using the frequency correlation function of speckle patterns

In this paper we present a new method for estimating the bandwidth of multimode optical fibers based on the frequency correlation function of the speckle patterns generated by the interference of fiber modes. This technique, which does not require a pulse or signal generator, can be utilized to estimate the bandwidth of a multimode fiber using a relatively short length of fiber. By applying this method to a test fiber we obtained a bandwidth of approximately 36 MHz km which is in relatively good agreement with the approximately 44-MHz x km bandwidth measured by a conventional pulsed technique.     

Correlation-based speckle velocimeter with self-mixing interference in a semiconductor laser diode

We propose a novel self-mixing laser diode speckle velocimeter based on autocorrelation. The self-mixing laser diode launches and receives reflected light from a moving surface that has a random reflection profile. Some portion of the scattered light backcouples into the laser cavity and causes random intensity variations in the form of speckle signals. These speckle signals obtained from a self-mixing laser diode are processed by use of autocorrelation. The linear relation between the velocity and the reciprocal of the correlation time of the speckle intensity fluctuations allows us to determine the velocity easily if proper calibration is performed. The range of the investigated velocity is 20-450 mm/s. For an aluminum target that moves at a velocity of 350 mm/s, the measurement error is less than 2%.