An image processing system for the analysis of speckle photographs

Mach-Zehnder Stationary Two-Beam Spectroscopy Using Compound Prisms

An interferometric optical setup for diffraction-less spectroscopy is tested as an optical design for control of interference frequency. Its design is based on a Mach-Zehnder interferometer in which a pair of compound prisms is introduced in the interferometer path to obtain interference patterns, which avoids the diffraction phenomena and nonlinear dispersion found on spectrometers that use gratings. Computer simulations of the interference patterns generated by the proposed optical setup are presented, and confirmed by the experimental results of the optical implementation. The theory that describes an ideal optical setup and the experimental results show that in order to reduce the combined uncertainties of wavelength measurement, a precise control in angle deviation and magnification are required for the reduction of measurement uncertainties.

Single-shot areal profilometry using hyperspectral interferometry with a microlens array

We describe a single-shot technique to measure areal profiles on optically smooth and stepped surfaces for applications where rapid data acquisition in non-cooperative environments is essential. It is based on hyperspectral interferometry (HSI), a technique in which the output of a white-light interferometer provides the input to a hyperspectral imaging system. Previous HSI implementations suffered from inefficient utilisation of the available pixels which limited the number of measured coordinates and/or unambiguous depth range. In the current paper a >20-fold increase in pixel utilisation is achieved through the use of a 2-D microlens array, that leads to a 35 × 35 channel system with an unambiguous depth range of 0.88 mm.

Scaling dielectrowetting optical shutters to higher resolution: microfluidic and optical implications

A detailed study is reported on the implications of scaling dielectrowetting optical shutters to higher resolutions. Reducing droplet sizes from millimeters to 100 μm in diameter increases the relevance of microfluidic physics such as pinning, film breakup, and dewetting speed as well as optical physics such as transmission and diffraction. In addition, in this work we present improved material systems, including optimized dielectric stacks which reduce electrochemical degradation, and blended lower-viscosity fluids which increase dewetting speed. A higher-resolution device of ~250 μm diameter demonstrates switching speeds of <100 ms and a clear, optically transmissive aperture of >70%. In addition to revealing science not previously discussed, this work has strong applied importance as scaling to higher resolutions is desirable for improving visual appearance in applications ranging from smart windows to electronic signage.

Flicker minimization in an LCoS Spatial Light Modulator

We present a method for reducing the phase flicker originated by the pulsed modulation of a Liquid Crystal on Silicon (LCoS) Spatial Light Modulator (SLM). It consists in reducing the temperature of the LCoS in a controlled way, in order to increase the viscosity of the liquid crystal. By doing this, we increase the time response of the liquid crystal, and thus reduce the amplitude of phase fluctuations. We evaluate the efficacy of this method quantifying the temporal evolution of phase shift using an experiment that is insensitive to optical polarization fluctuations. Additionally, we determine the effect of the temperature reduction on the effective phase modulation capability of the LCoS. We demonstrate that a reduction of up to 80% of the flicker initial value can be achieved when the LCoS is brought to -8 °C.

Temporal phase retrieval from a complex field in digital holographic interferometry

We describe a novel method of processing complex phasors in digital holographic interferometry (DHI). Unlike the commonly used digital phase subtraction method that operates on the phase itself, the proposed method operates on the complex phasor instead. Two temporal phase retrieval algorithms are developed in which the complex phasor of each pixel is measured and analyzed as a function of time. The developed algorithms are demonstrated in profile measurement of step heights. Experimental results show that the proposed phase retrieval algorithms for DHI perform well compared with conventional methods.

Second-order robust regularization cost function for detecting and reconstructing phase discontinuities

We propose a robust method for computing discontinuous phase maps from a fringe pattern with carrier frequency. Our algorithm is based on the minimization of an edge-preserving regularized cost function, specifically, on a robust regularized potential that uses a paradigm called the plate with adaptive rest condition, i.e., a second-order edge-preserving potential. Given that the proposed cost function is not convex, our method uses as its initial point an overly smoothed phase computed with a standard fringe analysis method and then reconstructs the phase discontinuities. Although the method is general purpose, it is introduced in the context of interferometric gauge-block calibration. The performance of the algorithm is demonstrated by numerical experiments with both synthetic and real data.

Laser speckle photography to measure surface displacements on cortical bone--verification of an automated analysis system

A non-contact strain measurement method that could be used in a physiological environment was adapted to determine accurately the mechanical properties of bone. The technique of laser speckle photography was applied to record in-plane surface displacements. An automated image analysis system, based on a Fast Fourier Transform algorithm, was developed for data acquisition and its accuracy and precision verified. It was established that the technique could be used at magnifications of up to 60x , providing an ultimate resolution of approximately 1 microm. Displacement measurements on cortical bone submerged in water were demonstrated, which is of great value in determining the true physiological properties of bone.

Iteration of phase window correlation and least-squares fit for Young's fringe pattern processing

Correlation by means of phase windows that artificially create phase shifts is combined with the least-squares fit to provide a processing algorithm. A Young's pattern is correlated by means of the phase windows to generate four patterns with phase shifts of 0 degrees, 90 degrees, 180 degrees, and 270 degrees. The phase of the Young's pattern is derived from the four patterns. Then the derived phase is least-squares fitted to a phase plane. The above steps are repeated once to improve accuracy. Speckle noise is suppressed by the correlation operations, as well as a loop including phase calculation, fringe reconstruction, and smoothing. The magnitude and direction of the displacement associated with Young's pattern are determined from the phase plane. The algorithm takes less calculation time than the fast Fourier transform method and does so with improved accuracy. Software has been developed and is used in the experiment.

Deformation, strengths and strains to failure of polymer bonded explosives

This paper describes a study of the strength and failure properties of a range of polymer bonded explosives (PBXS). These are composite systems in which small (typically micrometre up to millimetre-sized) explosive crystals are bonded by a polymer (typically 2–10% (by mass)). In PBXS it is important to optimise the mechanical properties, while maintaining a low sensitiveness (i. e. the material is safe to manufacture, store and handle) and high explosiveness (i. e. reacts powerfully to a prescribed stimulus). The Brazilian test, in which a disc-shaped specimen is loaded diametrically, was chosen for the study. The advantages are that relatively small specimens of typically 10 mm diameter and 4 mm thickness can be used, and that the tensile stresses on the central axis are achieved by applying compressive stresses at the anvil so that complicated gripping arrangements are not required. The technique of double-exposure laser speckle photography was chosen to measure the in-plane displacement field. The technique can measure displacements to sub-micrometre accuracy and provide information over the whole specimen surface. These are distinct advantages over strain gauge methods that involve attaching gauges to the specimen and which only give pointwise information. The double-exposure speckle pattern records were interpreted using an automated Young’s fringes method. The PBXS were of three explosive types and those based on HMX were studied systematically for two crystal sizes and three different binder materials, of two different weight percents. In general, compositions based on micronized crystals were the strongest. Polishing techniques were developed to study the deformation of the individual crystals, the points of nucleation of failure and the fracture paths through the PBXS. The failure modes are discussed in terms of various theoretical models. The mechanical twinning which was shown in earlier work to be an important failure mode in β -HMX also takes place in PBXS based on HMX. The general applicability of the techniques developed in this research for other composite systems is emphasized.

Fourier-transformation, phase-iteration, and least-square-fit image processing for Young's fringe pattern

The fast Fourier transform, phase iteration, and the least-square fit are combined into an automated processing technique for the analysis of Young's fringe patterns. A Young's fringe pattern is first fast-Fourier-transform filtered to get an initial phase, phase iteration is carried out to improve the phase if necessary, and then the phase is least-square fitted to a phase plane. The magnitude and the direction of the displacement associated with the Young's pattern are determined from the phase plane.

Phase-correlation techniques for quasi real-time measurement of deformations with digital speckle interferometry

A new approach of in-plane speckle-displacement analysis by binary phase-correlation evaluation is described. An optical implementation of the method based on digital speckle-pattern interferometry and one-focal-length correlator architecture that uses a liquid-crystal light valve is proposed.

Approach to automatic analysis of Young's fringes in speckle photography

A new flexible automatic method for analysis of Young's fringes that allows software, electronic hardware, and optoelectronic realizations is proposed. A displacement vector is sought in the two-dimensional spatial frequency domain, the separate slices of which are obtained through multiple use of the one-dimensional Fourier transform of the Radon-transformed fringe image. An estimate of fringe angle and spacing is found from a projection with the principal Fourier spectrum peak. Afterward its position is repeatedly refined until the desired accuracy is reached. Although the method is relevant mainly to speckle photography, our approach is also applicable to fringe patterns that are generated by a computer. The problem of fringe visibility is widely discussed, and a new estimate is proposed.

Parallel processing system for rapid analysis of speckle-photography and particle-image-velocimetry data

An automated system has been constructed to process double-exposure speckle-photography and particle-image-velocimetry images. A 3 × 3 array of laser beams probes the photograph, forming nine fringe patterns in parallel; these are then analyzed sequentially by digital computer and the use of a two-dimensional Fourier-transform method. Results are presented showing that the random errors in the measured displacements from such a system approach the expected speckle-noise-limited performance, with a total analysis time per displacement vector of 160 ms.

Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy

Replacing photographic recording by electronic processing has some obvious advantages. An algorithm used for electronic speckle pattern photography is presented, and the reliability and accuracy is analyzed by using computer-generated speckle patterns. The algorithm is based on a two-dimensional discrete cross correlation between subimages from different images. Subpixel accuracy is obtained by a Fourier series expansion of the discrete correlation surface. The accuracy of the algorithm was found to vary in proportion to sigma/n(1 - delta)(2), where sigma is the speckle size, n is the subimage size, and delta is the amount of decorrelation, with negligible systematic errors. For typical values the uncertainty in the displacement is approximately 0.05 pixels. The uncertainty is found to increase with increased displacement gradients.

Computer-aided speckle interferometry using spectral amplitude fringes

A fully automatic speckle metrology technique is developed. Two speckle patterns of a specimen, one before and one after the specimen deformation, are captured by a video camera. An equivalent double-exposure speckle pattern is obtained by superimposing the two digital images. The superimposed speckle pattern is then segmented into a series of small subimages. For each subimage a fast-Fourier transform is applied and a computer-generated Young's fringe pattern is obtained. The fringe pattern, which characterizes the local displacement vector, is analyzed by a second fast-Fourier transform. The local displacement vector is determined by a cardinal interpolation and a crest searching around a signal peak in the second spectral domain. An artificial rigid shift between the two images is introduced in the cases of extremely large or small displacements. From analysis of all subimage pairs of the whole superimposed speckle pattern a complete two-dimensional displacement field is deduced. Experimental results using laser as well as white-light speckle patterns are demonstrated.

Maximum-likelihood analysis of speckle photography fringe patterns

A new method for analyzing the Young's fringe patterns from a double-exposure speckle photograph is proposed based on maximum-likelihood estimation. Unlike previous linear algorithms, which rely on Fourier spectral analysis, the method permits knowledge of the speckle-noise statistics (in particular, that the noise is multiplicative rather than additive) to be incorporated in a systematic way. As a result, random errors in the measured displacement components are reduced, in the case of good visibility fringe patterns by a factor of up to 6. The proposed method is also applicable to the general problem of measuring the spatial frequency components of a two-dimensional sinusoid in the presence of signaldependent noise.

Speckle photography fringe analysis: effect of imaging geometry on displacement errors

Random errors in the measured displacement components from double-exposure speckle photographs recorded through a rectangular aperture are considered both by numerical simulations and by simple dimensional analysis.

Image processing for laser speckle velocimetry using the 2-D fast Fourier transform

An algorithm is described for the fringe analysis in laser speckle velocimetry. Based on the 2-D fast Fourier transform, the method relies on inherent features in the fringe pattern to remove efficiently the influence of the diffraction halo. A windowing operation is performed to enhance the reliability and reduce the influence of various noise contributions.

Speckle photography fringe analysis: assessment of current algorithms

The accuracy and reliability of four fringe analysis algorithms have been assessed, using Young's fringe patterns calculated from computer generated speckle patterns. The 1-D integration, 1-D autocorrelation, 2-D Fourier transform, and 2-D Walsh transform methods all estimated the two in-plane displacement components with negligible systematic error; the random errors were found to vary in proportion to sigma(2)/VR (speckle diameter = sigma, fringe visibility = V, and radius of laser probe beam = R), with the lowest errors given by the 2-D Fourier transform method.

Heterodyne readout system for dual plate speckle photography: analysis of error sources and performance evaluation

We describe the design, construction, and testing of a dual plate specklegram heterodyne readout system. The choice of the optical layout and mode of operation is based on the results of a detailed discussion on the sources of error associated both with optical noise and misalignments. Noise analysis includes the conventional scintillation noise and a recently described additional source, the speckle grain noise. Stability and reproducibility tests have been conducted and the accuracy of displacement measurement is 10(-6) of the recorded specklegram size, approximately five times worse than the ultimate noise limited value.

Automatic digital processing in speckle photography: comparison of two algorithms

Two algorithms for analyzing speckle photography fringes for spacing and orientation using a digital image processing system are compared. Each algorithm was tested for accuracy and computer run-time through a computer simulation which includes the degradation of data by noise.