Large in-plane displacement measurement in dual-beam speckle interferometry using temporal phase measurement

Abstract

Measurement of in-plane displacements of a diffuse object by observing the temporal fluctuation of the speckle pattern in a dual-beam illumination speckle interferometer is illustrated. To conceive the temporal changes the object is displaced in its plane continuously. A high-speed camera is used to acquire a number of frames of the image of the object motion sequentially. Through Fourier transformation and inverse Fourier transformation of the frames stacked together, the total phase is determined. Finally, the magnitude of the in-plane displacement of the object motion is extracted. The range of displacement that can be measured using this novel method lies between few microns and over 100 μm on the upper end. Theory together with experimental results are presented in this paper.     

Vibration Phase‐Based Ordering of Vibration Patterns Acquired With a Shearing Speckle Interferometer and Pulsed Illumination

Abstract: A method for both temporal and spatial characterisation of harmonic vibrations is presented. The method is based on simultaneous acquisition of phase‐stepped speckle interference patterns using a shearing speckle interferometer and the vibration phase for a series of vibration states within the vibration period. An unsynchronised free‐running pulse laser is used for illuminating a vibrating object yielding speckle interference patterns in random vibration phase order. Two π/2 phase‐stepped speckle interference patterns are acquired simultaneously for each recorded vibration state. The data set is sorted using vibration phase as the sorting key. The sorted speckle interference patterns are processed using a two‐bucket algorithm for the calculation of phase difference and by applying temporal phase unwrapping to finally obtain unwrapped phase distributions for any vibration state of the vibration cycle.     

Statistical Properties of Phase Variation in Shearing Speckle Interferometry and Its Effect on Fringe Visibility

Abstract

The statistical properties of two interfering speckle fields indicate a reduction in phase variation as the coherent correlation between them increases. In this paper, the impact of this phenomenon on fringe visibility in shearing speckle interferometry, where two laterally shifted speckle fields are super-imposed, is studied. Work is also done to correlate fringe visibility with the amount of lateral shear based on the limitations imposed by phase variance statistics.     

Phase shift calibration in speckle photography—a first step to practical real-time analysis of speckle correlation fringes

Abstract

The paper is focused on the implemention of phase shift calibration in speckle photography with a view to introducing the possibility of realtime analysis of displacement data obtained by the method. Phase reversal is accomplished by varying pressure within an air-filled quartz cell inserted in the pump beam in a conventional two-beam coupling arrangement. It is shown that phase reversal is achieved when a π-shifted speckle pattern overlaps on an unshifted speckle pattern at the observation plane. This phenomenon is exploited for calibration of the phase shift. Experimental results show good agreement with the theory.     

Phase measurement in temporal speckle pattern interferometry: comparison between the phase-shifting and the Fourier transform methods

The measurement of dynamic displacements by use of speckle pattern interferometry and temporal phase unwrapping allows for the evaluation of large-object displacement fields without the propagation of spatial unwrapping errors. If a temporal carrier is introduced in one of the beams of the interferometer, phase data for whole-object displacement can be retrieved by use of a temporal phase-shifting method or a temporal Fourier transformation approach. We present a comparison between both methods of temporal phase measurement in terms of precision and execution speed. We performed the analysis by using computer-simulated speckle interferograms, an approach that allowed us to know precisely the original phase distribution and also to determine the spatial rms phase error as a function of the phase change introduced between two consecutive speckle interferograms. The performance of both methods to process experimental data is also illustrated by use of the results from a high-speed speckle interferometry study of a carbon fiber panel.     

Spectral and Dispersion Analysis of Laser Sources and Multimode Fibres Via the Statistics of the Intensity Pattern

Abstract

The statistics of an intensity pattern at the exit face of a multimode fibre excited by a quasimonochromatic source is analysed by means of an expression for speckle pattern contrast. Theoretical considerations that take advantages of both classical coherence formalism and guided-mode field representation of light propagating in multimode fibres lead to two equivalent expressions for speckle pattern contrast; the first is expressed in the time domain by using a source temporal coherence function and the second is expressed in the frequency domain by using a frequency correlation function of the source spectral density. Moreover, the modal guiding conditions in multimode fibre are in both expressions governed by a maximum group delay time difference. The feasibility of both expressions, especially the second, is demonstrated by analytic expressions for the speckle pattern contrast for seven different spectra, that is the influence of the source temporal coherence as well as the modal dispersion is thus clearly shown.     

Phase measurement in temporal speckle pattern interferometry signals presenting low-modulated regions by means of the bidimensional empirical mode decomposition

We propose a phase measurement technique to retrieve optical phase distributions coded in noisy temporal speckle pattern interferometry signals presenting regions of adjacent low-modulated pixels, which is based on the bidimensional empirical mode decomposition and the Hilbert transform. It is shown that this approach can effectively remove noise and minimize the influence of large sets of adjacent nonmodulated pixels located in the time series of speckle interferograms. The performance of the phase retrieval approach is analyzed using computer-simulated speckle interferograms modulated with a temporal carrier. The results are also compared with those given by a technique based on the one-dimensional empirical mode decomposition. The advantages and limitations of the proposed approach are finally discussed.     

Carrier-modulated Object Step-loading Method of Automated Analysis in Digital Speckle Shearing Interferometry

Abstract

An object step-loading method has been recently reported to overcome the problems of phase unwrapping and decorrelation in digital speckle shearing interferometry. In this paper, a carrier modulation procedure is incorporated into the object step-loading method in order to improve the phase derivation accuracy. An added advantage with this approach is that the direction of deformation is also revealed.     

Hilbert transform analysis of a time series of speckle interferograms with a temporal carrier

We present an optical phase measurement method based on the Hilbert transform for the analysis of a time series of speckle interferograms modulated by a temporal carrier. We discuss the influence of nonmodulating pixels, modulation loss, and noise that affect the bias and modulation intensities of the interferometric signal and propose the application of the empirical mode decomposition method for its minimization. We also show the equivalence between the phase recovery approaches that are based on the Hilbert and the Fourier transforms. Finally, we present a numerical comparison between these methods using computer-simulated speckle interferograms modulated with a temporal carrier.     

Statistical Properties of the Interference Pattern Generated by a Partially Developed Speckle

Abstract

The fluctuations of fringe-pattern intensity are studied theoretically by means of Young's interference experiment applied to speckle. We have studied the fluctuations generated by partially developed Gaussian speckle produced in the far field. The formula for the average contrast of the fringe-pattern intensity is derived and the characteristic values of the contrast fringes are discussed. The theoretical results are compared with experimental data.     

Temporal response of a random medium from speckle intensity frequency correlations

We reconstruct the temporal response of a random medium by using speckle intensity frequency correlations. When the scattered field from a random medium is described by circular complex Gaussian statistics, we show that third-order correlations permit retrieval of the Fourier phase of the temporal response with bispectral techniques. Our experimental results for random media samples in the diffusion regime are in excellent agreement with the intensity temporal response measured directly with an ultrafast pulse laser and a streak camera. Our speckle correlation measurements also demonstrate sensitivity to inhomogeneous samples, highlighting the potential application for imaging within a scattering medium.     

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.     

Three-wavelength Speckle Interferometry: A Theoretical Study

Abstract

In this paper we discuss from a theoretical point of view the statistical properties of the rough-surface interferometry (ROSI) if more than two wavelengths are used. Starting from the Gaussian statistics of several correlated speckle fields we derive and discuss the probability density functions of the statistical errors induced by speckle noise for two different techniques involving three wavelengths. We show that the use of more than two wavelengths may only be advantageous if these statistical errors are small compared to the errors induced by the measuring equipment.     

Wavelength-shift speckle interferometry for absolute profilometry using a mode-hop free external cavity diode laser

Abstract

In this paper we present an absolute surface topography measurement with a tuneable diode laser with an external cavity that has a tuning range of as much as 25 nm without mode hops and a very high tuning speed of less than 1 s for the whole range. With this laser, an absolute wavelength-shift speckle pattern interferometer was realized, capable of measuring optically smooth and rough surfaces. We briefly explain the principles of operation, and the importance of wavelength tuning without mode hops. We discuss the capabilities, possible measuring ranges and some results as well as calibration methods of wavelength-shift speckle profilometry.     

Consideration of existence of phase information of object shape in zeroth-order diffraction beam using electromagnetic simulation with aperture in front of objective

ABSTRACT

It has been reported that the shape of a measured object can be determined by detecting the change in phase distribution generated by a lateral shift of the object using speckle interferometry. In speckle interferometry technique, it was also reported that the shape of the object beyond the diffraction limit can be measured. In this study, the principle of this method is discussed through experiments and electromagnetic analysis. Accordingly, the results of the experiments and electromagnetic analysis of phase change only under zeroth-order diffraction light through the lateral shift of the object are investigated by shutting out the higher harmonic diffraction lights using an aperture in front of the lens. The results indicate that even if the image of the object cannot be focused upon, three-dimensional shape measurement can be performed by analysing only the zeroth-order diffraction light from the object.     

Composite Displacement Measurement by Speckle Technique

Abstract

We present a simple method for measuring composite movements which comprise a longitudinal displacement and a rotation of a rough surface. The method is based on the direct analysis of the double exposure photographic recording obtained from two speckle patterns produced by the diffuser, before and after it is translated and rotated.     

Extended-range temporal electronic speckle pattern interferometry

In recent years the availability of high-speed digital video cameras has motivated the study of electronic speckle pattern interferometry (ESPI) in the time domain. To this end a properly sampled temporal sequence of N-fringe patterns is used to analyze the temporal experiment. Samples of temporal speckle images must fulfill the Nyquist criteria over the time axis. When the transient phenomena under study are too fast, the required sampling frequency over time may not be fulfilled. In that case one needs to extend the measuring range of the algorithm used to extract the modulating phase. We analyze how to use short laser pulses or short video acquisition times with fairly long temporal separation among them to estimate the modulating phase of a dynamic ESPI experiment. The only requirement is that the modulating phase being estimated be properly sampled in the spatial domain.     

Complex Degree of Coherence Due to Tilted Planar Sources

Abstract

The complex degree of coherence (CDC) due to a quasi-monochromatic spatially incoherent source can be displayed by performing a two-step procedure. The CDC information is encoded in the spectral content of the speckle pattern produced via a diffuser placed at the plane where the CDC is to be studied. In a second step, the recorded speckle is Fourier analysed. We apply this method to the study of tilted incoherent sources, for which the CDC is no longer an homogeneous function. A relationship is found that links the size of the speckle halo in the Fourier plane (where CDC information exists), and the tilt angle of the source plane. Some experimental results are shown in order to illustrate the method. Finally, some possible extensions and applications of our study are mentioned.     

Electronic speckle pattern interferometry based on spatial information using only two sheets of speckle patterns

Abstract

Speckle interferometry is an important deformation measurement method for an object with a rough surface. In this paper, a novel fringe analysis method is proposed that uses a new optical system, which uses a plane wave as the reference beam of the speckle interferometer. When the optical system is employed in fringe analysis, the deformation information and the bias components of the speckle patterns are clearly separated in the frequency domain. Therefore, the deformation information can be readily extracted using a Fourier transform, which gives a pair of real and imaginary components concerning the information. The specklegram is calculated using such a pair of components, and the phase map is obtained from the specklegram. Experimental results confirmed that the resolution power of this measurement method is higher than 1/261 of the wavelength of the light source of the optical system.     

Vibration-induced phase errors in high-speed phase-shifting speckle-pattern interferometry

We present results from numerical simulations of a dynamic phase-shifting speckle interferometer used in the presence of mechanical vibrations. The simulation is based on a detailed mathematical model of the system, which is used to predict the expected frequency response of the rms measurement error, in the time-varying phase difference maps, as a result of vibration. The performance of different phase-shifting algorithms is studied over a range of vibrational frequencies. Phase-difference evaluation is performed by means of temporal phase shifting and temporal phase unwrapping. It is demonstrated that longer sampling windows and higher framing rates are preferred in order to reduce the phase-change error that is due to vibration. A numerical criterion for an upper limit on the length of time window for the phase-shifting algorithm is also proposed. The numerical results are finally compared with experimental data, acquired with a phase-shifting speckle interferometer of 1000 frames/s.