Peak-locking Effect Research Articles

Improvements on the cross-correlation algorithm used for tracking fractional Bragg grating wavelength shifts in multimode fibres

Abstract In this paper we report on the deployment of Finite Impulse Response (FIR) filters as an extension to the common cross-correlation algorithm (CCA), for accurate peak tracking of multimode and single mode fibre Bragg gratings when dealing with wavelength shifts below the sampling resolution of the demodulator; the well-known peak-locking effect. The performance of the common CCA under these conditions was studied using simulations for single and multiple peak grating spectra and was compared with the performance of proposed, improved CCA method. We studied the cases where fibre Bragg gratings are wavelength-shifted with triangular and sinusoidal manner and how the proposed method behaves under these conditions. We experimentally evaluated our proposed method by utilising strain measurements using a fibre Bragg grating inscribed in a multimode gradient index CYTOP polymer fibre. The method and algorithm showed significant improvement concerning the peak-locking effect, while maintaining the response speed.

Correction of Peak Tracking Ripple in Solid State Spectrometers

Errors in peak wavelengths from fiber Bragg gratings (FBGs) when monitored using a pixel-based solid state spectrometer have been investigated. These errors show a pseudo-sinusoidal ripple superimposed upon the expected linear response. The error is analogous to a peak-locking effect common to subpixel resolution particle tracking by CCD camera in particle image velocimetry. The amplitude of the error is calibrated as a proportion of the scaled variation of the change in the peak power of the calculated peak as the spectral peak is scanned across the pixel array. An error correction algorithm has been developed and verified in order to provide an increase in the accuracy of sensing solutions when using pixel-based spectrometers. The methods presented here permit the correction of pixel induced ripple errors in real time using data commonly available from many interrogation spectrometers. Calibration prior to use can be achieved by scanning each FBG spectral peak across the width of a single pixel. The proposed method of error correction is applied to a fiber optic sensor array utilized for biomedical pressure and temperature measurement and demonstrates a clear ability to increase the accuracy of measured signals.

Fiber Bragg grating demodulation through innovative numerical procedures

ABSTRACTThe aim of this article is to introduce an innovative algorithm for the calculation of the shift of the maximum reflectivity wavelength of a Fiber Bragg Grating experiencing an applied strain. An accurate and precise evaluation of the FBG spectrum displacement is crucial for determining the amount of the physical quantity inducing such perturbations. The proposed method is based on the Fast Fourier Transform based Cross Correlation function. Such method is compared to Least Squares Fitting (LSF) and the centroid algorithms, pointing out remarkable improvements in accuracy, precision, and time consumption performance. In addition, a further improvement of the proposed algorithm is introduced. It consists in an iteratively performed Cross Correlation algorithm. It has been proved that such improvement leads to estimations characterized by better accuracy and precision, thanks also to a considerable reduction of the peak-locking effect due to the FBG spectral resolution.

Multispectral processing for color particle image velocimetry

Since the adoption of digital video cameras and cross-correlation methods for particle image velocimetry (PIV), the use of color images has largely been abandoned. Recently, however, with the re-emergence of color-based stereo and volumetric techniques, and the extensive use of color microscopy, color imaging for PIV has again become relevant. In this work, we explore the potential advantages of color PIV processing by developing and proposing new methods for handling multi-color images. The first method uses cross-correlation of every color channel independently to build a color vector cross-correlation plane. The vector cross-correlation can then be searched for one or more peaks corresponding to either the average displacement of several flow components using a color ensemble operation, or for the individual motion of colored particles, each with a different behavior. In the latter case, linear unmixing is used on the correlation plane to separate each known particle type as captured by the different color channels. The second method introduces the use of quaternions to encode the color data, and the cross-correlation is carried out simultaneously on all colors. The resulting correlation plane can be searched either for a single peak, corresponding to the mean flow or for multiple peaks, with velocity phase separation to determine which velocity corresponds to which particle type. Each of these methods was tested using synthetic images simulating the color recording of noisy particle fields both with and without the use of a Bayer filter and demosaicing operation. It was determined that for single-phase flow, both color methods decreased random errors by approximately a factor of two due to the noise signal being uncorrelated between color channels, while maintaining similar bias errors as compared to traditional monochrome PIV processing. In multi-component flows, the color vector correlation technique was able to successfully resolve displacements of two distinct yet coupled flow components with errors similar to traditional grayscale PIV processing of a single phase. It should be noted that traditional PIV processing is bound to fail entirely under such processing conditions. In contrast, the quaternion methods frequently failed to properly identify the correct velocity and phase and showed significant cross talk in the measurements between particle types. Finally, the color vector method was applied to experimental color images of a microchannel designed for contactless dielectrophoresis particle separation, and good results were obtained for both instantaneous and ensemble PIV processing. However, in both the synthetic color images that were generated using a Bayer filter and the experimental data, a significant peak-locking effect with a period of two pixels was observed. This effect is attributed to the inherent architecture of the Bayer filter. In order to mitigate this detrimental artifact, it is suggested that improved image interpolation or demosaicing algorithms tuned for use in PIV be developed and applied on the color images before processing, or that cameras that do not use a Bayer filter and therefore do not require a demosaicing algorithm be used for color PIV.

Quantitative evaluation of PIV peak locking through a multiple Δt strategy: relevance of the rms component

The possibility of using different times between laser pulses (Δt) in a PIV (Particle Image Velocimetry) measurement of the same real flow field for error assessment has already been proposed by the authors in a recent paper Nogueira et al. (Meas Sci Technol 20, 2009). It is a simple procedure that is available with the usual PIV setup. In that work, peak locking was considered basically as a bias error. Later measurements indicated that, using appropriate processing algorithms, this error is not the main peak-locking effect. Scenarios with the rms (root mean square) error due to peak locking as the most relevant contribution are more common than initially expected and require a differentiated approach. This issue is relevant due to the impact of the rms error in the evaluation of flow quantities like turbulent kinetic energy. The first part of this work is centred on showing that peak-locking error in PIV is not always a measurement bias towards the closest pixel integer displacement. Insight in the subject indicates that this is the case only for algorithm-induced peak locking. The peak locking coming out of image acquisition limitations (i.e. resolution) is not ‘a priory’ biased. It is a random error with a peculiar probability density function. Discussion on the subject is offered, and a particular approach to use a simple multiple Δt strategy to asses this error is proposed. The results reveal that in real images where amplitude of the peak-locking bias error is assessed to be as small as 0.02 pixels, rms errors can be in the order of 0.1 pixels. As PIV approaches maturity, providing a quantitative confidence interval by estimating measurement error seems essential. The method developed is robust enough to quantify these values in the presence of turbulence with rms up to ~0.6 pixels. This proposal constitutes a relevant step forward from the traditional histogram-based considerations that only reveal whether strong peak-locking error is present or not, without any information on its magnitude or whether its origin is bias or rms.

Elimination of peak-locking error in PIV analysis using the correlation mapping method

The peak-locking effect causes mean bias in most of the existing cross-correlation based algorithms for PIV data analysis. This phenomenon is inherent to the smooth curve-fitting through discrete correlation values, which is used to obtain the sub-pixel part of the displacement. Almost all of the existing effective methods to solve this problem require iterations. In this paper we introduce a new technique for obtaining sub-pixel accuracy, which bypasses the sub-pixel curve fitting, and eliminates the peak-locking effect, but does not require iterations. The principles of the ‘correlation mapping method’ (CMM) are based on the following logic: if one uses a bi-cubic interpolation to express the second image based on the first one and the unknown displacement, the correlation between them becomes a third-order polynomial of the displacement, whose coefficients depend on the first image. Matching this polynomial with the measured correlation provides an equation for the displacement for each point of the correlation map. A least-squares fit to the correlation values in the vicinity of the correlation peak (e.g. 5 × 5 points) provides an estimate for the particle displacement, including its sub-pixel part. We combine the new correlation mapping method with corrections for particle image distortion (PID) to further reduce the uncertainty in the velocity measurements. Three iterations typically achieve converged results. The CMM-PID method is tested using synthetic and experimental data. The peak-locking bias disappears in all cases. Even the ‘random’ error is substantially smaller than that obtained using a conventional sub-pixel curve fit. Issues related to streamline curvature and uncertainty in estimates of velocity gradients are also discussed.

A comparative study of five different PIV interrogation algorithms

Five different particle image velocimetry (PIV) interrogation algorithms are tested with numerically generated particle images and two real data sets measured in turbulent flows with relatively small particle images of size 1.0–2.5 pixels. The size distribution of the particle images is analyzed for both the synthetic and the real data in order to evaluate the tendency for peak-locking occurrence. First, the accuracy of the algorithms in terms of mean bias and rms error is compared to simulated data. Then, the algorithms’ ability to handle the peak-locking effect in an accelerating flow through a 2:1 contraction is compared, and their ability to estimate the rms and Reynolds shear stress profiles in a near-wall region of a turbulent boundary layer (TBL) at Re τ =510 is analyzed. The results of the latter case are compared to direct numerical simulation (DNS) data of a TBL. The algorithms are: standard fast Fourier transform cross-correlation (FFT-CC), direct normalized cross-correlation (DNCC), iterative FFT-CC with discrete window shift (DWS), iterative FFT-CC with continuous window shift (CWS), and iterative FFT-CC CWS with image deformation (CWD). Gaussian three-point peak fitting for sub-pixel estimation is used in all the algorithms. According to the tests with the non-deformation algorithms, DNCC seems to give the best rms estimation by the wall, and the CWS methods give slightly smaller peak-locking observations than the other methods. With the CWS methods, a bias error compensation method for the bilinear image interpolation, based on the particle image size analysis, is developed and tested, giving the same performance as the image interpolation based on the cardinal function. With the CWD algorithms, the effect of the spatial filter size between the iteration loops is analyzed, and it is found to have a strong effect on the results. In the near-wall region, the turbulence intensity varies by up to 4%, depending on the chosen interrogation algorithm. In addition, the algorithms’ computational performance is tested.

An improvement in the nine-point central difference image correction method for digital particle image velocimetry recording evaluation

A proper adjustment of the translation portion of pixel shifts for the multi-pass, nine-point (9P), central difference image correction (CDIC) method is found to be effective for further reducing the evaluation errors of digital particle image velocimetry recordings. In the improved central difference image correction scheme, the translation portion of pixel shifts is adjusted between the mean value of particle image displacements (initially introduced for the 9P method) and the particle image displacement at the centre (initially suggested for the four-point method) of the interrogation window, so that the evaluation errors of the iterated evaluation may converge to a lower level than both the initially introduced nine- and four-point methods. Based on a 50% overlap of interrogation windows, five possible algorithms to determine the pixel translation shift of the central difference image correction are discussed. Tests with synthetic particle image velocimetry recording pairs of simulated periodic flows demonstrate that the evaluation error of the 9P-central difference image correction method can be reduced to less than half of its initially introduced level, and it is obviously lower than that of the four-point method suggested by Wereley and Gui (2001 4th Int. Symp. on Particle Image Velocimetry (Göttingen, Germany, 17–19 Sept.); 2003 Exp. Fluids 34 42–51). Simulations and real image tests indicate that the error distribution and the peak-locking effect of the central difference image correction method have a two-pixel period.

A correlation-based continuous window-shift technique to reduce the peak-locking effect in digital PIV image evaluation

In this paper the peak-locking phenomenon is investigated in the evaluation of digital PIV recordings by using a correlation-based interrogation algorithm with a discrete window shift and a correlation-based tracking algorithm. Statistical analyses indicate that nonuniformly distributed bias errors are the main cause of the peak-locking effect, and the amplitude variation of the random error is also an important source of the peak locking. Simulations and experimental examples demonstrate that very strong peak-locking effects exist for the correlation-based interrogation algorithm with discrete window shift in the cases of large particle images, small interrogation windows, and very small particle images. Very strong peak-locking effects are also observed for the correlation-based tracking algorithm when the particle images are overexposed, binarized, or very small. These strong peak-locking effects can be avoided without loss of evaluation accuracy by using a continuous window-shift technique in combination with the correlation-based interrogation algorithm.

Identification of a new source of peak locking, analysis and its removal in conventional and super-resolution PIV techniques

One of the key factors that limit accuracy of particle image velocimetry (PIV) is the peak-locking effect. In this paper, a previously uncharacterised source of peak locking is presented. This source is neither related to the sensor geometry nor the subpixel resolution peak-fitting algorithms. It is present even when the particles are well described in terms of sensor spatial resolution (i.e. for particle diameters larger than 2 pixels). If no specific actions to avoid it are taken, its effect is especially important in those super-resolution systems that are based on iteratively reducing the size of the interrogation window. In this work, the mentioned source and its effects are studied and modelled. Based on this study, the actions required to avoid this type of peak locking are described. This includes the most usual correlation-based PIV systems, as well as super-resolution ones. Once this source of inaccuracy is avoided, it is possible to discriminate the performance of different types of correlation algorithms. As a consequence, specific proposals for the algorithms in the last steps of multigrid super-resolution PIV systems are given. The performances of the proposed solutions are verified using both synthetic and real PIV images.