Two-dimensional Cross-correlation Research Articles

VIMAP: AN INTERACTIVE PROGRAM PROVIDING RADIO SPECTRAL INDEX MAPS OF ACTIVE GALACTIC NUCLEI

We present a GUI-based interactive Python program, VIMAP, which generates radio spectral index maps of active galactic nuclei (AGN) from Very Long Baseline Interferometry (VLBI) maps obtained at different frequencies. VIMAP is a handy tool for the spectral analysis of synchrotron emission from AGN jets, specifically of spectral index distributions, turn-over frequencies, and core-shifts. In general, the required accurate image alignment is difficult to achieve because of a loss of absolute spatial coordinate information during VLBI data reduction (self-calibration) and/or intrinsic variations of source structure as function of frequency. These issues are overcome by VIMAP which in turn is based on the two-dimensional cross-correlation algorithm of Croke and Gabuzda (2008). In this paper, we briefly review the problem of aligning VLBI AGN maps, describe the workflow of VIMAP, and present an analysis of archival VLBI maps of the active nucleus 3C 120.

The Spatial Synchronization of Areal Measurement Data Sets by Multi-Probes

In this paper, to release this induced errors and improve the accuracy of the measured data, a new spatial synchronization method is proposed to spatially synchronize the three-dimensional surface data sets obtained by variety surface topography measuring instruments. The proposed spatial synchronization method minimizes the geometrical error components using the data interpolation, the least squares method, and the two-dimensional cross correlation function. For verification of the method, it was applied to the measured data sets measured with a chromatic confocal microscopy, a laser scanning confocal microscopy, and an ellipsometer. Based on the experimental results, the accuracy or the proposed method is analyzed and evaluated.

The analysis of in-air reverberation patterns from medical ultrasound transducers.

National guidelines for routine ultrasound quality assurance include the measurement of transducer sensitivity using the in-air reverberation pattern generated from a transducer operating in air. The in-air reverberation method has been compared with other well-known measures of transducer sensitivity, such as the Sonora FirstCall probe tester (Sonora Medical Systems Inc, Longmont, CO, USA) and phantom-based images. There is good agreement between the in-air reverberation images and the Sonora FirstCall probe data for individual crystal sensitivity. However, the in-air reverberation approach is cheaper and easier to implement for linear and curvilinear transducers. The methods used for measuring the in-air reverberation pattern and the influence of scanner parameters such as gain and output power have been investigated. In general, reliance on a visual assessment of reverberation depth can lead to inconsistencies in the measurement of reverberation depth, when taken over a period of several months. The value of scanner parameters, in particular scanner gain, is also important when trying to measure changes in reverberation depth due to changes in transducer performance. A more accurate assessment of changes in transducer sensitivity, using the in-air reverberation method, is found by measuring the peak pixel grey scale values within a chosen reverberation band in the image. This quantitative approach can be taken a step further by assessing changes within the whole in-air reverberation pattern, by applying a two-dimensional cross correlation between two reverberation images to assess changes in transducer performance.

In vivo full-field en face correlation mapping optical coherence tomography

A full-field optical coherence tomography (OCT) system has been developed for the purpose of performing nonscanning en face flow imaging. The light source is centered at 840 nm with a bandwidth of 50 nm resulting in an axial resolution of 8 μm in air. Microscope objectives with a numerical aperture of 0.1 were incorporated giving a transverse resolution of 5 μm. A magnification of 5.65 was measured, resulting in a field of view of 1260×945 μm. Pairs of interference fringe images are captured with opposing phase and a two-step phase image reconstruction method is applied to reconstruct each en face image. The OCT frame rate is 10 Hz. A two-dimensional cross-correlation technique is applied to pairs of consecutive en face images in order to distinguish dynamic from static light-scatterers. The feasibility of the method was examined by simulating blood flow by creating a phantom with 5% intralipid solution. In vivo imaging of a Xenopus laevis tadpole was also performed in order to investigate the feasibility of imaging the vascular system. We present for what we believe to be the first time, the application of correlation mapping optical coherence tomography to full-field OCT to provide in vivo functional imaging of blood vessels.

Orbital and physical parameters of eclipsing binaries from the ASAS catalogue – V. Investigation of subgiants and giants: the case of ASAS J010538−8003.7, ASAS J182510−2435.5 and V1980 Sgr★†

We present absolute physical and orbital parameters for three double-lined detached eclipsing binary systems from the All Sky Automated Survey (ASAS) catalogue with subgiant and giant components. These parameters were derived from archival V-band ASAS photometry and new radial velocities. The radial velocities were calculated from high quality optical spectra we obtained with the 8.2 m Subaru/HDS, ESO 3.6 m/HARPS, 1.9 m Radcliffe/GIRAFFE, CTIO 1.5 m/CHIRON, and 1.2 m Euler/CORALIE using the two-dimensional cross-correlation technique (TODCOR) and synthetic template spectra chosen for every system separately as references. The physical and orbital parameters of the systems were derived with the PHOEBE and JKTEBOP codes. We checked the evolutionary status of the systems with several sets of isochrones and determined distances for each system. The derived uncertainties for individual masses of ASAS J010538-8003.7, ASAS J182510-2435.5, and V1980 Sgr components vary from 0.7% to 3.6% while the radii are in the range 1% to 24%. For all of the investigated systems such a detailed orbital and physical analysis is presented for the first time.

RX J0513.1+0851 AND RX J0539.9+0956: TWO YOUNG, RAPIDLY ROTATING SPECTROSCOPIC BINARY STARS

RX J0513.1+0851 and RX J0539.9+0956 were previously identified as young, low-mass, single-lined spectroscopic binary systems and classified as weak-lined T Tauri stars at visible wavelengths. Here we present radial velocities, spectral types, vsini values, and flux ratios for the components in these systems resulting from two-dimensional cross-correlation analysis. These results are based on high-resolution, near-infrared spectroscopy taken with the Keck II telescope to provide a first characterization of these systems as double-lined rather than single-lined. It applies the power of infrared spectroscopy to the detection of cool secondaries; the flux scales as a less steep function of mass in the infrared than in the visible, thus enabling an identification of low-mass secondaries. We found that the RX J0513.1+0851 and RX J0539.9+0956 primary stars are fast rotators, 60 km/s and 80 km/s respectively; this introduces extra difficulty in the detection of the secondary component as a result of the quite broad absorption lines. To date, these are the highest rotational velocities measured for a pre-main sequence spectroscopic binary. The orbital parameters and mass ratios were determined by combining new visible light spectroscopy with our infrared data for both systems. For RX J0513.1+0851, we derived a period of ~4 days and a mass ratio of q = 0.46 +/- 0.01 and for RX J0539.9+0956, a period of ~1117 days and a mass ratio of q = 0.66 +/- 0.01. Based on our derived properties for the stellar components, we estimate the luminosities and hence distances to these binaries at 220 pc and 90 pc. They appear to be significantly closer than previously estimated.

Studies of red giants in eclipsing binaries

We present absolute physical and orbital parameters for double-lined detached eclipsing binary systems from the All Sky Automated Survey (ASAS) catalogue with subgiant and giant components. The radial velocities were calculated from high quality optical spectra we obtained with the 8.2 m Subaru/hds, ESO 3.6 m/harps, 1.9 m Radcliffe/giraffe, CTIO 1.5 m/chiron, and 1.2 m Euler/coralie using the two-dimensional cross-correlation technique (todcor) and synthetic template spectra chosen for every system separately as references. We checked the evolutionary status of the systems with several sets of evolutionary tracks and determined distances for each system. The derived uncertainties for individual masses and radii of components are better than 3% for several systems. Additionally, we performed atmospheric parameters determination and chemical abundances analysis for the system which spectra we disentangled.

Spectroscopic analysis of eclipsing SB2 stars: a case study

The investigation of eclipsing spectroscopic binaries provides basic parameters of stars in a direct way. Whereas the measurable absolute masses can be used to calibrate stellar evolutionary scenarios, the effective temperatures derived from spectroscopic analysis are an important input to light curve and asteroseismic modelling. We compare different methods for investigating eclipsing SB2 stars focusing on radial velocity determination and spectrum decomposition and analysis. Used methods are the two-dimensional cross-correlation technique todcor, spectral disentangling with the Fourier transform-based korel program, and a grid search-based method of spectrum analysis using spectrum synthesis. The study is based on the investigation of two eclipsing SB2 stars observed by the Kepler satellite mission.

In Vivo Classification of Breast Masses Using Features Derived From Axial-Strain and Axial-Shear Images

Breast cancer is currently the second leading cause of cancer deaths in women. Early detection and accurate classification of suspicious masses as benign or malignant is important for arriving at an appropriate treatment plan. In this article, we present classification results for features extracted from ultrasound-based, axial-strain and axial-shear images of breast masses. The breast-mass stiffness contrast, size ratio, and a normalized axial-shear strain area feature are evaluated for the classification of in vivo breast masses using a leave-one-out classifier. Radiofrequency echo data from 123 patients were acquired using Siemens Antares or Elegra clinical ultrasound systems during freehand palpation. Data from four different institutions were analyzed. Axial displacements and strains were estimated using a multilevel, pyramid-based two-dimensional cross-correlation algorithm, with final processing block dimensions of 0.385 mm × 0.507 mm (three A-lines). Since mass boundaries on B-mode images for 21 patients could not be delineated (isoechoic), the combined feature analysis was only performed for 102 patients. Results from receiver operating characteristic (ROC) demonstrate that the area under the curve was 0.90, 0.84, and 0.52 for the normalized axial-shear strain, size ratio, and stiffness contrast, respectively. When these three features were combined using a leave-one-out classifier and support vector machine approach, the overall area under the curve improved to 0.93.

Visualizing the radial and circumferential strain distribution within vessel phantoms using synthetic-aperture ultrasound elastography

Noninvasive elastography (NIVE) produces elastograms that are difficult to interpret because NIVE visualizes strain in the transducer coordinate system. In this paper, we hypothesized that transforming normal and shear strain elastograms to the vessel coordinate system will produce better strain elastograms. To corroborate this hypothesis, we acquired synthetic-aperture (SA) ultrasound data from simulated and physical vessel phantoms. In both studies, SA echo frames were reconstructed from data acquired with a sparse transducer array. The simulation study was performed with homogeneous and heterogenous phantoms, but in the experimental study we used a modified ultrasound scanner to acquire SA data from homogeneous (n = 1) and heterogeneous (n = 3) vessel phantoms. Axial and lateral displacements were estimated by performing two-dimensional cross-correlation analysis on the beamformed RF echo frames. We generated radial and circumferential strain elastograms by transforming normal and shear strain elastograms to the vessel coordinate system. The results revealed: 1) radial and circumferential strain elastograms acquired from simulated data had a relative root mean squared error on the order of 0.1%; 2) experimentally acquired radial and circumferential strain elastograms had elastographic contrast-to-noise ratio (CNRe) between 10 and 40 dB, and elastographic signal-to-noise ratio (SNRe) between 10 and 35 dB, depending on the number of active transmission elements employed during imaging; 3) radial and circumferential strain elastograms produced with fewer than 8 active transmission elements were inferior to those computed with a greater number of active elements; and 4) plaques were evident in the strain elastograms, except in those obtained with the sparsest transducer array. This study demonstrated that a syntheticaperture ultrasound system could visualize radial and circumferential strain noninvasively.

Correlation Analysis of Atomic and Single-Molecule Junction Conductance

The break-junction technique is widely used to measure electronic properties of nanoscale junctions including metal point-contacts and single-molecule junctions. In these measurements, conductance is measured as a function of electrode displacement yielding data that is analyzed by constructing conductance histograms to determine the most frequently observed conductance values in the nanoscale junctions. However much of the rich physics in these measurements is lost in this simple analysis technique. Conductance histograms cannot be used to study the statistical relation of distinct junction configurations, to distinguish structurally different configurations that have similar conductance values, or to obtain information on the relation between conductance and junction elongation. Here, we give a detailed introduction to a novel statistical analysis method based on the two-dimensional cross-correlation histogram (2DCH) analysis of conductance traces and show that this method provides new information about the relation of different junction configurations that occur during the formation and evolution of metal and single-molecule junctions. We first illustrate the different types of correlation effects by using simulated conductance traces. We then apply this analysis method to several different experimental examples. We show from break-junction measurements of different metal point-contacts that in aluminum, the first conductance histogram peak corresponds to two different junction structures. In tantalum, we identify the frequent absence of adhesive instability. We show that conductance plateaus shift in a correlated manner in iron and vanadium junctions. Finally, we highlight the applicability of the correlation analysis to single-molecule platinum-CO-platinum and gold-4,4'-bipyridine-gold junctions.

Finding proto-spectroscopic binaries

The formation of spectroscopic binaries (SB) may be a natural byproduct of star formation. The early dynamical evolution of multiple stellar systems after the initial fragmentation of molecular clouds leaves characteristic imprints on the properties of young, multiple stars. The discovery and the characterization of the youngest SB will allow us to infer the mechanisms and timescales involved in their formation. Our work aims to find spectroscopic companions around young stellar objects (YSO). We present a near-IR high-resolution (R ~ 60000) multi-epoch radial velocity survey of 7 YSO in the star forming region (SFR) rho-Ophiuchus. The radial velocities of each source were derived using a two-dimensional cross-correlation function, using the zero-point established by the Earth's atmosphere as reference. More than 14 spectral lines in the CO (0-2) bandhead window were used in the cross-correlation against LTE atmospheric models to compute the final results. We found that the spectra of the protostars in our sample agree well with the predicted stellar photospheric profiles, indicating that the radial velocities derived are indeed of stellar nature. Three of the targets analyzed exhibit large radial velocity variations during the three observation epochs. These objects - pending further confirmation and orbital characteristics - may become the first evidence for proto-spectroscopic binaries, and will provide important constraints on their formation. Our preliminary binary fraction (BF) of ~71% (when merging our results with those of previous studies) is in line with the notion that multiplicity is very high at young ages and therefore a byproduct of star formation

Sheared-flow induced confinement transition in a linear magnetized plasma

A magnetized plasma cylinder (12 cm in diameter) is induced by an annular shape obstacle at the Large Plasma Device [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)]. Sheared azimuthal flow is driven at the edge of the plasma cylinder through edge biasing. Strong fluctuations of density and potential ({delta}n/n{approx}e{delta}{phi}/kT{sub e}{approx}0.5) are observed at the plasma edge, accompanied by a large density gradient (L{sub n}={nabla}lnn{sup -1}{approx}2cm) and shearing rate ({gamma}{approx}300kHz). Edge turbulence and cross-field transport are modified by changing the bias voltage (V{sub bias}) on the obstacle and the axial magnetic field (B{sub z}) strength. In cases with low V{sub bias} and large B{sub z}, improved plasma confinement is observed, along with steeper edge density gradients. The radially sheared flow induced by ExB drift dramatically changes the cross-phase between density and potential fluctuations, which causes the wave-induced particle flux to reverse its direction across the shear layer. In cases with higher bias voltage or smaller B{sub z}, large radial transport and rapid depletion of the central plasma density are observed. Two-dimensional cross-correlation measurement shows that a mode with azimuthal mode number m=1 and large radial correlation length dominates themore » outward transport in these cases. Linear analysis based on a two-fluid Braginskii model suggests that the fluctuations are driven by both density gradient (drift wave like) and flow shear (Kelvin-Helmholtz like) at the plasma edge.« less

A fractional Fourier transform analysis of a bubble excited by an ultrasonic chirp

The fractional Fourier transform is proposed here as a model based, signal processing technique for determining the size of a bubble in a fluid. The bubble is insonified with an ultrasonic chirp and the radiated pressure field is recorded. This experimental bubble response is then compared with a series of theoretical model responses to identify the most accurate match between experiment and theory which allows the correct bubble size to be identified. The fractional Fourier transform is used to produce a more detailed description of each response, and two-dimensional cross correlation is then employed to identify the similarities between the experimental response and each theoretical response. In this paper the experimental bubble response is simulated by adding various levels of noise to the theoretical model output. The method is compared to the standard technique of using time-domain cross correlation. The proposed method is shown to be far more robust at correctly sizing the bubble and can cope with much lower signal to noise ratios.

Fast template tracking in video sequences

Tracking of poorly defined, rotating and/or distorted objects in a video sequence poses significant problems especially in medical diagnostics including ultrasound (sonographic) video used for examination and diagnosis of internal movement of tissue or muscle and nerve action. Cross-correlation techniques have been successful in retrieving dynamic information directly from ultrasound video data. We outline a fast implementation of tracking based on normalized cross-correlation using an adaptive template and present results from our application, developed in MATLAB™, which successfully tracks arbitrarily selected objects in deformed or severely compromised images. Common ultrasound image evaluation is qualitative but there is need to retrieve quantitative dynamic information such as the trajectory or velocity of selected areas. Our approach uses normalized two-dimensional cross-correlation to find the position of an initially selected template enclosing the feature of interest and map its trajectory frame-by-frame to produce displacement and velocity plots. We illustrate operation of the application using routine ultrasound data and demonstrate its performance using test video of objects rotating full circle and rolling down a ramp. We analyse errors associated with sampling to compare performance of our implementation with a more rigorous but tedious and computationally expensive correlation of a resampled, rotated, and shifted template.

Shaper-assisted full-phase characterization of UV pulses without a spectrometer

A full-phase measurement of low-energy femtosecond UV pulses is presented. The method relies on phase retrieval of measured sonogram traces and is greatly simplified by a two-dimensional shaper-assisted cross correlation setup. As all required pulses are generated by the pulse shaper, the method is free of external references and additional tunable filter setups.

Axial-Shear Strain Imaging for Differentiating Benign and Malignant Breast Masses

Axial strain imaging has been utilized for the characterization of breast masses for over a decade; however, another important feature namely the shear strain distribution around breast masses has only recently been used. In this article, we examine the feasibility of utilizing in vivo axial-shear strain imaging for differentiating benign from malignant breast masses. Radio-frequency data was acquired using a VFX 13-5 linear array transducer on 41 patients using a Siemens SONOLINE Antares real-time clinical scanner at the University of Wisconsin Breast Cancer Center. Free-hand palpation using deformations of up to 10% was utilized to generate axial strain and axial-shear strain images using a two-dimensional cross-correlation algorithm from the radio-frequency data loops. Axial-shear strain areas normalized to the lesion size, applied strain and lesion strain contrast was utilized as a feature for differentiating benign from malignant masses. The normalized axial-shear strain area feature estimated on eight patients with malignant tumors and 33 patients with fibroadenomas was utilized to demonstrate its potential for lesion differentiation. Biopsy results were considered the diagnostic standard for comparison. Our results indicate that the normalized axial-shear strain area is significantly larger for malignant tumors compared with benign masses such as fibroadenomas. Axial-shear strain pixel values greater than a specified threshold, including only those with correlation coefficient values greater than 0.75, were overlaid on the corresponding B-mode image to aid in diagnosis. A scatter plot of the normalized area feature demonstrates the feasibility of developing a linear classifier to differentiate benign from malignant masses. The area under the receiver operator characteristic curve utilizing the normalized axial-shear strain area feature was 0.996, demonstrating the potential of this feature to noninvasively differentiate between benign and malignant breast masses. (E-mail: tvarghese@wisc.edu)

Dynamic frame selection for in vivo ultrasound temperature estimation during radiofrequency ablation

Minimally invasive therapies such as radiofrequency ablation have been developed to treat cancers of the liver, prostate and kidney without invasive surgery. Prior work has demonstrated that ultrasound echo shifts due to temperature changes can be utilized to track the temperature distribution in real time. In this paper, a motion compensation algorithm is evaluated to reduce the impact of cardiac and respiratory motion on ultrasound-based temperature tracking methods. The algorithm dynamically selects the next suitable frame given a start frame (selected during the exhale or expiration phase where extraneous motion is reduced), enabling optimization of the computational time in addition to reducing displacement noise artifacts incurred with the estimation of smaller frame-to-frame displacements at the full frame rate. A region of interest that does not undergo ablation is selected in the first frame and the algorithm searches through subsequent frames to find a similarly located region of interest in subsequent frames, with a high value of the mean normalized cross-correlation coefficient value. In conjunction with dynamic frame selection, two different two-dimensional displacement estimation algorithms namely a block matching and multilevel cross-correlation are compared. The multi-level cross-correlation method incorporates tracking of the lateral tissue expansion in addition to the axial deformation to improve the estimation performance. Our results demonstrate the ability of the proposed motion compensation using dynamic frame selection in conjunction with the two-dimensional multilevel cross-correlation to track the temperature distribution.

Modeling and simulation of pinhole channels

This article presents a general pinhole channel reference model based on the cause of pinhole effect. On the base of this reference model, a deterministic simulation model is developed by keeping the difference of correlation properties between reference and simulation model as smaller as possible. The correlation properties include temporal autocorrelation function (ACF), two-dimensional (2-D) space cross-correlation function (CCF) and frequency correlation function (FCF). The results show that although pinhole channel has good correlation properties, the channel capacity is very low because of the low rank of channel transform matrix.

Absolute properties of the main-sequence eclipsing binary FM Leo

First spectroscopic and new photometric observations of the eclipsing binary FM Leo are presented. The main aims were to determine orbital and stellar parameters of two components and their evolutionary stage. First spectroscopic observations of the system were obtained with DDO and PST spectrographs. The results of the orbital solution from radial velocity curves are combined with those derived from the light-curve analysis (ASAS-3 photometry and supplementary observations of eclipses with 1 m and 0.35 m telescopes) to derive orbital and stellar parameters. JKTEBOP, Wilson-Devinney binary modelling codes and a two-dimensional cross-correlation (TODCOR) method were applied for the analysis. We find the masses to be M_1 = 1.318 $\pm$ 0.007 and M_2 = 1.287 $\pm$ 0.007 M_sun, the radii to be R_1 = 1.648 $\pm$ 0.043 and R_2 = 1.511 $\pm$ 0.049 R_sun for primary and secondary stars, respectively. The evolutionary stage of the system is briefly discussed by comparing physical parameters with current stellar evolution models. We find the components are located at the main sequence, with an age of about 3 Gyr.