Intensity Autocorrelation Function Research Articles

Simultaneously Extracting Multiple Parameters via Fitting One Single Autocorrelation Function Curve in Diffuse Correlation Spectroscopy

Near-infrared diffuse correlation spectroscopy (DCS) has recently been employed for noninvasive acquisition of blood flow information in deep tissues. Based on the established correlation diffusion equation, the light intensity autocorrelation function detected by DCS is determined by a blood flow index αD(B), tissue absorption coefficient μ(a), reduced scattering coefficient μ'(s), and a coherence factor β. This study is designed to investigate the possibility of extracting multiple parameters such as μ(a), μ'(s), β, and αD(B) through fitting one single autocorrelation function curve and evaluate the performance of different fitting methods. For this purpose, computer simulations, tissue-like phantom experiments, and in vivo tissue measurements were utilized. The results suggest that it is impractical to simultaneously fit αD(B) and μ(a) or αD(B) and μ'(s) from one single autocorrelation function curve due to the large crosstalk between these paired parameters. However, simultaneously fitting β and αD(B) is feasible and generates more accurate estimation with smaller standard deviation compared to the conventional two-step fitting method (i.e., first calculating β and then fitting αD(B)). The outcomes from this study provide a crucial guidance for DCS data analysis.

Anomalous dip observed in intensity autocorrelation function as an inherent nature of single-photon emitters

We report the observation of an anomalous antibunching dip in intensity autocorrelation function with photon correlation measurements on a single-photon emitter (SPE). We show that the anomalous dip observed is a manifestation of quantum nature of SPEs. Taking population dynamics in a quantum two-level system into account correctly, we redefine intensity autocorrelation function. This is of primary importance for precisely evaluating the lowest-level probability of multiphoton generation in SPEs toward realizing versatile pure SPEs for quantum information and communication.

Diffuse correlation spectroscopy with a fast Fourier transform-based software autocorrelator

Diffuse correlation spectroscopy (DCS) is an emerging noninvasive technique that probes the deep tissue blood flow, by using the time-averaged intensity autocorrelation function of the fluctuating diffuse reflectance signal. We present a fast Fourier transform (FFT)-based software autocorrelator that utilizes the graphical programming language LabVIEW (National Instruments) to complete data acquisition, recording, and processing tasks. The validation and evaluation experiments were conducted on an in-house flow phantom, human forearm, and photodynamic therapy (PDT) on mouse tumors under the acquisition rate of ∼400 kHz. The software autocorrelator in general has certain advantages, such as flexibility in raw photon count data preprocessing and low cost. In addition to that, our FFT-based software autocorrelator offers smoother starting and ending plateaus when compared to a hardware correlator, which could directly benefit the fitting results without too much sacrifice in speed. We show that the blood flow index (BFI) obtained by using a software autocorrelator exhibits better linear behavior in a phantom control experiment when compared to a hardware one. The results indicate that an FFT-based software autocorrelator can be an alternative solution to the conventional hardware ones in DCS systems with considerable benefits.

The application of dynamic light scattering to complex plasmas

The dynamic light scattering (DLS) technique is applied to the dust component of a complex (dusty) plasma, revealing a Gaussian intensity autocorrelation function for scattering angles between 4° and 175°. The Gaussian decay form represents free (ballistic) particle motion and allows determination of the one-dimensional squared particle velocity . At scattering angles below 1°, the intensity autocorrelation function is shown to be a combination of a Gaussian and an exponential function. This allows determination of the particle velocity and the diffusion constants at the same time. The dust system is fully described by the two components of motion in the horizontal and vertical directions. The two components are simultaneously measured on two scattering paths using only a single incident laser beam. In contrast to standard imaging techniques, the DLS method can be applied even to the disordered phase state where the dust particles have very high kinetic energies. In the ordered phase state, the assumptions of the DLS approach were verified by the independent Charge Coupled Device technique on the fundamental kinetic level. Furthermore, a careful discussion of the standard deviation of the DLS method proves that it can be used to study phase transitions of complex plasmas in detail.

One-particle correlation function in evanescent wave dynamic light scattering

In order to interpret measured intensity autocorrelation functions obtained in evanescent wave scattering, their initial decay rates have been analyzed recently [P. Holmqvist, J. K. G. Dhont, and P. R. Lang, Phys. Rev. E 74, 021402 (2006); B. Cichocki, E. Wajnryb, J. Blawzdziewicz, J. K. G. Dhont, and P. R. Lang, J. Chem. Phys. 132, 074704 (2010); J. W. Swan and J. F. Brady, ibid. 135, 014701 (2011)]. A theoretical analysis of the longer time dependence of evanescent wave autocorrelation functions, beyond the initial decay, is still lacking. In this paper we present such an analysis for very dilute suspensions of spherical colloids. We present simulation results, a comparison to cumulant expansions, and experiments. An efficient simulation method is developed which takes advantage of the particular mathematical structure of the time-evolution equation of the probability density function of the position coordinate of the colloidal sphere. The computer simulation results are compared with analytic, first and second order cumulant expansions. The only available analytical result for the full time dependence of evanescent wave autocorrelation functions [K. H. Lan, N. Ostrowsky, and D. Sornette, Phys. Rev. Lett. 57, 17 (1986)], that neglects hydrodynamic interactions between the colloidal spheres and the wall, is shown to be quite inaccurate. Experimental results are presented and compared to the simulations and cumulant expansions.

Size distribution of nanoparticles by dynamic light scattering. Comparison of Bayesian and Tikhonov inversion methods

The diameter distribution of nanometric particles is estimated from multiangle dynamic light scattering (MDLS) measurements by solving an ill-conditioned nonlinear inverse problem through Tikhonov and Bayesian methods. For both methods, the data inputs are the angle-dependent average diameters of the particle size distribution (PSD), which are in turn calculated from the measured autocorrelation functions of the light intensity scattered by a dilute sample of particles. The performances of both methods were tested on the basis of: (i) two simulated polymer latexes that involved PSDs of different shapes, widths and diameter ranges; and (ii) two real polystyrene latexes obtained by mixing two well-characterized standards of narrow PSDs (of known nominal diameters and standard deviations). For PSDs exhibiting highly asymmetric modes, or modes of quite different relative concentrations, the Bayesian method produced PSD estimates better than those obtained through Tikhonov regularization.

X-ray photon correlation spectroscopy during homogenous shear flow

We report x-ray photon correlation spectroscopy measurements of advective and diffusive dynamics in a dispersion of colloidal particles subjected to homogeneous shear flow in a rotating-disk shear cell. Intensity autocorrelation functions from scattering data collected using homodyne detection respond to the variation in velocity across the scattering volume when the scattering vector has a component parallel to the flow direction. Theoretical expressions for the impact of homogenous shear flow on the correlation function provide a quantitative prediction of the dependence of correlation functions on the scattering vector and shear rate. Under most circumstances, the applied shear deformation dominates the decay of the intensity correlation function. When scattering data are collected perpendicular to the flow direction, it is possible to measure the diffusive dynamics of the particles free from effects of the superimposed shear flow; however, this approach only works below some upper shear rate limit, beyond which data are affected either by shear effects (caused by the finite width of the detector) or by particle transit through the scattering volume.

Dynamics of charged gibbsite platelets in the isotropic phase

We report on depolarized and non-depolarized dynamic light scattering, static light scattering, and steady shear viscosity measurements on interacting charge-stabilized gibbsite platelets suspended in dimethyl sulfoxide (DMSO). The average collective and (long-time) translational self-diffusion coefficients, and the rotational diffusion coefficient, have been measured as functions of the platelet volume fraction ϕ, up to the isotropic–liquid crystal (I/LC) transition. The non-depolarized intensity autocorrelation function, measured at low scattering wavenumbers, consists of a fast and a slowly decaying mode which we interpret as the orientationally averaged collective and translational self-diffusion coefficients, respectively. Both the rotational and the long-time self-diffusion coefficients decrease very strongly, by more than two orders of magnitude, in going from the very dilute limit to the I/LC transition concentration. A similarly strong decrease, with increasing ϕ, is observed for the inverse zero-strain limiting steady shear viscosity. With increasing ϕ, increasingly strong shear-thinning is observed, accompanied by a shrinking of the low shear-rate Newtonian plateau. The measured diffusion coefficients are interpreted theoretically in terms of a simple model of effective charged spheres interacting by a screened Coulomb potential, with hydrodynamic interactions included. The disk-like particle shape, and the measured particle radius and thickness polydispersities, enter into the model calculations via the scattering amplitudes. The interaction-induced enhancement of the collective diffusion coefficient by more than a factor of 20 at larger ϕ is well captured in the effective sphere model, whereas the strong declines of the experimental translational and rotational self-diffusion coefficients are underestimated.

Dynamics of colloidal particles in ice

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration.

Extrapolation of the intensity autocorrelation function of a quantum-dot micropillar laser into the thermal emission regime

We present investigations on the coherence of the emission from the fundamental mode of an AlGaInAs/GaAs quantum-dot microcavity laser. We measure the first-order field-correlation function g(1)(τ) with a Michelson interferometer, from which we determine coherence times of up to 20 ns for the highest pump powers. To fully characterize the coherence properties of the cavity emission, we apply a phenomenological model that connects the first- and second-order correlation functions. Hereby it is possible to overcome the limited sensitivity of the streak camera used for photon-correlation measurements, and thus to extend the accessible excitation-power range for g(2)(τ) down to the thermal regime.

Particle Tracking Microrheology of Lyotropic Liquid Crystals

We present comprehensive results on the microrheological study of lyotropic liquid crystalline phases of various space groups constituted by water-monoglyceride (Dimodan) mixtures. In order to explore the viscoelastic properties of these systems, we use particle tracking of probe colloidal particles suitably dispersed in the liquid crystals and monitored by diffusing wave spectroscopy. The identification of the various liquid crystalline phases was separately carried out by small-angle X-ray scattering. The restricted motion of the particles was monitored and identified by the decay time of intensity autocorrelation function and the corresponding time-dependent mean square displacement (MSD), which revealed space group-dependent behavior. The characteristic time extracted by the intersection of the slopes of the MSD at short and long time scales, provided a characteristic time which could be directly compared with the relaxation time obtained by microrheology. Further direct comparison of microrheology and bulk rheology measurements was gained via the Laplace transform of the generalized time-dependent MSD, yielding the microrheology storage and loss moduli, G'(ω) and G''(ω), in the frequency domain ω. The general picture emerging from the microrheology data is that all liquid crystals exhibit viscoelastic properties in line with results from bulk rheology and the transition regime (elastic to viscous) differs according to the specific liquid crystal considered. In the case of the lamellar phase, a plastic fluid is measured by bulk rheology, while microrheology indicates viscoelastic behavior. Although we generally find good qualitative agreement between the two techniques, all liquid crystalline systems are found to relax faster when studied with microrheology. The most plausible explanation for this difference is due to the different length scales probed by the two techniques: that is, microscopical relaxation on these structured fluids, is likely to occur at shorter time scales which are more suitably probed by microrheology, whereas bulk, macroscopic relaxations occurring at longer time scales can only be probed by bulk rheology.

Single photon emitters based on Ni/Si related defects in single crystalline diamond

We present investigations on single Ni/Si related color centers produced via ion implantation into single crystalline type IIa CVD diamond. Testing different ion dose combinations we show that there is an upper limit for both the Ni and the Si dose 10^12/cm^2 and 10^10/cm^2 resp.) due to creation of excess fluorescent background. We demonstrate creation of Ni/Si related centers showing emission in the spectral range between 767nm and 775nm and narrow line-widths of 2nm FWHM at room temperature. Measurements of the intensity auto-correlation functions prove single-photon emission. The investigated color centers can be coarsely divided into two groups: Drawing from photon statistics and the degree of polarization in excitation and emission we find that some color centers behave as two-level, single-dipole systems whereas other centers exhibit three levels and contributions from two orthogonal dipoles. In addition, some color centers feature stable and bright emission with saturation count rates up to 78kcounts/s whereas others show fluctuating count rates and three-level blinking.

Quasi-elastic laser light scattering study of polyacrylamide hydrogel immersed in water and salt solutions

Polyacrylamide (PAAm) hydrogels immersed in water and aqueous NaCl solutions were investigated for their structure and dynamics using static and quasi-elastic laser light scattering (QELS) techniques. Ensemble-averaged electric field correlation function f(q, t) obtained from the non-ergodic analysis of intensity-autocorrelation function for PAAm gel immersed in water and in 5 M NaCl showed an exponential decay to a plateau with an initial decay followed by saturation at long times. The value of the plateau was found to depend on NaCl concentration and was higher than that of water. Collective diffusion coefficient, D, of the polymer network of the hydrogel immersed in water and in different concentrations of NaCl was determined by analysing f(q, t). The measured diffusion coefficient showed linear decrease with increase in concentration of NaCl. The characteristic network parameters were obtained by analyzing f(q, t) with harmonically bound Brownian particle model and from static light scattering studies.

Estimation of the $K$-Scattered Amplitude in Additive Noise

We recall a recent diffusion model by Field & Tough [4], in which stochastic differential equations accounting for the continuous dynamics of the ^-scattering have been proposed together with an expression for the intensity autocorrelation function. The finite impulse response Wiener filter enables the design of the optimal filter to retrieve the scattered amplitude when the clutter is placed in superposition with thermal noise. Two possible applications are discussed: the estimation of the parameter B (the reciprocal of which is a characteristic time for the autocorrelation function) and the inference of the scattering cross section.

Fluorescence Intermittency and Energy Transfer in Small Clusters of Semiconductor Quantum Dots

We have studied isolated semiconductor nanocrystal quantum dots (QDs) and small clusters of QDs by single-molecule time-correlated single-photon counting, from which fluorescence intensity trajectories, autocorrelation functions, decay histograms, and lifetime-intensity distributions have been constructed. These measurements confirm that QD clusters exhibit unique fluorescence behavior not observed in isolated QDs. In particular, the QD clusters exhibit a short-lifetime component in their fluorescence decay that is correlated with low fluorescence intensity of the cluster. A model based on nonradiative energy transfer to QDs within a cluster that have smaller energy gaps, combined with independent blinking for the QDs in a cluster, accounts for the main experimental features.

Synergistic interaction of Locust Bean Gum and Xanthan investigated by rheology and light scattering

The use of synergistic interactions between polysaccharides can represent an important approach for the preparation of physical networks with a wide range of industrial applications, such as in the food and biomedical fields. Locust Bean Gum and Xanthan, two biocompatible polymers, are able to form gels when mixed together. A detailed study was carried out on three samples, prepared at different weight ratios and two temperatures, by means of light scattering and rheological techniques. The solid-like character of each sample was evaluated by measurements of the viscoelastic spectrum and intensity autocorrelation function. The contribution of fast and slow fluctuations to the static light scattered intensity was also evaluated at different angles. The power law exponents for the sol–gel transitions were estimated together with the fractal dimensions. The scattering results were found in good agreement with the mechanical ones in revealing a strong dependence of the structural properties of the different samples on their preparation conditions. Indeed, results show that a fine tuning of the properties of the mixed gels is possible through the change of the temperature preparation and/or the polymer weight ratio.

Agglomeration of urinary nanocrystallites: Key factor to formation of urinary stones

With transmission electron microscopy (TEM) and nanoparticle size analyzer, comparative studies were conducted on the property variation of nanocrystallites in the urine of 5 lithogenic patients and 5 healthy subjects following the placement time ( t 1). These properties include average particle size ( d̄), size distribution, intensity–autocorrelation function, Zeta potential ( ζ) and aggregation state. With the prolongation of t 1 from 0 h to 4 h, d̄ value of the nanocrystallites in urine of lithogenic patients increased from 742 nm to 1667 nm, the autocorrelation time increased from 7.68 ms to 1050 ms and ζ decreased from −1.52 mV to −4.44 mV, respectively; the autocorrelation curves were of fluctuating and unsmooth, and TEM showed that most of the patient's urinary nanocrystallites were in aggregation state and three types of agglomeration were observed. However, for nanocrystallites in urine of healthy subjects, there was little variation in the above properties within 4 h. The autocorrelation curves were of regular and smooth, and TEM showed that healthy urinary nanocrystallites were well-dispersed. The above results show that the nanocrystallites in urine of healthy subjects can keep stability, whereas those of lithogenic patients are easier to agglomerate gradually; and the agglomeration of urinary nanocrystallites is the key factor to stone formation.

The intensity correlation function in evanescent wave scattering

As a first step toward the interpretation of dynamic light scattering with evanescent illumination from suspensions of interacting spheres, in order to probe their near wall dynamics, we develop a theory for the initial slope of the intensity autocorrelation function. An expression for the first cumulant is derived that is valid for arbitrary concentrations, which generalizes a well-known expression for the short-time, wave-vector dependent collective diffusion coefficient in bulk to the case where a wall is present. Explicit expressions and numerical results for the various contributions to the initial slope are obtained within a leading order virial expansion. The dependence of the initial slope on the components of the wave vector parallel and perpendicular to the wall, as well as the dependence on the evanescent-light penetration depth are discussed. For the hydrodynamic interactions between colloids and between the wall, which are essential for a correct description of the near-interface dynamics, we include both far-field and lubrication contributions. Lubrication contributions are essential to capture the dynamics as probed in experiments with small penetration depths. Simulations have been performed to verify the theory and to estimate the extent of the concentration range where the virial expansion is valid. The computer algorithm developed for this purpose will also be of future importance for the interpretation of experiments and to develop an understanding of near-interface dynamics, at high colloid concentrations.

Quantitative Determination of Spatial Protein-Protein Correlations in Fluorescence Confocal Microscopy

To quantify spatial protein-protein proximity (colocalization) in paired microscopic images of two sets of proteins labeled by distinct fluorophores, we showed that the cross-correlation and the autocorrelation functions of image intensity consisted of fast and slowly decaying components. The fast component resulted from clusters of proteins specifically labeled, and the slow component resulted from image heterogeneity and a broadly-distributed background. To better evaluate spatial proximity between the two specifically labeled proteins, we extracted the fast-decaying component by fitting the sharp peak in correlation functions to a Gaussian function, which was then used to obtain protein-protein proximity index and the Pearson's correlation coefficient. We also employed the median-filter method as a universal approach for background reduction to minimize nonspecific fluorescence. We illustrated our method by analyzing computer-simulated images and biological images.

Atom detection in a two-mode optical cavity with intermediate coupling: Autocorrelation studies

We use an optical cavity in the regime of intermediate coupling between atom and cavity mode to detect single moving atoms. Degenerate polarization modes allow excitation of the atoms in one mode and collection of spontaneous emission in the other while keeping separate the two sources of light; we obtain a higher confidence and efficiency of detection by adding cavity-enhanced Faraday rotation. Both methods greatly benefit from coincidence detection of photons, attaining fidelities in excess of 99% in less than $1\text{ }\ensuremath{\mu}\text{s}$. Detailed studies of the second-order intensity autocorrelation function of light from the signal mode reveal evidence of antibunched photon emissions and the dynamics of single-atom transits.