No Arabic abstract
Diffusing wave spectroscopy (DWS) is a well-known set of methods to measure the temporal dynamics of dynamic samples. In DWS, dynamic samples scatter the incident coherent light, and the information of the temporal dynamics is encoded in the scattered light. To record and analyze the light signal, there exist two types of methods - temporal sampling methods and speckle ensemble methods. Temporal sampling methods, including diffuse correlation spectroscopy (DCS), use one or multiple large bandwidth detectors to well sample and analyze the temporal light signal to infer the sample temporal dynamics. Speckle ensemble methods, including speckle visibility spectroscopy (SVS), use a high-pixel-count camera sensor to capture a speckle pattern and use the speckle contrast to infer sample temporal dynamics. In this paper, we theoretically and experimentally demonstrate that the decorrelation time ({tau}) measurement accuracy or SNR of the two types of methods has a unified and similar fundamental expression based on the number of independent observables (NIO) and the photon flux. Given a time measurement duration, NIO in temporal sampling methods is constrained by the measurement duration, while speckle ensemble methods can outperform by using simultaneous sampling channels to scale up NIO significantly. In the case of optical brain monitoring, the interplay of these factors favors speckle ensemble methods. We illustrate that this important engineering consideration is consistent with the previous research on blood pulsatile flow measurements, where a speckle ensemble method operating at 100-fold lower photon flux than a conventional temporal sampling system can achieve a comparable SNR.
We present a detection scheme for diffusing wave spectroscopy (DWS) based on a two cell geometry that allows efficient ensemble averaging. This is achieved by putting a fast rotating diffuser in the optical path between laser and sample. We show that the recorded (multi-speckle) correlation echoes provide an ensemble averaged signal that does not require additional time averaging. We find the performance of our experimental scheme comparable or even superior to camera based multi-speckle techniques that rely on direct spatial averaging. Furthermore, combined with traditional two-cell DWS, the full intensity autocorrelation function can be measured with a single experimental setup covering more than 10 decades in correlation time.
We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.
We introduce an elegant method which allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solid-like samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called multiplication rule, which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simple multiplication. To test the proposed method, we perform a series of DWS experiments using colloidal gels as model nonergodic media. Our experimental data are consistent with the theoretical predictions, allowing quantitative characterization of nonergodic media and demonstrating the validity of the proposed technique.
Mixing a small amount of liquid into a powder can give rise to dry-looking granules; increasing the amount of liquid eventually produces a flowing suspension. We perform experiments on these phenomena using Spheriglass, an industrially-realistic model powder. Drawing on recent advances in understanding friction-induced shear thickening and jamming in suspensions, we offer a unified description of granulation and suspension rheology. A liquid incorporation phase diagram explains the existence of permanent and transient granules and the increase of granule size with liquid content. Our results point to rheology-based design principles for industrial granulation.
The periodization of a stationary Gaussian random field on a sufficiently large torus comprising the spatial domain of interest is the basis of various efficient computational methods, such as the classical circulant embedding technique using the fast Fourier transform for generating samples on uniform grids. For the family of Matern covariances with smoothness index $ u$ and correlation length $lambda$, we analyse the nonsmooth periodization (corresponding to classical circulant embedding) and an alternative procedure using a smooth truncation of the covariance function. We solve two open problems: the first concerning the $ u$-dependent asymptotic decay of eigenvalues of the resulting circulant in the nonsmooth case, the second concerning the required size in terms of $ u$, $lambda$ of the torus when using a smooth periodization. In doing this we arrive at a complete characterisation of the performance of these two approaches. Both our theoretical estimates and the numerical tests provided here show substantial advantages of smooth truncation.