Time-resolved diffusion tomographic imaging in highly scattering turbid media

A method for imaging objects in highly scattering turbid media. According to one embodiment of the invention, the method involves using a plurality of intersecting source/detectors sets and time-resolving equipment to generate a plurality of time-resolved intensity curves for the diffusive component of light emergent from the medium. For each of the curves, the intensities at a plurality of times are then inputted into the following inverse reconstruction algorithm to form an image of the medium: X.sup.(k+1).spsp.T =?Y.sup.T W+X.sup.(k).spsp.T .LAMBDA.!?W.sup.T W+.LAMBDA.!.sup.-1 wherein W is a matrix relating output at detector position r.sub.d, at time t, to source at position r.sub.s, .LAMBDA. is a regularization matrix, chosen for convenience to be diagonal, but selected in a way related to the ratio of the noise, to fluctuations in the absorption (or diffusion) X.sub.j that we are trying to determine: .LAMBDA..sub.ij =.lambda..sub.j .delta..sub.ij with .lambda..sub.j =/ Here Y is the data collected at the detectors, and X.sup.k is the kth iterate toward the desired absoption information

Exact photocount statistics : lasers near threshold

A previously constructed laser model with quantum (noncommuting) noise sources was shown to lead near threshold to a quantum rotating-wave Van der Pol oscillator. A full dynamical correspondence between quantum and classical random processes allows one to compute the average of any time-ordered, normal-ordered operator function by averaging the associated function of classical random variables. Numerical calculations for the associated classical Van der Pol oscillator of the steady-state distribution, the total intensity fluctuations, and the linewidth versus operating point were amply confirmed experimentally. Measurements (and calculations) of higher than two-time correlations were sparse and contradictory. Photocount distributions, at times short compared to the intensity correlation time, confirm only the steady state of the laser. Pliotocount distributions at intermediate and longer times are difficut to compute because they involve multitime correlations of high (∞) order. By providing an exact solution for photocount distributions and their moments for all times, we expected to stimulate measurements near threshold which would provide an adequate test of the Van der Pol laser model. Comparison of the results reported here with recent photocount experiments of Meltzer, Davis, and Mandel and of Jakeman, Oliver, and Pike provides gratifying agreement and confirmation of our statistical understanding of laser fluctuations near threshold

Exact photocount statistics : lasers near threshold

A previously constructed laser model with quantum (noncommuting) noise sources was shown to lead near threshold to a quantum rotating-wave Van der Pol oscillator. A full dynamical correspondence between quantum and classical random processes allows one to compute the average of any time-ordered, normal-ordered operator function by averaging the associated function of classical random variables. Numerical calculations for the associated classical Van der Pol oscillator of the steady-state distribution, the total intensity fluctuations, and the linewidth versus operating point were amply confirmed experimentally. Measurements (and calculations) of higher than two-time correlations were sparse and contradictory. Photocount distributions, at times short compared to the intensity correlation time, confirm only the steady state of the laser. Pliotocount distributions at intermediate and longer times are difficut to compute because they involve multitime correlations of high (∞) order. By providing an exact solution for photocount distributions and their moments for all times, we expected to stimulate measurements near threshold which would provide an adequate test of the Van der Pol laser model. Comparison of the results reported here with recent photocount experiments of Meltzer, Davis, and Mandel and of Jakeman, Oliver, and Pike provides gratifying agreement and confirmation of our statistical understanding of laser fluctuations near threshold

Exact photocount distributions for laser near threshold

Photocount fluctuation problems, treated previously for Gaussian statistics only, or in the limit of short measurement times, have been extended to arbitrary times (compared with the intensity correlation time) and to general Markoffian processes. In particular, we calculate the distribution function of the time-integrated light intensity for a laser operated near threshold

Exact photocount distributions for laser near threshold

Photocount fluctuation problems, treated previously for Gaussian statistics only, or in the limit of short measurement times, have been extended to arbitrary times (compared with the intensity correlation time) and to general Markoffian processes. In particular, we calculate the distribution function of the time-integrated light intensity for a laser operated near threshold

Random Processes in Physics and Finance

This respected high-level text is aimed at students and professionals working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002) was a distinguished Professor of Physics at City College of New York and a member of the U. S. National Academy of Sciences, and is widely known for his contributions to our understanding of random processes in physics. Most chapters of this book are outcomes of the class notes which Lax taught at the City University of New York from 1985 to 2001. The material is unique as it presents the theoretical framework of Lax\u27s treatment of random processes, from basic probability theory to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanations of very narrow laser width, analytical solutions of the elastic Boltzmann transport equation, and a critical viewpoint of mathematics currently used in the world of finance. – Publisher descriptionhttps://digitalcommons.fairfield.edu/physics-books/1001/thumbnail.jp