Biomedical subjects

Timothy J Schulz

Publications and source records attributed to Timothy J Schulz.

5 recordsLinked to original sources

PubMed2005

Optimal beams for propagation through random media.

The problem of maximizing the intensity that is transferred from a transmitter aperture to a receiver aperture is considered in which the propagation medium is random. Two optimization criteria are considered: maximal expected intensity transfer and minimal scintillation index. The beam that maximizes the expected intensity is shown to be fully coherent. Its coherent mode is determined as the principal eigenfunction for a kernel that is determined through the second-order moments of the propagation Green's function. The beam that minimizes the scintillation index is shown to be partially coherent in general, with its coherent modes determined by minimizing a quadratic form that has nonlinear dependence on the coherent-mode fields, and on the second- and fourth-order moments of the propagation Green's function.

Journal Article↗

PubMed2005

Signal recovery from autocorrelation and cross-correlation data.

A signal recovery technique is motivated and derived for the recovery of several nonnegative signals from measurements of their autocorrelation and cross-correlation functions. The iterative technique is shown to preserve nonnegativity of the signal estimates and to produce a sequence of estimates whose correlations better approximate the measured correlations as the iterations proceed. The method is demonstrated on simulated data for active imaging with dual-frequency or dual-polarization illumination.

Algorithms↗

PubMed2004

Iterative transform algorithm for the computation of optimal beams.

The problem of maximizing the integrated-weighted intensity of a transmitted beam in a receiver plane is equivalent to the problem of finding the largest eigenvalue's eigenfunction for a particular Hermitian operator. Application of the power method for the determination of this eigenfunction, along with its associated eigen-value, results in an iterative transform algorithm that can be applied to arbitrary apertures, nonnegative windows, and propagation media. The computational complexity of each iteration of this algorithm is equivalent to the numerical propagation of an arbitrary beam through the transmission medium.

Journal Article↗

PubMed2003

Experimental estimation of the spatial statistics of turbulence-induced index of refraction fluctuations in the upper atmosphere.

We present results from an experiment to estimate the parameters of homogeneous, isotropic optical turbulence in the upper atmosphere. The balloon-borne experiment made high-resolution temperature measurements at seven points on a hexagonal grid for altitudes from 12,000 to 18,000 m. From the temperature data, we obtained index of refraction fluctuations that can be used to compute a sample-based estimate for a parameterized description of the spatial autocorrelation of the turbulence. The three parameters of interest were a proportionality constant Pc, the power-law parameter alpha, and the outer scale L0. The results obtained for Pc are within the expected range and agree well with independent measurements made from a standard rising thermosonde measurement made approximately simultaneously with the data collection. Values for a were in the range 1.52 < or = alpha < or = 1.73 were observed, which are significantly less than the power law used in the Kolmogorov and von Karman models, alpha = 1.833. Values observed for L0 were in the range 5 < or = L0 < or = 19 m. Evidence that alpha may be consistently less than that used in the Kolmogorov and von Karman models likely has the most significant implications for systems that must work in or through the tropopause.

Journal Article↗

PubMed2002

Measurement and data processing approach for detecting anisotropic spatial statistics of the turbulence-induced index of refraction fluctuations in the upper atmosphere.

We discuss a method of data reduction and analysis that has been developed for a novel experiment to detect anisotropic turbulence in the tropopause and to measure the spatial statistics of these flows. The experimental concept is to make measurements of temperature at 15 points on a hexagonal grid for altitudes from 12,000 to 18,000 m while suspended from a balloon performing a controlled descent. From the temperature data, we estimate the index of refraction and study the spatial statistics of the turbulence-induced index of refraction fluctuations. We present and evaluate the performance of a processing approach to estimate the parameters of an anisotropic model for the spatial power spectrum of the turbulence-induced index of refraction fluctuations. A Gaussian correlation model and a least-squares optimization routine are used to estimate the parameters of the model from the measurements. In addition, we implemented a quick-look algorithm to have a computationally nonintensive way of viewing the autocorrelation function of the index fluctuations. The autocorrelation of the index of refraction fluctuations is binned and interpolated onto a uniform grid from the sparse points that exist in our experiment. This allows the autocorrelation to be viewed with a three-dimensional plot to determine whether anisotropy exists in a specific data slab. Simulation results presented here show that, in the presence of the anticipated levels of measurement noise, the least-squares estimation technique allows turbulence parameters to be estimated with low rms error.

Journal Article↗