Estimation and Tracking of Atmospheric Delay Noise in a Long-Baseline Optical Stellar Interferometer and Determination of the Expected Estimation Error

Details Estimation and Tracking of Atmospheric Delay Noise in a Long-Baseline Optical Stellar Interferometer and Determination of the Expected Estimation Error Estimation and Tracking of Atmospheric Delay Noise in a Long-Baseline Optical Stellar Interferometer and Determination of the Expected Estimation Error

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........6m&link_type=abstract

Thesis (PH.D.)--UNIVERSITY OF MINNESOTA, 1995.Source: Dissertation Abstracts International, Volume: 56-04, Section: B, page: 210

Mathematics

Probability

4

Coherence

Scientific paper

A long-baseline optical stellar interferometer is capable of performing superior measurements of optical correlation (or "fringe visibility") in much shorter observation times if the instantaneous atmospheric delay tau (t), can be accurately tracked to well within an optical wavelength. This permits coherent integration of the optical correlation, among other advantages. The conventional approach to "fringe tracking" involves a control system that serves a rapidly responding path-length compensator in real-time. At marginal signal levels, the reliability of such a real-time delay-tracking system suffers. Precise delay-tracking can be achieved at somewhat lower signal levels by employing an off-line delay-tracking system, in which the raw data measured by the interferometer is stored for subsequent analysis. Then it is possible to estimate the delay error at time t using raw data collected both before and after time t, resulting in a superior estimate. As opposed to point estimation procedures based upon the estimation of tau at a point in time, the optimum estimation of tau is based upon the comparison of all possible functions, tau(t), over a time period. Such a path estimation procedure fully incorporates the a priori statistics of the atmospheric delay process. Solutions are found using an iterative procedure to maximize the a posteriori probability of the function tau(t), determined by employing Bayes' theorem. However there will be more than one local maximum of a posteriori probability. At lower signal-to-noise ratios it becomes increasingly difficult to differentiate among these multiple solutions, and the resultant estimate contains ambiguities. However by properly evaluating the array of solutions, sufficient information can be retained for the purpose of integrating the measurement of correlation. Very acceptable results are obtained at signal-to-noise ratios as low as 3.0, corresponding to 9 detected photons per T_0 with full optical correlation, |V| = 1. T_0 is defined as r _0/V_0) where r _0 is the Fried parameter, and V _0 is the velocity of the "wind" driving the atmospheric delay process according to the Taylor model. At this signal level the r.m.s. estimation error of the correctly identified solution is.7 radians.

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