Optimal weighting of phase data with varying signal to noise ratio

Christoph Arndt; Otmar Loffeld

doi:10.1117/12.281262

25 September 1997 Optimal weighting of phase data with varying signal to noise ratio

Christoph Arndt, Otmar Loffeld

Proceedings Volume 3100, Sensors, Sensor Systems, and Sensor Data Processing; (1997) https://doi.org/10.1117/12.281262
Event: Lasers and Optics in Manufacturing III, 1997, Munich, Germany

Abstract

In treating 2D arrays we may use either the cartesian coordinate system or the cylindrical coordinate system to describe pictures, fields, etc. Both descriptions must contain the same amount of information about the device, that is to be examined. As a consequence the joint distribution density of real and imaginary part of a vector and the joint distribution density of absolute value and phase of the same vector have to contain the same information. Approximating the phase density by a gaussian density we take the variance of the phase density to generate the gaussian density. In worst case this variance becomes (Delta) ²/12 (where (Delta) is the width of the phase interval (Delta) equals 2(pi) ). However, that would suggest that the phase data would contain information through the distribution density of the phase is an uniform density, where we cannot favor any value of the phase, i.e. we do not have any information about which value the phase estimate should have. In the following paper we are going to find a solution to this problem by examining the difference between information and inverse variance in the phase distribution.

Citation Download Citation

Christoph Arndt and Otmar Loffeld "Optimal weighting of phase data with varying signal to noise ratio", Proc. SPIE 3100, Sensors, Sensor Systems, and Sensor Data Processing, (25 September 1997); https://doi.org/10.1117/12.281262

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