General fringe decomposition and statistical bias correction in optical interferometry

Details General fringe decomposition and statistical bias correction in optical interferometry General fringe decomposition and statistical bias correction in optical interferometry

Oct 2004

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004spie.5491.1498t&link_type=abstract

New Frontiers in Stellar Interferometry, Proceedings of SPIE Volume 5491. Edited by Wesley A. Traub. Bellingham, WA: The Intern

Mathematics

Scientific paper

Interferometric fringes are traditionally decomposed using the Discrete Fourier Transform (DFT). However, the application of the DFT is only correct in cases where the fringes are sampled evenly with delay and over integer number of fringe periods. This ideal case is often not achieved in Optical Interferometry. Fringe spectrography, non-linear fringe sweeps and image-plane beam combiners are typical cases of where the DFT approach fails to make most efficient use of the data. The authors assert that in many cases alternative and more efficient fringe decompositions exist but which may exhibit considerably different noise behaviour to the DFT. The authors present the mathematical results important for correcting for statistical bias in the powerspectrum and bispectrum constructs of a completely general fringe decomposition. An estimator for the noise in the powerspectrum has also been derived. The authors believe this to be the first analytical derivation of statistical bias and noise in interferometry that treats both photon counting noise as well as Gaussian read out noise.

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