Model fitting and error analysis for differential interferometry. I. General formalism.

Details Model fitting and error analysis for differential interferometry. I. General formalism. Model fitting and error analysis for differential interferometry. I. General formalism.

Feb 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26as..109..389c&link_type=abstract

Astronomy and Astrophysics Suppl. 109, 389-399 (1995)

Astronomy and Astrophysics

Astrophysics

15

Atmospheric Effects, Techniques: Interferometric, Techniques: Image Processing, Methods: Data Analysis

Scientific paper

A combination between high angular and high spectral resolution techniques, Differential Interferometry (DI) yields seeing independent information with a resolution much higher than the telescope diffraction limit. This paper, first in a series of two, presents a formalism for the estimation of the parameters modelling the brightness and velocity fields of unresolved or partially resolved astronomical candidates. We use the average cross spectrum of speckle patterns recorded in different spectral channels to define an estimator which contains all the seeing independent DI data and is to be minimised in a non linear iterative least square fit of the model parameters. From this general estimator, we derive a simpler one based on the phase of the average cross spectrum which remains seeing independent whatever the spectral bandwidth is. We apply it to non resolved sources, when all the information is contained in the object spectrum and in the angular vectorial function ɛ(λ) representing the variation of the object photocenter with wavelength. Then, we give a simple formal expression of the parameters errors and, as a first application, we determine the optimum size for the slit of the spectrograph used in a one dimensional DI experiment. In the second paper, we describe the application of this general formalism to rotating stars and binary systems and discuss its performances as a function of the visual magnitude.

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