MODEL-FITTING AND ERROR ANALYSIS FOR DIFFERENTIAL INTERFEROMETRY .1. GENERAL FORMALISM

A combination between high angular and high spectral resolution techni ques, Differential Interferometry (DI) yields seeing independent infor mation with a resolution much higher than the telescope diffraction li mit. This paper, first in a series of two, presents a formalism for th e estimation of the parameters modelling the brightness and velocity f ields of unresolved or partially resolved astronomical candidates. We use the average cross spectrum of speckle patterns recorded in differe nt spectral channels to define an estimator which contains all the see ing independent DI data and is to be minimised in a non linear iterati ve least square fit of the model parameters. From this general estimat or, we derive a simpler one based on the phase of the average cross sp ectrum which remains seeing independent whatever the spectral bandwidt h is. We apply it to non resolved sources, when ail the information is contained in the object spectrum and in the angular vectorial functio n epsilon(lambda) representing the variation of the object photocenter with wavelength. Then, we give a simple formal expression of the para meters errors and, as a first application, we determine the optimum si ze for the slit of the spectrograph used in a one dimensional DI exper iment. In the second paper, we describe the application of this genera l formalism to rotating stars and binary systems and discuss its perfo rmances as a function of the visual magnitude.