Statistical approach to noise in stellar speckle interferometry

In this paper we describe a new method to derive the variances of the power spectrum and the autocorrelation function of images recorded in the photon-counting mode. The formalism is different from that of Goodman and Belsher. The variances are written as functions of the tri-spectrum and the quadri-correlation function. For the power spectrum, we recover the result of Goodman and that of Dainty and Greenaway. For the autocorrelation function, a new expression is obtained. No remarkable effect corresponding to Goodman's 'half-frequency' phenomenon is observed, but the variance at the space lag rho is found to be influenced by cuts of the triple correlations of the classical image intensity for space lags equals to rho and 2 rho. A crude simplification of the expression of the variance of the autocorrelation function is used to derive results in terms of the signal-to-noise ratio (SNR).