Estimating angular position of optical radiation source when received by array of photodetectors

The angular position of an optical radiation source is measured; its field is detected by an array of photodetectors in the focal (diffraction) plane of an optical antenna. The signal and background fields are of unknown intensity. The position is determined from the coordinates of the center of diffraction pattern of the signal field in the focal plane, assuming that each element of the array filters no more than one spatial, while the signal and background fields are both broadband and a Poisson model applies to the electron count fields when the radiation is detected. Similitude theory is used in order to derive an optimal estimate of the vector to the source and the special case where the radiation field is received by a four-element array is analyzed. It is shown that the covariation of the estimates of the coordinates is zero in the absence of background noise. The expressions provided permit the calculations of these optimal estimates when the diffraction pattern of the signal field does not coincide with the center of the array (nontracking meter) and there are no a priori data on the intensities of the signal and background noise fields.