Resolvability of Objects from the Standpoint of Statistical Parameter Estimation*

The values of the radiance at points of an incoherently radiating object are considered as parameters of the statistical description of the field at the aperture of an observing optical instrument. By means of the Cramér–Rao inequality, a lower bound is set to the mean-square errors of unbiased estimates of the radiance values. The errors are shown to increase rapidly when the object is sampled at points separated by less than a conventional resolution interval.