Abstract

The mutual information between the radiance of an incoherently radiating object plane and the field at the aperture of an observing system is calculated on a classical basis. A formula of the Shannon type is obtained when the time–bandwidth product of the object light is large, the average radiance from the object plane is small enough to permit the threshold approximation, and the radiance of the object plane is modeled as a spatial gaussian process. It includes the dependence on the bandwidth of the object light and the effective temperature of the background, assumed spatially and temporally white. A set of sufficient statistics for the aperture field, based on Fourier sampling of the object plane, is introduced, and its bearing on the resolution of fine details of the object is brought out.

© 1970 Optical Society of America

Modal Decomposition of Aperture Fields in Detection and Estimation of Incoherent Objects*

Carl W. Helstrom
J. Opt. Soc. Am. 60(4) 521-530 (1970)

Linear Restoration of Incoherently Radiating Objects

Carl W. Helstrom
J. Opt. Soc. Am. 62(3) 416-423 (1972)

Resolvability of Objects from the Standpoint of Statistical Parameter Estimation*

Carl W. Helstrom
J. Opt. Soc. Am. 60(5) 659-666 (1970)

Detection and Resolution of Incoherent Objects by a Background-Limited Optical System*

Carl W. Helstrom
J. Opt. Soc. Am. 59(2) 164-175 (1969)

Detection and Resolution of Incoherent Objects Seen through a Turbulent Medium*

Carl W. Helstrom
J. Opt. Soc. Am. 59(3) 331-341 (1969)