Abstract

The Shannon number is shown to specify the number of degrees of freedom that can be resolved in a coherent object scrutinized by a distant optical instrument that extracts information about the object from the light passing through its aperture. The quantum-mechanical nature of the light is taken into account, and the problem of determining the object amplitude distribution is treated by means of quantum estimation theory, which defines a limitation on the accuracy of an estimate of the object distribution that cannot be surpassed by any means of processing the received light. Fundamentally, the limitation arises from the inability of more than a finite number of modes of excitation of the object to deposit a significant number of photons in the aperture.

© 1977 Optical Society of America

A priori information and the degrees of freedom of noisy images

Bahaa Saleh
J. Opt. Soc. Am. 67(1) 71-76 (1977)

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

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

Resolvability of Objects from the Standpoint of Statistical Parameter Estimation*

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

Estimation of Object Parameters by a Quantum-Limited Optical System

CARL W. HELSTROM
J. Opt. Soc. Am. 60(2) 233-239 (1970)

Effects of Coherence on the Degrees of Freedom of an Image

F. Gori and G. Guattari
J. Opt. Soc. Am. 61(1) 36-39 (1971)