Abstract

By means of the quantum-mechanical form of the Cramér–Rao inequality, a lower bound is set to the mean-square error in an unbiased estimate of a parameter of an incoherently radiating object observed in the presence of thermal background light by an optical system collecting light through a finite aperture. Estimates of absolute radiance, frequency, and position of the object are specifically analyzed. The bounds reduce in the classical limit to those previously obtained, but are valid in the quantum limit as well. When the background vanishes, the bounds depend only weakly on the effective number of independent spatial and temporal degrees of freedom of the object light at the aperture.

© 1970 Optical Society of America

Resolvability of Objects from the Standpoint of Statistical Parameter Estimation*

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

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

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

Detection of Incoherent Objects by a Quantum-Limited Optical System*

Carl W. Helstrom
J. Opt. Soc. Am. 59(8) 924-936 (1969)

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

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

Information Transfer from Incoherently Radiating Objects

Carl W. Helstrom
J. Opt. Soc. Am. 60(12) 1608-1616 (1970)