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The application of signal detection theory to optics Quarterly progress report

Carl W. Helstrom

Published Jan 1, 1969• 0 citations
OpenAlex

Abstract

By means of the quantum-mechanical form of the Cram&-Rao inequality, a lower bound is set t o the mean-square error i n an unbiased estimate of a parameter of an incoherently radiating object observed i n the presence of thermal background l i g h t by an optical system'admitting light through a f i n i t e aperture.

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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.
The detection of an incoherent object, light from which is received in the presence of thermal radiant energy, is treated by quantum detection theory under the assumption that the product of the observation time and the bandwidth of the object light is large. The threshold detector measures a quantum-mechanical operator that is a quadratic functional of the field at the aperture of the receiver. The statistics of the outcome of this measurement are approximately Poisson, and the detectability of the object depends—as under a background limitation—on the number of effectively independent spatio-temporal modes of the field. The detectabilities of objects with a rectangular and a Lorentz spectrum are compared under the assumption that the light from each possesses first-order coherence at the aperture.