[OPTICAL REVIEW Vol. 7, No. 1 (2000) 34-43]

## An Operator Method of the Theory of Optical Coherence and Radiometry

Kyu YOSHIMORI^{1} and Kazuyoshi ITOH^{2}

^{1}Earth Observation Research Center, National Space Development Agency of Japan, 1-9-9, Roppongi, Minato-ku, Tokyo, 106-0032 Japan, ^{2}Department of Applied Physics, Graduate School of Engineering, Osaka University, 2-1, Yamadaoka, Suita, 565-0871 Japan

(Received September 11, 1999; Accepted November 5, 1999)

This paper presents a quantum mechanical formalism of the classical coherence theory, within which the generalized radiance function defined in the time domain is regarded as a phase space representative of a time-dependent correlation operator of a polychromatic field. The theory deals with both stationary and nonstationary fields and, for a stationary field, provides a new operator formalism of the usual theory of optical coherence developed in the space-frequency domain. New results include an operator representation of the mutual coherence function, an operator version of the Wiener-Khintchine theorem, and an operator theorem that projects the correlation operator of a polychromatic field onto a particular spectral component. As illustrative examples, the previous formulas regarding the relationship between temporal coherence and spatial coherence, and the relationship between spectral properties and coherence properties are derived from the new operator formulas. The correspondence of the present formalism to the usual formalism using Dirac notation to describe the propagation of a stationary, partially coherent, quasi-monochromatic field is also considered.

Key words : coherence, generalized radiometry, Wigner function, phase space, nonstationary field