We find that the new generalized radiance function that was derived from Walther’s first generalized radiance function by the present authors for a polychromatic field [J. Opt. Soc. Am. A 14, 3379 (1997)] cannot generally be identified with Walther’s first original function, even if the field is stationary in time. The identification of the new generalized radiance function with Walther’s first original function requires an additional condition of quasi-homogeneity of the field. In contrast, the new complex radiance function for a polychromatic field that was also derived in our previous paper can be derived from the complex version of Walther’s second generalized radiance function, regardless of the state of coherence of the field.
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