Propagation law for Walther’s first generalized radiance function and its short-wavelength limit with quasi-homogeneous sources

An exact law is derived for the propagation in free space of the first generalized radiance function introduced by Walther. A simplified form of this law is obtained for the case when the source is quasi-homogeneous. It is also shown that when the source is quasi-homogeneous and the wave number is large enough (the wavelength is sufficiently short) the first generalized radiance acquires all the properties of the radiance of traditional radiometry.