Dirac bra-ket in radiometry of quasi-homogeneous sources

The concept of "throughput" is used in traditional radiometry of Lambertian sources for computing and estimating the radiant flux passed through a pair of stops, in particular through the window and the pupil of an optical system. It is shown that in a more general case of quasi-homogeneous sources for energetic calculations of the perfect optical system, one must use instead of the throughput a functional that is similar to the famous "Dirac bra-ket." This functional takes into account the radiation pattern of the source. As the Dirac bra-ket satisfies the axioms of the inner product, powerful mathematical tools of functional analysis for the energy calculation of the optical systems are used. The main equations and principles of radiometry (the principle of reversibility and Maxwell's principle) are reformulated from the concept "throughput" into the concept "Dirac bra-ket." For generalization of Maxwell's principle to the class of quasi-homogeneous sources the concept of "effective stops" is introduced.