Etendue - Derivation via wave optics possible?

Question

I recently learned about etendue - which is important because it is conserved.
The only derivation of etendue conservation which I was able to understand is via hamiltonian optics (https://en.wikipedia.org/wiki/Hamiltonian_optics).

Questions:
a) Is it possible to define etendue at wave optics level?
b) If not, does this mean that etendue isn't a proper physical thing?

Pointers to literature are welcome.

Comments

background: https://en.wikipedia.org/wiki/Etendue

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The etendue in wave optics may be understood as the number of modes of a multimode beam or similarily as the phase space volume of the optical Wigner function. As such, it is preserved through unitary transformations.

Mathematically, etendue is to the optical, classical Wigner function what the inverse of the purity is to the quantum Wigner function.