The propagation filter is a matrix where every row is the previous one rotated one place to the right. The diagonal form is very easy to multiply by, thus the FFT steps. This important property is lost as soon as we begin multiplying them by one another. Though such a matrix can represent any possible scene in its entirety, and can be subjected to arbitrary illumination by multiplying it by an illumination wavefront, the scale is out of hand. I've tried commuting the matrix chain to condense at least some of them together while preserving the diagonal property, but this does not appear possible.
Matrix transposes keep getting in the way.
The wavefront can be moved across an entirely empty gap in a single FFT step by raising each coefficient in the FFT of the half wavelength propagation filter by an integer power equal to the number of half wavelengths in the gap width. The scene properties are different for the different light types. Diffraction effects will be seen. For full diffuse and scattered indirect lighting the wave method is much more efficient than ray tracing. Calculations that involve coincident rays generated by scattering from different illumination sources off the same surface points are handled separately in all existing ray models.