Coherers, Acoustic Lenses, Phase shields and more

Recently I've been building a small bookshelf speaker for myself and I came across the research performed by Purifi Audio. In the SPK16 speaker, the tweeter has constant directivity from 2khz to 20khz with only a -6db loss at 60 degrees. this is a very impressive feat of engineering. Using a one inch tweeter like they are using, the driver begins to beam at around 10khz, meaning the response below that can be controlled with a waveguide. I've been able to optimize a waveguide to hit the same result below 10khz, but once we hit the beaming frequency the speaker narrows from -6 at 60 degrees to about -6 at 30 degrees. In their log, Purifi documents that they increased the directivity of the tweeter by using a "coherer" which looks much like a lens, or a phase shield. They state "a collection of ring-shaped objects that shape the wavefront around the throat of the wave guide in order to direct energy to the further of axis directions"

My question is, what principle does this "coherer" operate on?
Could it be that the rings are creating points of diffraction which spread out the highest frequencies?
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https://purifi-audio.com/blog/tech-notes-1/spk16-reference-design-12
 
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yes, the function of the coherer can be explained by the concept of diffraction: waves hit the boundaries and wave are re-emitted. this is another way to describe the boundary condition along hard surfaces: the particle velocity is zero (incoming and exiting wave velocity cancel). A lens is normally somewhat larger than the wavelength so this is why we felt that lens was not the appropriate term.

BTW: the -6dB beam width more like +/-70 deg
 
A -6db, 70-degree dispersion pattern through to 20k is a mental achievement. Some of the best-measuring speakers from high-end manufacturers only get to around 50 degrees, and the response after 10k tends to narrow to about 35-40 degrees.

The science and mathematics of this are likely over my head at this point so I may be oversimplifying.
But In the most basic case, to increase the directivity at a certain frequency you'd need to introduce a source of diffraction at the selected frequency near the speaker driver. That diffraction point widens the radiation pattern so that it can be controlled by the waveguide rather than changing depending on your listening angle (like seen with typical edge diffraction). Would you go about calculating that circle diameter the same way you would calculate the diameter at which baffle diffraction occurs?