Kirkus, again I have to kindly disagree on some points. Also omnidirectional source directivity is constant, and in power response terms the driver type has no inherent effect. In most practical cases the limited radiation angle is achieved in a certain bandwidth, not from 20 to 20k. Horns and waveguides can both be mathematically modeled and optimized and there are several BEM packages doing this. They usually model also the diaphragm radiating into the waveguide, as without that the picture is incomplete. The modern directivity control appeared first in sound reinforcement field, where the coverage is important. Altec made their Mantaray horns, using basically two flares and an abrupt joint between them. First expansion created the vertical pattern, opening into a narrow arc-like slit - being in itself a (horizontally) wide radiator- and the second flare controlled the horizontal pattern. The JBL Bi-radial horns use the same principle. In very simple terms a waveguide could be interpreted as the outer flare of a constant directivity horn, if you so wish. The fact that the throat area is equal to diaphragm area, i.e. there is no compression, mainly affects efficiency, which is higher with horn drivers. However, also waveguide improves efficiency in two ways: the actual radiating impedance is better matched, and the same energy is radiated into smaller solid angle than without waveguide. These factors are connected and the net result can be seen in the raw responses of the link, the sensitivity at the low end of the tweeter passband is higher. This is very good result as the improved sensitivity is easy to equalize and it improves tweeter reliability.
I do not understand what you actually mean with saying, that "for true constant-directivity performance to be possible, the wave-front propegation has to be constant with frequency." For constant directivity the radiation angle has to be independent of frequency. In practice the radiation angle vs. frequency has some ripple, as can be seen also from the O500 graph. O500 has a 300 mm woofer and its radiation angle (-3 dB) can be seen changing from 180 degrees at around 140 Hz( there seems to be measurement errors due to room limitations) to about 80 degrees at 500 Hz, then there is small ripple at upper crossover around 3 kHz,because the soft dome midrange becomes a more directive ring radiator, then it is getting narrower to about 40 degrees and again widening to 80 degrees at 15 kHz and getting narrower above that. As a whole this is can be regarded a good practical approximation of constant directivity, just like the performance of its predecessors, Genelec 1037, having also a 300 mm woofer and a bit smaller MF/HF waveguide, and 1038, having 385 mm woofer and larger waveguide. Those came to market already in early 90's (about 10 years before K+H O500) while their first predecessor, Genelec 1022A came to market in 1985.
Two-way speakers can be designed to constant directivity as well, but due to smaller woofer, the bandwidth of this behavior is not as wide and starts at least one octave higher. Even then the practical improvements are clearly audible. To make the woofer more directive at lower frequencies you can naturally use cardioid designs and accept the consequences in available power.
