Thiel CS1.2 loudspeaker Phase Coherence
Phase coherence is a subject every bit as complex as loudspeaker waveform radiation. Purists such as Thiel maintain that their 6dB/octave slopes are the only way to truly maintain phase coherence; John Bau of Spica can show you on his Tecron analyzer that the Bessel 4th-order low-pass filter he uses to cross his tweeter down to the woofer on his TC-50 and Angelus, when used with the particular drivers he chooses, is also phase coherent.
Not mentioned by any of these designers, but surely important, is that the loudspeaker radiation is phase coherent and thus aligned in time (the term "Time-aligned" is a trademark of Ed Long and thus cannot be used by others; the idea cannot be patented) only with respect to one listener-seating position (and only one listening height, something that is always proving a problem for JGH, who is notably shorter than average). And that the off-axis radiation of the speaker, which can provide up to about 35% of the acoustic energy at your ears (depending on the deadness of your room), cannot possibly be phase coherent and time-aligned.
Contrast this to a French horn, for instance. Although far from an omnidirectional radiator—why do you think horn players vary the direction of their bell depending on the importance of their part?—the French horn is optimally coherent in a way that no multiple-driver loudspeaker can ever be. This is one reason why planar loudspeakers, particularly those with no crossovers, have retained their popularity over the years. Planar loudspeakers are nevertheless plagued by many problems, and cannot, in my opinion, make any claims for inherent phase coherence.
For me, the proof is in the pudding. The hallmarks of phase coherence, whether we're talking about speakers where "Coherent Source" is a copyrighted trademark, as with the Thiels, or simply an important design factor, are solidity of image, correctness of timbre even with significant movement within the listening position, and a general sense of everything within the soundstage hanging together.—Larry Archibald