Apologies if I’m misunderstanding the whole directivity issue but what (in layman's terms) is the purpose of such testing?
In simple terms, think of directivity like this. Measure the speaker on-axis, and you get one amplitude response. Measure 15deg, 30deg (etc) off-axis, and you get a different amplitude response. What this means is that if you have them toed in so they fire at you on-axis, you hear the on-axis response. But if they are firing straight ahead and the angle between you and the loudspeaker is 15deg, you will hear the 15deg response. "Higher directivity" means that a speaker shoots out a narrow beam of sound, so if you measure off-axis you get a dramatically different amplitude response.
What this also means is that sound that emanates off-axis will reflect off the walls/floor/ceiling and arrive at the listening position with a slight delay. You want this reflected sound to be as similar as possible to the direct sound, otherwise it can throw off the tonality if it arrives early enough. We know from psychoacoustic studies that reflections that arrive <20ms to the direct sound are integrated by our ears so that it's the same sound.
You will find that loudspeakers with smooth directivity are prized on ASR, and earn top marks from Amir. I personally don't think that directivity has to be perfect, it just has to be "good enough". IMO all those guys who complain at small jiggles are the audio equivalent of navel gazing. The room itself will spectrally distort the sound. Having said that, from a speaker design perspective, you DO want to get your directivity as perfect as possible because it is worth striving for. But I think a more balanced position is to be a bit more forgiving of small directivity errors. What is the
most important is to get the on-axis sound spectrally correct, and fortunately this is something that DSP can offer you.
Nobody knows what ideal directivity is, but most people accept that somewhere between a -6dB point at 30-45 deg is best. You will find some people on ASR believing that narrower directivity is better (fewer reflections at the expense of a smaller sweet spot), and some others thinking that wider directivity is better because reflections are beneficial. You don't want to open that can of worms here, do what is best for you, and your own personal audio philosophy.
Or is this something that is inherent to the driver and cannot be physically corrected?
It is inherent in the total physical design of the loudspeaker. The driver will have a certain directivity, but it will be influenced by the baffle (x, y location and width), shape of the baffle, presence of waveguides, whether the corners of the baffle are radiused, and even whether the driver is flush mounted or not.
When you take your measurements, you will find that what you get won't match what the manufacturer published. This is because manufacturers measure their drivers on a test baffle which likely won't be the same as yours.
I gave you a link to Vance Dickason's book earlier. Please buy it and read it. I can not recommend it strongly enough, I think it is mandatory reading for anybody who is interested in speakers, ESPECIALLY people who DIY speakers.
