It assumes it is an arbitrary source radiating sound.
That is exactly the problem with NFS in my understanding, that it tries via iteration, to calculate a number of imaginary sound sources at unknown positions, which would fit to the soundfield it has actually measured at numerous positions in what is neither nearfield nor farfield. If the actual number of sound sources is closer to indefinite, they are far away from each other compared to the wavelength, or their phase relations towards each other are chaotic, that cannot be as accurate as claimed, as some measurements with bending-wave planar transducers or cardioids have proven.
And yes, I am understanding how the NFS calculation works, and that it would in theory be perfectly working for any planar diaphragm moving in a pistonic manner with no major chaotic cancellation effects at play.
I have yet to see an anechoic chamber that is flat down to 20 Hz which Klippel NFS is. You also need an awfully large anechoic chamber to be able to measure at 3 meters.
With a very huge room, you can go pretty low just with the help of time windowing. Have you been to the cube in Struer?
Btw you do not need to go flat as low as 20Hz. Klippel does not do that accurately as well. Otherwise you would never get a reading of negative directivity index with speakers that solely employ omnidirectional bass sources without major phase differences. Not a big deal, though, as the frequency plot itself is not too far off in most of standard cases, but indirect indication of limitations of the calculation. It simply should not happen.
Now take this to Nth degree of many stones thrown in the water, representing the drivers, cabinet, etc. of the a speaker. A complex sum is now radiating into 3-D space but it can be modeled using simple set of functions. Finding this model is what Klippel NFS does.
It is a good analogy. Now imagine an indefinite number of stones being thrown, slightly delayed in a chaotic manner, plus stones being thrown from under the water hitting the surface of the water, or little pumps sucking it in. That is basically what a bending-wave transducer like a huge planar does. In my understanding, even the most sophisticated model comes to its limits trying to calculate an accurate representation of that chaos. You have indirect indication for this, the moment the error rate increases.
the Klippel NFS measures at very near distance the speaker chassis and then computes the sound field at a distance. So you claim the sophisticated mathematic give right results.
I have the advantage of having worked with truly anechoic measurements of existing loudspeakers for decades, manyfold the number of what Amir has measured, as well as with Klippel systems, so I had the chance to compare.
Can tell you that if the aforementioned conditions for potential miscalculations, such as chaotic out-of-phase behavior of parts of the diaphragm, huge distances or cancellation effects between sound sources (as typically found with large planar transducers, cardioids, dipoles, line sources and alike), are NOT in play, and the wavelengths are not overly long (i.e. everything above 100Hz for a room of normal size), the NFS calculation is very very accurate. I have no reasons to doubt the results except for very unusual cases.