Would that still be true for a light (or w/e) beam that is perfectly collimated?
I was thinking of a hypothetical case.
>In a vacuum.
Read more.
> Achieving a truly collimated beam where the divergence is 0 is not possible, but achieving an approximately collimated beam by either minimizing the divergence or maximizing the distance between the point of observation and the nearest beam waist is possible.
In practice the situation is even worse and you can't even get the performance that a perfect Gaussian beam would allow. We often express the performance of real beams by a thing called M^2 or beam quality parameter [2]. In some sense is measures how much wider the beam is than it needs to be, and this number is never less than one.
[1] Btw such a beam would have infinite brilliance. [2] https://en.wikipedia.org/wiki/M_squared
That's not written in stone yet, it's a good approximation but still falls down under specific conditions.
EIRP is describing that the total flux through a sphere at a given radius is constant regardless of the beam shape, but we are only interested in a specific cross section and are not accounting for the rest of it.
And yes, the inverse square law is strictly speaking only true for point sources. But it is an extremely good approximation once you are much further away than the size of the source (a distance ten times the diameter of the source is usually totally sufficient).