This is going to be a bit too specialist for most people, but here goes...
Normally we treat LEDs as point sources. However, they are actually flat chips that emit light from the surface. I am assuming that the emission is not uniform across the chip. If this is so does the uniformity of the relative emission across the chip remain constant under varying current? Or do changes in current result in different areas of the chip lightening or darkening relative to each other?
Good news first: the plastic dome that you typically see on LEDs is a lens / diffusor and probably designed to counter any significant variation.
The amount of photons emitted is proportional to the number of (desired) charge carrier recombinations in the junction.
That boils down to the population of the bands in your semiconductor crystal; you'll need the right states to be available for such a photon-emitting combination to happen.
For that, you'll have to have the necessary electric potential to be present at any place – in other word, for perfectly uniform emission, you'd need a perfectly uniform electric field!
Of course, even assuming your LED's die is infinitely large and perfectly flat, that's impossible if you don't build your electrodes from a perfect conductor; in reality, you'll always observe that there's higher current where there's the "electrically shortest path" between the two electrodes, which implies you'll get less light emission at the edges of your die, far away from the contacting.
And also, the higher the current, the more it will "spread out" across the whole surface.
Now, clever contacting will minimize try to minimize the non-uniformity: in the end, wafer is expensive enough to make manufacturers want to avoid that. And while that will certainly strive to homogenize the current density under maximum I_f, it's unlikely to be wildly suboptimal for lower currents.
Overall:
Or do changes in current result in different areas of the chip lightening or darkening relative to each other?
Yes!
Also, don't disregard thermal aspects: an LED is a semiconductor device, which has higher electron mobility with higher temperature, but also higher number of non-emitting recombinations. But, a well-cooled part of the die might act as a small current "barrier" and distinctively shape how current is distributed in a situation where the temperature delta to the environment becomes large.
this just in:
We are using light from a small single chip IR diode to locate a piece of metal for within nanometres using a split beam and then recombining to get a zero.
Ah! Yeah, well, aren't you aiming for a laser diode here instead of a plain LED?
