Converting between brilliance, intensity, and flux

Question

This one should be a bit of a softball, but I can't find it explicitly stated anywhere on the internet, and my basic unit analysis doesn't seem to work.

Suppose you have a beam of synchrotron radiation with a brilliance $B$ at a given energy. (For instance, the brilliance of the Advanced Light Source at Berkeley is given in a graph form here). If I know the distance $d$ from the source and the area $A$ of the (for simplicity, unfocused) spot on my sample, how do I calculate the flux (units photons/sec) to my sample? Another way to phrase the same question is given the distance from the source and the brilliance, how do I calculate the intensity (units photons/sec/area) of the photon source at my sample? Am I missing some parameter?

Answer 1

Brilliance is as stated in literature:

number of photons per second per mm$^2$ per rad$^2$ per $0.001BW$,

where $BW = \Delta\omega/\omega$ is the like the "binning" size over which the equation was integrated over. So the number of photons that will arrive at your sample depends on what frequency range you are measuring over. If you are measuring the number of photons over an infinitely narrow window of frequencies then the number of photons/second approaches zero.

Therefore (for a rough average if the brilliance curve is $\approx$ constant over your frequency range)

number of photons/second/mm$^2$ = Brilliance $\cdot \frac{A}{L^2} \cdot 0.001 \cdot \Delta\omega/\omega_0$

where $\Delta\omega$ = the window of frequencies you are detecting and $\omega_0$ the center frequency. If however the brilliance curve changes over the frequency range you are detecting you will have to integrate the function.

Answer 2

Genie already stated the definition of brilliance:

Number of photons per second per mm2 per rad2 per 0.1% bandwidth.

Of the parameters you have listed, you are missing the divergence of the beam (needed to get rid of the "per rad2" in the formula for brilliance). However, I see at the APS link given that for each beamline, the APS provides pure flux graphs. I think those graphs will answer your question nicely.