# USRBIN averaging over the 3rd coordinate in a 2d projection

Hello,

It’s my understanding that when you plot a 2d projection with USRBIN, it will average the values over the 3rd coordinate. I’m wondering if someone can give me a more specific explanation on how this averaging works. I’ll explain my situation:

I’m scoring the dose-eq around a target (approximately a disc of radius 5cm and thickness 1cm) after irradiation. Suppose the target is at (0,0,0) and I was looking at a data point on my plot with (x,y) coordinates of (0,50cm). My understanding is that the value here would be averaged over all values with coordinates (0,50,z) where z extends between some range that I’ve chosen on my USRBIN card. However, dose-eq drops radially, so we’d have to expect that the dose-eq at (0,50,0) would be much higher than at (0,50,50), since the latter is further from the target. Thus averaging over the line (0,50,z) seems to give an arbitrary value that changes depending on the limits I set on my USRBIN card. Increasing the range of z would always lower the value since I’m introducing more data points that are further away.

I’m wondering if there is some kind of weighting that goes into getting the value. If not, is it recommended that I simply choose a small range (ie from z=-1 to z=1) to get a good estimate?

Hallo,

That’s correct.

The weighting is automatically provided by the bin volume, which is constant in case of Cartesian mesh, but is not in case of cylindrical mesh (bins at larger radius have a larger volume).
There is no need to limit a priori the third dimension range, you can do it at plotting level by specifying its extension at will in Flair (select the z-limits when plotting a x-y cut).
Note that it’s up to you to define a physically meaningful resolution for a good estimate. In particular, if you need to determine a maximum value, you may want to increase the resolution (i.e. reduce the volume of averaging) up to convergence. Of course the latter cannot be attained if using an ideal pencil beam.