Where I 0 is the total intensity stemming from the supersonic expansion nozzle (taken as a constant in the optimisation problem), r p h is the radius of the pinhole, S is the speed ratio of the beam, r S is the radius of the skimmer, R F is the radius of the supersonic expansion quitting surface (the point in the expansion from which atoms can be considered to travel in a straight line), x S is the distance between the nozzle and the skimmer and a is the distance between the skimmer and the pinhole. There are several other versions of this equation that depend on the intensity model, but they all show a quadratic dependency on the pinhole radius (the bigger the pinhole, the more intensity) and an inverse quadratic dependency with the distance between the skimmer and the pinhole (the more the atoms spread, the less intensity).