An Optimal Lookup Table Construction for Charge Division with respect to Efficiency Flatness

Static lookup tables as often used in the position calculation electronics in position sensitive detectors suffer from the well known problem that the propagation of digitization errors in the division leads to unequal efficiencies for the different output channels. In this paper we present a solution to the construction of such a lookup table which is optimal in the sense that the least possible efficiency errors are committed in the class of monotone lookup tables. The obtained resolution is comparable to what is obtained using the standard implementation of the fixed point division. After a theoretical explanation, we present some experimental results confirming our claim.