Design of a Real Time FPGA-based Three Dimensional Positioning Algorithm.

We report on the implementation and hardware platform of a real time Statistics-Based Processing (SBP) method with depth of interaction processing for continuous miniature crystal element (cMiCE) detectors using a sensor on the entrance surface design. Our group previously reported on a Field Programmable Gate Array (FPGA) SBP implementation that provided a two dimensional (2D) solution of the detector's intrinsic spatial resolution. This new implementation extends that work to take advantage of three dimensional (3D) look up tables to provide a 3D positioning solution that improves intrinsic spatial resolution. Resolution is most improved along the edges of the crystal, an area where the 2D algorithm's performance suffers. The algorithm allows an intrinsic spatial resolution of ~0.90 mm FWHM in X and Y and a resolution of ~1.90 mm FWHM in Z (i.e., the depth of the crystal) based upon DETECT2000 simulation results that include the effects of Compton scatter in the crystal. A pipelined FPGA implementation is able to process events in excess of 220k events per second, which is greater than the maximum expected coincidence rate for an individual detector. In contrast to all detectors being processed at a centralized host, as in the current system, a separate FPGA is available at each detector, thus dividing the computational load. A prototype design has been implemented and tested using a reduced word size due to memory limitations of our commercial prototyping board.