Modification of backgammon shape cathode and graded charge division readout method for a novel triple charge division centroid finding method

The triple charge division (TCD) centred finding method that uses a modified pattern of a backgammon shape cathode (MBSC) is introduced for medium range length position sensitive detectors with optimum numbers of cathode segments. The MBSC pattern has three separated areas and uses sawtooth like insulator gaps for separating the areas. The side areas of the MBSC pattern are severed by a central common area. The size of the central area is twice the size of both sides. Whereas the central area is the widest area among three, both sides areas have the main role in position sensing. With the same resolution and linearity, the active region of the original backgammon pattern increases twice by using the MBSC pattern, and with the same length, the linearity of TCD centred finding is much better than the backgammon charge division readout method. The linearity prediction of TCD centred finding and experimental results necessitated us to find an optimum truncation of the apices of the MBCS pattern in the central area. The TCD centred finding has a special readout method since charges must be collected from two segments in both sides and from three segments in the central area of the MBSC pattern. The so called graded charge division (GCD) is the special readout method for TCD. The GCD readout is a combination of the charge division readout and sequence grading of serial segments. Position sensing with TCD centred finding and GCD readout were done by two sizes of MBSC patterns (200 mm and 80 mm) and a spatial resolution of about 1% of the detector length is achieved