General spatial distortion correction method for solid-state position sensitive detectors in PET

Solid-state position sensitive detectors such as position sensitive avalanche photodiodes (PSAPD) and position sensitive solid-state photomultipliers (PS-SSPM) are attractive for use in high resolution PET. The position-sensitive design scheme allows the resolution of small crystal elements. It significantly reduces the number of costly preamplifiers and analogue-to-digital converters, and the complexity of interconnection design compared to pixel based array detectors. However, “pin-cushion” distortions are found in the corner of flood histograms generated by Anger logic, which make automatic peak segmentation difficult. Thus, an accurate crystal segmentation algorithm is highly desired. Alternative calculation formulae have been proposed to reduce the “pin-cushion” distortions but they are only effective for certain PSDs. In this paper, we propose a new set of calculation formulae to produce less distorted flood histograms and larger peak separations in the corner. Our hypothesis is that reduced distortions will facilitate crystal segmentation algorithms. This reduced pin-cushion will manifest itself through an increased separation between peaks in the corner of the flood histogram. Our formulae still rely on simple arithmetic of four corner signals with introduction of two parameters which can be easily adjusted for different PSDs. Our formulae have been applied to both clean and noisy flood measurement data from two PSAPDs as well as an dataset from a PS-SSPM. The angles of the lines connecting adjacent peaks in the horizontal and vertical direction are more than 75 degrees from our method, compared to 30-40 degrees from Anger logic in the corner of the flood histograms. The orthogonality of these two lines directly links to distortion reduction. Our formulae give more than 100% increase in peak separations in corners for all data and 20% increase in figure of merit in corners for noisy data. In the future, it will be tested with- segmentation algorithms.