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Efficient Fan Beam Calibration for k Nearest Position 

Monolithic scintillator detectors can achieve excellent spatial resolution and coincidence resolving time. However, their practical use for positron emission tomography (PET) and other applications in the medicalimaging field is still limited due to drawbacks of the different methods used to estimate the position of interaction. Common statistical methods for example require the collection of an extensive dataset of reference events with a narrow pencil beam aimed at a fine grid of reference positions. Such procedures are time consuming and not straightforwardly implemented in systems composed of many detectors. Here, we experimentally demonstrate for the first time a new calibration procedure for $k$-nearest neighbor ($k$-NN) position estimation that utilizes reference data acquired with a fan beam.The procedure is tested on two detectors consisting of $16~hbox{mm} times 16~hbox{mm} times 10~hbox{mm}$ and $16~hbox{mm} times 16~hbox{mm} times 20~hbox{mm}$ monolithic, Ca-codoped LSO:Ce crystals and digital photon counter (DPC) arrays.

For both detectors, the spatial resolution and the bias obtained with the new method are found to be practically the same as those obtained with the previously used method based on pencil-beam irradiation, while the calibration time is reduced by a factor of $sim 20$. Specifically, a FWHM of $sim 1.1~hbox{mm}$ and a FWTM of $sim 2.7~hbox{mm}$ were obtained using the fan-beam method with the 10 mm crystal, whereas a FWHM of $sim 1.5~hbox{mm}$ and a FWTM of $sim 6~hbox{mm}$ were achieved with the 20 mm crystal. Using a fan beam made with a $sim 4.5~hbox{MBq}quad ^{22}{rm Na}$point-source and a tungsten slit collimator with 0.5 mm aperture, the total measurement time needed to acquire the reference dataset was $sim 3$hours for the thinner crystal and $sim 2$ hours for the thicker one.

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