Techniques for precise energy calibration of particle pixel detectors

We demonstrate techniques to improve the accuracy of the energy calibration of Timepix pixel detectors, used for the measurement of energetic particles. The typical signal from such particles spreads among many pixels due to charge sharing effects. As a consequence, the deposited energy in each pixel cannot be reconstructed unless the detector is calibrated, limiting the usability of such signals for calibration. To avoid this shortcoming, we calibrate using low energy X-rays. However, charge sharing effects still occur, resulting in part of the energy being deposited in adjacent pixels and possibly lost. This systematic error in the calibration process results in an error of about 5% in the energy measurements of calibrated devices. We use FLUKA simulations to assess the magnitude of charge sharing effects, allowing a corrected energy calibration to be performed on several Timepix pixel detectors and resulting in substantial improvement in energy deposition measurements. Next, we address shortcomings in calibration associated with the huge range (from kiloelectron-volts to megaelectron-volts) of energy deposited per pixel which result in a nonlinear energy response over the full range. We introduce a new method to characterize the non-linear response of the Timepix detectors at high input energies. We demonstrate improvement using a broad range of particle types and energies, showing that the new method reduces the energy measurement errors, in some cases by more than 90%.