Flat field calibration methods are commonly used in computed tomography (CT) to correct for system imperfections. Unfortunately, they cannot be applied in energy-resolving CT when using bow-tie filters owing to spectral distortions imprinted by the filter. This work presents a novel semi-analytical calibration method for photon-counting spectral CT systems, which is applicable with a bow-tie filter in place and efficiently compensates pile-up effects at fourfold increased photon flux compared to a previously published method without degradation of image quality. The achieved reduction of the scan time enabled the first K-edge imaging in-vivo. The method employs a calibration measurement with a set of flat sheets of only a single absorber material and utilizes an analytical model to predict the expected photon counts, taking into account factors such as x-ray spectrum and detector response. From the ratios of the measured x-ray intensities and the corresponding simulated photon counts, a look-up table is generated. By use of this look-up table, measured photon-counts can be corrected yielding data in line with the analytical model. The corrected data show low pixel-to-pixel variations and pile-up effects are mitigated. Consequently, operations like material decomposition based on the same analytical model yield accurate results. The method was validated on a experimental spectral CT system equipped with a bow-tie filter in a phantom experiment and an in-vivo animal study. The level of artifacts in the resulting images is considerably lower than in images generated with a previously published method. First in-vivo K-edge images of a rabbit selectively depict vessel occlusion by an ytterbium-based thermoresponsive polymer.
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