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Purpose: Spectral information of the output of x-ray tubes in (dual source) computer tomography (CT) scanners can be used to improve the conversion of CT numbers to proton stopping power and can be used to advantage in CT scanner quality assurance. The purpose of this study is to design, validate, and apply a compact portable Compton spectrometer that was constructed to accurately measure x-ray spectra of CT scanners., Methods: In the design of the Compton spectrometer, the shielding materials were carefully chosen and positioned to reduce background by x-ray fluorescence from the materials used. The spectrum of Compton scattered x-rays alters from the original source spectrum due to various physical processes. Reconstruction of the original x-ray spectrum from the Compton scattered spectrum is based on Monte Carlo simulations of the processes involved. This reconstruction is validated by comparing directly and indirectly measured spectra of a mobile x-ray tube. The Compton spectrometer is assessed in a clinical setting by measuring x-ray spectra at various tube voltages of three different medical CT scanner x-ray tubes., Results: The directly and indirectly measured spectra are in good agreement (their ratio being 0.99) thereby validating the reconstruction method. The measured spectra of the medical CT scanners are consistent with theoretical spectra and spectra obtained from the x-ray tube manufacturer., Conclusions: A Compton spectrometer has been successfully designed, constructed, validated, and applied in the measurement of x-ray spectra of CT scanners. These measurements show that our compact Compton spectrometer can be rapidly set-up using the alignment lasers of the CT scanner, thereby enabling its use in commissioning, troubleshooting, and, e.g., annual performance check-ups of CT scanners.