Ring artifacts reduce image quality in tomography, and arise from faulty detector calibration. In microtomography, we have identified that ring artifacts can arise due to high-spatial frequency variations in the scintillator thickness. Such variations are normally removed by a flat-field correction. However, as the spectrum changes, e.g. due to beam hardening, the detector response varies non-uniformly introducing ring artifacts that persist after flat-field correction. In this paper, we present a method to correct for ring artifacts from variations in scintillator thickness by using a simple method to characterize the local scintillator response. The method addresses the actual physical cause of the ring artifacts, in contrary to many other ring artifact removal methods which rely only on image post-processing. By applying the technique to an experimental phantom tomography, we show that ring artifacts are strongly reduced compared to only making a flat-field correction.