The size of the field of measurement (FOM) in computed tomography is limited by the size of the x-ray detector. In general, the detector is mounted symmetrically with respect to the rotation axis such that the transaxial FOM diameter approximately equals the lateral dimensions of the detector when being demagnified to the isocenter. To enlarge the FOM one may laterally shift the detector by up to 50% of its size. Well-known weighting functions must then be applied to the raw data prior to convolution and backprojection. In this case, a full scan or a scan with more than 360 degrees angular coverage is required to obtain complete data. However, there is a small region, the inner FOM, that is covered redundantly and where a partial scan reconstruction may be sufficient. A new weighting function is proposed that allows one to reconstruct partial scans in that inner FOM while it reconstructs full scan or overscan data for the outer FOM, which is the part that contains no redundancies. The presented shifted detector partial scan algorithm achieves a high temporal resolution in the inner FOM while maintaining truncation-free images for the outer part. The partial scan window can be arbitrarily shifted in the angular direction, what corresponds to shifting the temporal window of the data shown in the inner FOM. This feature allows for the reconstruction of dynamic CT data with high temporal resolution. The approach presented here is evaluated using simulated and measured data for a dual source micro-CT scanner with rotating gantry.