Linear optical coherence tomography (LOCT) systems are a simple and robust alternative to time-domain optical coherence tomography systems, but a detector with approximately 10(4) pixels is needed for an imaging depth of 2 mm. We present a new system for LOCT with a special mask attached to the image sensor. The mask essentially performs a downconversion of the spatial frequencies by multiplication with a second spatial frequency. This reduces the fringe frequency of the optical coherence tomography signal so that the signal can be sampled with fewer pixels.