We describe an original microscope for high-resolution optical coherence tomography applications. Our system is based on a Linnik interference microscope with high-numerical-aperture objectives. Lock-in detection of the interference signal is achieved in parallel on a CCD by use of a photoelastic birefringence modulator and full-field stroboscopic illumination with an infrared LED. Transverse cross-section (en-face, or XY) images can be obtained in real time with better than 1-microm axial (Z) resolution and 0.5-microm transverse (XY) resolution. A sensitivity of approximately 80 dB is reached at a 1-image/s acquisition rate, which allows tomography in scattering media such as biological tissues.