An optical coherence tomography system is described which can image up to video rate. The system utilizes a high power broadband source and real time image acquisition hardware and features a high speed scanning delay line in the reference arm based on Fourier-transform pulse shaping technology. The theory of low coherence interferometry with a dispersive delay line, and the operation of the delay line are detailed and the design equations of the system are presented. Real time imaging is demonstrated in vivo in tissues relevant to early human disease diagnosis (skin, eye) and in an important model in developmental biology (Xenopus laevis).