Temporal imaging with a time lens

We extend the well-known analogy between the problems of paraxial diffraction in space and dispersion in time to optical pulse compression and propose a time-domain analog to spatial imaging that allows for the distortionless expansion or compression of optical power waveforms. We call this new concept temporal imaging and derive equivalent expressions for the focal length and the f-number of a time lens and the magnification of an imaging system. It should now become possible, with a temporal microscope, to expand ultrafast optical phenomena to a time scale that is accessible to conventional high-speed photodiodes.