Generalization of the concepts of focal length and f-number to space and time

One can exploit the duality between the parabolic equations of diffraction and dispersion to create the time-domain equivalent of a spatial imaging system. A key element in this temporal imaging system is the time lens (quadratic phase modulator) with attributes analogous to the focal length and the f-number of conventional space lenses. These temporal analogs are analyzed and compared with their spatial counterparts in a generalized framework, from which we conclude that chirp rate and fractional bandwidth are the defining quantities in both systems.