We present a new apparatus for converting between spectral and temporal representation of optical information, designed for operating with pulsed light sources. Every input pulse is converted into a pulse train in which the pulse intensities represent the spatial or temporal frequency spectrum of the original pulse. This method enables spectral measurements to be performed by following the temporal response of a single detector and, thus, is useful for real-time spectroscopy and imaging, and for spectral correlation measurements. The apparatus is based on multiple round-trips inside a 2f-cavity-like mirror arrangement in which the spectrum is spread on the back focal plane, and a small section of it is allowed to escape after each round-trip. Unlike existing methods, it relies neither on fibers nor on interference effects. It offers easy wavelength range tunability, and a prototype built achieves over 10% average efficiency in the near infrared (NIR). We demonstrate the application of the prototype for an efficient measurement of the joint spectrum of a non-degenerate bi-photon source in which one of the photons is in the NIR.