  Fourier-transform spectroscopy (FTS) has been widely used as a standard
analytical technique over the past half-century. FTS is a simple and robust
autocorrelation-based technique that is compatible with both temporally
coherent and incoherent light sources, which functions as an active or passive
spectrometer. However, this technique has been mostly used for static
measurements due to the low scan rate imposed by technological restrictions.
This has impeded its application to continuous rapid measurements, which would
be of significant interest for a variety of fields, especially when monitoring
of non-repeating/transient complex dynamics is desirable. Here, we demonstrate
highly efficient FTS operating at a high spectral acquisition rate with a
simple delay line based on a dynamic phase-control technique. The independent
adjustability of phase and group delays allows us to achieve the
Nyquist-limited spectral acquisition rate over 10,000 spectra per second, while
maintaining a large spectral bandwidth and high resolution. In addition, we
demonstrate the ability of this passive spectrometer working with an incoherent
light source.
