Abstract
We theoretically derive the analytic relationship between experimental parameters and the measured incident (or illumination) optical power spectrum for a new form of spectroscopy, entitled light labeling spectroscopy. The light labeling signals are shown to arise from the interference between fields diffracted from a grating with time varying ruling density. A Gaussian model is used to illustrate the bounds of the method for recovering power spectra without artificial spectral apodization. Finally, several example systems are tabulated to give numerical insight into the possible system performances across a range of wavelength regions.