Measurement of power spectral density of broad-spectrum visible light with heterodyne near field scattering and its scalability to betatron radiation

We exploit the speckle field generated by scattering from a colloidal suspension to access both spatial and temporal coherence properties of broadband radiation. By applying the Wiener-Khinchine theorem to the retrieved temporal coherence function, information about the emission spectrum of the source is obtained in good agreement with the results of a grating spectrometer. Experiments have been performed with visible light. We prove more generally that our approach can be considered as a tool for modeling a variety of cases. Here we discuss how to apply such diagnostics to broad-spectrum betatron radiation produced in the laser-driven wakefield accelerator under development at SPARC LAB facility in Frascati.