The second-order correlation function of incoherent light, which is usually measured in the time domain, can be alternatively measured in the frequency domain. Here, we use an all-optical technique in a highly nonlinear fiber for measuring the full spectrum of the fluctuations of the photocurrent (rf spectrum) generated by broadband radiation with different spectral coherence properties. Our experiments reveal that the rf spectrum of a light signal depends strongly on its spectral coherence properties. From a practical perspective, this ultrafast technique constitutes an alternative for measuring the intensity correlations of spectrally incoherent radiation.