Lighthill's theory of jet noise, as extended and developed by Ribner (self and shear noise), has successfully described many features of the jet noise outside the 'refraction valley'. However, attempts to measure the self and shear noise source terms directly by means of a cross-correlation technique have been only partially successful. The major difficulty has been suspected as spurious 'probe noise' generated by turbulence - hot wire interaction. Thus, to avoid this problem, the traditional hot wire anemometer has been replaced in the present investigation by a non-intrusive device: a Laser Doppler Velocimeter. Substantial modifications were made to meet the constraints imposed by the correlation experiment; a major feature was provision to measure u(x), the component of turbulent velocity in the observer direction x. Self and shear noise spectra have been constructed from the measured cross-spectral densities by a method consistent with the postulated self/shear noise formalism. The two spectra exhibit comparable amplitudes and virtually identical shapes, but are displaced substantially in frequency: all this is predicted by the theory. Self and shear noise spectra extracted from far field jet noise intensities via an algorithm of Nossier and Ribner exhibit the same behavior. On the whole both sets of spectra, although derived from vastly different experimental procedures, are compatible.