We theoretically and experimentally demonstrate a method for measuring the phase and intensity noise and their correlation in superluminescent diodes. A Michelson interferometer containing strongly unbalanced paths has been developed to measure the noise. By the spectral analysis of the photocurrents in detectors, the intensity noise is about twice the value of the phase noise in the superluminescent diode. The more interesting result we obtained is the experimental evidence that the intensity noise and the phase noise are mutually independent. The correlation coefficient of the intensity noise and the phase noise fluctuates between -0.08 and 0, which shows scarcely any sign of amplitude-phase noise correlation. The results offer a basic premise for the analysis of broadband light sources.