A complete analysis and measurement of the noise figure of Raman amplifiers is reported. The standard noise figure definition derived from the amplified spontaneous emission approach is discussed. A new approach, based on the field fluctuations, is proposed. It takes into account the vacuum fluctuation as a minimum noise level fit the amplifier input and as a contribution to the noise generation. As a result, the noise of a phase-insensitive amplifier is shown to be generated by the input noise amplification, the intrinsic amplification and attenuation mechanisms. This model enables to exactly define the noise figure as the degradation of the optical signal-to-noise ratio, which is in complete agreement with the practice of the IEEE standard.