The close-in AM noise is often neglected, under the assumption that it is a minor problem as compared to phase noise. With the progress of technology and of experimental science, this assumption is no longer true. Yet, information in the literature is scarce or absent.This report describes the measurement of the AM noise of rf/microwave sources in terms of Sα(f ), i.e., the power spectrum density of the fractional amplitude fluctuation α. The proposed schemes make use of commercial power detectors based on Schottky and tunnel diodes, in single-channel and correlation configuration.There follow the analysis of the front-end amplifier at the detector output, the analysis of the methods for the measurement of the powerdetector noise, and a digression about the calibration procedures.The measurement methods are extended to the relative intensity noise (RIN) of optical beams, and to the AM noise of the rf/microwave modulation in photonic systems.Some rf/microwave synthesizers and oscillators have been measured, using correlation and moderate averaging. As an example, the flicker noise of a low-noise quartz oscillator (Wenzel 501-04623E) is Sα = 1.15×10 −13 /f , which is equivalent to an Allan deviation of σα = 4×10 −7 . The measurement systems described exhibit the world-record lowest background noise.