Phase and synchronous detector theory as applied to beam position and intensity measurements

A popular signal processing technique for beam position measurements uses the principle of amplitude-modulation-to-phase-modulation (AM/PM) conversion and phase detection. This technique processes position-sensitive beam-image-current probe-signals into output signals that are proportional to the beam´s position. These same probe signals may be summed and processed in a different fashion to provide output signals that are proportional to the peak beam current. This paper derives the transfer functions for the AM/PM beam position and peak beam current processors