One of the most useful recent ion cyclotron resonance (ICR) developments is the conversion of magnetron motion to cyclotron motion by azimuthal quadrupolar excitation in the presence of ion-neutral collisions. The technique offers a mass-selective means for "shrink-wrapping" an ion cloud into a tight packet along the central axis of an ICR ion trap for enhanced signal to noise ratio, mass resolving power, and other advantages. However, the process itself is not directly observable. In this paper, we show that the conversion may be rendered observable by converting coherent magnetron motion (produced by off-axis ionization during a period short compared to the magnetron frequency) to coherent cyclotron motion, followed by subsequent dipole detection at omega(+) (reduced cyclotron frequency) or quadrupolar detection at omega(c) (unperturbed cyclotron frequency) and 2 omega(+). Detection at omega(c) eliminates the ICR frequency shift due to the electrostatic trapping potential, providing for increased mass accuracy; detection at 2 omega(+) may offer increased mass resolving power. The observed signal behavior as a function of excitation amplitude-duration product is predicted theoretically and confirmed experimentally for both types of detection. Unlike the otherwise analogous 180 degrees pulse in nuclear magnetic resonance (NMR), the magnetron-to-cyclotron interconversion may be phase-coherent with respect to both initial and final states. Finally, we show dow coherent magnetron motion of two ion packets of different magnetron phase can be converted eo cyclotron motion of two ion packets of different cyclotron phase, and we discuss the implications of that process.