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We describe a computer-controlled stroboscopic phase-shifting interferometer system for measuring out-of-plane motions and deformations of MEMS structures with nanometer accuracy. To aid rapid device characterization, our system incorporates (1) an imaging interferometer that records motion at many points simultaneously without point-by-point scanning, (2) an integrated computer-control and data-acquisition unit to automate measurement, and (3) an analysis package that generates sequences of time-resolved surface-height maps from the captured data. The system can generate a detailed picture of microstructure dynamics in minutes. A pulsed laser diode serves as the stroboscopic light source permitting measurement of large-amplitude motion (tens of micrometers out-of-plane) at kilohertz frequencies. The high out-of-plane sensitivity of the method makes it particularly suitable for characterizing actuated micro-optical elements for which even nanometer-scale deformations can produce substantial performance degradation. We illustrate the capabilities of the system with a study of the dynamic behavior of a polysilicon surface-micromachined scanning mirror that was fabricated in the MCNC MUMPS foundry process.