  We introduce a new modality for dynamic phase imaging in confocal microscopy
based on synthetic optical holography. By temporal demultiplexing of the
detector signal into a series of holograms, we record time-resolved phase
images directly in the time domain at a bandwidth as determined by the photo
detector and digitizer. We demonstrate our method by optical imaging of
transient vibrations in an atomic force microscope cantilever with 100 ns time
resolution, and observe the dynamic deformation of the cantilever surface after
excitation with broadband mechanical pulses. Temporal Fourier transform of a
single data set acquired in 4.2 minutes yields frequency and mode profile of
all excited out-of-plane vibration modes with sub-picometer vertical
sensitivity and sub-micrometer lateral resolution. Our method has the potential
for transient and spectroscopic vibration imaging of micromechanical systems at
nano- and picosecond scale time resolution.
