We have developed a new ring-down technique that does not require a shutter to turn a probe laser on and off. With a rapid cavity scan we can measure a simple exponential cavity decay from which a cavity finesse can be found. When the cavity is scanned slowly, the cavity decay exhibits an amplitude modulation, and an analytic expression is derived for this modulation. With this new technique we measured the ultraslow relative velocity of the mirrors (of the order of micrometers per second) as well as the linewidth (~100 kHz) of the probe laser.
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