Velocimetry of fast surfaces using Fabry–Perot interferometry

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Abstract
This article describes the use of the Fabry–Perot laser interferometer in the fringe mode to measure velocities of fast-moving reflecting surfaces, and includes a review of previously published work. We begin by describing the theory of the Doppler shift that applies to these situations, and include an experimental test of whether surface normal direction affects Doppler shift. Formulas are derived for the analysis of the effects of shocked, dispersive, moving transparent media on velocity measurements, including expressions for the velocity of light in a moving medium with moving boundaries. The Fabry–Perot method is compared with other techniques such as the VISAR interferometer. We then describe in detail a standard configuration developed at our facilities, discuss other configurations using optical fibers and more than one cylinder lens, and describe a new laser amplifier developed specifically for velocimetry. Methods of alignment, instrument calibration, surface preparation, and operation are included. Next, we present several methods of analysis, the choice of which depends on the absolute accuracy required, and examine many sources of possible error. These analytical techniques allow the motion of surfaces of reflectivity of at least 1% to be measured with an absolute precision of 0.5%. Time resolution can be a few nanoseconds, and is traded off for velocity resolution. One can make continuous velocity records of surfaces whose reflectivity under shock loading decreases to less than 1% of its initial value. We have simultaneously recorded three distinct velocity–time histories without ambiguity.