## Abstract

An investigation of the minimum number of intersecting beams that is required for laser Doppler anemometry (LDA) incorporating only a single detector is presented. We aim to provide decisive arguments for using four beams as the minimum requirement for complete three-dimensional velocity reconstruction even though three beams supply three velocity components. We derive expressions for the detected signals of the most general LDA system. From a matrix analysis of these expressions, we conclude that there is no physically realizable arrangement of three beams that results in complete three-dimensional velocity reconstruction and that four beams is the minimum number of beams required. We also determine the optimal arrangement of the four incident beams for unambiguous LDA and for best signal separation and immunity to minor optical alignment errors. To ascertain the velocity components, we scan the specimen in a precise manner relative to the point of focus of the beams, whereas some other researchers alter the frequency of the incident beams. The results obtained with these two methods are equivalent. However, scanning is mechanically simpler than frequency shifting and also allows for the formation of velocity images—images of the flow velocity over a region in two- or three-dimensional space. In particular, we examine systems that are limited by the common practice of using only a single high-numerical-aperture objective for both focusing and detection. We show that using high-numerical-aperture objectives results in the best signal differentiation and immunity to minor alignment errors.

© 2000 Optical Society of America

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