Time-of-flight anemometry using a displacement plate-beamsplitter

Abstract

We propose the use of a second surface mirror as a displacement plate-beamsplitter to provide significant simplification and cost reduction of time-of-flight anemometry (ToFA), without sacrificing precision and accuracy. These benefits are most pronounced for long-range applications. Our method's principle benefits are due to the few and simple components it requires as well as low sensitivity to both temperature effects and light source incoherence. We found that precise and accurate results are possible using a common consumer mirror as the main optical element and an inexpensive diode laser as the light source, which could broaden access to laser anemometry and make many industry applications economically feasible. The nature of the design also permits an increase in range for a given laser power since the method can utilize the entire optical area of the focusing lens/mirror independent of other design considerations and the cost of a flat second-surface mirror is usually negligible. To characterize the performance of this method, we develop a Cramer–Rao bound (CRB) for a general class of ToFA's with multiple Gaussian beams under signal-independent Gaussian white noise. For a given measurement volume, the lowest velocity uncertainty is achieved by creating a standard two-sheet geometry: power-matching the first two beams by adjusting the beamsplitter and blocking the rest of the beams is optimal. However, keeping the higher order beams permits determination of flow direction. Conditions to achieve beam power-matching are given. An anemometer is built using a diode laser with 12 mw 405 nm beam using a total of just three transmitting optical components. Our setup has an accuracy of 99.1%. The worst-case precision of 96.7% nearly achieves the CRB, although optimizing the setup more can lower the bound, and therefore allow increase in the performance by an order of magnitude or more.

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