Fundamental flow measurement capabilities of optical Doppler and time-of-flight principles

Abstract In order to understand the fundamental measurement capabilities of different flow velocity principles based on Mie scattering, a equation how calculate shot noise limit for respective signal model is derived. The derivation well-known rules uncertainty propagation and yields Cramér–Rao bound without necessity Fisher information. derived next applied compare Doppler time-of-flight including laser anemometry (LDA), planar velocimetry (PDV), laser-two-focus (L2F), particle tracking (PTV) image (PIV). comparison performed an identical mean power, while two cases are studied in detail: measuring single seeding as well multiple particles averaging. LDA, L2F PTV/PIV obey similar limit. For case particles, minimal achievable directly proportional absolute value measured component inversely spatial resolution. PDV almost independent Since sensitive with respect depending observation direction, other only reasonable certain extent. However, all limits show expected inverse proportionality square root total number detected photons thus also time. Considering comparable spatiotemporal resolution, light power typical configurations, largest. As final result, it that each principle obeys between position wave vector, which agreement Heisenberg’s principle. Therefore, common basis provided assess systems what possible within quantum mechanical constraints. Graphic abstract