Low-magnification particle positioning for 3D velocimetry applications
Three-dimensional (3D) position and velocity information can be extracted by directly analysing the scattering patterns in velocimetry imaging of seeding particles using real-time CCD cameras. A Fraunhöfer diffraction simplification of generalised Lorenz–Mie theory is shown to yield a representative model of particle position, such that particle position can be approximately deduced from typical experimental particle images. Data are obtained by pattern-matching theoretical to experimental images using a Nelder–Mead algorithm, subject to digitisation considerations and the concept of “locales”. In this way, information about the characteristics of positional error as a function of magnification, pixel size, intensity resolution, and spatial resolution can be derived. This work shows that an optimum magnification exists, beneath which error begins to increase drastically. A practical application is demonstrated. The theory, simulations and experimental verification of this basic problem are discussed.