Abstract
BackgroundFlow visualization techniques such as uPIV and droplet imaging determine the measurement volume by the focal plane. Thus, an understanding of how the focal plane moves in reference to the camera is necessary when planar interfaces are present between the camera and the focal plane.MethodsUsing geometric optics, a focus model for a camera imaging through multiple parallel interfaces with different refractive indices is derived. This model is based on the thin lens camera model and gives the location of the focal plane, the depth of field, and the change in the location of the focal plane for a change of camera position. The theoretical model is validated by both simulation and experimental results.ResultsSignificant results are that while the magnification of a camera for an in-focus object does not vary for changes in the camera position, the position of the focal plane does. The change of the focal plane location depends only on the refractive indices of the media surrounding the camera and the focal plane regardless of the number or type of other media in between.ConclusionThe derived model provides a simple, accurate relationship between the focal plane location and the number and location of planar interfaces, thus avoiding potentially incorrect results for measurement plane depth.
Highlights
Flow visualization techniques such as uPIV and droplet imaging determine the measurement volume by the focal plane
Various challenges arise when applying this technique to small scales, including diffraction effects, errors due to Brownian motion and spurious reflections, and the necessity of setting the measurement volume using the depth of field instead of light sheet thickness
From this focus model, the location of the focal plane, implications about the magnification of the system, and how these factors change with movement of the camera or for different orientations of the planar interfaces can be inferred
Summary
Flow visualization techniques such as uPIV and droplet imaging determine the measurement volume by the focal plane. Particle image velocimetry (PIV) is one of the most prominent measurement techniques for full-field flow quantification. Various challenges arise when applying this technique to small scales, including diffraction effects, errors due to Brownian motion and spurious reflections, and the necessity of setting the measurement volume using the depth of field instead of light sheet thickness. The latter of these challenges shifts the responsibility of accurately locating the measurement volume to the imaging rather than light sheet optics. Wieneke proposed a self-calibration scheme where the location of the laser light sheet was inferred without a calibration target using the disparity map from de-warped images from two stereoscopic
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