Focal plane model for flat refractive geometry

Abstract

Flow 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.

Using 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.

Significant 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.

The 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.