8.4 Multi-plane Dewarping
8.4.2 Multi-plane Dewarping Procedure
The multi-plane dewarping procedure is quite simple. The idea is to photograph a precision grid of dots with a known spacing at several planes throughout the probe volume, starting with the reference plane. Three processing steps in the software generate a mapping between the imaged grid and a perfect one, and this mapping is used during the reconstruction of the point clouds in
Figure 8.4-1: The dewarping target, as imaged by the one sensor during an actual dewarping run with the Ian Camera.
This is the image at the focal plane so the origin (the dot isolated by the three diagonal spaces) is very close to the center of the image.
Figure 8.4-2: The dewarping target, as an RGB-composite of all three apertures’ images (from the Ian Camera). This is the image at the focal plane so any mismatch between the three apertures is due to lens distortion and manufacturing error.
Figure 8.4-3: Typical multi-plane dewarping setup for calibration in a fluid other than air. The target frame holds the grid target and diffuser. The traverse moves the target through the probe volume; the stages are used to align the target. There areXandY stages for positioning the origin and a rotation stage for aligning the grid to the horizontal. Alignment of the target face to the camera faceplate is achieved by shimming between the bracket and the traverse.
processing of experimental data.
Because the internal pinhole model is forced to fit the images of the dewarping grid, any errors in traversing the grid during calibration are propagated to experimental data directly. Thus it is absolutely key to align the target so that it is parallel to the faceplate of the camera and that theZ traverse be aligned with the optical axis of the camera, and that at each station, theZ coordinate be known to satisfactory precision. Thus the dewarping setup is carefully aligned and components are bolted in a repeatable manner. The frame that holds the target is made to be relatively thick to minimize warping or vibration.
The first step in creating a dewarping set is to turn on the camera and let it warm up. Typically the warm up period takes about 30 minutes since the faceplates for the two third-generation cameras weigh around 25 pounds. The beauty of the phenomenon is that it is easy to check for, since a calibration done at the wrong temperature will yield a poorly reconstructed particle field.
The central laser diode in the third-generation cameras is carefully aligned during assembly to be perpendicular to the faceplate, so by placing a flat mirror at the target and checking for the reflection on the facplate it is easy to precisely align the target parallel to the faceplate. The outer diode is aimed to emanate from the camera’s aperture separation so that it traverses toward the optical axis at the same angle as the sensor axis. Because of this, it will be refracted similarly through media as would the light scattered by the seeding particles. The crossing of the two beams provides a quick way to “find” the reference plane in multi-medium experiments.
Note that since multi-plane dewarping forces the parameters to fit reality the reference plane
is really an arbitrary location chosen during the design of the camera to maximize the mappable region at a particular working distance and characterize the camera there. However it is possible to simply start the calibration at a differentZ location and thus “move” the reference plane, allowing some flexibility in the working distance and/or mappable region size for a particular camera. The geometry of the high-sensitivity cameras, exemplified in figure8.4-4, makes it impossible to increase the size of the mappable region, and if the working distance is extended it is done so at the expense of resolution and sensitivity.
Figure 8.4-4: Anywhere in space where the fields of view intersect is in theory mappable—including the region behind the reference plane. In this particular layout (the same of figure4.1-1but showing the mapping to a distance 2Lfrom the aperture plane) the mappable region does not necessarily grow in size. In a “more sensitive” camera, the mappable region may shrink in size as the distance from the reference plane grows, whereas a “less sensitive” camera will exhibit a growing mappable region.
original reference plane aperture plane image plane sensor
camera axis sensoraxis
sensor field of view mappable region
LL LL
Images should be taken through the desired mapping region at every 5 to 10 millimeters inZ. Too many planes and the error introduced by dewarping may become destructive in the reconstruction;
too few and the set may not be able to properly correct for the optical path difference between planes to a satisfactory level.
The grid images are processed in three steps. In the first, DDPIV is used to perform Gaussian fitting on the dot images themselves to build a list of the sub-pixel locations of the grid dots as imaged. gridfindis then used to “walk” the grid, assigning each dot image a “perfect grid” location.
dewarpC takes the correspondence list and performs a least squares fit of a second, third, and fourth order function that can generate the perfect grid point locations from the imaged ones, thus
“dewarping” the image. Each plane is processed separately—that is, the correction is independent
ofZ location.
Chapter 9
Defocusing Camera Design
9.1 Introduction
The design of a defocusing camera happens in two parts. First, because characteristics such as the mappable region size and position and the sensitivity of the camera depend on the geometric layout of the apertures, the parameters are finalized by iterating with the pinhole relationships of chapter4.
ECG Designeris a Mathematica program written just for that. The second part involves mechanical design to try to approximate the results of ECG Designeror adjustments thereof in a real camera.
The two can be linked if the CAD software used supports the definition of relations between sketch segments and individual parts.
Detailed information about DDPIV camera design and construction can be found in partIII:De- sign and ConstructionofGraff[2007a].