Particle Image Velocimetry (PIV) was born in the late 1970’s, first receiving its name in 1984 [Adrian, 2005]. It was evident in these early years that PIV would be an immensely powerful experimental flow analysis tool. However, the method at the time was difficult to implement, requiring complex optical setups and meticulous image analysis. The method was greatly simplified once both digital acquisition and image analysis was shown to be feasible [Willert and Gharib,1991]. The simplifica- tion of the method together with the rapid advances in digital camera technology over the years has made Digital PIV (DPIV) commonplace in fluid mechanics laboratories.
In either its analog or digital form, PIV was limited to a two-dimensional measurement averaged over the thickness of the illumination volume, which was, for this reason, made to be as thin as possible. In DPIV the velocity of a section of the field of view is measured by cross-correlating the same section of two exposures. The average displacement of the contents of this section of the image (images of the flow markers) divided by the time elapsed between the exposures is taken to be the velocity of the fluid there.
Because standard PIV measures two components of velocity in one plane (a two-dimensional volume), recent convention in the field is to refer to the method is referred as a “2D2C” measurement.
1.3.1 Stereo PIV
Perhaps the most direct extension of PIV into the third dimension is Stereo PIV (SPIV), whereby, in essence, the single digital camera is replaced by two cameras separated by a considerable space.
Perhaps the earliest publication of the currently popular method is that of Prasad and Jensen in Prasad and Jensen [1995]. The two points of view are used to extract the third component of velocity from the illuminated volume by parallax. Thus it is still a measurement of the average velocity within the illumination volume which, as in standard PIV, is made to be thin. Stereo PIV is thus a 2D3C measurement, although much of the literature, even recently, refers to it as 3D PIV.
The velocity is measured exactly as in standard PIV, with the third component reconstructed from the two 2D2C measurements.
In an attempt to create a 3D3C system based on Stereo PIV, some researchers have attempted to combine two or more independent SPIV setups to create a multi-plane measurement. In essence, multiple systems operating at optically separable wavelengths acquire simultaneous images of the experiment. One obvious drawback is the need for multiple wavelengths of light and an ever in- creasing number of cameras and computers. Although some published results exist, the painstaking setup procedure has limited the technique.
1.3.2 Photogrammetry
Photogrammetry is the science of measuring from photographs. It has a long and rich history associated with cartography, aerial photography, and surveying. In the machine vision world, pho- togrammetry came to mean the reconstruction of a three-dimensional domain from several points of view. Multiple cameras are synchronized spatially through a calibration [Tsai,1987] which also builds a mathematical pinhole model for each camera containing some distortion correction parame- ters. Typically the position of points in the volume is ascertained by tracing rays backwards from the image plane through the camera model into space. The result is a discrete set of points, or a point cloud. In the PIV field, this type of 3D3C is typically referred to as Particle Tracking Velocimetry (PTV) or 3D-PTV, though it can also refer to 2D2C measurements where seeding is too low to perform image correlation as is done in PIV. It has been used primarily for domains of considerable size, such as quarter-scale wind tunnels. Because typically the location of the flow markers must be reconstructed, seeding concentration is relatively low simply because all the particles in the depth of the volume must be visible in the two-dimensional space that is the camera sensor. In other words, spatial resolution is limited by the depth of the volume keeping in mind that the maximum number of flow markers that can be reliably reconstructed is in the tens of thousands (though common results are in the neighborhood of 3000 tracers per frame). Although typically these systems should be as mobile as a stereo PIV setup, they usually stay in once place, that is, they are built around the test facility.
1.3.3 Holographic PIV
Holographic PIV (HPIV) generates holograms rather than images at different instances in time, thus it has the potential to overcome the spacial resolution systems of photogrammetric systems.
Unforunately this comes at the expense of a very complex and costly setup that is more an installation than an instrument. The HPIV method is reminiscent of the early days of PIV, when both the acquisition and reconstruction required a lot of skill and specialized equipment. Measurements with orders of magnitude higher seeding density than in photogrammetry are possible. A beautiful example of this technique—showing both its potential and complexity—is Barnhart, Adrian, and Papen[1994].
1.3.4 Tomographic PIV
Unveiled in Elsinga, Scarano, Wieneke, and van Oudheusden [2005], Tomographic PIV systems consist of four cameras in a bi-axial Scheimpflug arrangement aimed at the volume of interest, which is in the shape of a slab (depth is considerably shorter than the width or the height). This is an interesting 3D3C approach which could very well be considered the direct extension of SPIV
into the third dimension. The images acquired are fed into a feedback loop that uses them to reconstruct a volumetric image of the domain iteratively. The seeding particles are never strictly identified; instead, the reconstruction result is a three-dimensional intensity map consisting of three- dimensional pixels. This is similar to the result of true tomographic imaging systems, such as confocal microscopy or CAT scans, where individual image slices are joined together to generate a volumetric image.
Velocity is then obtained by performing a three-dimensional image correlation. Spatial resolu- tions are reported to be considerably higher than those of photogrammetric systems, presumably because higher seeding densities are acceptable since reconstruction errors do not propagate past the cross-correlation stage.
1.3.5 Defocusing DPIV
Defocusing DPIV (DDPIV) can be interpreted as a subset of photogrammetry, the main advantage over which being that the reconstruction is much simpler due to the optical layout. Like photogram- metry, it can track discrete particles in place, which gives it an advantage over all the other methods in that it can also track the movement of surfaces in three dimensions. The single assembly makes it a very compact system, and, being fully digital, is much simpler to operate than HPIV. The calibration method, derived from that of SPIV, indirectly provides a more accurate camera model than the one used in photogrammetry. Its optimal arrangement requires three sensors, and thus it is he least expensive volumetric setup, with both photogrammetry and Tomo PIV requiring at least 4 sensors.
Chapter 2
Defocusing DPIV
2.1 Introduction
Defocusing DPIV (DDPIV), at its core, is a special subset of photogrammetry. Three sensors are assembled into a common faceplate such that they are coplanar and their fields of view intersect in a predetermined region called themappable region. In general terms, DDPIV can estimate the depth of features based on the relative location of their images on the three sensors. In the case of fluid measurements, images of the flow markers are used to reconstruct discrete point clouds for instants in time. Velocity is computed either through tracking algorithms or three-dimensional cross-correlation on the discrete clouds.
The primary difference between the defocusing technique and photogrammetry lies in the optical layout and the calibration scheme. The optical layout affords a reconstruction method simpler than backwards ray-tracing—if the sensors are parallel, the position of the image of a point is decoupled relative to the point’sZ and X, Y position.
The calibration scheme used in DDPIV is based loosely on that developed for SPIV and thus is a completely different paradigm than that used in photogrammetry (commonly based on the methods ofTsai[1987]). Rather than generating a pinhole model of the sensors with coefficients to correct for distortion, multi-plane dewarping, as DDPIV’s calibration is called, is given the pinhole model and is made to correct the location of the images so that they fit this model. This yields more precise result than typical Photogrammetry methods, especially for volumes on the order of the instrument size, because it also accounts for differences between the pinhole model and the optical reality that do not propagate themselves as measurable distortion.