How PIV Works
Multi-pass
What is Multi-pass?
Multi-pass is a method for reducing the negative aspects of a large Interrogation Region (IR) size and small IR concurrently. To begin, readers should be familiar with the correlation plane (see: How PIV Works?) and how a larger IR decreases resolution but enables larger particle displacements, while a smaller IR increases resolution but enables smaller particle displacements (see: Region Size). This trade-off is unfortunate, but luckily PIV algorithms now have means for “cheating” this trade-off. The solution we will discuss is called discrete window offset, and essentially conducts one iteration of PIV (the first pass) with a large IR (thereby capturing larger displacements). With the result of this first pass, the algorithm can implement an informed second pass with a smaller IR (thereby providing greater resolution). This process can be repeated as desired for multiple passes. With this general idea, let’s look at an example of the process for a single interrogation region. To begin, Figure 1 demonstrates a single synthetic IR pair, each of size 64 pixels and the corresponding correlation Plane.
Figure 1. A synthetic 64x64 pixel interrogation region pair with a displacement of 14.5 pixels in the positive $x$ direction.
This is a useful result, but our window size of 64 pixels is large, and we can do better. To do so, we will use the vector result from our first pass to select two smaller IRs within the 64-pixel IRs. Specifically, we will select a new, smaller IR from the first image, whose center is located half of the output vector (in the opposite direction of the vector) from the larger IR center. In the same manner, we will select a new, smaller IR from the second image, whose center is located half of the output vector (in the same direction as the vector) from the larger IR center. Figure 3 shows the same IRs from Figure 1, but with the new IRs outlined in red.
Figure 2. The interrogation region pair from Figure 1, with second pass interrogation regions outlined in red. With a displacement of (14.5,0) pixels, the first interrogation region is centered 7 pixels in the negative $x$ direction, and the second region is centered 7 pixels in the positive $x$ direction (from the first region centers).
This increases the likelihood of maintaining a valid correlation despite decreasing the IR size, by increasing the likelihood that the same particles are maintained between the first and second image. Figure 4 demonstrates the correlation plane for this result.
Figure 3. The 32x32 pixel second pass interrogation region pair and corresponding correlation plane.
A few important notes exist for this method. To begin, for those inspecting Figure 4 closely, the output vector from the second pass must have the window offsets added to the new output vector, as the correlation maximum is for the shifted interrogation regions. Second, a post-processing scheme is necessary between each pass to remove spurious vector from providing a divergent offset (i.e., if the first pass correlation is incorrect, the second pass will not provide a valid result either).
Author: Jack Elliott
Date Published: June, 2022