Holographic Particle Image Velocimetry

Pushing the Boundaries of Informatics
Contributed editorial appearing in
Scientific Computing & Instrumentation 19:2, January 2002, pg. 45.

An excellent way to build a reputation as a skilled political adviser is to provide information freely without providing knowledge. Important information is often buried in mountains of ancillary and unrelated signals, forcing the recipient to devote precious resources to data mining and knowledge extraction. Often, the target quantity of data acquisition is obtained indirectly through the fastidious analysis of measured supporting values. Velocity is one such abstract quantity that can be deduced only by observing the motion of a system as a function of time.

One optical method employed to obtain object velocity uses a stationary camera that records images of object position at two instants in time. If the objects under study are small particles entrained in fluid flow, the technique is known as Particle Image Velocimetry (PIV). Early PIV measurement systems used strobe lights and photographic film to capture both instants in time on the same negative. After the film was developed, a technician would manually connect identical particles by drawing an arrow on the film. As the images of each particle are separated by the same known amount of time, the length of the arrow is proportional to its speed. Each arrow points in the direction of particle motion.

As PIV matured, film was digitally scanned and numerical algorithms were employed to automate the process. A maximum likelihood algorithm mimicked the manual method by searching for identical pairs of particles. As the density of particles increased, so too did the difficulty in tracking individual particles. The digital images were segmented into small areas that could be spatially autocorrelated to yield average displacement information. The resulting autocorrelation images contain a large centroid peak representing the correlation of each image with itself, which is flanked by two smaller peaks resulting from the particle displacement. One smaller peak represents the second exposure offset from the first; the other, the first exposure offset from the second. If the actual flow direction is known, the displacement is measured by calculating the distance between the centroid and the correct satellite peak.

In regions of highly complex flow, it is difficult to choose the correct satellite peak. Using two colors of light in conjunction with color film, the first and second exposure can be identified, removing temporal ambiguity. The color negative can be digitized by a color scanner, and two separate images produced based on the differences in chromaticity. These images are cross-correlated, and a single cross-correlation peak is calculated for each image segment. Two-color PIV can be improved by using a color digital camera. Another hurdle for PIV to overcome was its limitation to two dimensions. A single imaging device only acquires a flat, 2-D cross-sectional view of the flow. Particle movement in the third dimension cannot be calculated. Particles that travel out of the observation plane between exposures create noise. Stereoscopic PIV uses two digital cameras that view the same flow region from two positions. Using algorithms that are aware of the viewing geometry, the 3-D flow field can be reconstructed.

The most recent development is Holographic PIV (HPIV), wherein the 3-D image of the flow is captured on doubly exposed holographic film. When the hologram is reconstructed, traditional 2-D PIV equipment can be used to analyze cross-sectional images of the hologram. Most recently, a digital camera has replaced the holographic film. Known as Direct-to-Digital Holography (DDH), multiple coherent laser beams are used to image a diffraction pattern onto the digital camera. As particles flow through the beams, the resulting interference fringes are recorded digitally. Using the Fresnel transform or a Fresnel-derived wavelet set known as Fresnelets, the 2-D digital interference patterns are numerically reconstructed into 3-D images of the flow field and the velocity vectors are extracted. As the HP1IV technique evolves into 3-D movies of the flow, the current limitation is how to glean the simple knowledge of a particle moving here to there among so many terabytes of information.