ASYMMETRIC AUTOCORRELATION FUNCTION TO RESOLVE DIRECTIONAL AMBIGUITY IN PIV IMAGES

Autocorrelation of a double-exposed image, unlike cross-correlation be tween two images, produces a correlation function that is symmetric ab out the origin. Thus, while it is possible to calculate the speed and direction of tracer particles in a particle image velocimetry (PIV) im age using autocorrelation, it is impossible to tell whether the veloci ty is in the positive or negative direction. This ambiguity can be res olved by spatially shifting one exposure relative to the next or label ing exposures with color or polarization, but the complexity and limit ations of these methods can be prohibitive. It is, however, possible t o resolve the sign of the velocity from a triple-exposed image using u nequal time intervals between exposures. Triple-exposed images, like d ouble-exposed images, correlate symmetrically about zero. The directio nal ambiguity, however, can be resolved by calculating the probability that the three exposures occur in a specific temporal order; that is, by assuming that the correlation has a specific sign and testing to s ee if the assumption is correct. Traditional spectral and statistical correlation techniques are unable to accomplish this. Presented herein is a computationally efficient asymmetric correlation function that i s able to differentiate the temporal order of triple exposed images. I ncluded is a discussion of the limitations of this function and of dif ficulties in experimental implementation.