A new Method for Processing Time Averaged Vibration Patterns: Linear Regression

Speckle-based interferometry systems are useful tools for measuring vibration patterns at harmonically vibrating objects. The standard method for processing the speckle patterns acquired is to eliminate additive background noise and speckle phase, yielding Bessel-type fringe patterns whose values are proportional to the absolute value of the Bessel function. Fringes are covered by multiplicative speckle intensity noise on the Bessel-modulated vibration amplitude. Sine–cosine filtering is not an option because the Bessel-type fringe pattern is not a phase pattern, and thus, sine–cosine filtering would only degrade the results. Improvements can be reached by involving additional measurements acquired in the stationary state. An alternative method for processing vibration patterns using linear regression is proposed, yielding patterns where the vibration amplitude is an argument of a true Bessel function, not its absolute value. As a result, spatial frequencies of the vibration fringe pattern are only half of those obtained with standard methods, and results can be filtered and normalised conveniently. While other contributions to improve the results rely on determining indexed skeletons for high Bessel fringe densities, the proposed method aims at a very limited number of low-order fringes, allowing demodulation of the Bessel fringe pattern based on the actual Bessel values in the pattern. The method provides an effective alternative for spatial filtering. Phase differences between the stationary and vibrating states have an adverse effect on the results. Two methods, capable of handling phase jumps of 2π in the phase difference distribution, are presented to correct this.