Detection and evaluation of droplet and bubble fringe patterns in images of planar interferometric measurement techniques using the wavelet transform

The acquired images of interferometric particle sizing techniques are characterized by intense fringe pattern overlapping in dense droplet and bubble areas, which hinders the image processing process and subsequent information extraction. Methods employed, such as thresholding and the Hough transform and template cross-correlation, exhibit weaknesses when processing such dense areas of interest. We investigate the viability of applying the wavelet transform (WT) for the detection of the fringe pattern centers and the evaluation of the particle size. We present the basics of the WT using the Mexican hat, which exhibits excellent localization properties and present two different alternatives routes in detecting the fringe patterns in the compressed and uncompressed fringe pattern cases. We found that in comparison to the most reported methods for image evaluation, such as intensity thresholding and plain cross-correlation, the WT is a very efficient tool for detecting the patterns, even in images with high-number fringe pattern areas. The usage of the WT for the sizing of the imaged droplets and bubbles is also examined, in comparison to the Fast Fourier Transform (FFT).