An adaptive sampling algorithm for Doppler-shift fluorescence velocimetry in high-speed flows

We present an approach to improving the efficiency of obtaining samples over a given domain for the peak location of Gaussian line-shapes. The method uses parameter estimates obtained from previous measurements to determine subsequent sampling locations. The method may be applied to determine the location of a spectral peak, where the monetary or time cost is too high to allow a less efficient search method, such as sampling at uniformly distributed domain locations, to be used. We demonstrate the algorithm using linear least-squares fitting of log-scaled planar laser-induced fluorescence data combined with Monte-Carlo simulation of measurements, to accurately determine the Doppler-shifted fluorescence peak frequency for each pixel of a fluorescence image. A simulated comparison between this approach and a uniformly spaced sampling approach is carried out using fits both for a single pixel and for a collection of pixels representing the fluorescence images that would be obtained in a hypersonic flow facility. In all cases, the peak location of Doppler-shifted line-shapes were determined to a similar precision with fewer samples than could be achieved using the more typical uniformly distributed sampling approach.