In situ calibration of an interferometric velocity sensor for measuring small scale flow structures using a Talbot-pattern

Abstract

Small scale flow phenomena play an important role across engineering, biological and chemical sciences. To gain deeper understanding of the influence of those flow phenomena involved, measurement techniques with high spatial resolution are often required, presuming a calibration of very low uncertainty. To enable such measurements, a method for the in situ calibration of an interferometric flow velocity profile sensor is presented. This sensor, with demonstrated spatial resolution better than 1 μm, allows for spatially-resolving measurements with low velocity uncertainty in flows with high velocity gradients, on condition that the spatial behavior of the interference fringe systems is well-known by calibration with low uncertainty, especially challenging to obtain at applications with geometries difficult to access. The calibration method described herein uses three interfering beams to form the interference fringe systems of the sensor, yielding Doppler burst signals exhibiting two peaks in the frequency domain whose amplitude ratio varies periodically along the measurement volume major z-axis, giving a further independent value of the axial tracer particle position that can be used to determine the calibration functions of the sensor during the flow measurement. A flow measurement in a microchannel experimentally validates that the presented approach allows for simultaneously estimating the calibration functions and the velocity profile, providing flow measurements with very low systematic measurement errors of the particle position of less than 400 nm (confidence interval 95%). In that way, the interferometric flow velocity profile sensor utilizing the in situ self-calibration method promises valuable insights on small scale flow phenomena, such as those given in shear and boundary layer flows, by featuring reliable flow measurements due to minimum systematic and statistical measurement errors.