Optimization of in-line phase contrast particle image velocimetry using a laboratory x-ray source

Phase contrast particle image velocimetry (PIV) using a laboratory x-ray microfocus source is investigated using a numerical model. Phase contrast images of 75 μm air bubbles, embedded within water exhibiting steady-state vortical flow, are generated under the paraxial approximation using a tungsten x-ray spectrum at 30 kVp. Propagation-based x-ray phase-contrast speckle images at a range of source–object and object–detector distances are generated, and used as input into a simulated PIV measurement. The effects of source-size-induced penumbral blurring, together with the finite dynamic range of the detector, are accounted for in the simulation. The PIV measurement procedure involves using the cross-correlation between temporally sequential speckle images to estimate the transverse displacement field for the fluid. The global error in the PIV reconstruction, for the set of simulations that was performed, suggests that geometric magnification is the key parameter for designing a laboratory-based x-ray phase-contrast PIV system. For the modeled system, x-ray phase-contrast PIV data measurement can be optimized to obtain low error (<0.2 effective pixel of the detector) in the system with magnification lying in the range between 1.5 and 3. For large effective pixel size (>15 μm) of the detector, high geometric magnification (>2.5) is desired, while for large source size system (FWHM > 30 μm), low magnification (<1.5) would be suggested instead. The methods developed in this paper can be applied to optimizing phase-contrast velocimetry using a variety of laboratory x-ray sources.