Phase critical angle scattering for measurement of transient nanoscale growth rate of a micron-sized bubble

We developed phase critical angle scattering (PCAS) to simultaneously measure the spherical and transparent bubble size at the micron scale and transient bubble growth at the nanoscale. The theoretical derivation of PCAS reveals that the phase of the fine structure of critical angle scattering caused by reflection and first-order refraction is highly sensitive to and linearly shifts with bubble diameter growth. Experiments on a single growing bubble are implemented with a Fourier imaging system. The results show that the PCAS technique can measure the tiny bubble growth down to tens of nanometers, providing a promising tool for accurate characterization of bubble dynamics.