Optical distortion correction for liquid droplet visualization using the ray tracing method: further considerations

Abstract

The original work of Kang et al (2004 Meas. Sci. Technol. 15 1104–12) presents a scheme for correcting optical distortion caused by the curved surface of a droplet, and illustrates its application in PIV measurements of the velocity field inside evaporating liquid droplets. In this work we re-derive the correction algorithm and show that several terms in the original algorithm proposed by Kang et al are erroneous. This was not evident in the original work because the erroneous terms are negligible for droplets with approximately hemispherical shapes. However, for the more general situation of droplets that have shapes closer to that of a sphere, with heights much larger than their contact-line radii, these errors become quite significant. The corrected algorithm is presented and its application illustrated in comparison with that of Kang et al.