Hybrid measurement of droplet contact angle and refractive index using transmission fringe (TF) technique: Theoretical study

This work presents the development of a hybrid measurement of droplet contact angle and refractive index (RI) using the transmission fringe (TF) technique. Firstly, the transmission fringe (TF) technique is developed, which can determine the droplet contact angle on a surface by measuring the transmitted beam fringe radius on the projected screen. An analytic expression for the contact angle as a function of the measured fringe radius (FR) from geometric modeling has been formulated and simulated as critical angle versus fringe radius at various incidence angles. The analytical formulation shows that the contact angle is a function of the interference FR, the incidence angle, the working distance from the droplet to the interference fringe, and the refractive indices (RI) of the liquid and the substrate. The contact angles in the range of 0 to 90 degrees are simulated for the droplets with a few millimeters in the radius and tens to thousands of micrometers in height. Secondly, different RI liquids are simulated (RI 1.0~2.0) to demonstrate the RI determination of the unknown liquids. The FR from the transmission fringe (TF) and the contact angles from the side view imaging can determine the RI of liquids in a unique way. This new optical detection technique can be used to determine the RI of unknown liquids with a simple optical setup, not requiring a sophisticated microscope. This technique can determine the contact angle of the liquids with known RI by measuring the fringe radius in a simple optical set-up of a TF formation. Furthermore, with a separately measured contact angle from sideview imaging, the RI of unknown liquids can be determined by the measured FR.