Measurement of contact angles of microscopic droplets by focal length method

We present a method to measure contact angles of microscopic droplets with a conventional microscope that possesses a precision focus adjustment stage. The droplets are modeled as spherical caps that act as lenses. Their focal length is determined by measuring the distance from the substrate surface to the level where a sharp image of the aperture stop is observed. The lens diameter is found by edge detection of a microscope image of the microdroplets. The spherical cap model relates the focal length and diameter of such lenses to the contact angle of the used liquid with known refractive index. The measurement procedure was applied to condensed water droplets on a silicon substrate covered by its native oxide layer. The results are found to be in good agreement with conventional, goniometric sessile drop measurements of the advancing contact angle.