Calibrating interference microscopes by measuring the equilibrium shape and contact angle of fluid drops

摘要

Abstract: Calibration of the axial response of interference microscopes has received considerable attention in the past two decades. In addition to systematic errors which could be caused by components in the microscope or measurement technique, a numerical correction factor associated with imaging at high apertures must be determined. Unfortunately, the cost of reference height standards increases sharply with their spatial homogeneity and calibration accuracy and these standards may be easily contaminated and therefore require sophisticated cleaning and re-calibration. To address these problems, we have investigated the interferometric measurement of the equilibrium shape of static fluid drops on coated substrates. For drops with small Bond number (the Bond number is a ratio of gravitational to capillary forces), the surface of the drop forms a spherical cap. It appears that nature forms a highly smooth, curved surface. By varying the surface energy, it is possible to obtain a wide range of static contact angles. For example, silicone oil $LB@polydimethylsiloxane (PDMS)$RB on glass forms a contact angle of about 5 degrees, while it forms an angle of 38 degrees on Teflon and 68 degrees on a fluorinated silicon surface. We have measured contact angles as large as 68 degrees for PDMS on a single crystal silicon wafer with a 50 $MUL@/0.8 NA objective using a custom-made phase-shifted, laser feedback microscope. The method for preparing these static drops is simple and we envision that microscopists will be able to prepare easily disposable calibration standards in their laboratories. !13