The accuracy of measuring confined fluid properties using white light interferometry

Thin-film interferometry (type: Fabry-Pérot) with visible white-light illumination can detect sub-nanometer changes in optical path and, therefore, be utilized to study the thickness and refractive index (RI) of nano-confined fluids at a typical resolution ≤ λ/104. This type of white light interferometry is understandably at the core of the surface forces apparatus technique, where two mica sheets with identical thickness (e.g., 1-5 µm) are used to confine a fluid between their surfaces at nanometer separations and measure surface forces as a function of surface separation. In this context, the absolute accuracy of white light interferometry has received little attention historically, although accuracy is the key limiting factor for certain types of experiments, such as the measurements of RI of nanometer thin fluid films. At its root, the accuracy of interferometric RI measurement critically depends on exactly detecting secondary spectral modulations. The following spectral evaluation requires a theory based on an interferometer definition that consists of accurate values for thickness and dispersive RI for all optical layers involved. This work aims at complementing the partially existing literature toward a systematic treatment of the most relevant accuracy-limiting factors; in addition, systematic errors in the interferometer definition include the choice of dispersive RI mathematical model or other experimentally variable factors like the mechanical deformations occurring inside the interferometer under the influence of surface forces. We conclude that an accurate optical description of the layers contributing most to the optical path (e.g., mica surfaces) is currently the leading source of systematic error and that the present methodology of thin film interferometry is not sufficiently accurate to detect and quantify a change of density <10% in a nanometer confined fluid.