Optimizing multiple beam interferometry in the surface forces apparatus: Novel optics, reflection mode modeling, metal layer thicknesses, birefringence, and rotation of anisotropic layers

Abstract

Multiple beam interferometry (MBI) evolved as a powerful tool for the simultaneous evaluation of thin film thicknesses and refractive indices in Surface Forces Apparatus (SFA) measurements. However, analysis has relied on simplifications for providing fast or simplified analysis of recorded interference spectra. Here, we describe the implementation of new optics and a generalized fitting approach to 4 × 4 transfer matrix method simulations for the SFA. Layers are described by dispersive complex refractive indices, thicknesses, and Euler angles that can be fitted, providing modeling for birefringent or colored layers. Normalization of data by incident light intensities is essential for the implementation of a fitting approach. Therefore, a modular optical system is described that can be retrofit to any existing SFA setup. Real-time normalization of spectra by white light is realized, alignment procedures are considerably simplified, and direct switching between transmission and reflection modes is possible. A numerical approach is introduced for constructing transfer matrices for birefringent materials. Full fitting of data to the simulation is implemented for arbitrary multilayered stacks used in SFA. This enables self-consistent fitting of mirror thicknesses, birefringence, and relative rotation of anisotropic layers (e.g., mica), evaluation of reflection and transmission mode spectra, and simultaneous fitting of thicknesses and refractive indices of media confined between two surfaces. In addition, a fast full spectral fitting method is implemented for providing a possible real-time analysis with up to 30 fps. We measure and analyze refractive indices of confined cyclohexane, the thickness of lipid bilayers, the thickness of metal layers, the relative rotation of birefringent materials, contact widths, as well as simultaneous fitting of both reflection and transmission mode spectra of typical interferometers. Our analyses suggest a number of best practices for conducting SFA and open MBI in an SFA for increasingly complex systems, including metamaterials, multilayered anisotropic layers, and chiral layers.