Calibration of a fan-shaped beam surface plasmon resonance instrument for quantitative adsorbed thin film studies—No metal film thickness or optical properties required

A popular instrument configuration for the fast tracking of the resonance angle position during time-dependent surface plasmon resonance (SPR) measurements uses stationary optics, a convergent or divergent fan-shaped beam from a light source of finite spectral bandwidth, and an array photodetector to simultaneously cover a range of incident angles. This type of instrument must be properly calibrated for quantitative thin film studies to determine an exact relationship between the angle of the incident light and the detector pixel element that the light strikes upon reflection from the metal sensing surface. A simple method is presented to calibrate a divergent fan-shaped light beam instrument that produces reflectivity curves that include both the critical (Θcrit) and resonance (Θmin) angles in aqueous-based solution. Unlike previously reported calibrations, the method does not require additional hardware (precision goniometer) or knowledge of the thickness and optical properties of the surface plasmon-supporting metal layer. The proposed approach is based on the dependence of the position of the critical angle edge on the dielectric constant (or refractive index) of the contacting solution. Pixel–incident angle relations are established by relating the critical angle positions of the experimental reflectivity curves with those generated using standard Fresnel thin film calculations. The accuracy of the pixel–angle relation obtained using Θcrit is compared with the relation obtained using Θmin, the position used in literature reports for calibration purposes. The pixel–angle relation derived using the bulk refractive index variation of Θcrit is applied to quantify the change in film thickness that results upon the electrochemical oxidation of a self-assembled monolayer (SAM) of ferrocenyldodecanethiolate on gold.