Backside absorbing layer microscopy: a universal relationship between physical thickness and reflectivity

Abstract

The Backside Absorbing Layer Microscopy (BALM) is a recently introduced surface imaging technique in reflected light with an unprecedented combination of sensitivity and lateral resolution, hence very promising for the development of imaging sensors. This requires to turn BALM images into quantitative measurements. The usual way to analyze reflectivity measurements is to compare the optical signal and a numerical model with many adjustable parameters. Here we demonstrate a universal relationship between the sample reflectivity and the physical thickness of the sample, ruled by three measurable quantities. Mapping the true sample thickness becomes possible whatever the instrument configuration and the sample refractive index. Application to kinetic measurements is discussed.

BALM: Watching the Formation of Tethered Bilayer Lipid Membranes with Submicron Lateral Resolution

“…The BALM reflectivity R(e) finds a real or virtual minimum (e min , R min ) for a low value of |e min | because the thickness e gold of the gold layer corresponds itself to a reflectivity minimum. In these conditions, it was shown that the BALM reflectivity obeys a parabolic variation with the thickness e of the added layer, 91 with (e min , R min ) being the minimum of this parabola. The position and amplitude of the parabola, and hence the values of e min and R min , are very sensitive to many factors, including the exact composition of the BALM substrate, the aperture of the microscope, the wavelength or the spectrum of the light source, the spectral response of the camera, and the refractive index of the solvent and of the added layer.…”

“…The key point is that the variation R ( e ) remains parabolic whatever the detail of all of the instrumental parameters. Based on this remark, the strategy proposed in ref was therefore not to try to precisely handle all of these parameters but to determine case-by-case the three parameters that govern the exact shape of the parabola. As long as the refractive index of the added layer remains constant, knowledge of the three parameters is sufficient to convert the measured reflectivity into quantitative thickness measurements.…”

“…In such conditions, the red signal is weakly nonlinear and closely resembles the SPR signal. Following Abou Khachfe et al, the BALM analysis lies on the fundamental equation …”

“…90 Recently, an universal relationship has been established between the BALM reflectivity and the physical thickness of a layer sample, ruled by three measurable quantities. 91 This relationship can be used without any knowledge of the microscope settings or the ARA coating in order to obtain a thickness map of the sample, whatever its (constant) complex refractive index, in a typical thickness range going from 0 to 30 nm. The thickness unit can be further determined with the help of a single reference measurement.…”

“…The performance of the technique was already demonstrated by imaging 2D flakes of various materials, by following, in situ and in real time, their evolution upon small-molecule adsorption or by detecting in operando the electrochemical reduction of individual sub-10 nm nanoparticles . Recently, a universal relationship was established between the BALM reflectivity and the physical thickness of a layer sample, ruled by three measurable quantities . This relationship can be used without any knowledge of the microscope settings or the ARA coating to obtain a thickness map of the sample, whatever its (constant) complex refractive index, in a typical thickness range going from 0 to 30 nm.…”