Figure 4: Fringe-spacing analysis based on simplified non-planar RICM.
(a) Simplified non-planar RICM image formation model. The intensity I(x) is produced by the interference of rays I1 and I2, which correspond to the single set of complementary rays I0 with the maximum OPLD (determined by geometric parameters S(xβ), β and θR defined at position xβ) among all possible contributions (shaded area). Complementary I0 originate from within the illumination cone (θ1≤αIA, where αIA is given by the illumination numerical aperture, INA, of the microscope); then, they are reflected back from planar (substrate/layer 1 at x) and non-planar (layer 1/object at xβ) interfaces producing rays I1 and I2, respectively, which interfere at position x only if they are incident within the cone of detected light (θ2≤αDA, where αDA is determined by the numerical aperture, NA, of the objective). (b) The formulation of the simplified non-planar RICM model is completed when NRL/non-NRL regimes are identified at OPLDmax, as illustrated with a normalized OPLD plot for the range of detection angles corresponding to a series of wedge inclination angles with INA=0.48 and water surroundings. (c) Despite the intrinsic fringe-spacing variability, which produces the scattered data points, the behaviour of ΔSPf/Δxf with inclination angle observed in simulations from several different wedge systems is in excellent agreement with equation (4), where INA, n1 (surroundings composition) and θR (reflected light regime) are the main parameters. (d) Percentage error of inclination angles retrieved from the averages of all fringe-spacing values originated from simulations of comparable wedge systems. Closed and open symbols represent βretrieved, using NRL and non-NRL models, respectively. In all figures, simulations are performed with numerical aperture=1.25 for wedge angles ranging from 0° to βmax.
