Figure 2. Adaptive fitting for enhanced resolution and accuracy.

Superposition fit to g⁽⁰⁾(x) = 1 (to calculate mass) using the first four modes of a doubly-clamped beam, showing the effect of measurement zone reduction. a, Initial superposition (black curve) before the initial values for the location and size of the particle are determined. After determination of the location and size of the particle, the measurement zone can be reduced. In this case, the position is determined to be near x/L = 0.35 (dotted vertical line) and a measurement zone smaller than the original is chosen (pink shaded area). This measurement zone (pink shaded area) is centred on the particle position and commensurate with particle size. With this reduction in measurement zone, a new superposition can be calculated (blue curve: solid is within zone, dashed is outside). b, Zoomed-in view of new superposition. Further reduction of the measurement zone by a factor of 10 leads to another superposition (green curve: solid is within zone, dashed is outside). This is again superior to the previous superposition (blue curve). c, Zoomed-in view of final superposition (dotted vertical line is the position of the particle). Error is reduced by six orders of magnitude from a.