Equivalence of constant-height and constant-intensity images in scanning near-field optical microscopy

We present an analytical proof of the equivalence of scanning near-field optical images of small objects obtained by two alternative operating modes: (1) scanning at a constant distance from the mean plane of the surface and recording the detected intensity (constant-height images) and (2) keeping the detected intensity constant and recording the vertical motion of the tip (constant-intensity images). Numerical simulations with homogeneous and inhomogeneous samples illustrate this result.