In apertureless near-field optical microscopy the vertical dithering of the tip, associated with demodulation at higher harmonics , allows us to suppress the far-field background, providing artifact free elastic scattering images. This paper analyzes, both theoretically and experimentally, the physical origin of the background signal at the different harmonics and the mechanisms underlying its rejection for the general case of propagative-field illumination. We show that Fourier components of the background must be expected at every harmonic, evidencing why demodulation at higher harmonics is not an inherently background-free technique, and assessing the experimental conditions in which it becomes like that. In particular, we put forward the fundamental roles of both the harmonic order and the tip oscillation amplitude in the background suppression mechanisms. Furthermore, we outline how the lock-in detection of the signals amplitude can enhance the nonlinear dependence of the background on the tip-sample distance. Such effect provides a more subtle source of topography artifacts since the optical maps become qualitatively uncorrelated from the topographic counterpart, requiring an upgrade of the criteria to assess the absence of artifacts from the optical maps.
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Here is considered as the ratio between the BKG amplitude and the amplitude of the dc component calculated in the small oscillations approximation .
The periodicity is exactly halved only if the offset is null.
