Heterodyne detection is most common technique in apertureless scattering near-field optical microscopy (A-SNOM), because it can get better signal-to-noise ration (S/N ratio) than the homodyne detection. Fore-researchers provided a rough way to express the heterodyne detection signals in order to avoid the complicated interference signal expressions. Therefore, the explanation is not clear and missing much information in signal processing. In this study, we analyze and verify the amplitude and phase of heterodyne detection signals in complete interference model which including the tip enhancement phenomena and tip reflective background electric field in different harmonics of tip vibration frequency. From our analytical results, we propose meaningful concepts: (1) the high order harmonic tip scattering noise decays faster with high order Bessel function in small phase modulation depth than the near-field interaction signal; (2) longer wavelength and smaller incident angle of incident electric field has better signal contrast, and it opposites traditional optical microscope about shorter wavelength has better resolution.
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