Near-field microscopy offers the opportunity to reveal optical contrast at deep subwavelength scales. In scanning near-field optical microscopy (SNOM), the diffraction limit is overcome by a nanoscopic probe in close proximity to the sample. The interaction of the probe with the sample fields necessarily perturbs the bare sample response, and a critical issue is the interpretation of recorded signals. For a few specific SNOM configurations, individual descriptions have been modeled, but a general and intuitive framework is still lacking. Here, we give an exact formulation of the measurable signals in SNOM which is easily applicable to experimental configurations. Our results are in close analogy with the description Tersoff and Hamann have derived for the tunneling currents in scanning tunneling microscopy. For point-like scattering probe tips, such as used in apertureless SNOM, the theory simplifies dramatically to a single scalar relation. We find that the measured signal is directly proportional to the field of the coupled tip-sample system at the position of the tip. For weakly interacting probes, the model thus verifies the empirical findings that the recorded signal is proportional to the unperturbed field of the bare sample. In the more general case, it provides guidance to an intuitive and faithful interpretation of recorded images, facilitating the characterization of tip-related distortions and the evaluation of novel SNOM configurations, both for aperture-based and apertureless SNOM.