Measurements monitoring the inductive coupling between oscillating radio-frequency magnetic fields and objects of interest create versatile platforms for non-destructive testing. The benefits of ultra-low-frequency measurements, i.e., below 3 kHz, are sometimes outweighed by the fundamental and technical difficulties related to operating pick-up coils or other field sensors in this frequency range. Inductive measurements with the detection based on a two-photon interaction in rf atomic magnetometers address some of these issues as the sensor gains an uplift in its operational frequency. The developments reported here integrate the fundamental and applied aspects of the two-photon process in magnetic induction measurements. In this paper, all the spectral components of the two-photon process are identified, which result from the non-linear interactions between the rf fields and atoms. For the first time, a method for the retrieval of the two-photon phase information, which is critical for inductive measurements, is also demonstrated. Furthermore, a self-compensation configuration is introduced, whereby high-contrast measurements of defects can be obtained due to its insensitivity to the primary field, including using simplified instrumentation for this configuration by producing two rf fields with a single rf coil.
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