Small displacement measurements with subatomic resolution by beat frequency measurements

Abstract

In this paper a novel method for high-resolution measurement of displacements with sub-atomic resolution is described. With this method, a length change of an optical resonator is directly transformed to a radio-frequency signal. A tunable He–Ne laser is locked to a mode of the resonator using a digital signal processing technique. Heterodyne mixing of this locked laser with an iodine-stabilized He–Ne laser converts the frequency of the laser locked to the cavity into the radio-frequency region. A HF counter measures the beat frequency from which the displacement can be derived directly. This method delivers inherent linearity and sub-nanometre resolution of the displacement over a range of several micrometres. An example of the capabilities of this system is given in this paper, where it is used for checking periodic deviations of a laser interferometer system. Emphasis is put on the construction of the optical resonator, on how its narrow resonance line-width is achieved, and how the required mechanical stability is achieved. The measurement range and the scale linearity are discussed in detail. Possible applications of this method are the calibration of nano-position systems based on PZT transducers, as well as inductive and capacitive sensors.