Approaching attometer laser vibrometry

The heterodyne two-beam interferometer has been proven to be the optimal solution for laser-Doppler vibrometry (LDV) regarding accuracy and signal robustness. The theoretical resolution limit for a two-beam interferometer of laser class 3R (up to 5 mW visible measurement-light) is in the regime of a few femtometer per square-root Hertz and well suited to study vibrations in microstructures. However, some new applications of radio-frequency microelectromechanical (RF-MEM) resonators, nanostructures, and surface-nano-defect detection require resolutions beyond that limit. The resolution depends only on the photodetector noise and the sensor sensitivity to specimen displacements. The noise is already defined in present systems by the quantum nature of light for a properly designed optical sensor and more light would lead to an inacceptable influence like heating of the tiny specimen. Noise can only be improved by squeezed-light techniques which require a negligible loss of measurement light which is impossible to realize for almost all technical measurement tasks. Thus, improving the sensitivity is the only path which could make attometer laser vibrometry possible. Decreasing the measurement wavelength would increase the sensitivity but would also increase the photon shot noise. In this paper, we discuss an approach to increase the sensitivity by assembling an additional mirror between interferometer and specimen to form an optical cavity. A detailed theoretical analysis of this setup is presented and we derive the resolution limit, discuss the main contributions to the uncertainty budget, and show a first experiment proving the sensitivity and resolution improvement of our approach.