Pure modulation and accurate measurement of optical beam's tilt and displacement

We developed a tilt modulation technique of a laser beam with a wedged crystal. Combined with a phase-compensating crystal, a pure tilt modulation with a wide bandwidth (actually determined by the bandwidth of electro-optic crystals) is realized. By Fourier transformation with a lens, the tilt signal is transformed into displacement. With homodyne detection using a local oscillator of the first-order Hermite-Gauss mode (HG₁₀) and a 4F phase-monitoring system, we measure the displacement and tilt of a laser probe beam. This technique can be used in metrology, such as Newtonian gravitational constant determination and gravitational wave detection, or the calibration of a spatial sensor, such as tilt/displacement sensors.