Fabry–Perot metrology for displacements up to 50 mm

Abstract

A system designed to apply Fabry-Perot interferometry to the measurement of displacements is described. Two adjacent modes of a Fabry-Perot cavity are probed, and both the absolute optical frequencies and their difference are used to determine displacements via changes in cavity length. Light is coupled to the cavity via an optical fiber, making the system ideal for remote sensing applications. Continuous interrogation is not necessary, as the cavity length is encoded in the free spectral range. The absolute uncertainty is determined to be below 10 pm, which for the largest displacement measured corresponds to a relative uncertainty of 4 x 10(-10). To my knowledge this is the smallest relative uncertainty in a displacement measurement ever demonstrated.

Accurate Gouy phase measurement in an astigmatic optical cavity

“…Additional sources of uncertainty are the presence of the nearby TEM 20 and TEM 02 modes (Fig. 2), which slightly shift the laser lock point from the TEM 11 resonance frequency, and parasitic cavities [25,26] which can also shift the resonances. We estimate (type B evaluation) these contributions to be 0:03 lrad and 0:06 lrad, respectively.…”

Comb mode filtering silver mirror cavity for spectroscopic distance measurement

“…The input mirror M 1 was flat and the output mirror M 2 was set to 150 mm from the first one and had radius of curvature of 800 mm. The laser modes were mode matched to the cavity 23 with a lens pair, with focal lengths of 200 mm and 150 mm, placed in front of the input mirror. The beam waist at the input mirror was 390 µm.…”

“…The resulting cavity finesse is approximately 166. 23 To decrease the effects of thermal expansion, the cavity mirror's layers were made on fused silica substrates of 12.3 mm diameter. The mirrors were coated homogeneously by the deposition technique on the RF magnetron sputtering 30 with silver over the 11 mm diameter of each substrate.…”

Study of a large range metrological atomic force microscope applied for calibration of a vertical PZT stage

“…. Calibration systems for nanosensors or stages have been successfully demonstrated by using X-ray interferometry [1], laser Fabry-Perot method [2][3][4] and laser interferomtry with enhanced interpolation resolutions [5][6][7][8][9]. Among these systems, a moving target attached on a PZT stage is commonly used as a measuring mirror with respect to the reference mirror in the optical interferometric configuration to introduce an optical path change in the measuring optical beam and the movement of the PZT stage can then be properly calibrated.…”