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We present an interferometric technique for measuring ultrasmall tilts. The information of a tilt in one of the mirrors of a modified Sagnac interferometer is carried by the phase difference between the counter-propagating laser beams. Using a small misalignment of the interferometer, orthogonal to the plane of the tilt, a bimodal (or two-fringe) pattern is induced in the beam’s transverse power distribution. By tracking the mean of such a distribution, using a split detector, a sensitive measurement of the phase is performed. With 1.2 mW of continuous-wave laser power, the technique has a shot noise limited sensitivity of 56 frad/Hz−−−√ and a measured noise floor of 200 frad/Hz−−−√ for tilt frequencies above 2 Hz. A tilt of 200 frad corresponds to a differential displacement of 4.0 fm in our setup. The novelty of the protocol relies on signal amplification due to the misalignment and on good performance at low frequencies. A noise floor of about 70 prad/Hz−−−√ is observed between 2 and 100 mHz.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Optics Letters, volume 42, issue 13, in 2017 following peer review. This article may not exactly replicate the final published version. The definitive publisher-authenticated version is available online at

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