TY - JOUR

T1 - Applying differential wave-front sensing and differential power sensing for simultaneous precise and wide-range test-mass rotation measurements

AU - Meshksar, Neda

AU - Mehmet, Moritz

AU - Isleif, Katharina Sophie

AU - Heinzel, Gerhard

N1 - Funding Information: This research was funded by ETH Research Grant ETH-05 16-2 and the Max Planck Society (MPG) in the framework of the LEGACY cooperation on low-frequency gravitational wave astronomy (M.IF.A.QOP18098) and Deutsche Forschungsgemeinschaft (DFG) within Sonderforschungsbereich (SFB) 1128 Relativistic Geodesy and Gravimetry with Quantum Sensors (geo-Q), projects A06,A07, and Germany?s Excellence Strategy Grant No. EXC-2123 QuantumFrontiers?390837967.

PY - 2021/1

Y1 - 2021/1

N2 - We propose to combine differential wave-front sensing (DWS) and differential power sensing (DPS) in a Mach-Zehnder type interferometer for measuring the rotational dynamics of a test-mass. Using the DWS method, a high sensitive measurement of 6 nrad Hz−1/2 in sub-Hz frequencies can be provided around the test-mass nominal position (±0.11 mrad), whereas the measurement of a wide rotation range (±5 mrad) is realized by the DPS method. The interferometer can be combined with deep frequency modulation (DFM) interferometry for measurement of the test-mass translational dynamics. The setup and the resulting interferometric signals are verified by simulations. An optimization algorithm is applied to find suitable positions of the lenses and the waist size of the input laser in order to determine the best trade of between the slope of DWS, dynamic range of DPS, and the interferometric contrast. Our simulation further allows to investigate the layout for robustness and design tolerances. We compare our device with a recent experimental realization of a DFM interferometer and find that a practical implementation of the interferometer proposed here has the potential to provide translational and rotational test-mass tracking with state-of-the-art sensitivity. The simple and compact design, and especially the capability of sensing the test-mass rotation in a wide range and simultaneously providing a high-precision measurement close to the test-mass nominal position makes the design especially suitable for example for employment in torsion pendulum setups.

AB - We propose to combine differential wave-front sensing (DWS) and differential power sensing (DPS) in a Mach-Zehnder type interferometer for measuring the rotational dynamics of a test-mass. Using the DWS method, a high sensitive measurement of 6 nrad Hz−1/2 in sub-Hz frequencies can be provided around the test-mass nominal position (±0.11 mrad), whereas the measurement of a wide rotation range (±5 mrad) is realized by the DPS method. The interferometer can be combined with deep frequency modulation (DFM) interferometry for measurement of the test-mass translational dynamics. The setup and the resulting interferometric signals are verified by simulations. An optimization algorithm is applied to find suitable positions of the lenses and the waist size of the input laser in order to determine the best trade of between the slope of DWS, dynamic range of DPS, and the interferometric contrast. Our simulation further allows to investigate the layout for robustness and design tolerances. We compare our device with a recent experimental realization of a DFM interferometer and find that a practical implementation of the interferometer proposed here has the potential to provide translational and rotational test-mass tracking with state-of-the-art sensitivity. The simple and compact design, and especially the capability of sensing the test-mass rotation in a wide range and simultaneously providing a high-precision measurement close to the test-mass nominal position makes the design especially suitable for example for employment in torsion pendulum setups.

KW - Deep frequency modulation interferometry

KW - Differential power sensing

KW - Differential wave-front sensing

KW - Test-mass readout

KW - Torsion balance

UR - http://www.scopus.com/inward/record.url?scp=85098569487&partnerID=8YFLogxK

U2 - 10.3390/s21010164

DO - 10.3390/s21010164

M3 - Letter

C2 - 33383766

AN - SCOPUS:85098569487

VL - 21

JO - Sensors (Switzerland)

JF - Sensors (Switzerland)

SN - 1424-8220

IS - 1

M1 - 164

ER -