Development of a MEMS Xylophone Bar Magnetometer Using Optical Interferometry for Detection
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(1).
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Mat. Res. Soc. Symp. Proc. Vol. 605 © 2000 Materials Research Society
In this expression, Icis the bar length, I is the bar current, B is the magnitude of the magnetic field, and E is the angle between I and B. The Lorentz force generates an orthogonal displacement of the xylophone bar, do, which alternates at the frequency of the driving current, f, and is expressed by ddC
2 2 d [l1- (f / fo) ] + (f / Qfo)
2 .(2)
In Eq. 2, fo is the fundamental resonance frequency of the bar, 0 is the resonance quality factor, and ddocis the midpoint deflection at constant current [5]. The latter parameter is proportional to the product of the cube of the bar length and the magnitude of the Lorentz force. Therefore, Eqs. 1 and 2 show that the magnetic force,
which is directed orthogonal to the bar surface, will cause the bar to vibrate at the frequency of the driving current with an amplitude that is linearly proportional to the drive current , magnetic field, and the mechanical quality factor of the resonator. Under nano- to micro-Tesla operation, it has been determined that the displacement of a miniature xylophone bar via the Lorentz force is on the order of 1 to 10 A at the resonance frequency of the bar [5]. Therefore, the use of an optical transduction mechanism for detection of the xylophone bar deflection must be able to sense and resolve bar displacements that are significantly less than the wavelength of optical radiation. In the previous xylophone bar magnetometer investigations, a simple optical beam deflection approach was demonstrated to have nanoTesla field sensitivity when using a high Q, 5 mm x 0.5 mm x 0.125 mm copper beryllium (CuBe) xylophone bar [3]. The sub-A and nanoTesla sensitivity was obtained by placing a position sensitive detector a
-e
distance of 20 centimeters from the bar surface and detecting the reflected intensity from the beam
Detector
Feedback and
surface. This transduction approach relies on the use of long reflection distances to the detector, since the angular deflection at the detector is linearly proportional to the separation
between
the
detector
and
stabilization electronics
is
the
long
,
,
Beam splitter Las1
9_ Reference miror
bar.
on piezoelectric stage
Therefore, a true limiting factor for the nanoTesla sensitivity in optical beam deflection
Output ectopuc
ylophone drive
electronics
distance
I bXp
between the detector and xylophone bar and not the xylophone bar dimensions. An alternative transduction Figure 1. Schematic of the path-stabilized Michelson used inthe magnetometer studies. scheme to the beam deflection interferometer Details of the experimental setup are discussed inthe approach is optical interferometry, text. which relies on the ability to detect
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The optical path length differences rather than angular beam displacements. interferometric platform provides for significantly smaller sensor systems relative to optical beam deflection technology. In addition, a recent review of bar displacement transduction technologies has sh
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