Fiber-optic directional sensor schematic.
(Left): Diagram of the two-fiber probe showing input and collection fibers, the normal gap distance D, and the distance T between the fiber probe center and the edge of the reflector. (Right): Plan-view diagram showing rotational misalignment of the edge reflector by an angle φ. The equations give the rate of optical power change with reflector translation along the X and Y axes for small values of φ.
Measured detected light power level versus distance T between the fiber probe center and the reflector's edge (here φ ∼ 0).
Geometry used for development of the analytic model for predicting the cantilever tip displacement in response to a plane acoustic wave traveling in the x direction.
log10 of the cantilever tip displacement versus acoustic frequency computed with analytic model (solid line) and finite-element model (dashed line), and log10 of the particle displacement in the acoustic wave (dotted line) for solid rod cantilever in water and no attachment or viscous loss. The 345 μm radius, 2 cm long rod is made from a material with E of 4.5 GPa and ρ of 2200 kg/m3.
Plan and side views of the experimental arrangement used to measure the acoustic response of the cantilever-probe directional sensor versus frequency in air.
(a) log10 of cantilever tip displacement for a normally incident acoustic wave versus frequency (solid line) and log10 of acoustic wave particle displacement (dashed line) for a 4.86 cm long, 1.666 mm diameter acrylic rod cantilever in air having attachment loss γ att = 15 s−1: analytic (solid line); measurements (crosses). (b) Normalized sensor response at 200 Hz versus the angle θ between the acoustic wave direction and the normal to the cantilever axis: cos θ (solid line); measurements (crosses).
log10 of the forces as computed analytically for a 4.86 cm long, 1.666 mm diameter acrylic cantilever in a fluid with no attachment loss versus acoustic frequency: (a) In air and (b) in water. Applied acoustic drag force (solid line); applied acoustic gradient force (dashed line).
log10 of the cantilever tip displacement versus acoustic frequency with flow force included (solid line) and no flow force (dashed line) for the 4.86 cm long, 1.666 mm diameter acrylic rod cantilever with no attachment loss: (a) In water and (b) In air.
Cross section of the two-fiber probe (upper) and the design for a proposed five-fiber probe for displacement measurement in two orthogonal directions (lower). The reflector is shown only for the five-fiber probe. (The five fiber design effectively has two two-fiber probes along each axis.)
Minimum detectable sound pressure levels for 4.86 cm long, 1.67 mm diameter acrylic cantilever with two-fiber probe for various limiting factors.
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