As stated above, the detection mechanism is that ultrasonic pressure waves cause strains in the optical fiber, thus modulating the phase of the light passing through the fiber. The fiber-based Michelson and Mach-Zehnder interferometers used to measure the strains are shown in . The sensing arm contains the segment wound around the sensor, while the reference arm contains a segment wound on a piezoceramic cylinder. Low-frequency thermal fluctuations and external perturbations cause phase drift between the two arms, leading to light intensity fluctuations at the output. These are compensated with a negative feedback circuit, providing voltage to the piezoceramic cylinder in the reference arm. The feedback circuit responds to audio and lower frequency fluctuations, so there is no signal loss in the ultrasound range. The gain and dc offset of the feedback voltage are adjusted to maintain a phase difference of 90° between the two arms. If the light intensity in each arm is I0
, any small strain ΔL
induced by the ultrasonic waves results in a phase change Δ
in the sensing arm and a change in the light output of the interferometer ΔI
where λ is the laser wavelength within the optical fiber, and ΔL
is much smaller than λ.
FIG. 1 Fiberized laser interferometers used to measure the ultrasound-induced strain in the fiber-optic sensors. (A) Mach-Zehnder interferometer. The high coherence light from the laser is split into the reference arm and the sensor arm, then recombined. The (more ...)
Two different sensor designs are tested. In the first design,8
a single-mode optical fiber is wound in a helix and glued to a thin flexible backing disk. The design is shown in . For testing, the sensor is immersed in a water tank. Ultrasonic waves produced in the tank may cause volumetric expansion and compression of the backing disk (the breathing mode), or they may cause it to wobble. Both forms of deformation change the strain in the fiber disk, which is detected by the interferometer.
Design of first sensor. The optical fiber is wound into a planar disk and glued to a backing disk of polyethylene.
A limitation of the planar disk geometry is that glass-core optical fibers have minimum bending diameters of 5 mm or larger. In order to keep the thickness of the fiber disk small compared to the acoustic wavelength, only one or two layers of fiber can be used. To wind a sufficient length of fiber to improve sensitivity, the diameter of the disk needs to be 25 mm or larger. This is larger than most single element probes used in medical ultrasound. The thin flexible backing disk may also change shape when pressed against the sample, thus changing the acoustic profile of the sensor.
The second design overcomes these limitations by manipulating the ultrasound wave-front. In this design, the optical fiber is wound into a cylinder. Placed inside the cylinder is a coaxial conical reflector, with the tip of the cone facing the incoming ultrasonic wave (). When immersed in the test tank, incoming waves propagating parallel to the axis of the cylinder are reflected radially outward toward the cylindrical surface of the fiber spool. If the angle of the cone is 45°, an incoming planar wavefront is reflected into a cylindrically-outgoing wavefront, and impacts the fiber cylinder simultaneously. The overall length change in the fiber is the sum of the changes in all the turns of the cylinder, which magnifies the signal many fold. This geometry also allows the sensor diameter to be as small as 5 mm, the minimum bending diameter of the fiber.
Design of second sensor. The optical fiber is wound on a thin polyethylene cylinder. A coaxial aluminum cone ultrasound reflector is inserted into the cylinder to direct the ultrasonic wavefront toward the fiber cylinder.
In a more robust construction, the fiber is wound around a solid cylindrical form with a cone-shaped hollowing at one end (). The form is made of a plastic material with acoustic impedance similar to water. The plastic-air interface of the cone serves as the reflector. The reflection is nearly complete since the acoustic impedance of air is orders of magnitude lower than that of solid material. To receive an ultrasound signal from an object such as tissue, all that is necessary is to make a good acoustic contact between the object and the flat end of the form. Compared to the immersion design in , there is some sensitivity loss from the acoustic impedance mismatch between the plastic material and water. This loss can be recovered with impedance matching layer(s).
Practical construction of second design. The optical fiber is wound on a plexiglass cylinder with a conical hollowing in the back as the ultrasound reflector.
The sensitivity of the cylindrical sensors can be estimated from the relationship between the ultrasound pressure and changes in the radius of the fiber cylinder. Consider a plane wave of pressure P incident on the sensor. Denote the acoustic impedance of the cylinder as Z, the number of turns of the fiber as N, the linear Young’s modulus of the fiber as Y (force-strain ratio along the fiber), the laser wavelength in the fiber as λ, the radius of the cylinder as R, the pressure-induced radius change as ΔR, and the stretch in the fiber length as ΔL. The incident plane wave is reflected by the cone and propagates radially to the fiber cylinder (). Because of this process, the pressure on the cylinder decreases from P at the base level of the cone to near zero at the tip level of the cone. For approximate estimates, the average pressure on the cylinder is taken as P/2. To obtain the change of radius ΔR under this pressure, one needs to include the constrictive pressure on the cylinder by the expansion of the fiber spool. This pressure is
The incident pressure on the cylinder wall will approximately balance the sum of this and the internal stress associated with the radial strain in the cylinder:
The laser phase change can be expressed as
It should be noted that all the fiber-optic sensors described here are displacement based—displacements in the medium directly translate into fiber length changes. As expressed in Eq. (1)
, this results in a proportional change in the light output of the laser interferometer. Because displacements are proportional to pressure divided by frequency, the sensitivity of the sensors in radians per unit pressure decreases with frequency. This is seen in the measurements described below. Other mechanical and optical factors that may affect the performance of the sensors at higher frequencies will be described later in the Discussion section.