Ultrasonic Interferometer

Ultrasonic Interferometer EED 104

INTRODUCTION:

Modern fast development of high-precision machinery construction, robotics and other

branches of technology demands an adequate progress on spatial metrology of

machines’ fast-moving parts. The accuracy of measurements required is 10-6 while

motion velocity of mechanical parts runs up to several meters per second.

Any solution of this problem is not possible without application of some new physical

and systematic principles. A subject of this investigation is the possibility to use

acoustic continuous wave process for high-precision absolute spatial measurements

performing with high speed.

An Ultrasonic Interferometer is a simple and direct device to determine the ultrasonic

velocity in solids, liquids and gases with a high degree of accuracy. The principle used

in the measurement of velocity (V) is based on the accurate determination of the

wavelength () in the medium. Ultrasonic waves of known frequency (f) are produced

by a quartz plate fixed at the bottom of the cell. These waves are reflected by a movable

metallic plate kept parallel to the

quartz plate. If the separation

between these two plates is exactly

a whole multiple of the sound

wavelength, standing waves are

formed in the medium. This

acoustic resonance gives rise to an

electrical reaction on the generator

driving the quartz plate and the anode current of the generator becomes maximum. If

the distance is now increased or decreased and the variation is exactly one half wave

length (/2) or multiple of it, anode current again becomes maximum. If the separation

between quartz plate and metallic plate is changed by d between two successive

maximum anode current, then

d = /2 … (1)

From the knowledge of wavelength (), the velocity (V) can be obtained by the relation:

V = × f =2df. … (2)


ULTRASONIC INTERFEROMETERMain idea of the technique proposed is the use of coherent running acoustic wave

propagation along homogeneous solid waveguide as a linear measuring scale. That is, a

special kind of ultrasonic interferometry is proposed as an application for high-precision

linear and (or) angular measurement.

An obvious advantage of

coherent running wave

interferometers as opposed to

any pulse system is the

possibility to provide high-

accurate phase measurements

with averaging over a lot of

wave periods. The proposed

principle is very close to

optical interferometry.

Advantages1) Most optical interferometric measurements are being performed in air. Index of

air refraction spatial and thermal instability is limiting the accuracy by the value

of 10-5 in any case. To perform these measurements in vacuum is not possible.

Any solid waveguide is much more stable, but solid waveguides can be used

only with the acoustic variant.

2) Because optical waves are very short (about 1 μm) in comparison to acoustic

ones, it is hardly possible to carry out optical interferometric measurement of

fast-changing distance. In this case the repetition rate of interferential

maximums is rather high for reliable acquisition and exact processing even for

any modern electronic system. Acoustic systems are free of these problems.

3) Acoustic elements and systems are much more simple and cheaper than optical

ones.


DisadvantagesA measurement technique using ultrasonic interferometry is described for non-contact,

quantitative measurement of acoustic vibrations. A pair of low-cost ultrasonic

transducers was used in a transmit–receive mode to direct a 40 kHz carrier wave to the

surface of a solid target vibrating acoustically, such as a speaker cone. Demodulation of

return signals consisted of a phase sensitive detection circuit to assess interference

between the carrier wave and return signal. Recovered signals were enhanced using

real-time digital signal processing hardware to improve signal-to-noise ratios for audio

vibration measurements. Phase resolution of at least 3.4 Mrads has been demonstrated

in the audio frequency range. This represented an equivalent displacement of 2.3 µm in

air.

PHYSICOCHEMICAL MEASUREMENTS

THE USE OF AN ULTRASONIC INTERFEROMETER

FOR MEASUREMENTS IN THE CRITICAL REGION OF

LIGHT AND HEAVY WATER

An interferometer and a procedure for measuring the velocity and absorption coefficient

of ultrasound in light and heavy water close to the critical point are developed.

Measurements of the velocity and absorption coefficient of ultrasound in the critical

region of the states of light and heavy water are not only of independent interest in

acoustics, but are also extremely important for the further development of the theory of

the liquid state (phase transitions, equations of states, and thermodynamic properties)

and for thermal-power engineering, physical chemistry, etc. However, the high critical

parameters of light and heavy water (Tc = 373.946°C, pc = 22.064 MPa and Tc =

370.74°C, pc = 21.671 MPa, respectively), and the high chemical activity and electrical

conductivity have made this region of these states extremely difficult to investigate. For

a correct check of the different theoretical hypotheses, data of systematic measurements

of the velocity and absorption coefficient of ultrasound of increased accuracy are


required, and the physical state of the water must be adequate for the measured

parameters. If one neglects to take into account the duration for which equilibrium is

established in the critical region, hysteresis phenomena occur. Hence, there is a need for

new instruments and procedures for investigating the velocity and absorption coefficient

of ultrasound at high temperatures and pressures of the water. Interferometer methods

can make a considerable contribution to solving these problems, since they enable

measurements to be made when there is high absorption of the ultrasonic energy.

However, existing methods of measuring the velocity and absorption coefficient by an

ultrasonic interferometer with one or two generating piezoelectric transducers, and with

one generating and one receiving piezoelectric transducers have a number of drawbacks.

In some cases, it is necessary to determine a large number of quantities and to draw

graphs, which complicates the calculation procedure and reduces the measurement

accuracy; in other cases, the presence of even small satellites on the response curve

leads to considerable errors; in the third cases, the measurements of the velocity and

absorption coefficient of ultrasound are shifted in time (the measurements are made

separately), and, consequently, their values relate to different states of the medium, or

these methods are insufficiently sensitive at high temperatures and pressures.

We were presented with the problem of designing an ultrasonic interferometer and

developing a procedure for measuring the velocity and absorption of ultrasound in light

and heavy water as a function of the temperature, pressure and frequency, in small steps

of their variations along different thermodynamic paths (isotherms and isochroous in the

liquid and vapour phases along the equilibrium line) in the critical region. The accuracy

of the measurements, for example, of the ultrasonic velocity should not be inferior to the

accuracy of measurements of the equilibrium or kinetic properties, which is necessary

for correct calculations and analysis of other properties (the adiabatic compressibility,

the second viscosity, dispersion of the velocity, relaxation time, etc.).

In the course of this research, we constructed and tested different types of

interferometers, operating in the standing-wave and traveling-wave modes, and also in

the pulsed mode. It turned out that only the interferometer operating in the traveling-

wave mode with a variable base and two piezoelectric transducers, placed directly in the

liquid or vapour phase of light or heavy water in an autoclave, is the most sensitive and

multifunctional for measurements in the region of the critical point. Due to its


insufficient sensitivity, an interferometer operating in the pulsed mode was unable to

measure the absorption of ultrasound in the critical region of water.

The main procedural, technological and apparatus solutions, required for measurements

in light and heavy water in the critical region are as follows. A search was made for the

material for the piezoelectric transducers, which, when in direct contact, would not

dissolve in the vapour or liquid phases of the water and possessed a high Curie point

and a high electromechanical coupling coefficient. Tests were made in small autoclaves

with water at high temperatures (up to 600°C) and pressures (up to 60 MPa) of lead

zirconate-titanate, quartz and lithium niobate with a contact duration of more than three

months. Whereas the first materials dissolved considerably, single crystals of lithium

niobate turned out to be insoluble, and no decomposition tracks or corrosion were

detected (a considerable change in the colour to light beige was observed, but a

cleavage surface always remained shiny), and they preserve their high sensitivity and

resonance properties under test.

The much higher electromechanical coupling coefficient of lithium niobate compared

with quartz enabled acceptable conditions for measuring the velocity and absorption

coefficient of ultrasound to be obtained. Moreover, lithium niobate did not change the

refractive index, transparency and electrical conductivity of the water.

These positive qualities of lithium niobate provided a basis for using it to manufacture

all the electrical insulation components inside the electrical leads and the autoclave.

Additional tests of different materials for use in the construction of the ultrasonic

interferometer (high-pressure electrical leads, the reduction gear, the mechanical parts

of the interferometer and the autoclave, the holders of the piezoelectric transducers, etc.)

showed that the most suitable constructional material is Kh18N10T stainless and acid-

resistant steel. The correspondence of the measured parameters to the physical state of

the sample of water ensured high accuracy in maintaining and measuring the

temperature and pressure, a small ballast volume, instrumental backup, and the

constructional features of the equipment. To measure the temperature, we used a

standard PTS-10 platinum resistance thermometer with an error of ±0.01°C and an

R348 potentiometer of accuracy class 0.002. The temperature in the autoclave with the

water sample was kept constant using a thermostat with an error of ±0.01°C. The

temperature gradient along the autoclave of length 30 cm at 400°C did not exceed


6×10–4K/cm. The pressure was measured with an MP-600 piston manometer of

accuracy class 0.05 through a mercury separator. We developed a construction of the

main parts of the continuous interferometer of variable base: an electromechanical

device for varying the base of the interferometer with high accuracy, and the electrical

part, required to obtain an acoustic signal and to provide the conditions for the

occurrence and monitoring of the superposition of the signals. The electromechanical

system and the electromagnet unit are shown schematically in Fig. 1. The main

supporting platform, on which all the components of the electromechanical system are

fastened, is the upper flange 1, which is hermetically connected to the autoclave by the

“cone on cone” method 2 without gaskets, which would degrade the purity of the water

being investigated. All the communications of the interferometers passed through it.

The mechanical part of the interferometer is placed inside the guiding cylinder 3,

connected with a flange. It consists of the reduction gear 4, which transfers rotational

motion to the micrometre screw 5, situated in the outer ring bearing 6, between which

there are spheres 7 of diameter 3.15 mm. The reduction gear is made of Kh18N10T

stainless steel and has a reduction factor of 9:1 with a 0.3 gear module. Particular

attention was given to the technology by which the micrometre screw was

manufactured, since the clearances, high ductility of the stainless steel, and the low

degree of cleanliness with which the surfaces were processed could produce vibrations

of the screw 5 and of the piston 8, leading to a reduction in the accuracy with which the

displacement of the piston is measured and a degradation of the conditions under which

the interference is obtained. Final processing of the screw (the seating in the bearing,

screw thread M10×0.5) was carried out on a cutting-polishing lathe with a diamond

instrument. The whole surface of the micrometre screw was chromium plated and after

this it was finished with GOI paste. To displace the piston by the micro shaft along the

axis of the cylinder, a guiding screw 10 was fastened to the latter, and a groove 9 was

cut in the piston. The surfaces of the cylinder and the piston, the screw threads of the

micrometre screw and the grooves on the piston, the seating of the screw and the

external ring bearing were lapped, chromium plated, and then polished in order to

increase the surface hardness and reduce friction.

The electrically conducting part of the interferometer, designed to supply (extract) the

electrical signal to the radiating piezoelectric transducer and the receiving piezoelectric


transducer, should provide reliable conditions for the transducer voltage to depend in a

stable manner on the base (the distance between the transducers). This relationship (the

response curve of the interferometer) is recorded on the tape of a recording instrument.

The water, since its electrical conductivity is independent of the degree of purity, may

considerably shunt the generator circuit and the input amplifier, while any unreliable

contact(even mechanical) may change the position of the “zero” level of the recording

instrument, which affects the accuracy of the measurements, particularly of the

absorption coefficient of ultrasound. This manifests itself as one approach the critical

point, where the absorption of the ultrasound has an anomalously rapid increase. To

reduce the effect of factors which reduce the sensitivity and accuracy of the

measurements, and to produce the conditions for measurements in the traveling-wave

mode, a clamp holder 11 of piezoelectric transducer 12 of lithium niobate of diameter

20 mm and thickness 7.2 mm (without backings) was attached to the lower part of the

piston. In order not to damp and not to reduce the sensitivity of the piezoelectric

Transducers, the latter were fastened in clamp holders in the nodal plane. The

interferometer was adjusted by the device 13. The signal on the transducers is applied

using springs 14, made of chromium-plated strips of stainless steel 0.08 mm thick

having low stiffness. The signal to the transducers is applied along thin wires 16

(platinum wires), which pass inside the insulators 15, made of lithium niobate. The

wires are screened with thin-walled tubes 17 of diameter 4 mm, made of stainless steel.

Beads 18 of lithium niobate are used to insulate the wires inside the tubes. A diamond

instrument was used to manufacture the insulators (cutting and boring). Reliable

vacuum-sealed packing of the electrical lead is achieved by connecting a “cone on

cone” connecting pipe 19, so that the inner wire passes freely through the flange.

It was necessary to develop a construction of the electrical lead which could withstand

high pressures and high temperatures, without degrading the degree of purity of the

water (impurities shift the critical point and introduce uncontrolled interference) and

reducing the effect of the electrical conductivity of the water. For this purpose, using a

tube (external diameter 4 mm and length 28 cm) of stainless steel 20, a high-pressure

electrical lead, based on a glass-metal joint, was taken out into the room-temperature

zone, and the free space was filled with a dielectric – lithium niobate (the second


Fig. 1. Sketch of the electromechanical part of the interferometer: 1) upper flange; 2)

conical packing; 3) guiding cylinder; 4) reduction gear; 5) micrometre screw; 6) ring

bearing; 7) spheres; 8) piston; 9) groove; 10) guiding screw; 11) clamp holder; 12)

piezoelectric transducers; 13) adjusting device; 14) springs; 15) insulators; 16) thin

wires; 17) thin-walled tubes; 18) beads; 19) connecting pipe; 20) rustproof tube; 21)

electric lead; 22) drop of molybdenum glass; 23) conical connecting pipe;

24) molybdenum wire; 25) electromagnet system; 26) armature; 27) electromagnet; 28)

side nonmagnetic sections of the armature; 29) central magnetic section; 30) weld

contour; 31) rustproof bearing; 32) capillary; 33) micro shaft; 34) shut-off valve; 35)

shut-off valve cone; 36) cone opening.


electrical lead, situated symmetrically with respect to the axis of the flange, is not

shown). The joint then does not lose its strength and remains hermetically sealed, the

glass does not leach out at low temperatures and does not affect the purity of the water,

while its shunting action is reduced. The tube 20 is connected hermetically to the

connecting pipe 19 and the body of the electrical lead 21 by argon-arc welding.

Hermetic sealing of the electric lead 21 is ensured by soldering a drop of molybdenum

glass 22 with a molybdenum wire 24 and a conical connecting pipe 23, made of kovar.

The kovar was sealed to the body of the electric lead by the “cone on cone” method. All

the touching surfaces of the components made of stainless steel were chromium plated,

thereby producing a reliable electrical contact. These constructions considerably

reduced the effect of the electrical conductivity of the water, and ensured that the

acoustic-electrical channel was sufficiently sensitive for extended measurements of the

velocity and absorption coefficient of the ultrasound (a requirement for measurements

in the critical region). The black dots in Fig. 1 indicate where the parts of the electrically

conducting wires are connected.

The purpose of the electromagnet unit 25 is to change the base of the interferometer and

it simultaneously performs two functions. First, dose setting and cleansing of the sample

of water and measurements of the pressure by the piston manometer through the

mercury separator are carried out through it by means of a stainless capillary tube with

an external diameter of 2.3 mm and a length of 50 cm. Second, it considerably reduces

the temperature gradients in the medium being investigated and enables rotation to be

transferred inside the autoclave using small torques (the micro shaft has no seal). This

unit(like all the hermetically sealed units and devices which are at room temperature)

should have a small ballast volume compared with the volume of the sample of water

being investigated. It consists of an armature 26, situated inside the hermetically sealed

body of nonmagnetic stainless steel. The armature rotates the electromagnet 27 (with an

angle of rotation counter), and takes the form of a three-section disk, the side sections

28 of which are made of Kh18N10T nonmagnetic steel, while the central section 29 is

made of 4Kh13 magnetic stainless steel.

The technology for manufacturing the armature is as follows. A groove is cut in a

previously turned blank of nonmagnetic stainless steel, into which the magnet section is

inserted. The sections, along the edges of which bevels have been removed, are tightly


clamped to one another and are joined along the contour 30 by argon-arc welding. After

this, the armature in the assembly is finally machined in the centres to the free

dimensions of the inner container of the body of the electromagnet and the armature is

secured in it using the bearing 31 of stainless steel. This enables the ballast volume (the

volume of water which is outside the measuring chamber), which would reduce the

measurement accuracy, to be reduced considerably. In order to ensure that the hermetic

seals hold at high temperatures and pressures, one end of the capillary 32 is welded to

the body of the electromagnet system 25 while the second is welded to the conical

connecting pipe 19. To transfer the rotational torque from the armature 26 to the input

shaft of the reduction gear 4, a micro shaft 33 with a diameter of 1.4 mm is inserted into

the capillary. One other function of the micro shaft is to expel liquid from the capillary

in order to reduce the ballast volume. The shut-off valve 34 is for evacuating and

supplying water when the cone 35 is raised through the opening 36 (the evacuating and

supply systems are disconnected from the shut-off valve during measurements and do

not produce any additional temperature gradients).

The electrical part of the interferometer consists mainly of instruments made by

commercial organizations. We will merely point out some procedural aspects which

enable correct measurements of the velocity and absorption coefficient of ultrasound to

be made in the critical region of such a specific object as water (with a large number of

anomalies), in which similar measurements have not so far been made. The absorption

of ultrasound is determined by the molecular structure of the material and its state, but it

is theoretically difficult to carry out a calculation specifically in the critical region,

where the relaxation processes are unusual. It is well known that only frequency and

temperature measurements of the velocity and absorption coefficient of ultrasound give

the main information for investigating relaxation processes.

We will describe in more detail the procedure for determining the velocity and

absorption coefficient of ultrasound using an interferometer with a variable base with

radiating and receiving piezoelectric transducers, operating in the traveling-wave mode.

In this case, unlike the standing-wave mode, due to the considerable absorption of the

ultrasound by the medium, there is no reaction on the radiator, which is due to the

reflected wave from the receiving piezoelectric transducer.


For this, it is necessary to satisfy the condition Re–2αl << 1, where R is the transmission

coefficient of the receiving piezoelectric transducer and l is the distance between the

transducers. The amplitude of the oscillations of the radiator ξ0 is then independent of l,

and we can obtain the following relation for the displacement and phase of the surface

of the receiving piezoelectric transducer:

ξ (l,t) = ξ0e- αl(1+2RCosɸ0+R2)1\2ei(ωt-kl+ɸ1)

Tanφ1 = R Sinφ0

1+RCosφ0

The receiving piezoelectric transducer is equivalent to a source of current Ieq(t) =

2eijSωiξ(l, t)/d, loaded with an admittance iωC0 + Z¿−1, where C0 is the inherent

capacitance of the piezoelectric transducer, Zin is the input impedance of the amplifier,

and eij is the piezoelectric constant of the transducer.

For the voltage on the receiving piezoelectric transducer, we obtain

U1(l, t) = 2eijS ωiξ(l , t)(iω C 0+Z¿

−1)d,

which can be represented in the form

U1(l, t) = U01(l)sin(ωt – kl + Φ01), (1)

where U01(l) = U0(1 + 2RcosΦ0 + R2)1/2e–αl = C1e–αl; U0 and Φ01 do not depend on the

distance l. It follows from (1) that, in the traveling-wave mode, the amplitude of the

voltage on the receiving piezoelectric transducer decreases exponentially as l increases

(it does not pulsate). As mentioned earlier, to measure the velocity and absorption

coefficient, two electric signals are applied to the input of the amplifier and are

summed: one from the receiving piezoelectric transducer with a voltage U1(l, t), and the

other a reference signal with voltage

U2(t) = U02 sin (ωt + Φ02)

from the generator attenuator. We will assume that the amplitude U02 and the initial

phase Φ02 of the reference voltage are constant, while the frequencies of the summed

voltages are the same (since the same generator is employed). We obtain for the

amplitude of the summed voltage

U0(l) = [C12e-2αl + U 02

2 + 2C1e-αl U02 Cos(kl + Δ Φ12)]1/2 (2)

where ΔΦ12 = Φ02 – Φ01, and U02 and Φ02 are independent of the interferometer base. It

follows from relation (2) that the amplitude of the summed signal is a quasi-periodic


function of the distance between the piezoelectric transducers with a period equal to the

wavelength λ, which can be determined from the response curve.

We will simplify the procedure for determining the theoretical formula for the

absorption coefficient of ultrasound. To do this, we will change from the expressions for

the voltage on the receiving piezoelectric transducer, the reference-signal voltage and

the summed voltage at the amplifier input to the corresponding levels of displacements

of the pen of the recording instrument (in view of the fact that they are proportional).

This holds provided the amplifier, detector and the dc amplifier are linear and the scale

of the recording instrument is also linear. Then, we can write the following expression

for the envelopes of the maxima and minima:

Ymax(l) = Y0 + Y1e–αl + Y2; Ymin(l) = Y0 – Y1e–αl + Y2, (3)

where Y0 is the displacement due to the constant component at the output of the dc

amplifier; Y1e–αl and Y2 are the displacements due to the voltage on the plates of the

receiving piezoelectric transducer and the reference voltage, respectively.


References

1. A. Aleksandrov, The Thermal Properties of Water and Water Vapour, Moscow,

(1999).

2. E. A. Kolesnikov, Ultrasonic Measurements, Moscow (1970).

3. G. Mikhailov,V. A. Solov’ev, and Yu. P. Syrnikov, Principles of Molecular

Acoustics, Moscow (1964).

4. Measurement Science Review, Volume 9, No. 6, 20095. Transducers of Linear Displacement, 2004.

Ultrasonic Interferometer

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