- Email: [email protected]
Continuous recording of ultrasonic velocity by laser Bragg diffraction
Continuous recording of ultrasonic velocity by laser Bragg diffraction S. ITO, K. YONEDA,
T. OKURA,
S. HATTORI
A method for improving the measuring accuracy of ultrasonic wave velocities in a liquid sample is given. This utilizes the Bragg diffraction angle. Continuous recording of the ultrasonic velocity for a continuously varying sample temperature is also described. An analogue of the Czerny-Turner mount in the grating monochromater is used for the determination of the angle of diffraction. A frequency modulated ultrasonic wave produces an oscillating photo-electric signal from a diffracted light component incident on a photomultiplier tube. Using this signal, the peak point in the intensity distribution of the component is determined with extremely high accuracy. Applying the phase-sensitively detected output of this signal to a servo motor which drives the angle of a plane mirror (replacing the grating in the Czerny-Turner mount), gives automatic tracking of the angle of diffraction. This in turn allows the possibility of continuous recording of the velocity dispersion as a function of sample temperature.
The phenomenon of light diffraction in a transparent medium perturbed by externally introduced ultrasonic waves provides information about the acoustical and optical properties of the medium. With the development of laser technology, many experimental techniques which take advantage of a monochromatic, high intensity light source have been proposed for the investigation and application of this phenomenon.lt2 Because a narrow light beam can be obtained from a laser, and the measurements performed without having to use an ultrasonic receiver, the light diffraction method becomes advantageous in the higher frequency range or at higher sample viscosities where the attenuation of the ultrasonic wave is greater. It is thus reasonable that optical methods have been gathering much attention. Ultrasonic techniques have so far played a very important role in research on relaxation processes. This is because they fulfill the experimental condition that the time scale of measurement must be much shorter than the time scale of the structural rearrangement considered.3 With the development of ultrasonic techniques, the measuring accuracy in these regions has been much improved in recent S. Ito and S. Hattori are with the Faculty of Engineering, Nagoya University, Nagoya, Japan. K. Yoneda is with the Faculty of Science and Engineering, Meijyo University, Nagoya, Japan. T. Okura is with the Japan Spectroscopic Company Ltd. Hachioji, Tokyo, Japan. Received 1 January 1973.
OPTICS AND LASER TECHNOLOGY.
OCTOBER
1973
years.4 The information required, that is the ultrasonic absorption and velocities in the medium, is also given by the angular broadening and the angle of diffraction. Optical methods have not been considered of primary importance in the field of ultrasonic relaxation study, despite the advantages already mentioned. This is because of their poor accuracy. For instance, in 1965 McSkimin measured sound velocities with errors less than 0.008% by the acoustic phase comparison method,4 while in 1967 Gordon and Cohen measured them with 0.3% errors;l the measurements by Mori and Suminokura in 1969 are the best with a laser light source. 5 We have thus engaged in studies to refine the accuracy of angle of diffraction measurements. This paper describes the techniques used, and the results of continuous recording of velocity dispersion curves. Apparatus for measuring the angle of diffraction Light diffracted by ultrasonic waves in a liquid medium has an angular distribution corresponding to the aberration of the optical system, the diffraction limited divergence of the incident light source, and also the amplitude attenuation of ultrasonic waves in the sample. Thus the most important consideration in improving the measuring accuracy of the angle of diffraction is the method of finding and determining the angle at which the intensity of the diffracted light component takes maximum value.
221
(PotentioneterH II
Fig.1
Schematic
t?ecorderl
diagram of the experimental
apparatus
To refine the accuracy, an analogue of the Czerny-Turner mount in the grating monochromater and a frequency modulated ultrasonic wave are used. Fig.1 shows a schema‘tic diagram of the experimental apparatus. The light beam from slit one is collimated by the first concave mirror and is focused again by second concave mirror onto slit two. The two concave mirrors both have focal lengths of 680 mm. Images of light components of different diffraction orders from the liquid cell that have been focused by the second concave mirror fall on the second slit in turn - analogous to the different spectral components in a grating monochromater. A rotating plane mirror replaces the grating of the Czerny-Turner monochromater. The revolving table on which the plane mirror is fixed is connected to a stage driven by a micrometer screw-gauge through a bar 300 mm in length. Revolving angles of the plane mirror can be read on the scale of the micrometer screw-gauge which is made to have backlash less than 2 pm. The plane mirror and the liquid cell are revolved by an interlocking mechanism. This keeps the liquid cell in the Bragg condition, in which incident and diffracted light wave vectors are arranged symmetrically to the ultrasonic wave vector for any angle of diffraction. As shown in Fig.2, the increment of rotation angle which lets one of the diffracted light beam components pass through the second slit is one half the increment of the diffraction angle. The increment of the Bragg angle is also one half that of the angle of diffraction. Thus the Bragg condition is always satisfied if the liquid cell is rotated in the same direction as the plane mirror with the ratio 1 : 1. Since the angle of diffraction is proportional to the ultrasonic frequency, the frequency modulated ultrasonic wave causes the angle of diffraction of the beam to oscillate with the same period as the modulation signal. When such a beam illuminates the photomultiplier placed behind the fixed slit, an ac component having the modulation frequency appears on the photomultiplier tube output, superimposed on the dc component which is nearly proportional to the light intensity. The ac component is proportional to the derivative of the angular intensity distribution curve of the diffracted light component. The phase-sensitively detected ac component of the photo-current with reference to the modulation signal is thus proportional to the deviation of the centre of the angular distribution from the second slit position. For the ultrasonic transducer, an x-cut crystal of
222
7.950 MHz fundamental by the third harmonic.
frequency
was used. It was driven
It should be noted here that the position of the zero order diffracted light component cannot be determined by this method. Therefore the angle between the + 1 order diffracted components, namely twice the angle of diffraction, is measured. However, this is favourable when we apply the Raman-Nath equation to the relation between the micrometer screw-gauge readings and the ultrasonic velocities (see the appendix). The variation of the photomultiplier tube output due to the electrically induced light intensity fluctuation of the source and to the angular vibration mechanically induced from the ultrasonic transducer is not distinguishable from the pertinent signal when this method is used. It is thus necessary to adjust the centre frequency of the fm oscillator carefully to the resonance frequency of the transducer. If this adjustment is not made, measured values contain a noticeable error. Measurement
of diffraction
angles
The rotation angle of the revolving table is measured in terms of the micrometer screw-gauge reading between centres of the + 1 and - 1 order diffracted components. Both the frequency modulation and phase sensitive detection method and the ordinary dc photo-detection method were used, and eight measurements made in each case. The former and the latter gave a peak centre separation 2 and a root mean square deviation (ar) rms of 3.0170 f 0.0005 and 3.0178 + 0.0021 respectively. This result indicates the extent of the improvement in measuring accuracy, and allows us to claim a 0.02% accuracy for the present method. Although special precautions are taken to obtain mechanical resetability of the revolving table bearing and of the contact point between the bar and the micrometer screw-gauge, it is these factors which limit the reproducibility of the measurement.
The ultrasonic
wave velocity is given by:
(1) where F,, is the frequency of the ultrasonic wave, X is the wavelength of the light source in air, I is the micrometer
mirror
Fig.2 Interlocking of liquid cell and plane mirror. This ensures that the Bragg condition is satisfied for any diffraction angle
OPTICS AND LASER TECHNOLOGY.
OCTOBER
1973
Table 1. Comparisonofknown and measured valuesof uhrasonicvelocity in distilled water. v ub - known ValUeS quoted from a paper by Greenspan and e, schiegg;6 Vmeas values determined by using the optical diffraction method; T - measured temperature of distilled water; F - centre frequency of the frequency modulated ultrasonic wave; / - micrometer screwgauge reading (used in obtaining the effective bar length L); s - diffraction angle which corresponds to the value of /
T
F
I
[MHz1
[mm]
Vpub s [ms-'1 [103rad]
vmeas
ctl 10.0
23.901
3.089
1447.6 10.45
1447.2
11.0
23.900
3.078
1451.5 10.41
1452.3
12.0
23.900
3.074
1455.3 10.40
1453.2
13.0
23.901
3.066
1459.1 10.37
1458.1
14.0
23.918
3.060
1462.7 10.35
1462.0
15.0
23.916
3.051
1466.3 10.32
1466.2
16.0
23.908
3.041
1469.7 10.29
1470.5
17.0
23.908
3.035
1473.1 10.27
1473.4
18.0
23.907
3.029
1476.4 10.25
1476.3
19.0
23.906
3.021
1479.6 10.22
1480.1
20.0
23.905
3.015
1482.7 10.20
1483.0
[ms-ll
screw-gauge. As one can see in Fig. 1, once the plane mirror comes up to the required position - that which gives a light output between two maximum slope points of the angular distribution of a diffracted light component incident on the second slit - a closed servo-control loop operates so as to keep the centre of the angular distribution at the second slit. To test the operation of the servo-control loop, artificial disturbance experiments were made. The results are shown in Fig.3. The ordinate indicates the reading of the micrometer screw-gauge. This corresponds linearly to the abscissa of the diffracted light component’s angular distribution curve, which is shown together with the record
screw-gauge reading in mm, Lo is the length of the bar in mm, and (cos cr/cos Gs)is an instrumental constant defined in the appendix. The last constant is hard to measure, but it is acceptable to regard it as a constant through,out the measurement. An effective bar length L, defined as: cos
cl
(2)
L=L,-cos 6s
is calculated from the measured micrometer readings and known ultrasonic velocities in distilled water at various temperatures. Measured temperatures, the ultrasonic frequencies, and the micrometer readings are listed in the first three columns in Table 1. Known ultrasonic velocities taken from the paper by Greenspan and Tschiegg 6 are listed in the forth column. From these values of F. and Y the best-fit value of L is found to be 295.578 -+0.007 mm. From this L value the ultrasonic velocities for the measurement are recalculated using (1); they are listed in the fifth column. From comparison of the known with the measured velocities in Table 1, one can see the overall accuracy of the ultrasonic velocity measurement is greatly improved by using the optical diffraction method.
R@sponse ot servo
Artificial
offset
ZO&bmkOOl4
mradl
-
Continuous recording of velocity dispersions The output of the phase sensitive detector is converted to the line frequency ac signal by a chopper. This line frequency error signal is amplified and connected to the control input of a servo motor which drives the micrometer
OPTICS
AND
LASER
TECHNOLOGY.
OCTOBER
1973
Record of the output of the potentiometer that is connected Fig.3 directly to the micrometer screw-gauge, showing the response of the servo system. Above is the angular intensity distribution of the diffracted light component; the angle along its abscissa corresponds to the ordinate of the record
223
in Fig.3. The cause functions used for the disturbance experiment are additional line frequency signals. These have a rectangular pulse envelope which is just sufficient to offset from the equilibrium point one and then the other maximum slope point in the angular distribution curve. The response is composed of one overshoot, then one backshoot; the slow exponential response has a time constant of 0.5 min, and the shift of the equilibrium point corresponds to about 1.6 pm. The latter obviously originates from the play in the whole mechanical transmission system, and results in unavoidable errors in the continuous recording of ultrasonic velocities. Determining the origin of the slow response is more difficult. However, it will only give rise to an error of 0.5 pm at most in the case of the rapidly changing ultrasonic velocities. In addition to the response to a pulse disturbance, the record in Fig.3 shows random noise around the equilibrium point. This has a value of about 1.4 pm rms. The output voltage of the potentiometer that is directly connected to the micrometer screw-gauge gives a continuous recording of the ultrasonic wavelength. Meanwhile, the temperature of the sample liquid changes slowly, a thermostat being employed. The resulting record gives a sort of dispersion curve provided the relaxation time of the sample liquid undergoes a temperature dependent change across a certain time - that which corresponds to the period of the ultrasonic wave in the temperature range of the record. The mean square amplitude of the noise shows a dependence on the ultrasonic power. It is assumed that it can be decomposed into the ultrasonic power dependent part which is obviously caused by the light intensity fluctuation due to the ultrasonic power induced density fluctuation of the sample liquid, the mechanically induced disturbance of the servo control loop, and the electronic noise. Reduction of the ultrasonic power results in reduction of the response speed of the servo control system and in the increase in disturbance of the servo control system due to the decrease of loop gain. Consequently, the optimum value of the ultrasonic power is chosen so as to minimize the resultant random fluctuation of the servo control system. The speed of temperature change can be so chosen that the corresponding speed of change of wavelength accompanying the temperature dispersion does not exceed the slow response of the apparatus. The error in the recorded wavelength then amounts to 0.11%. 0.05% of it comes from the resetability uncertainty of the mechanical system, and 0.04% comes from the random fluctuation of the servo control system. The remainder should be attributed to uncertainty in the zero level determination of the coordinate that corresponds to the centre of the zero order component’s angular distribution. Conclusion An attempt to improve the measuring accuracy of the ultrasonic wave velocity by a Bragg diffraction method has been described. An analogue of the Czerny-Turner mount of the grating monochromater was used. Zero indication of the centre of the diffracted light distribution was given by a phase sensitively detected light intensity with reference to a modulation signal of ultrasonic wave frequency. The root mean square deviation of the measured ultrasonic velocity in distilled water from the known values was 0.6 m set-l . This corresponds to an accuracy of 0.04%.
224
It Fig.4 Relation between the micrometer screw-gauge scale readings and the rotation of the plane mirror. The arrow indicates the direction of movement of the micrometer screw-gauge in measurement. Lo is the bar length. An effective bar length L is defined in (2)
Apparatus for the continuous recording of ultrasonic wavelength versus temperature of the sample liquid was constructed. It was confirmed that it worked successfully within an error of 0.11%.
Acknowledgements The authors are greatly indebted to A. Nishiwaki, E. Uchida, M. Tawada, and M. Yamanoi for many fruitful discussions in the course of this work.
Appendix The Raman-Nath
equation is:
h sin 8 + sin $ = A
(Al)
where 0 is the angle of incidence between the ultrasonic plane wave and the incident light beam in medium, r#~is the angle between. the direction of the outgoing light and the ultrasonic plane wave, and A and A are the wavelengths of the ultrasonic wave and the incident light respectively. When the Bragg condition is fulfilled, 8 is equal to I$, so that the diffraction angle s is equal to 26 or 24:
2
sin ? =
1
2
A
642)
However, in experiment this condition is accompanied by some.error. If there is a small constant deviation 6s from the condition, the ratio of (Al) and (A2) is:
{sin
5
(t+&)
+sin
tF-6s)
f2sin;
co&
OPTICS AND LASER TECHNOLOGY.
(A3)
OCTOBER
1973
Therefore the true value of X/A is related to 4 as follows:
2sin i COSSS= ;
and an angle s, that is 5 = s = 4. Therefore, the following relation is obtained from (A4) and (AS):
(A4) (A@
On the other hand, in a Czerny-Turner mount, the relation between the micrometer screw-gauge scale 1 and the rotation angle of the plane mirror 5 is given by the following equation (Fig.4): 1 -
5 = 2sin z cos (Y
References Cordon, E. I., Cohen, M. G. ‘High-resolution Brillouin scattering’ Whys Rev 153 (1967) 201-‘207 U&i&, N. ‘Direct measurement of photoelastic coefficients by an ultrasonic light diffraction technique. Jup JAppZ P/zys 8 (1969) 329-333 Mason, W. P.: Physical Acoustics Vol 2 Part A (Academic Press, 1965) 282-349 McSkimin, H. J. ‘Variations of the ultrasonic pulse superposition method for increasing the sensitivity of delay-time measurement.’ JAcousf Sot Am 37 (1965) 864-871 Mori, H., Suminokura, T., Suzuki, T. ‘An interferometric method for measuring ultrasonic light diffraction spectra and its application to the measurements of sound velocity and absorp tion’. Ohyo Butsuri (The Japanese Society of Applied Physics) 38 (1969) 112661132 Greenspan, M., Tschiegg, C. E. ‘Tables of the speed of sound in water’, JAcoust Sot Am 31 (1959) 75-76
(A5)
LO
where Lo indicates the bar length, and (Yis the angle between the direction perpendicular to the micrometer screw-gauge movement and the bar position where the penetrated light peak passes through the second slit. When the angle between *I diffraction order components is measured, it corresponds to the rotation angle of the plane mirror, the half value of the two-fold diffraction angle,
n
~~~~~~~~~
The development of techniques for dielectric measurement at high frequencies (1 to 1000 GHz) is relatively recent; the application of these techniques to the characterization and standardization of materials has scarcely begun. There is, therefore, much to be learned and much to be discussed.
Hl4h1 1
I Dielectric
1
Thus was the background to a tutorial conference, held at the UK’s National Physical Laboratory in March 1972, the proceedings of which have now been oublished under the title H&h Freauencv Dielectric Measurerner&. The book contains twenty papers covering the following topics: -
I
dielectric measurements on liquids at frequencies between 250 MHz and 170 GHz
Measurement
transmission methods for the measurement of dielectric loss
1
optical materials for the submillimetre waveband
-
closed cavity methods
microwave open resonators thin-film
dielectric
measurements
spectroscopic
measurements
This book fills an important gap in the literature on dielectrics, and is one volume that you should have on your bookshelf. Price $26 a CODVfrom IPC Science and Technoloav Press Ltd (ref: OE3). IPC House, 32 High Street, Guildford, Surrey GUl 3EW,
J. Chamberlain
OPTICS AND LASER TECHNOLOGY.
-
1 time-domain
Edited by
and G.W.Chantry
1
submillimetre-wave techniques
1
OCTOBER
England.
1973
225
T. OKURA,
S. HATTORI
A method for improving the measuring accuracy of ultrasonic wave velocities in a liquid sample is given. This utilizes the Bragg diffraction angle. Continuous recording of the ultrasonic velocity for a continuously varying sample temperature is also described. An analogue of the Czerny-Turner mount in the grating monochromater is used for the determination of the angle of diffraction. A frequency modulated ultrasonic wave produces an oscillating photo-electric signal from a diffracted light component incident on a photomultiplier tube. Using this signal, the peak point in the intensity distribution of the component is determined with extremely high accuracy. Applying the phase-sensitively detected output of this signal to a servo motor which drives the angle of a plane mirror (replacing the grating in the Czerny-Turner mount), gives automatic tracking of the angle of diffraction. This in turn allows the possibility of continuous recording of the velocity dispersion as a function of sample temperature.
The phenomenon of light diffraction in a transparent medium perturbed by externally introduced ultrasonic waves provides information about the acoustical and optical properties of the medium. With the development of laser technology, many experimental techniques which take advantage of a monochromatic, high intensity light source have been proposed for the investigation and application of this phenomenon.lt2 Because a narrow light beam can be obtained from a laser, and the measurements performed without having to use an ultrasonic receiver, the light diffraction method becomes advantageous in the higher frequency range or at higher sample viscosities where the attenuation of the ultrasonic wave is greater. It is thus reasonable that optical methods have been gathering much attention. Ultrasonic techniques have so far played a very important role in research on relaxation processes. This is because they fulfill the experimental condition that the time scale of measurement must be much shorter than the time scale of the structural rearrangement considered.3 With the development of ultrasonic techniques, the measuring accuracy in these regions has been much improved in recent S. Ito and S. Hattori are with the Faculty of Engineering, Nagoya University, Nagoya, Japan. K. Yoneda is with the Faculty of Science and Engineering, Meijyo University, Nagoya, Japan. T. Okura is with the Japan Spectroscopic Company Ltd. Hachioji, Tokyo, Japan. Received 1 January 1973.
OPTICS AND LASER TECHNOLOGY.
OCTOBER
1973
years.4 The information required, that is the ultrasonic absorption and velocities in the medium, is also given by the angular broadening and the angle of diffraction. Optical methods have not been considered of primary importance in the field of ultrasonic relaxation study, despite the advantages already mentioned. This is because of their poor accuracy. For instance, in 1965 McSkimin measured sound velocities with errors less than 0.008% by the acoustic phase comparison method,4 while in 1967 Gordon and Cohen measured them with 0.3% errors;l the measurements by Mori and Suminokura in 1969 are the best with a laser light source. 5 We have thus engaged in studies to refine the accuracy of angle of diffraction measurements. This paper describes the techniques used, and the results of continuous recording of velocity dispersion curves. Apparatus for measuring the angle of diffraction Light diffracted by ultrasonic waves in a liquid medium has an angular distribution corresponding to the aberration of the optical system, the diffraction limited divergence of the incident light source, and also the amplitude attenuation of ultrasonic waves in the sample. Thus the most important consideration in improving the measuring accuracy of the angle of diffraction is the method of finding and determining the angle at which the intensity of the diffracted light component takes maximum value.
221
(PotentioneterH II
Fig.1
Schematic
t?ecorderl
diagram of the experimental
apparatus
To refine the accuracy, an analogue of the Czerny-Turner mount in the grating monochromater and a frequency modulated ultrasonic wave are used. Fig.1 shows a schema‘tic diagram of the experimental apparatus. The light beam from slit one is collimated by the first concave mirror and is focused again by second concave mirror onto slit two. The two concave mirrors both have focal lengths of 680 mm. Images of light components of different diffraction orders from the liquid cell that have been focused by the second concave mirror fall on the second slit in turn - analogous to the different spectral components in a grating monochromater. A rotating plane mirror replaces the grating of the Czerny-Turner monochromater. The revolving table on which the plane mirror is fixed is connected to a stage driven by a micrometer screw-gauge through a bar 300 mm in length. Revolving angles of the plane mirror can be read on the scale of the micrometer screw-gauge which is made to have backlash less than 2 pm. The plane mirror and the liquid cell are revolved by an interlocking mechanism. This keeps the liquid cell in the Bragg condition, in which incident and diffracted light wave vectors are arranged symmetrically to the ultrasonic wave vector for any angle of diffraction. As shown in Fig.2, the increment of rotation angle which lets one of the diffracted light beam components pass through the second slit is one half the increment of the diffraction angle. The increment of the Bragg angle is also one half that of the angle of diffraction. Thus the Bragg condition is always satisfied if the liquid cell is rotated in the same direction as the plane mirror with the ratio 1 : 1. Since the angle of diffraction is proportional to the ultrasonic frequency, the frequency modulated ultrasonic wave causes the angle of diffraction of the beam to oscillate with the same period as the modulation signal. When such a beam illuminates the photomultiplier placed behind the fixed slit, an ac component having the modulation frequency appears on the photomultiplier tube output, superimposed on the dc component which is nearly proportional to the light intensity. The ac component is proportional to the derivative of the angular intensity distribution curve of the diffracted light component. The phase-sensitively detected ac component of the photo-current with reference to the modulation signal is thus proportional to the deviation of the centre of the angular distribution from the second slit position. For the ultrasonic transducer, an x-cut crystal of
222
7.950 MHz fundamental by the third harmonic.
frequency
was used. It was driven
It should be noted here that the position of the zero order diffracted light component cannot be determined by this method. Therefore the angle between the + 1 order diffracted components, namely twice the angle of diffraction, is measured. However, this is favourable when we apply the Raman-Nath equation to the relation between the micrometer screw-gauge readings and the ultrasonic velocities (see the appendix). The variation of the photomultiplier tube output due to the electrically induced light intensity fluctuation of the source and to the angular vibration mechanically induced from the ultrasonic transducer is not distinguishable from the pertinent signal when this method is used. It is thus necessary to adjust the centre frequency of the fm oscillator carefully to the resonance frequency of the transducer. If this adjustment is not made, measured values contain a noticeable error. Measurement
of diffraction
angles
The rotation angle of the revolving table is measured in terms of the micrometer screw-gauge reading between centres of the + 1 and - 1 order diffracted components. Both the frequency modulation and phase sensitive detection method and the ordinary dc photo-detection method were used, and eight measurements made in each case. The former and the latter gave a peak centre separation 2 and a root mean square deviation (ar) rms of 3.0170 f 0.0005 and 3.0178 + 0.0021 respectively. This result indicates the extent of the improvement in measuring accuracy, and allows us to claim a 0.02% accuracy for the present method. Although special precautions are taken to obtain mechanical resetability of the revolving table bearing and of the contact point between the bar and the micrometer screw-gauge, it is these factors which limit the reproducibility of the measurement.
The ultrasonic
wave velocity is given by:
(1) where F,, is the frequency of the ultrasonic wave, X is the wavelength of the light source in air, I is the micrometer
mirror
Fig.2 Interlocking of liquid cell and plane mirror. This ensures that the Bragg condition is satisfied for any diffraction angle
OPTICS AND LASER TECHNOLOGY.
OCTOBER
1973
Table 1. Comparisonofknown and measured valuesof uhrasonicvelocity in distilled water. v ub - known ValUeS quoted from a paper by Greenspan and e, schiegg;6 Vmeas values determined by using the optical diffraction method; T - measured temperature of distilled water; F - centre frequency of the frequency modulated ultrasonic wave; / - micrometer screwgauge reading (used in obtaining the effective bar length L); s - diffraction angle which corresponds to the value of /
T
F
I
[MHz1
[mm]
Vpub s [ms-'1 [103rad]
vmeas
ctl 10.0
23.901
3.089
1447.6 10.45
1447.2
11.0
23.900
3.078
1451.5 10.41
1452.3
12.0
23.900
3.074
1455.3 10.40
1453.2
13.0
23.901
3.066
1459.1 10.37
1458.1
14.0
23.918
3.060
1462.7 10.35
1462.0
15.0
23.916
3.051
1466.3 10.32
1466.2
16.0
23.908
3.041
1469.7 10.29
1470.5
17.0
23.908
3.035
1473.1 10.27
1473.4
18.0
23.907
3.029
1476.4 10.25
1476.3
19.0
23.906
3.021
1479.6 10.22
1480.1
20.0
23.905
3.015
1482.7 10.20
1483.0
[ms-ll
screw-gauge. As one can see in Fig. 1, once the plane mirror comes up to the required position - that which gives a light output between two maximum slope points of the angular distribution of a diffracted light component incident on the second slit - a closed servo-control loop operates so as to keep the centre of the angular distribution at the second slit. To test the operation of the servo-control loop, artificial disturbance experiments were made. The results are shown in Fig.3. The ordinate indicates the reading of the micrometer screw-gauge. This corresponds linearly to the abscissa of the diffracted light component’s angular distribution curve, which is shown together with the record
screw-gauge reading in mm, Lo is the length of the bar in mm, and (cos cr/cos Gs)is an instrumental constant defined in the appendix. The last constant is hard to measure, but it is acceptable to regard it as a constant through,out the measurement. An effective bar length L, defined as: cos
cl
(2)
L=L,-cos 6s
is calculated from the measured micrometer readings and known ultrasonic velocities in distilled water at various temperatures. Measured temperatures, the ultrasonic frequencies, and the micrometer readings are listed in the first three columns in Table 1. Known ultrasonic velocities taken from the paper by Greenspan and Tschiegg 6 are listed in the forth column. From these values of F. and Y the best-fit value of L is found to be 295.578 -+0.007 mm. From this L value the ultrasonic velocities for the measurement are recalculated using (1); they are listed in the fifth column. From comparison of the known with the measured velocities in Table 1, one can see the overall accuracy of the ultrasonic velocity measurement is greatly improved by using the optical diffraction method.
R@sponse ot servo
Artificial
offset
ZO&bmkOOl4
mradl
-
Continuous recording of velocity dispersions The output of the phase sensitive detector is converted to the line frequency ac signal by a chopper. This line frequency error signal is amplified and connected to the control input of a servo motor which drives the micrometer
OPTICS
AND
LASER
TECHNOLOGY.
OCTOBER
1973
Record of the output of the potentiometer that is connected Fig.3 directly to the micrometer screw-gauge, showing the response of the servo system. Above is the angular intensity distribution of the diffracted light component; the angle along its abscissa corresponds to the ordinate of the record
223
in Fig.3. The cause functions used for the disturbance experiment are additional line frequency signals. These have a rectangular pulse envelope which is just sufficient to offset from the equilibrium point one and then the other maximum slope point in the angular distribution curve. The response is composed of one overshoot, then one backshoot; the slow exponential response has a time constant of 0.5 min, and the shift of the equilibrium point corresponds to about 1.6 pm. The latter obviously originates from the play in the whole mechanical transmission system, and results in unavoidable errors in the continuous recording of ultrasonic velocities. Determining the origin of the slow response is more difficult. However, it will only give rise to an error of 0.5 pm at most in the case of the rapidly changing ultrasonic velocities. In addition to the response to a pulse disturbance, the record in Fig.3 shows random noise around the equilibrium point. This has a value of about 1.4 pm rms. The output voltage of the potentiometer that is directly connected to the micrometer screw-gauge gives a continuous recording of the ultrasonic wavelength. Meanwhile, the temperature of the sample liquid changes slowly, a thermostat being employed. The resulting record gives a sort of dispersion curve provided the relaxation time of the sample liquid undergoes a temperature dependent change across a certain time - that which corresponds to the period of the ultrasonic wave in the temperature range of the record. The mean square amplitude of the noise shows a dependence on the ultrasonic power. It is assumed that it can be decomposed into the ultrasonic power dependent part which is obviously caused by the light intensity fluctuation due to the ultrasonic power induced density fluctuation of the sample liquid, the mechanically induced disturbance of the servo control loop, and the electronic noise. Reduction of the ultrasonic power results in reduction of the response speed of the servo control system and in the increase in disturbance of the servo control system due to the decrease of loop gain. Consequently, the optimum value of the ultrasonic power is chosen so as to minimize the resultant random fluctuation of the servo control system. The speed of temperature change can be so chosen that the corresponding speed of change of wavelength accompanying the temperature dispersion does not exceed the slow response of the apparatus. The error in the recorded wavelength then amounts to 0.11%. 0.05% of it comes from the resetability uncertainty of the mechanical system, and 0.04% comes from the random fluctuation of the servo control system. The remainder should be attributed to uncertainty in the zero level determination of the coordinate that corresponds to the centre of the zero order component’s angular distribution. Conclusion An attempt to improve the measuring accuracy of the ultrasonic wave velocity by a Bragg diffraction method has been described. An analogue of the Czerny-Turner mount of the grating monochromater was used. Zero indication of the centre of the diffracted light distribution was given by a phase sensitively detected light intensity with reference to a modulation signal of ultrasonic wave frequency. The root mean square deviation of the measured ultrasonic velocity in distilled water from the known values was 0.6 m set-l . This corresponds to an accuracy of 0.04%.
224
It Fig.4 Relation between the micrometer screw-gauge scale readings and the rotation of the plane mirror. The arrow indicates the direction of movement of the micrometer screw-gauge in measurement. Lo is the bar length. An effective bar length L is defined in (2)
Apparatus for the continuous recording of ultrasonic wavelength versus temperature of the sample liquid was constructed. It was confirmed that it worked successfully within an error of 0.11%.
Acknowledgements The authors are greatly indebted to A. Nishiwaki, E. Uchida, M. Tawada, and M. Yamanoi for many fruitful discussions in the course of this work.
Appendix The Raman-Nath
equation is:
h sin 8 + sin $ = A
(Al)
where 0 is the angle of incidence between the ultrasonic plane wave and the incident light beam in medium, r#~is the angle between. the direction of the outgoing light and the ultrasonic plane wave, and A and A are the wavelengths of the ultrasonic wave and the incident light respectively. When the Bragg condition is fulfilled, 8 is equal to I$, so that the diffraction angle s is equal to 26 or 24:
2
sin ? =
1
2
A
642)
However, in experiment this condition is accompanied by some.error. If there is a small constant deviation 6s from the condition, the ratio of (Al) and (A2) is:
{sin
5
(t+&)
+sin
tF-6s)
f2sin;
co&
OPTICS AND LASER TECHNOLOGY.
(A3)
OCTOBER
1973
Therefore the true value of X/A is related to 4 as follows:
2sin i COSSS= ;
and an angle s, that is 5 = s = 4. Therefore, the following relation is obtained from (A4) and (AS):
(A4) (A@
On the other hand, in a Czerny-Turner mount, the relation between the micrometer screw-gauge scale 1 and the rotation angle of the plane mirror 5 is given by the following equation (Fig.4): 1 -
5 = 2sin z cos (Y
References Cordon, E. I., Cohen, M. G. ‘High-resolution Brillouin scattering’ Whys Rev 153 (1967) 201-‘207 U&i&, N. ‘Direct measurement of photoelastic coefficients by an ultrasonic light diffraction technique. Jup JAppZ P/zys 8 (1969) 329-333 Mason, W. P.: Physical Acoustics Vol 2 Part A (Academic Press, 1965) 282-349 McSkimin, H. J. ‘Variations of the ultrasonic pulse superposition method for increasing the sensitivity of delay-time measurement.’ JAcousf Sot Am 37 (1965) 864-871 Mori, H., Suminokura, T., Suzuki, T. ‘An interferometric method for measuring ultrasonic light diffraction spectra and its application to the measurements of sound velocity and absorp tion’. Ohyo Butsuri (The Japanese Society of Applied Physics) 38 (1969) 112661132 Greenspan, M., Tschiegg, C. E. ‘Tables of the speed of sound in water’, JAcoust Sot Am 31 (1959) 75-76
(A5)
LO
where Lo indicates the bar length, and (Yis the angle between the direction perpendicular to the micrometer screw-gauge movement and the bar position where the penetrated light peak passes through the second slit. When the angle between *I diffraction order components is measured, it corresponds to the rotation angle of the plane mirror, the half value of the two-fold diffraction angle,
n
~~~~~~~~~
The development of techniques for dielectric measurement at high frequencies (1 to 1000 GHz) is relatively recent; the application of these techniques to the characterization and standardization of materials has scarcely begun. There is, therefore, much to be learned and much to be discussed.
Hl4h1 1
I Dielectric
1
Thus was the background to a tutorial conference, held at the UK’s National Physical Laboratory in March 1972, the proceedings of which have now been oublished under the title H&h Freauencv Dielectric Measurerner&. The book contains twenty papers covering the following topics: -
I
dielectric measurements on liquids at frequencies between 250 MHz and 170 GHz
Measurement
transmission methods for the measurement of dielectric loss
1
optical materials for the submillimetre waveband
-
closed cavity methods
microwave open resonators thin-film
dielectric
measurements
spectroscopic
measurements
This book fills an important gap in the literature on dielectrics, and is one volume that you should have on your bookshelf. Price $26 a CODVfrom IPC Science and Technoloav Press Ltd (ref: OE3). IPC House, 32 High Street, Guildford, Surrey GUl 3EW,
J. Chamberlain
OPTICS AND LASER TECHNOLOGY.
-
1 time-domain
Edited by
and G.W.Chantry
1
submillimetre-wave techniques
1
OCTOBER
England.
1973
225