Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement
This paper addresses the problem of experimental verification of a recently proposed two-probe method for displacement measurement based on microwave interferometry. The aim of this paper is to develop a technique that would allow one to verify that method by comparing the measured displacement vs....
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Інститут технічної механіки НАН України і НКА України
2018
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| Цитувати: | Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement / O.V. Pylypenko, A.V. Doronin, N.B. Gorev, I.F. Kodzhespirova // Технічна механіка. — 2018. — № 1. — С. 5-12. — Бібліогр.: 12 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1737842025-02-09T23:35:06Z Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement Экспериментальная проверка двухзондовой реализации сверхвысокочастотной интерферометрии для измерения перемещения Експериментальна перевірка двозондової реалізації надвисокочастотної інтерферометрії для вимірювання переміщення Pylypenko, O.V. Doronin, A.V. Gorev, N.B. Kodzhespirova, I.F. This paper addresses the problem of experimental verification of a recently proposed two-probe method for displacement measurement based on microwave interferometry. The aim of this paper is to develop a technique that would allow one to verify that method by comparing the measured displacement vs. time relationship of a moving target with the actual one without recourse to complex photorecording equipment. This aim is achieved by the target being put in motion using a crank mechanism so that the actual target displacement can be calculated from the crank radius and arm length, the crank rotation period, and the crank angle at the initial time. Рассматривается задача экспериментальной проверки недавно предложенного двухзондового метода измерения перемещения на основе сверхвысокочастотной интерферометрии. Целью данной статьи является разработка методики, позволяющей провести проверку этого метода путем сравнения измеренной и фактической временной зависимости перемещения движущегося объекта без использования сложного оборудования для фоторегистрации. Данная цель достигается тем, что объект приводится в движение с помощью кривошипно-шатунного механизма, так что фактическое перемещение объекта можно рассчитать по радиусу и длине плеча кривошипа, периоду вращения кривошипа и углу поворота кривошипа в начальный момент времени. Розглядається задача експериментальної перевірки нещодавно запропонованого двозондового метода вимірювання переміщення на основі надвисокочастотної інтерферометрії. Метою цієї роботи є розробка методики, що дозволяє провести перевірку цього метода шляхом порівняння виміряної й фактичної часової залежності переміщення об’єкта, що рухається, без використання складного обладнання для фотореєстрації. Ця мета досягається тим, що об’єкт приводиться до руху за допомогою кривошипно-шатунного механізму, так що фактичне переміщення об’єкта можна розрахувати за радіусом і довжиною плеча кривошипа, періодом обертання кривошипа та кутом повороту кривошипа у початковий момент часу. 2018 Article Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement / O.V. Pylypenko, A.V. Doronin, N.B. Gorev, I.F. Kodzhespirova // Технічна механіка. — 2018. — № 1. — С. 5-12. — Бібліогр.: 12 назв. — англ. 1561-9184 https://nasplib.isofts.kiev.ua/handle/123456789/173784 621.002.56 en Технічна механіка application/pdf Інститут технічної механіки НАН України і НКА України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This paper addresses the problem of experimental verification of a recently proposed two-probe method for displacement measurement based on microwave interferometry. The aim of this paper is to develop a technique that would allow one to verify that method by comparing the measured displacement vs. time relationship of a moving target with the actual one without recourse to complex photorecording equipment. This aim is achieved by the target being put in motion using a crank mechanism so that the actual target displacement can be calculated from the crank radius and arm length, the crank rotation period, and the crank angle at the initial time. |
| format |
Article |
| author |
Pylypenko, O.V. Doronin, A.V. Gorev, N.B. Kodzhespirova, I.F. |
| spellingShingle |
Pylypenko, O.V. Doronin, A.V. Gorev, N.B. Kodzhespirova, I.F. Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement Технічна механіка |
| author_facet |
Pylypenko, O.V. Doronin, A.V. Gorev, N.B. Kodzhespirova, I.F. |
| author_sort |
Pylypenko, O.V. |
| title |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| title_short |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| title_full |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| title_fullStr |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| title_full_unstemmed |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| title_sort |
experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement |
| publisher |
Інститут технічної механіки НАН України і НКА України |
| publishDate |
2018 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/173784 |
| citation_txt |
Experimental verification of a two-probe implemetration of microwave interferometry for displacement measurement / O.V. Pylypenko, A.V. Doronin, N.B. Gorev, I.F. Kodzhespirova // Технічна механіка. — 2018. — № 1. — С. 5-12. — Бібліогр.: 12 назв. — англ. |
| series |
Технічна механіка |
| work_keys_str_mv |
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5
UDC 621.002.56
O. V. PYLYPENKO, A. V. DORONIN, N. B. GOREV, I. F. KODZHESPIROVA
EXPERIMENTAL VERIFICATION OF A TWO-PROBE IMPLEMETRATION OF
MICROWAVE INTERFEROMETRY FOR DISPLACEMENT MEASUREMENT
Institute of Technical Mechanics
of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine,
15 Leshko-Popel St., Dnipro 49005, Ukraine; e-mail: ifk56@ukr.net
Розглядається задача експериментальної перевірки нещодавно запропонованого двозондового мето-
да вимірювання переміщення на основі надвисокочастотної інтерферометрії. Метою цієї роботи є розроб-
ка методики, що дозволяє провести перевірку цього метода шляхом порівняння виміряної й фактичної
часової залежності переміщення об’єкта, що рухається, без використання складного обладнання для фото-
реєстрації. Ця мета досягається тим, що об’єкт приводиться до руху за допомогою кривошипно-шатунного
механізму, так що фактичне переміщення об’єкта можна розрахувати за радіусом і довжиною плеча кри-
вошипа, періодом обертання кривошипа та кутом повороту кривошипа у початковий момент часу. Описа-
ні в цій роботі експерименти підтвердили працездатність вищевказаного двозондового метода вимірюван-
ня переміщення, тим самим підтвердивши, що для вимірювання переміщення при невідомому коефіцієнті
відбиття достатньо двох зондів. При довжині хвилі зондуючого електромагнітного випромінювання 3 см,
розмасі коливань об’єкта 10 см і 15 см і частоті коливань об’єкта близько 2 Гц цей метод дозволяє визна-
чити миттєве значення переміщення з максимальною похибкою близько 3 мм і середньою похибкою бли-
зько 1 мм без будь-якої попередньої обробки даних вимірювань, такої як фільтрація, згладжування тощо.
У порівнянні із загальноприйнятими тризондовими вимірюваннями зменшення кількості зондів дозволяє
спростити конструкцію й виготовлення хвилевідної секції, а також послабити паразитний ефект перевід-
биттів між зондами. Простота апаратної реалізації метода дозволяє використати його при розробці борто-
вих давачів для вимірювання переміщення об’єктів космічного сміття відносно космічного апарата для
видалення космічного сміття.
Рассматривается задача экспериментальной проверки недавно предложенного двухзондового метода
измерения перемещения на основе сверхвысокочастотной интерферометрии. Целью данной статьи являет-
ся разработка методики, позволяющей провести проверку этого метода путем сравнения измеренной и
фактической временной зависимости перемещения движущегося объекта без использования сложного
оборудования для фоторегистрации. Данная цель достигается тем, что объект приводится в движение с
помощью кривошипно-шатунного механизма, так что фактическое перемещение объекта можно рассчи-
тать по радиусу и длине плеча кривошипа, периоду вращения кривошипа и углу поворота кривошипа в
начальный момент времени. Описанные в данной работе эксперименты подтвердили работоспособность
вышеуказанного двухзондового метода измерения перемещения, тем самым подтвердив, что для измере-
ния перемещения при неизвестном коэффициенте отражения достаточно двух зондов. При длине волны
зондирующего электромагнитного излучения 3 см, размахе колебаний объекта 10 см и 15 см и частоте
колебаний объекта около 2 Гц этот метод позволяет определить мгновенное значение перемещения объек-
та с максимальной погрешностью около 3 мм и средней погрешностью около 1 мм без какой-либо предва-
рительной обработки данных измерений, такой как фильтрация, сглаживание и т. п. По сравнению с об-
щепринятыми трехзондовыми измерениями уменьшение количества зондов позволяет упросить конст-
рукцию и изготовление волноводной секции и ослабить паразитный эффект переотражений между зонда-
ми. Простота аппаратной реализации метода позволяет использовать его при разработке бортовых датчи-
ков для измерения перемещения объектов космического мусора относительно космического аппарата для
удаления комического мусора.
This paper addresses the problem of experimental verification of a recently proposed two-probe method for
displacement measurement based on microwave interferometry. The aim of this paper is to develop a technique
that would allow one to verify that method by comparing the measured displacement vs. time relationship of a
moving target with the actual one without recourse to complex photorecording equipment. This aim is achieved
by the target being put in motion using a crank mechanism so that the actual target displacement can be calcu-
lated from the crank radius and arm length, the crank rotation period, and the crank angle at the initial time. The
experiments described in this paper have verified the above-mentioned two-probe displacement measurement
method, thus confirming that the displacement can be determined from probe measurements at an unknown re-
flection coefficient using as few as two probes. At an operating wavelength of 3 cm, a target double amplitude of
10 cm and 15 cm, and a target vibration frequency of about 2 Hz, the method allows one to determine the instan-
taneous target displacement with a maximum error of about 3 mm and an average error of about 1 mm without
any preprocessing of the measured data, such as filtering, smoothing, etc. In comparison with conventional three-
probe measurements, the reduction in the number of probes simplifies the design and manufacture of the measur-
ing waveguide section and alleviates the problem of interprobe interference. The simple hardware implementation
of the above-mentioned displacement measurement method allows one to use it in the development of motion
sensors to measure the displacement of space debris objects onboard a dedicated spacecraft for space debris re-
moval.
O. V. Pylypenko, A. V. Doronin, N. B. Gorev, I. F. Kodzhespirova, 2018
Техн. механіка. – 2018. – № 1.
6
Keywords: complex reflection coefficient, displacement, electrical probe, ex-
perimental verification, semiconductor detector, waveguide section.
Microwave interferometry is an ideal means for displacement measurement in
various engineering applications [1]. This is due to its ability to provide fast non-
contact measurements, applicability to dusty or smoky environments (as distinct
from laser Doppler sensors [2 – 4] or vision-based systems using digital image
processing techniques [5]), and simple hardware implementation. In microwave
interferometry, the displacement of the object under measurement (target) is ex-
tracted from the phase shift between the signal reflected from the target and the
reference signal. Recently, a two-probe displacement measurement method based
on microwave interferometry was proposed [6]. In that method, the quadrature sig-
nals needed for the determination of the phase shift are extracted from the outputs
of two probes placed in a waveguide section one eighth of the guided operating
wavelength g apart. In hardware implementation, the method is far simpler than
conventional techniques based on quadrature mixing [7, 8], which need special
hardware incorporating a power divider and a phase-detecting processor (an analog
[7] or a digital [8] quadrature mixer) and face the problem of minimization of the
nonlinear phase response of the quadrature mixer arising from its phase and ampli-
tude unbalances. A distinctive feature of the method proposed in [6] is the possi-
bility of displacement measurement at an unknown reflection coefficient with as
few as two probes, while since the classic text by Tischer [9] it has been univer-
sally believed that at least three probes are needed to determine or eliminate the
unknown reflection coefficient. Theoretically, the method gives the exact value of
the displacement for reflection coefficients (at the location of the probes) no
greater than 21 and in the general case determines it to a worst-case accuracy of
about 4.4 % of the operating wavelength.
In [6], the method was verified by comparing the measured target double am-
plitude with the actual one. Clearly it is of much more interest to verify the method
by comparing the measured displacement vs. time relationship of a moving target
with the actual one. The aim of this paper is to develop a technique that would al-
low one to do this without recourse to complex photorecording equipment.
This aim may be achieved using a target put in motion by a crank mechanism
as shown in Fig. 1.
Fig. 1
As can be seen from Fig. 1, the displacement x of the target at time t relative
to its initial position at 0t is
tOAOAtx crcr 0)( (1)
crcrcrcrcrcr RRLOA cossin)( 222 , (2)
7
T
tt crcr
2)( 0 (3)
where cr is the crank angle, cr0 is the crank angle at t = 0, OA is the distance
from the rotation center to the end of the crank arm, Lcr is the crank arm length, Rcr
is the crank radius, and T is the rotation period.
As can be seen from Eqs. (1) to (3), the displacement is a periodical time
function with a period equal to T. The derivative of x with respect to the time is
crcrcr
crcr
crcr
crcrcr
crcrcr
RL
ROA
T
R
RL
R
Tdt
xd
222222
2
sin
sin2sin
sin
cossin2 . (4)
For convenience, define 20Ttt cr . It follows from Eq. (4) that the de-
rivative becomes zero at ,...,2,1,0,2 nnTt and it changes its sign from
positive to negative and from negative to positive at ,...,2,1,0, mmTt and
at ,...,2,1,0,21 kTkt respectively. Because of this, the function x(t)
reaches one minimum and one maximum over a period. So the crank rotation pe-
riod may be determined from the measured dependence x(t) as the distance along
the abscissa axis between two adjacent minima or two adjacent maxima.
It follows from the aforesaid that the initial phase cr0 may be determined
from the measured dependence x(t) as follows
T
t
cr
1
0
2
(5)
where t1 is the time at which the measured dependence x(t) shows its first maxi-
mum (the procedure of finding T and t1 from the measured dependence x(t) is
illustrated in Fig. 2).
Fig. 2
In view of Eq. (5), the expression of (3) for cr (t) becomes
T
tttcr 12)(
. (6)
Given T and t1, the actual target displacement can be calculated from Eqs. (1),
(2), and (6) and compared with the measured one.
8
However, T and t1 can be determined from the measured time dependence of
the displacement only approximately. Because of this, the displacement measure-
ment error, i. e. the difference of the measured displacement and the actual one
may be found by the following algorithm.
1. From the measured time dependence of the target displacement x(t), esti-
mate the crank rotation period T and the time t1 at which the measured dependence
x(t) shows its first maximum (in the following, the estimated values of T and the
time t1 will be denoted as Tap and t1ap, respectively).
2. Vary T and t1 with a specified step on the intervals apap TTT 1.19.0 and
apap ttt 111 1.19.0 .
3. For each pair (T, t1), calculate the target displacement at each time point
from Eqs. (1), (2), and (6).
4. For each time point, calculate the displacement measurement error xer as
the difference of the measured displacement x(t) and the calculated displacement
xc(t).
5. Find the maximum value |xer|max of the displacement error magnitude for
the given pair (T, t1).
6. Find the pair (T, t1) such that |xer|max is a minimum and take these values
of T and t1 as the actual values Tact and t1act of the crank rotation period T and the
time t1.
7. For T = Tact and t1 = t1act`, calculate the target displacement at each time
point from Eqs. (1), (2), and (6).
8. Run Step 4 to find the actual displacement measurement error xer.
To verify the method proposed in [6] by the above algorithm, the displacement
of a target (a brass disc or a brass square) put into a reciprocal motion by an
electrically driven crank mechanism was measured. The target vibration frequency
was controlled by the voltage across the driving motor. The target vibration ampli-
tude was controlled by varying the crank radius.
The measuring setup comprised a microwave oscillator, a circulator with a
dummy load, a waveguide section with two probes installed therein and two semi-
conductor detectors connected to the probes, a horn antenna mounted at the end of
the waveguide section, two amplifiers, an analog-to-digital converter, and a per-
sonal computer. A schematic of the setup is shown in Fig. 3. The electromagnetic
wave generated by the oscillator passes through the circulator, enters the
waveguide section, is emitted by the horn antenna, reaches the target, and reflects
therefrom. The reflected wave passes through the horn antenna, enters the
waveguide section, and is directed by the circulator to the dummy load. The elec-
tromagnetic wave generated by the microwave oscillator and the wave reflected
from the target interfere in the waveguide section to form a standing wave, whose
amplitude is measured with the electrical probes and the semiconductor detectors
connected thereto. The amplifiers amplify the detector currents, and the amplified
currents arrive at the analog-to-digital convertor, which converts them into digital
signals. From the digital signals, the personal computer determinates the relative
displacement of the target by the method proposed in [6].
9
Fig. 3
The experiments were conducted at different values of the target double am-
plitude equal to twice the crank radius and the minimum distance between the an-
tenna and the target. In all the cases, the free-space operating wavelength was
3 cm, with corresponds to an operating frequency of 10 GHz.
In Experiment 1, the target was a brass disc of diameter 128 mm, the target
double amplitude was 15 cm, and the minimum distance between the antenna and
the target was 100 cm. In Experiment 2, the target was the same in Experiment 1,
the target double amplitude was 10 cm, and the minimum distance between the
antenna and the target was 15 cm. In Experiment 3, the target was a 70x70 mm
brass square, the target double amplitude was 10 cm, and the minimum distance
between the antenna and the target was 5 cm.
Figs. 4 to 6 show the target displacement x measured by the method pro-
posed in [6] and the actual target displacement xact found by the algorithm de-
scribed above for Experiments 1, 2, and 3, respectively. As can be seen from the
figures, the target vibration period is about 0.5 sec, i.e. the vibration frequency is
about 2 Hz. It can also be seen that the curves of the measured and the actual dis-
placement coincide to within the line thickness.
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
-140
-120
-100
-80
-60
-40
-20
0
20
t (sec)
x, xact (mm) measured displacement
actual displacement
Fig. 4
10
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-100
-80
-60
-40
-20
0
t (sec)
x, xact (mm)
measured displacement
actual displacement
Fig. 5
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-100
-80
-60
-40
-20
0
t (sec)
x, xact (mm) measured displacement
actual displacement
Fig. 6
The peak-to-peak amplitude was determined to an accuracy of 0.7 mm in Ex-
periment 1, 1.1 mm in Experiment 2, and 0.2 mm in Experiment 3.
Figs. 7 to 9 show the displacement measurement error xer equal to the differ-
ence of the measured displacement x and the actual displacement xact versus the
time and the apparent reflection coefficient rap versus the target displacement x0
from the position closest to the antenna for Experiments 1, 2, and 3, respectively.
The apparent reflection coefficient rap is defined as the smaller positive root of the
biquadratic equation that relates the actual reflection coefficient of the target ract to
the currents of the semiconductor detectors [6]. As shown in [6], rap coincides with
ract if the latter is no greater than 21 0,707; otherwise, rap may not be equal to
ract. If rap ract, the displacement is determined with an error, which, however,
does not exceed 4.4 % of the free-space operating wavelength.
11
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
-3
-2
-1
0
1
2
3
x
0
(mm)
xer (mm)
t (sec)
0 20 40 60 80 100 120 140
0.035
0.040
0.045
0.050
0.055
0.060
0.065
rap
Fig. 7
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-3
-2
-1
0
1
2
3
xer (mm)
0 10 20 30 40 50 60 70 80 90 100
0.2
0.3
0.4
0.5
0.6
rap
x
0
(mm)
t (sec)
Fig. 8
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
-3
-2
-1
0
1
2
3
0 20 40 60 80 100
0.2
0.4
0.6
0.8
rap
x
0
(mm)
xer (mm)
t (sec)
21
Fig. 9
12
The maximum and the average error in the determination of the instantaneous
relative displacement was 2.9 mm and 0.8 mm in Experiment 1, 2.2 mm and
1.0 mm in Experiment 2, and 3.3 mm and 1.1 mm in Experiment 3. In Experiments
1 and 2, the apparent reflection coefficient varied between 0.04 and 0.066 and be-
tween 0.12 and 0.58, respectively, i. e. it was less than 21 0.707. Because of
this, in those experiments the smaller positive root of the biquadratic equation gave
the actual reflection coefficient, and thus the error was due to other factors such as
deviation of the reflected wave from the plane waveform, reflections from the an-
tenna, noise, etc. In Experiment 3, the apparent reflection coefficient varied be-
tween 0.2 and 0.76, i. e. at some of the measurement points the smaller positive
root of the biquadratic equation might be extraneous. However, as can be seen
from the data given above, this did not contribute much to the error in comparison
with Experiments 1 and 2. As can be seen from Figs. 6 and 9 (Experiment 3), the
two-probe method proposed in [6] performs well for a minimum antenna–target
distance of 5 cm too, while the standing-wave radar proposed in [10] fails to oper-
ate at distances less than 14 cm due to positional interference between the target
and the antenna.
So the experiments described in this paper have verified the two-probe dis-
placement measurement method proposed in [6], thus confirming that the dis-
placement can be determined from probe measurements at an unknown reflection
coefficient using as few as two probes. In comparison with conventional three-
probe measurements [11], the reduction in the number of probes simplifies the de-
sign and manufacture of the measuring waveguide section and alleviates the prob-
lem of interprobe interference. The simple hardware implementation of the above-
mentioned displacement measurement method allows one to use it in the devel-
opment of motion sensors to measure the displacement of space debris objects on-
board a dedicated spacecraft for space debris removal [12].
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Received 02.01.2018,
in final form 22.01.2018
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