Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж
The paper is focused on a new concept of a cryogenic-optical sensor intended for use in the space industry, geodynamics, and fundamental experiments. The basis of the sensor is a magnetic suspension with a levitating test body, a high-precision optical recorder of mechanical coordinates of the levit...
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| author | Yatsenko, Vitaly Kruchinin, Sergii Bidyuk, Petro |
| author_facet | Yatsenko, Vitaly Kruchinin, Sergii Bidyuk, Petro |
| author_sort | Yatsenko, Vitaly |
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| datestamp_date | 2022-12-21T22:15:21Z |
| description | The paper is focused on a new concept of a cryogenic-optical sensor intended for use in the space industry, geodynamics, and fundamental experiments. The basis of the sensor is a magnetic suspension with a levitating test body, a high-precision optical recorder of mechanical coordinates of the levitating body, and a signal-processing system. A Michelson-type interferometer with a laser diode and a single-mode optical fiber was used to measure the test body's displacements. The coordination of the laser diode coherence length and the difference in the interferometer optical lengths of the arms made it possible to eliminate coherent noise caused by interference from spurious reflections. The minimum recorded shift of the test body was 0.1 nm. The design of the sensor and the mathematical model of the superconducting suspension dynamics are presented. The results of experimental studies of a magnetic suspension together with an optical interferometric displacement sensor having a subnanometer sensitivity are shown. |
| doi_str_mv | 10.20535/SRIT.2308-8893.2022.3.02 |
| first_indexed | 2025-07-17T10:28:01Z |
| format | Article |
| fulltext |
V. Yatsenko, S. Kruchinin, P. Bidyuk, 2022
30 ISSN 1681–6048 System Research & Information Technologies, 2022, № 3
TIДC
ПРОГРЕСИВНІ ІНФОРМАЦІЙНІ ТЕХНОЛОГІЇ,
ВИСОКОПРОДУКТИВНІ КОМП’ЮТЕРНІ
СИСТЕМИ
UDC 004.942+004.383.3
DOI: 10.20535/SRIT.2308-8893.2022.3.02
SUPERCONDUCTING GRAVIMETERS BASED ON ADVANCED
NANOMATERIALS AND QUANTUM NEURAL NETWORK
V. YATSENKO, S. KRUCHININ, P. BIDYUK
Abstract. The paper is focused on a new concept of a cryogenic-optical sensor in-
tended for use in the space industry, geodynamics, and fundamental experiments.
The basis of the sensor is a magnetic suspension with a levitating test body, a high-
precision optical recorder of mechanical coordinates of the levitating body, and a
signal-processing system. A Michelson-type interferometer with a laser diode and a
single-mode optical fiber was used to measure the test body's displacements. The
coordination of the laser diode coherence length and the difference in the interfer-
ometer optical lengths of the arms made it possible to eliminate coherent noise
caused by interference from spurious reflections. The minimum recorded shift of the
test body was 0.1 nm. The design of the sensor and the mathematical model of the
superconducting suspension dynamics are presented. The results of experimental
studies of a magnetic suspension together with an optical interferometric displace-
ment sensor having a subnanometer sensitivity are shown.
Keywords: magnetic suspension, laser interferometer, optical fiber, displacement
measurement, quantum neural network.
INTRODUCTION
Remote sensing today is one of the rapidly growing modern measurement tech-
nologies. This direction of studies and applications is an industry with the cost of
billions of dollars, and the number of distant specific images of different parts of
the Earth is continuously growing. Solutions of many practical problems depend
on the widespread use of measuring systems and different principles they use.
These problems include monitoring of natural resources based upon analysis of
gravitational anomalies, study of global geodynamic processes, the Earth’s gravi-
tational field, motions of Earth’s poles, etc. To increase accuracy of the observa-
tions, determining the location and orientation for long-term air flights and un-
derwater vehicle navigations require knowledge of Earth’s gravitational field,
including its anomalies. Detailed information on the Earth’s gravitational field is
needed by many industries and applied sciences (space research, geology, naviga-
tion, science of the Earth’s shape). An accurate fast detection of geodynamic pro-
cesses can provide data on the origin and development of critical local and global
environmental conditions. Another practical problem is in the need to obtain more
accurate information on undiscovered minerals of the Earth.
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 31
A gravimeter is a very accurate tool [1, 2, 6] for measuring the gravity accel-
eration g. At present, accuracy of the best stationary ground-based gravimeters is
810 g. For sea-based gravimeters, it is 710 g, and the aviation uses its value of
about 610 g. Most gravimeters manufactured by industry are based on the prop-
erties of a stretched spring or elastic properties of springs made of quartz or some
special alloys. Their accuracy is not sufficient to solve these problems. Since the
accuracy of gravimeters based on traditional principles has become fundamentally
exhausted, many developers over the past decades have tried to use unconven-
tional approaches in attempts to create ultraprecise gravimeters [1, 2]. These at-
tempts can be grouped by the method of non-contact suspension of the gravimeter
sensitive mass, by the use of electric or magnetic forces, by the methods of meas-
uring the gravimeter sensitive mass displacements (optical recording systems,
Josephson effects as the basis of measurements, etc.), as well as by computer
based methods of signal processing. A great advance in the improvement of gra-
vimeters was made due to the financing of development of superconducting gra-
vimeters. J. M. Goodkind described in detail a superconducting gravimeter [1]. As
he stated, the basic design of a superconducting gravimeter has been unchanged
for almost 30 years since his first publication [2]. The free-state (levitation) of a
sensitive mass of this gravimeter is achieved due to the Brownback-Meissner ef-
fect [3, 4]. An alternative approach is based on the phenomenon of magnetic levi-
tation. The research in this field began in the late 1960s as a natural consequence
of development of a low-temperature applied superconductivity, the theory of
electromechanical conversion of energy and methods of control theory, as well as
the development of defense navigation systems in the xUSSR. The phenomenon
of “magnetic potential pit” (MPP) [4–6], discovered in 1975, means that the mag-
netic attraction between two distant magnets can change to the magnetic repulsion
only as a result of growing distance between them. In this case the attractive force
between two distant magnets was considered as a force that increases as the dis-
tance decreases. In other words, MPP considers the minimum magnetic potential
energy as a function of the distance, although, by the time MPP was discovered,
the magnetic interaction was considered monotonic, i.e. without the possibility of
having a minimum anywhere except for points on the boundary.
The objective of this study is to present the results on the development of a
sensitive element and a method for assessing the gravitational perturbation that
affects a levitating test body. The paper presents the concept of a cryogenic opti-
cal sensor, its design, a mathematical model of dynamics of a superconducting
suspension, and its stability analysis. The results of experimental studies of
a magnetic suspension and an optical interferometric displacement sensor with
subnanometer sensitivity are presented.
CONCEPT OF A CRYOGENIC OPTICAL SENSOR
The sensor concept is based on three features and their combination [1, 2, 6, 7, 8].
First, this is a new type of superconducting suspension of a test body of highly
sensitive gravimeter in a free state. Known superconducting suspensions [1–5]
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 32
use the concept of levitation based on the Brownback–Meissner effect [3], when
the stable magnetic confinement without contact with other bodies arises due to
the ideal diamagnetism of the superconductor, which ensures the expulsion of
another magnet from its volume. As an example can be a superconducting magnet
coil powered by the direct current. The test body of known gravimeters is, as
a rule, continuous sphere. Instead of the superconductor diamagnetism, the new
concept uses the zero resistance of a superconductor in the form of a thin closed
loop, for example, a ring. Under certain conditions, due to the manifestation of the
MPP phenomenon, such ring can steadily hang in a free state despite its diamag-
netism that is practically not manifested and, according to well-known physical
principles, makes the suspension inoperative. Another feature is the laser method
for measuring the displacements of the test body, while known superconducting
gravimeters use on the purpose sensors based on the Josephson effect (supercon-
ducting quantum interferometer sensors). The third feature is the use of modern
signal processing methods to isolate very small disturbances against a background
of significant noise levels that correspond to parameters of the measured gravita-
tional field.
The choice of MPP as the basis for the levitation is explained by the two fac-
tors. The first of them is the desire to increase the sensitivity of the superconduct-
ing gravimeter, the second is to expand its dynamic range. The use of optical reg-
istration of the levitating sensitive mass displacements is also a new approach in
the field of ultra-precise gravimseters. To process the signals of cryogenic optical
gravimeter, it is proposed to use several processing steps. The first step is to com-
pensate the noise affecting the base of the device. The second processing stage is
focused on the use of the sensor inverse dynamic model [10]. The adaptive digital
filtering is performed in the third stage of processing. In general, the novelty of
the concept lies in the combination of a free sensitive mass suspension, an optical
registration system, and new signal processing facilities. To our opinion, this ap-
proach to the sensor construction is implemented for the first time.
A superconducting gravimeter is a spring-type meter, in which, however,
a magnetic returning force works as mechanical spring acting on a test supercon-
ducting body in an inhomogeneous magnetic field of superconducting rings or
a permanent magnet. Due to the high stability of the superconducting currents,
a highly stable non-dissipative spring is created. In equilibrium, the test body levi-
tates in a position, where the gravitational force is balanced by a magnetic force
acting in the opposite direction. When the gravity changes, the test body begins to
shift from the zero position, and the electronic displacement sensor produces an
error signal. By changing the current in the control ring, the auto-tuning system
creates an additional magnetic field proportional to this signal, which keeps the
test body in zero position. Since the returning force is proportional to the current,
measuring the current in the control ring provides linear measurement of changes
in the force of gravity.
In the model of sensitive element (Fig. 1), the test mass was in the form of
a cylinder on which superconducting rings and a mirror for interferometric meas-
urements were placed. Additional structural elements necessary for technological
reasons were attached to this cylinder.
An effective use of the advantages of MSS (magnetic suspension system)
which have almost unlimited sensitivity requires an appropriate system of regis-
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 33
tration of the test body displacement. To determine the test body positions in cry-
ogenic element (CE), the use of a laser sensor was proposed. This made it possi-
ble to exclude probable disturbances in the position of test body caused by electric
and magnetic fields as opposed to the conventional sensors used in previous sys-
tems. The modern interferometric methods and dynamic effects in the laser gen-
eration caused by weak external signals are used to detect ultra-small movements
of the test body. The interferometric method can ensure the measuring accuracy
of the test body coordinates not worse than 0.1 nm, what is sufficient to achieve
the necessary sensor sensitivity. We have selected and implemented experimental
schemes with laser displacement detectors, which provide measurements of the
test body displacements and transformation of the signal into digital form for sub-
sequent processing. It was shown that an optical sensor based on a diode laser
with external resonator as a source of monochromatic radiation and a single-mode
optical fiber as a channel for transporting light to a test body with maintaining the
coherence of optical radiation that satisfies set requirements.
SENSOR DESIGN
The suspension is coaxial, i.e. the holding magnets are displaced from the coaxial
position to the position, where their axes are parallel to the axis of the suspension
(Fig. 2). From various options for the number of holding magnets (two, three,
four), a system of four rare earth permanent magnets with a vertical axis was
selected. Each magnet in the horizontal plane has a rectangular shape. The
vertical positions of all four sets of magnets were shifted from the axis of the
suspension so that a space of 18 mm in diameter was formed to accommodate the
optical sensor. The problem of the non-vertical position of the suspended free
sample, which arose as a result of the unequal magnetic properties of the sets of
permanent magnets, was solved by two structural changes. One of them was an
increase in the pendulous feature of the test mass and the other was reduced to a
Fig. 1. The layout of the opto-cryogenic sensor
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 34
thin ferromagnetic ring, which compensated for the azimuthal inhomogeneity of
the suspension magnetic field.
After theoretical and experimental studies of the suspension, optical sensor,
and measurement software, the feasibility of the implementation of selected de-
sign as a whole was analyzed. As for the suspension, the main work concerned
changes in the design of the magnetic system, when instead of placing remaining
magnets on the axis of the suspension they had to be biased from the axis so that
to place an optical laser sensor on it.
The new design of the working model (Fig. 3, 4) included four sets of per-
manent rare earth magnets, whose vertical axes of which were shifted from the
suspension axis in four radial directions. The new design of the test mass had two
niobium-titanium rings. The upper plane of the sample was polished as a
reflective plane for laser beams. The levitation gap, depending on the weight of
the test body, was from 7 to 15 mm. Based on this working model, theoretical and
experimental studies of the joint operation of the suspension – registration system
were carried out. The influence of the physical state of helium (liquid or gas) on
the joint operation of the suspension – registration system was analyzed. The
effect of a passive filter on the accuracy of the measurements was studied as well.
The factors that influence a decrease in the suspension stiffness, in particular the
presence of an additional ferromagnetic mass on a free sample wecre analyzed.
Experimental studies of the system were carried out to determine the proper-
ties of working model of a gravimeter, the dynamic characteristics of the mag-
netic suspension of free trial mass of the working layout of the gravimeter as well
as the refinement of the sensitive element as a part of magnetic suspension, which
was dictated by the experimental studies.
Fig. 2. Design of the opto-cryogenic sensor
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 35
SIGNAL PROCESSING SYSTEM
The signal processing system consists of an adaptive compensator, inverse dy-
namic sensor model, adaptive Kalman filter, and a digital filter. Instead of a
reverse model, a special type of neural network can be used. The software
integrates gravity perturbation estimation algorithms with data processing models.
It also includes a subsystem for interaction of the program core with the database,
as well as with algorithms for its interaction with the sensor. It is supposed to in-
clude the software modules implemented in Matlab. Special tools are provided to
Fig. 4. Magnetic suspension system and optical system for the measurement of mechani-
cal coordinates
Fig. 3. Magnetic suspension system of four sets of holding permanent magnets
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 36
significantly reduce the levels of internal and light-generating noises based on the
use of the features of the detector operation and software.
The analysis of the noise intensity characteristics of the optical coordinate
meter was conducted. The correlation function and spectral density of the noise
were obtained with regard for the properties of the bandpass filtering in an
interferometer and the arbitrary modulation of a wavefront. The analysis included
the modulation of a fractional noise as a special case of noises. To detect a signal
limited by a fractional noise, the signal-noise ratio was found as a function of the
modulation parameters. And the procedure for optimizing the noise-signal ratio
corresponding to the signal demodulation was developed.
A noise compensation algorithm based on the global optimization approach
is proposed. The compensator can extract useful information from a noisy optical
signal. The noise compensation system allows the use of two types of sensors.
The primary sensor generates a noisy source signal, whereas the secondary sensor
measures the noise that is not correlated with the useful signal, but is correlated
with a noise in the primary sensor.
Neural network algorithms for the signal analysis and estimation of gravita-
tional perturbations based on the information approach have been developed. The
error of the entropy minimization approach in identifying the dynamics of a test
body was studied. An influence of the Parsen clock window on the search for a
minimum of the entropy was studied. It has been analytically proved that the min-
imum of the entropy can be local. At the same time, the global minimum of the
entropy with nonparametric estimation can be found by using information from
the Shannon and Gaussian kernels. A comparative analysis of minimizing the en-
tropy of the error and minimizing the entropy of the least squared error of a short-
term prediction of experimental data is carried out. The statistical properties of the
error in estimating the high-order central moments of the experimental time series
and forecasting are used as comparison criteria. A mathematical description of a
new structure of the inhibitor-type neural network which belongs to an important
class of neural networks is developed. The necessary conditions for the behavior
stability of a competitive inhibitory neural network are determined, and an algo-
rithm based on stability conditions is developed. An algorithm of implementation
of an inhibitory neural network for the evaluation of a signal characterizing the
position of a levitating body in space has been also proposed.
Testing of the software for estimation of gravity perturbations affecting the
levitating test body was performed. A module for the asymptotic estimation of
gravitational perturbations by optical measurements has been added to the soft-
ware. The analysis of the signal evaluation quality of the levitating body distur-
bance using the sequential processing of “optimal filter – inverse model – adap-
tive filter” was made. To compare the evaluation qualities, the following criteria
were used: the ratio of standard deviations of the estimated signals, least-square
error of the estimate, and the correlation coefficient of the signal without noise
and the estimated signal.
LASER DISPLACEMENT SENSOR OF A SUPERCONDUCTING GRAVIMETER
Recent advances in development of diode lasers and the fiber optic technology,
progress in the development of laser interferometry methods offer an alternative
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 37
to commonly used electronic displacement sensors. The use of fiberoptic interfer-
ometers has several important potential advantages [1], providing: 1) the possibil-
ity of creating a linear highly sensitive displacement detector; 2) absolute dis-
placement measurements with a natural scale such as the laser radiation
wavelength; 3) a dynamic range sufficient to record the largest seismic distur-
bances; 4) minimal electrical noise; 5) minimum size, relatively easy production,
and the lack of electromagnetic and thermal noises; 6) the ability to reduce drifts
while using frequency-stabilized lasers.
Optical Measurement System Design
In the model of a superconducting gravimeter investigated in this paper, the
motion of the test body was studied, by using an optical sensor — a laser
fiberoptic interferometer. The laser interferometer is based on a 5-m long single-
mode optical fiber, which made it possible to conveniently place the laser-optical
unit relative to the cryogenic one. The test body had the shape of a cylinder on
which a mirror was placed for interferometric measurements (Fig. 5).
The general scheme of the optical measuring system is shown in Fig. 6. It
included:
a source of laser radiation;
fiber optic cable;
photodetector;
signal recording system;
laser radiation monitoring system.
The laser diode radiation was fed into the optical fiber using a collimating
lens. The reference beam of the interferometer was formed by reflecting part of
the laser radiation that was fed into the fiber from the output end of the light
guide, and the signal beam was formed by the reflection from the polished
aluminum surface of the test body. In order to reduce the sensitivity of the device
to the angular deviations of the test body, the output collimating optics was not
installed, the amplitude of the signal beam rapidly decreased with increasing the
distance from the output end of the fiber to the test body. A normal operating
range was considered at distances in the interval 0.2 – 0.8 mm.
Fig. 5. The scheme of the insert in a cryostat with an optical gage head mounted on a
supporting plane and with the levitating test body
Reference surface
Head
of optical
sensor
Miror surface
of levitating
test body
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 38
The reference and signal beams were returned through the fiber back to the
laser optical unit, then reflected from the beam splitter and recorded by
a photodetector.
The laser radiation source was based on a Hitachi semiconductor continuous
laser HL6320G (emission wavelength 635 nm, output power 10 mW). The laser
was placed in a TCLDM9 thermoelectric cooled laser head of Thorlabs Inc.,
which allowed the installation of diodes with a case diameter of 9 mm and
5.6 mm, allowing the modulation of a supply current in the frequency range from
100 kHz to 1 GHz and the precise control over the laser diode temperature. To
feed the laser an LDC-500-EC electronic unit (Thorlabs Inc.) was used, which
made it possible to set the laser diode current in the interval from zero to 500 mA
with an accuracy of ± 0.2 mA. Noise in the frequency range of 10 Hz – 10 MHz
does not exceed 5 μA. The power supply had a mode for controlling the laser
radiation power using the photodetector integrated in the laser diode case. The
power supply current of the laser diode could be modulated using an external
generator in the frequency range from DC to 150 kHz, the modulation coefficient
is 50 mA / V.
The temperature of the laser diode was stabilized using a thermoelectric
cooler built in a laser head, which was controlled by the TEC2000-EC thermal
stabilization unit (Thorlabs Inc.). The temperature stability was 0.001 K, the ad-
justment accuracy was 0.01 °С.
The interferometer used a fiber optic cable P-3224-FC-5 (Thorlabs Inc.). The
cable at both ends had ceramic caps, a numerical aperture of 0.12, a cut-off wave-
length of 620 nm, is single-mode with a core diameter of 4 μm, and a sheath di-
ameter of 125 μm. The cable length was 5 m. From the laser side, the radiation
was fed into the optical fiber using an F230FFC-B collimating lens (Thorlabs
Fig. 6. Block diagram of the optical measuring system: 1 — cryostat with an insert on
which an optical head is mounted; 2 — optical cable; 3 — focusing lens; 4 — a laser
head with a laser diode; 5 — power supply of the laser diode; 6 — temperature
stabilization unit; 7 — Fabry-Perot IFP-1 interferometer; 8 — screen; 9 — synchronous
detector; 10 — analog-to-digital oerter; 11 — modulator; 12 — computer
SD
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 39
Inc.) with a diameter of 3.8 mm, a numerical aperture of 0.55, and a focal length
of 4.5 mm. Optics were enlightened in the interval of 600–1050 nm.
As a photodetector, PDA55-EC silicon photodiode (Thorlabs Inc.) was used
with a large receiving window area (13 mm2) with a low-noise amplifier, the gain
of which was adjustable from 4105.1 V/A to 61.5 10 V/A. With a minimum
gain, the receiver bandwidth was at least 10 MHz.
The signal from the photodetector was either fed directly into an analog-
digital 12-bit converter of MC-PC20 type or firstly into a synchronous detector to
increase the signal-to-noise ratio, and then through an ADC to a personal computer.
To form the reference signal for the synchronous detector and to modulate
the interference signal, we used a modulator, which generated an alternating high-
voltage signal for supplying to the piezoelectric element to modulate the position
of the reference plane of the interferometer. The recording system made it possi-
ble to record a continuous signal lasting 16s.
Properties of the fiber optic interference sensor and its maximum sensitivity
Interference signal. The light intensity detected by a photodetector depends on the
distance x between the test body and the end of the fiber and can be represented as
x
RRRTTRRRRII 4cos)()1(2)1( 111100 , (1.1)
where I is the light intensity at the photodetector, 0I is the intensity of the laser
radiation fed into the fiber, 0R is the reflection coefficient of the dividing plate,
1R is the reflection coefficient of the fiber end, R is the reflection coefficient of
the surface of the test body, T is the collection efficiency of the fiber reflected
from the surface of the test body, )( is the correlation function of laser radia-
tion, cll / , where xisl 2 the difference in the paths of the signal and refer-
ence rays, cl is the coherence length of the laser radiation ( vxlc , where c is
the speed of light, and Δν is the width of the laser radiation spectrum). In the case
of white frequency noise, the laser emission spectrum has a Lorentzian shape, and
the correlation function has the form )(exp)( .
The effect of laser radiation coherence. Thus, the interference is possible,
if the path difference is less than the coherence length. The coherence length sub-
stantially depends on the type of laser. For example, for a gas single-mode laser, it
is 3cl km, while for laser diodes that were used in the described experiments,
this value is less than 1cm. The relative smallness of the coherence length for la-
ser diodes plays a very important role in the operation of a developed laser meter.
In reality, in addition to the interference between the waves reflected from the test
body and the end of the fiber, some of other interferences can be observed (e.g.,
the interference of waves reflected from the input and output ends of the fiber,
etc.).This interference is an unwanted spurious effect that can significantly distort
the useful signal. It is important that in the proposed scheme only a useful signal
takes place, when the difference in the paths of the interfering waves is minimal,
while, for all others, the difference in the courses contains the length of the fiber,
which is 5 m in this experiment. Therefore, it can be expected that when using
“bad” lasers with a short coherence length (but greater than the distance from the
end of the fiber to the test body), the useful signal will not be distorted by the spu-
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 40
Fig. 7. Dependence of the photodetector
signal on the displacement of the reflecting
surface in the case of using a He-Ne laser
(upper figure) and a laser diode (lower figure).
2.4
2,3
2,2
2,1
2,0
1.9
1.0
0.0 0.2 0.4 0.6 0.8 1.08.0
7,5
7.0
6.,5
6.0
0.0 0.2 0.4 0.6 0.8 1.0
S
i
g
n
a
l
V
/L
rious interference. At the same time, the use of “good” gas lasers will lead to a
significant distortion of the signal.
To confirm this conclusion, an optical meter was experimentally tested for
two cases where a He–Ne laser and a laser diode were used as a source. Fig. 7
illustrates the need to use low-coherence lasers. In this figure, the upper curve
shows the interference signal, when using a gas laser, and the lower curve shows
the interference signal for a laser di-
ode. It can be seen that, in the first
case, the interference pattern is dis-
torted due to spurious reflections,
whereas, in the other case, the ideal
sinusoidal dependence of the signal is
observed, when the position of the
test body changes.
The sensitivity of the method.
For experimental determination of the
minimum displacement of a test body
which can be recorded by the devel-
oped optical sensor, the scheme
shown in Fig. 8 was used. The mirror
simulating the test body was mounted
on a piezoelectric element to which a
constant voltage was applied to control
the movement of the mirror with sub-
nanometer accuracy. The magnitude of
a mirror displacement was determined
by the magnitude of the applied
voltage, based on the fact that the
displacement of the mirror by a half
of the laser radiation wavelength )m32.02/( would be at a voltage of 48V.
The sensitivity of the interferometer was determined when tuning the region of the
highest steepness of the dependence of the signal on the displacement of the mirror.
Fig. 8. Sensitivity calibration scheme of the optical sensor: 1 — piezoelectric element;
2 — mirror mounted on the piezoelectric element; 3 — optical sensor head; 4 — voltage
source. The input end of the fiber is cut at an angle of 8°
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Using a modulation technique to increase the sensitivity. The analysis of
the noise of the optical measuring system showed that, with an increase in the fre-
quency of observations, the spectral density of the noise rapidly decreases, reach-
ing a constant value at frequencies above 5kHz, which is two orders of magnitude
lower than the spectral density at low frequencies. Therefore, to increase the accu-
racy of the optical sensor, the modulation technique can be used, which makes it
possible to transfer the registration frequency to the spectral region, where the
system noise is minimal.
According to (1.1), the dependence of the interference signal on the position
of the mirror x can be written as
kxbaS 2sin ,
where /2k , a and b are constants. To eliminate the coordinate-independent
component of the signal a, which makes the main contribution to low-frequency
fluctuations, we modulate the distance to the test body with a frequency of ,
)(cos0 txxx .
The signal is recorded at the modulation frequency (or triple frequency) ac-
cording to the formula
/2
0
)(cos)( dttktSsk ,
where 3.1k . After integration, we obtain, respectively:
)2(coscos)2,1(J01 xkkbs
and
xk
xk
xk
xk
xk
xkbs
)2(J2
)2(J
)(
)2(J2
2coscos 0
12
1
3 ,
where )(zJn is the Bessel function.
Experimentally, the efficiency of the modulation technique was tested by
changing the mirror position (or the position of the sensor optical head) with a
frequency of 65Hz and with amplitude of about 0.1μm. The signal from
the photodetector was fed to a selective amplifier, asynchronous detector, and an
integrator and recorded by a computer. The registration of signals was performed
at a frequency of 65 Hzin a
narrow frequency band (the
averaging time was equal to
1 s), and the signal-to-noise
ratio significantly increases.
Fig. 7 shows the change in the
signal with a stepwise
displacement of the mirror with
a step of 0.8nm. It can be seen
that the use of the modulation
technique even at a not very
high modulation frequency
leads to a significant reduction
in the noise and, con-
sequently, to a significant
increase in the method
sensitivity. As follows from Fig. 9, the developed sensor allows to register
displacements at the level of about 0.1 nm.
Fig. 9. Registration of oscillations of a test
body with an amplitude of about 1.0 μm and
an oscillation period of about 0.25 s
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 42
Model experiments
Given high cost of cryogenic experiments with relatively short levitation sessions
in the gas phase, the development of the necessary technical solutions was carried
out using models that recreate, as closely as possible, the real working conditions
of a superconducting gravimeter. Based on the fact that the natural frequency of
the developed test body was as low as several Hz, a scheme that recreates the dy-
namics of the test body by placing a reflecting mirror on a floating base was im-
plemented.
It can be shown that the vertical oscillations of the body with an area of S
that floats on the surface of a liquid with density ρ are described by the relation
gSxxm ,
where m is the mass of the float with a mirror, is the density of a liquid, and g
is the acceleration of gravity. The natural frequency of such a system is deter-
mined by the value mgS / and can easily be changed by choosing the ap-
propriate values of the system parameters. For model experiments, a system was
used with 05.0m kg, 310 kg / m3 (water), the float had the shape of a cyl-
inder with a diameter of 50 mm. The oscillation frequency of such a system was
about 3 Hz.
Fig. 10 shows the signal from an optical sensor, when the oscillation ampli-
tude was about 1 nm. It can be seen that, during the period of oscillations, the mir-
Fig. 10. An interference signal in the case of a levitating test body: a–c — fragments (0.2 s)
of consecutive 16-second recordings of the interference signal, which were carried out
after 3–5 min one by one. Levitating test body is in a gas environment without direct con-
tact with liquid helium. d — the levitating test body is in direct contact with liquid helium
a Time, s b Time, s
c Time, s d Time, s
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 43
ror surface shifts by several half-waves, and the signal follows relation (1.1), in
which the distance varies by the harmonic law.
The model experiments showed that the developed system makes it possible
to register, after the appropriate mathematical processing of the obtained data, the
vibrational motion of the test body with an amplitude greater than or comparable
to the wavelength.
QUANTUM NEURAL NETWORKS
It is planned to use in gravimeter a quantum neural network based upon quantum
automates. We studied the quantum computing within the constraints of using a
polylogarithmic ( 1\,)(log kknO ) number of qubits and a polylogarithmic num-
ber of computation steps. The current research in the literature has focused on
using a polynomial number of qubits. A new mathematical model of computation
called Quantum Neural Networks (QNNs) is defined, building on Deutsch’s mod-
el of quantum computational network. The model introduces a nonlinear and irre-
versible gate, similar to the speculative operator defined by Abrams and Lloyd.
The precise dynamics of this operator are defined and while giving examples in
which nonlinear Schrödinger’s equations are applied, we speculate on its possible
implementation. Many practical problems associated with the current model of
quantum computing are alleviated in the new model. It is shown that QNNs of
logarithmic size and constant depth have the same computational power as
threshold circuits, which are used for modeling neural networks. QNNs of poly-
logarithmic size and polylogarithmic depth can solve the problems in NC, the
class of problems with theoretically fast parallel solutions. Thus, the new model
may indeed provide an approach for building scalable parallel computers.
Our quantum neural network based on quantum automatons. This useful
possibility was introduced by V. Yatsenko. He used controllable Schrödinger’s
equations and it was shown how converts it to a quantum automaton. We formu-
late a new paradigm for computing with cellular automata (CAS) composed of
arrays of quantum devices-quantum cellular automata. Computing in such a para-
digm is edge driven. Input, output, and power are delivered at the edge of the CA
array only; no direct flow of information or energy to internal cells is required.
Computing in this paradigm is also computing with the ground state. The archi-
tecture is so designed that the ground-state configuration of the array, subject to
boundary conditions determined by the input, yields the computational result. We
propose a specific realization of these ideas using two-electron cells composed of
quantum dots. The charge density in the cell is very highly polarized (aligned)
along one of the two cell axes, suggestive of a two-state CA. The polarization of
one cell induces a polarization in a neighboring cell through the Coulomb interac-
tion in a very non-linear fashion. Quantum cellular automata can perform useful
computing. The authors showed that AND gates, OR gates, and inverters can be
constructed and interconnected. This opens new way for implementation of the
gravimeter proposed.
CONCLUSIONS
A gravimeter based on an optical sensor and a magnetic suspension of a super-
conducting test body was developed and experimentally investigated. The sensor
V. Yatsenko, S. Kruchinin, P. Bidyuk
ISSN 1681–6048 System Research & Information Technologies, 2022, № 3 44
was studied at cryogenic temperatures, and procedures of data collection and pro-
cessing were developed. Using the developed sensor, we studied the dynamics of
a levitating test body in different environments (liquefied helium, cold helium
vapor, etc.). On the studies of sensor’s model its elements were refined to increase
the sensitivity and to reduce the noise level.
An optical interferometric displacement sensor with subnanometer sensitiv-
ity was developed, created, and studied. The sensor was used to study the dynam-
ics of oscillations of a test body with micron amplitudes, and it was shown that
the proposed and experimentally implemented method for detecting the small dis-
placements of the test body provides the possibility of using this method in super-
conducting gravimeters with adequate parameters of the sensitive element of
a gravimeter. The achieved sensitivity of the optical sensor makes it possible to
record a minimum displacement of the test body of the order of 100 pm, which
with a natural frequency of oscillations of the test body of 0.2 Hz makes it possi-
ble to detect a change in the acceleration of gravity at a level of 1010 g. For esti-
mation makes the acceleration of gravity at a level of 1010 g we propose to use a
quantum neural network based on quantum automatons.
REFERENCES
1. W.A. Prothero and J.M. Goodkind, “A superconducting gravimeter,” Rev. Sci. Instr.,
vol. 39, pp. 1257–1261, 1968.
2. J.M. Goodkind and R.J. Warburton, “Superconductivity applied to gravimetry,”
IEEE Trans. on Magn., vol. 11, iss. 2, 1975.
3. J.M. Goodkind, “The superconducting gravimeter,” Rev. Sci. Instrum., vol. 70,
no. 11, pp. 4131–4152, 1999.
4. F.C. Moon, Superconducting Levitation: Application to bearings and magnetic
transportation. NY: John Willey & Sons, 1994, 295 p.
5. S. Kruchinin, Modern Aspect of Superconductivity: Theory of Superconductivity.
World Scientic, 2010, 232 p.
6. V. Kozoriz, Novel Magnetic Levitation and Propulsion Phenomena. Zaporizhya,
1999, 271 p.
7. V. Yatsenko and P. Pardalos, “Global optimization of cryogenic-optical sensor,” in
Sensors, Systems, and Next-Generation Satellites, Proc. SPIE, 4550, pp. 433–441,
2001.
8. V. Yatsenko, “Functional structure of cryogenic optical sensor and mathematical
modeling of signal,” SPIE Conference ‘Optical Science and Technologies’,
3-8 August 2003, San Diego, CA, USA, Proc. of SPIE, vol. 5172.
Received 03.08.2022
INFORMATION ON THE ARTICLE
Vitaly O. Yatsenko, ORCID: 0000-0002-7159-3312, National Technical University
of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Ukraine, e-mail: gsaudr-
sai@gmail.com
Sergii P. Kruchinin, ORCID: 0000-0002-0674-5826, Bogolyubov Institute of Theoreti-
cal Physics, NASU, Ukraine, e-mail: skruchin@i.com.ua
Superconducting gravimeters based on advanced nanomaterials and quantum neural network
Системні дослідження та інформаційні технології, 2022, № 3 45
Petro I. Bidyuk, ORCID: 0000-0002-7421-3565, Educational and Research Institute for
Applied System Analysis of the National Technical University of Ukraine “Igor Sikorsky
Kyiv Polytechnic Institute”, Ukraine, e-mail: pbidyuke_00@ukr.net
НАДПРОВІДНІ ГРАВІМЕТРИ НА ОСНОВІ СУЧАСНИХ НАНОМАТЕРІАЛІВ І
КВАНТОВИХ НЕЙРОННИХ МЕРЕЖ / В.O. Яценко, С.П. Кручинін, П.І. Бідюк
Анотація. Описано нову концепцію кріогенно-оптичного датчика, призначе-
ного для використання у космічних дослідженнях, геодинаміці та фундамента-
льних експериментах. В основу датчика покладено магнітний підвіс з левітую-
чим тестовим тілом, високоточний оптичний реєстратор механічних координат
левітуючого тіла і система оброблення сигналів. Як вимірювальну систему для
визначення зміщень тестового тіла використано інтерферометр Міхельсона з
лазерним діодом і оптоволокном. Координація когерентної довжини лазерного
діода і різниці оптичних довжин плечей інтерферометра дала змогу видалити
когерентний шум, зумовлений інтерференцією від випадкових відбитків. Мі-
німально зареєстроване відхилення тестового тіла становило 0,1 нм. Подано
процедуру проектування датчика, а також математичну модель динаміки над-
провідної підвіски. Наведено результати експериментальних досліджень маг-
нітної підвіски й оптичного інтерферометричного датчика відхилень, який має
субнанометричну чутливість.
Ключові слова: магнітна підвіска, лазерний інтерферометр, оптичне волокно,
вимірювання зміщення, квантова нейронна мережі.
|
| id | journaliasakpiua-article-269237 |
| institution | System research and information technologies |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-07-17T10:28:01Z |
| publishDate | 2022 |
| publisher | The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" |
| record_format | ojs |
| resource_txt_mv | journaliasakpiua/0d/e7cba95b6b29172aa631397ff11e900d.pdf |
| spelling | journaliasakpiua-article-2692372022-12-21T22:15:21Z Superconducting gravimeters based on advanced nanomaterials and quantum neural network Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж Yatsenko, Vitaly Kruchinin, Sergii Bidyuk, Petro магнітна підвіска лазерний інтерферометр оптичне волокно вимірювання зміщення квантова нейронна мережі magnetic suspension laser interferometer optical fiber displacement measurement quantum neural network The paper is focused on a new concept of a cryogenic-optical sensor intended for use in the space industry, geodynamics, and fundamental experiments. The basis of the sensor is a magnetic suspension with a levitating test body, a high-precision optical recorder of mechanical coordinates of the levitating body, and a signal-processing system. A Michelson-type interferometer with a laser diode and a single-mode optical fiber was used to measure the test body's displacements. The coordination of the laser diode coherence length and the difference in the interferometer optical lengths of the arms made it possible to eliminate coherent noise caused by interference from spurious reflections. The minimum recorded shift of the test body was 0.1 nm. The design of the sensor and the mathematical model of the superconducting suspension dynamics are presented. The results of experimental studies of a magnetic suspension together with an optical interferometric displacement sensor having a subnanometer sensitivity are shown. Описано нову концепцію кріогенно-оптичного датчика, призначеного для використання у космічних дослідженнях, геодинаміці та фундаментальних експериментах. В основу датчика покладено магнітний підвіс з левітуючим тестовим тілом, високоточний оптичний реєстратор механічних координат левітуючого тіла і система оброблення сигналів. Як вимірювальну систему для визначення зміщень тестового тіла використано інтерферометр Міхельсона з лазерним діодом і оптоволокном. Координація когерентної довжини лазерного діода і різниці оптичних довжин плечей інтерферометра дала змогу видалити когерентний шум, зумовлений інтерференцією від випадкових відбитків. Мінімально зареєстроване відхилення тестового тіла становило 0,1 нм. Подано процедуру проектування датчика, а також математичну модель динаміки надпровідної підвіски. Наведено результати експериментальних досліджень магнітної підвіски й оптичного інтерферометричного датчика відхилень, який має субнанометричну чутливість. The National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute" 2022-10-30 Article Article application/pdf https://journal.iasa.kpi.ua/article/view/269237 10.20535/SRIT.2308-8893.2022.3.02 System research and information technologies; No. 3 (2022); 30-45 Системные исследования и информационные технологии; № 3 (2022); 30-45 Системні дослідження та інформаційні технології; № 3 (2022); 30-45 2308-8893 1681-6048 en https://journal.iasa.kpi.ua/article/view/269237/264730 |
| spellingShingle | магнітна підвіска лазерний інтерферометр оптичне волокно вимірювання зміщення квантова нейронна мережі Yatsenko, Vitaly Kruchinin, Sergii Bidyuk, Petro Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title | Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title_alt | Superconducting gravimeters based on advanced nanomaterials and quantum neural network |
| title_full | Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title_fullStr | Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title_full_unstemmed | Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title_short | Надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| title_sort | надпровідні гравіметри на основі сучасних наноматеріалів і квантових нейронних мереж |
| topic | магнітна підвіска лазерний інтерферометр оптичне волокно вимірювання зміщення квантова нейронна мережі |
| topic_facet | магнітна підвіска лазерний інтерферометр оптичне волокно вимірювання зміщення квантова нейронна мережі magnetic suspension laser interferometer optical fiber displacement measurement quantum neural network |
| url | https://journal.iasa.kpi.ua/article/view/269237 |
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