Crystal optical method for temperature measuring
A new crystal optical method for temperature measuring based on the sign inversion of birefringence ∆n and temperature dependence of ∆n(T) is substantiated. The respective characteristics of some crystals are presented, which confirm good metrological and exploitation properties of the method. I...
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irk-123456789-1206602017-06-13T03:03:36Z Crystal optical method for temperature measuring Romanyuk, M.O. Andriyevsky, B. Kostetsky, O. Romanyuk, M.M. Stadnyk, V. A new crystal optical method for temperature measuring based on the sign inversion of birefringence ∆n and temperature dependence of ∆n(T) is substantiated. The respective characteristics of some crystals are presented, which confirm good metrological and exploitation properties of the method. It is noted that the method solves some problems which arise in thermometry based on thermoelectricity and thermoresistance. The proposed method also gives better possibilities for measuring the temperature in hard conditions (in the region of high electric and magnetic fields, rotating workpieces etc.). Обгрунтовується новий кристалооптичний метод вимірювання температури на базі інверсії знаку двозаломлення ∆n та температурної залежності ∆n(T). Наведено відповідні характеристики деяких кристалів, які підтверджують високі метрологічні та експлуатаційні характеристики методу. Відзначається, що метод розв’язує деякі проблеми, що виникають перед термометрією на базі термоелектрики і термоопору, а також відкриває більш високі можливості вимірювань температури у важких умовах (в області високих електричних та магнітних полів, деталей, що обертаються і ін.). 2002 Article Crystal optical method for temperature measuring / M.O. Romanyuk, B. Andriyevsky, O. Kostetsky, M.M. Romanyuk, V. Stadnyk // Condensed Matter Physics. — 2002. — Т. 5, № 3(31). — С. 579-586. — Бібліогр.: 14 назв. — англ. 1607-324X PACS: 78.20.Nv, 07.20.Dt DOI:10.5488/CMP.5.3.579 http://dspace.nbuv.gov.ua/handle/123456789/120660 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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DSpace DC |
| language |
English |
| description |
A new crystal optical method for temperature measuring based on the sign
inversion of birefringence ∆n and temperature dependence of ∆n(T)
is substantiated. The respective characteristics of some crystals are presented,
which confirm good metrological and exploitation properties of the
method. It is noted that the method solves some problems which arise in
thermometry based on thermoelectricity and thermoresistance. The proposed
method also gives better possibilities for measuring the temperature
in hard conditions (in the region of high electric and magnetic fields, rotating
workpieces etc.). |
| format |
Article |
| author |
Romanyuk, M.O. Andriyevsky, B. Kostetsky, O. Romanyuk, M.M. Stadnyk, V. |
| spellingShingle |
Romanyuk, M.O. Andriyevsky, B. Kostetsky, O. Romanyuk, M.M. Stadnyk, V. Crystal optical method for temperature measuring Condensed Matter Physics |
| author_facet |
Romanyuk, M.O. Andriyevsky, B. Kostetsky, O. Romanyuk, M.M. Stadnyk, V. |
| author_sort |
Romanyuk, M.O. |
| title |
Crystal optical method for temperature measuring |
| title_short |
Crystal optical method for temperature measuring |
| title_full |
Crystal optical method for temperature measuring |
| title_fullStr |
Crystal optical method for temperature measuring |
| title_full_unstemmed |
Crystal optical method for temperature measuring |
| title_sort |
crystal optical method for temperature measuring |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2002 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120660 |
| citation_txt |
Crystal optical method for temperature
measuring / M.O. Romanyuk, B. Andriyevsky, O. Kostetsky, M.M. Romanyuk, V. Stadnyk // Condensed Matter Physics. — 2002. — Т. 5, № 3(31). — С. 579-586. — Бібліогр.: 14 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT romanyukmo crystalopticalmethodfortemperaturemeasuring AT andriyevskyb crystalopticalmethodfortemperaturemeasuring AT kostetskyo crystalopticalmethodfortemperaturemeasuring AT romanyukmm crystalopticalmethodfortemperaturemeasuring AT stadnykv crystalopticalmethodfortemperaturemeasuring |
| first_indexed |
2025-07-08T18:17:52Z |
| last_indexed |
2025-07-08T18:17:52Z |
| _version_ |
1837103761414160384 |
| fulltext |
Condensed Matter Physics, 2002, Vol. 5, No. 3(31), pp. 579–586
Crystal optical method for temperature
measuring
M.O.Romanyuk 1 , B.Andriyevsky 1 , O.Kostetsky 2 ,
M.M.Romanyuk 3 , V.Stadnyk 1
1 The Ivan Franko National University of Lviv,
8 Kyryla i Mefodiya Str., 79005 Lviv, Ukraine
2 Lviv State Agrarian University, 80381 Dublyany, Ukraine
3 The National University “Lviv Politekhnika”,
12 Stepana Bandery Str., 79013 Lviv, Ukraine
Received August 7, 2001
A new crystal optical method for temperature measuring based on the sign
inversion of birefringence ∆n and temperature dependence of ∆n(T )
is substantiated. The respective characteristics of some crystals are pre-
sented, which confirm good metrological and exploitation properties of the
method. It is noted that the method solves some problems which arise in
thermometry based on thermoelectricity and thermoresistance. The pro-
posed method also gives better possibilities for measuring the temperature
in hard conditions (in the region of high electric and magnetic fields, rotat-
ing workpieces etc.).
Key words: temperature, inversion of birefringence sign, scale of
temperature
PACS: 78.20.Nv, 07.20.Dt
1. General statements
Some physical laws are used for assigning and measuring a temperature as well as
for creating the reference temperature points [1]. Thermodetectors based on thermo-
electricity and on thermoresistance are the most prevalent [2,3]. They need separate
calibration and periodical verification of its stability. It is important to ensure that
the magnitude of the electric current or the voltage detected have a single tempera-
ture origin. All these peculiarities are connected with diffusion of components in the
contacts of two melted metals of a thermocouple, impurities in thermoresistance,
and the change of crystalline structure of active elements of the sensor.
This leads to the idea of a thermocouple based on single crystals [4], substitution
or improvement of the galvanic connection of sensor with the indicator, and creating
a sensor with the intrinsic reference point of temperature [5]. The latter purpose is
c© M.O.Romanyuk, B.Andriyevsky, O.Kostetsky, M.M.Romanyuk, V.Stadnyk 579
M.O.Romanyuk et al.
achieved through the use of a special headpiece on a thermocouple of certain metal,
the temperature of which determines the reference temperature point in which the
rate of increase or decrease of temperature is changed at the constant power of the
heater or the cooler. Another metal of a headpiece is needed to obtain a different
reference point.
Galvanic connections can be avoided using the optical sensors of temperature.
One of this type of sensors is the optical scattering cell [6] filled with liquid and
glass powder. This liquid and powder differ by the magnitude of refractive indices,
its temperature and spectral dependence. When these refractive indices differ, the
cell scatters the incident light strongly. When a crossing of the refractive index dis-
persions ni(λ) (i = 1, 2) takes place, the cell medium becomes optically homogeneous
for a certain wavelength, and thereby the light scattering decreases. This peculiarity
shows the magnitude of temperature.
The proposed method of defining and measuring the temperature is based on
the sign inversion of birefringence ∆n of optically biaxial crystals [7]. This makes
it possible to satisfy the above mentioned requirements of thermometry that arise
based on thermoelectromotion and thermoresistance. In the proposed method a sin-
gle crystal of good optical quality plays a role of the sensor, the point of birefringence
inversion appears as an internal reference point, and the laser light beam ensures
optical connection between the sensor and the indicator (screen or photodetector in
the region of interference pattern). In this case the respective temperature point is
fixed based on the interference pattern form or on the photocurrent minimum . This
is the positive and clear peculiarity of the method. In such a way, having a set of
monochromatic light sources one can fix different temperature points. When a sin-
gle light source is presented (laser, for instance), then the deviation of temperature
(T −Ti) from the point of sign inversion of birefringence can be determined based on
temperature changes of birefringence ∆n(T −Ti) (optical path difference ∆ = d·∆n)
of the same sensor measured in the direction of sign inversion of birefringence. The
latter value can be determined using the known methods [6].
2. Sign inversion of birefringence
Several dozens of crystals are known today in which the curves of spectral depen-
dences ni(λ) (i = 1, 2) cross one another in the point λ0. The symmetry of optical
indicatrix increases and the sign of birefringence for the respective direction of light
propagation is changed in this point. In the case of optically uniaxial crystals such a
point is called an isotropic one and a crystal becomes optically isotropic. The change
of birefringence sign can be determined using only appropriate compensators. An
optically biaxial crystal becomes optically uniaxial in this point, so one deals with
an isotropic direction and this point can be seen through the appearance of a cono-
scopic pattern, characteristic of the cut of optically uniaxial crystal perpendicular
to the optical axis. The change of a corresponding sign can be seen by the change of
spatial orientation of the plane of the optical axes by 90◦ of optically biaxial states
of the crystal [6].
580
Crystal optical method
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Figure 1. Spectral dependence of
birefringence ∆nx(λ) of deuterated
Rochelle salt crystal at the tempera-
ture 4.2 K.
Figure 2. Temperature dependences of
the birefringence ∆nx(T ) for light wave-
length λ = 600 nm and the wavelength
of sign inversion of birefringence λi(T )
for deuterated Rochelle salt crystal.
Spectral inversion of the sign of birefringence (SISB) in crystals has been studied
by several authors [8–10]. Several dozens of crystals are known at present which
possess this property, and thus the temperature and baric shifts of this point are
determined.
Figures 1 and 2 show spectral (figure 1) and temperature (figure 2) dependences
of birefringence ∆nx and the wavelength of sign inversion of birefringence λi for
deuterated Rochelle salt crystal [11]. Points of the dotted curve correspond to a
conoscopic pattern characteristic of the uniaxial crystal for the cut perpendicular to
the optical axes. Analogous dependences for a set of other crystals are presented in
[12]. General information about some of these crystals is presented in table 1.
Analytically, SISB can be described based on the multioscillator Selmeier disper-
sion formula. This way, the factors determinative for the spectral-and-temperature
dependence of the isotropic state can be determined. So far there is no microscopic
theory of this phenomenon.
Temperature sensitivity of the spectral position of the isotropic state depends
upon spectral and temperature dependence of birefringence ∆n which can be easily
determined in the experiment:
∂λ0
∂T
= −
(
∂∆n
∂T
)
/
(
∂∆n
∂λ
)
. (1)
This relation is important from practical viewpoint.
3. Principles of crystal-and-optical thermometer based on the
inversion of sign of birefringence
The use of ISB for measuring the temperature and for creating the reference
temperature points has been proposed in [13].
581
M.O.Romanyuk et al.
Ti
I
T
P
C
A S
DII o
V
Figure 3. Scheme of the crystal optical thermometer based on the ISB (a) and
the method of identification of temperature for a given wavelength λ (b). I0, I –
intensities of light; P, A – polarizers; C – crystal optical sensor of temperature;
V – volume of measured temperature; S – screen with a hole in its middle; D –
photodetector.
The plane parallel plate of a transparent optically biaxial crystal with ISB point
cut perpendicularly to the acute bisectrix between optical axes acts here as a sensor
of temperature. The entering plane of a plate is mat, and the exit plane is polished.
This plate is placed in a zone of measuring the temperature by diagonal manner
relating the directions of light polarization in crossed light polarizers. It is placed
in this zone perpendicularly to the laser beam, and two mutually perpendicular
directions of light polarization in this crystalline plate are rotated by the angle of
45◦ relating the other two mutually perpendicular directions of light polarization in
the polarizer and in the analyzer. In this case, the object detected is an interference
conoscopic pattern or an electric signal of the photodetector (figure 3).
A signal of the photodetector is determined by the intensity I of an exit light
according to the known relation,
I = I0 sin2 2α sin2
πd (n′ − n′′)
λ
, (2)
where I0, α, d, (n′ − n′′), λ are the intensity of the incident light, the angle between
the directions of light polarization in the crystal and in the polarizers, the thickness
of the sample in the direction of the light beam, corresponding to birefringence,
wavelength, respectively. It is obvious that the best arrangement corresponds to the
case α = 45◦.
Sensitivity of the method is determined by the parameters of the sensor and the
receiving apparatus and is placed in the range of 10−1–10−3 K. For instance, in the
case of δI ∼ 0.01I0, d = 0.1 cm, ∂∆n/∂T ∼ 5 ·10−5 K−1, λ = 600 nm the inaccuracy
of temperature determination is δT ≈ 2 · 10−2 K.
582
Crystal optical method
Table 1. Characteristics of the temperature-and-spectral diagrams of the inver-
sion of sign of birefringence (ISB) for several crystals [14].
Crystal,
cut
Ranges of the exis-
tence of ISB
Temperature sen-
sitivity of spectr-
al position of the
ISP
∂λ0/∂T , nm/K
Temperature
range, K
Spectral
range, nm
∆λ, nm ∆T , K averaged maximal
KNaC4H4O6·4H2O
X
465–280 4.2–330 –0.56 –0.8 20–250
295–465
KNaC4H4O6·4D2O
X
463–279 4.2–330 –0.57 –0.8 20–250
295–465
NH4NaC4H4O6·4H2O
Z
1200–380 130–330 –4.1 –14 130–180
500–1200
NH4NaC4H4O6·4H2O
X
295–250 4.2–95 –0.5 –1.0 20–95
290–250
K2Ca(SO4)2·H2O
X
1000–200 270–470 –0.4 –4.0 270–470
200–1000
(C6H4)COOHCOOK
Z
500–350 4.2–560 –0.26 –0.29 50–560
350–500
Rb2SO4, Y 1100–250 72–160 –10 –80 500–1100
X 1100–300 270–350 –10 –20 500–1100
K2SO4, Y 850–250 617 ∞ ∞ 850–250
X 850–250 700 850–250
LiKSO4, Z 360–240 180–420 –0.5 –0.8 180–420
240–360
(NH4)2BeF4, Y 1100–240
1100–240
76–78
304–312
–110 ∞
∞
76 – Tmelt
400–1100
312 – Tmelt
500
LiNbO3, X 600 1100
583
M.O.Romanyuk et al.
4. Distinctive features of the method
1. One crystalline sample can be used for installation of several reference tem-
perature points by changing the wavelength of light at which the ISB takes
place.
2. A reference temperature point can be found through the qualitative charac-
teristic (minimum of photosignal) or through the form of conoscopic pattern,
characteristic of the uniaxial crystal cut perpendicularly to the optical axis.
3. The degree of selective light absorption (by wavelength) of the intermediate
surrounding does not influence the nongalvanic connection of sensors and the
receiver. For instance, the latter influence takes place in the case of optical
pirometry.
4. The proposed method enables us to measure the temperature of the rotating
workpieces and the workpieces being under high electric voltage.
Drawbacks of the method:
1. Relatively high inertiality of the sensor is caused by low thermal conductivity
of the sensitive dielectric crystal.
2. It is necessary to calibrate the sensor for different sensitive elements (as a
secondary temperature sensor) and to align it with the laser light beam.
3. A necessity of using a set of monochromatic light sources (filters, monochro-
mator, lasers).
5. Combination of birefringence and inversion of sign of bire-
fringence
It is convenient to work with a single source of monochromatic light when mea-
suring the temperature. In this case the point of ISB can be regarded as an internal
reference temperature point and the change of temperature δT can be estimated
based on birefringence change δ∆n. In this case one can use the crystals, for which
the corresponding points of ISB are placed in inconvenient spectral regions. An idea
of this method is clear from figure 4. Taking into account the number of character-
istic conoscopic patterns (lemniscates) and their orientation one can estimate the
magnitude and the sign of deviation from the point of ISB for the wavelength of
the light used. Extrema of photocurrent are registered by inversion counter, which
is one of the possible versions of accounting a sign of the birefringence change [14].
Thus, the use of temperature-and-spectral dependence of ISB makes it possible to
determine reference temperature points based the on light wavelength of interference
conoscopic pattern. Combination of such a point for one wavelength with a change
of birefringence for this wavelength enables us to measure the temperature simply
in a wide range relating the point of ISB.
584
Crystal optical method
Figure 4. Conoscopic patterns for DRS crystal at the temperatures T < Ti (left
pattern), T = Ti (middle pattern), and T > Ti (rigth pattern) for the light prop-
agation along X -axes (λ = 632.8 nm). Ti is the temperature of sign birefringence
inversion.
Crystalline sensor of temperature, internal reference point as ISB and optical
connection of the sensor with the indicator create new possibilities for thermometry
of special objects.
Authors are thankful to Corresponding Member Natl. Acad. Sci. of Ukraine
Prof. I.V.Stasyuk, Prof. R.R.Levytsky, and Dr. A.P.Moina for stimulating interest
to this paper and for useful discussions.
References
1. Kuinn T. Temperature. Moskow, Mir, 1985.
2. Gerashchenko O.A., Yeriomina A.N., Stadnik B.I. Temperature Measuring. Kyiv,
Tekhnika, 1989.
3. Anatychuk L.M. Thermoelements and Thermoelectric Arrangements. Kyiv, Tekhnika,
1979.
4. Kuritnykh I.P., Burkhanov G.S., Stadnik B.I. Materials of High Temperature Ther-
mometry. Moskow, 1986.
5. Sachenko A.A., Milchenko V.Yu., Kogan V.V. Measure of Temperature by Sensors
with Build-in Calibrators. Moskow, 1986.
6. Chernyakova M.M., Steblyk V.A., Voitsekhov Yu.R. Devices for Measure of Temper-
ature. Patent USSR, No. 402762. Information Bulletine, No. 2, 1973.
7. Romanyuk M.O. Crystal Optics. Kyiv, 1997.
8. Brodin M.S. Optical properties of single crystals CdS. // Solid State Physics, 1960,
vol. 2, No. 9, p. 2152–2157.
9. Solovyov L.E., Rudakov V.S. Phenomena of pseudo crossing of dispersional curves. //
Vesnik Leningradskogo universiteta. Fisika i khimiya, 1968, No. 4, p. 23–26.
10. Suslikov L.M., Khasitarchanov Yu.A., Gadmashi Z.P. Birefringence of uniaxially
stressed crystals of AgGaSe2. // Solid State Physics, 1990, vol. 32, No. 2, p. 632–
634.
11. Gaba V.M., Romanyuk N.A., Franiv A.V. Properties of optical indicatrix of deuterated
Rochelle salt crystals. // Ukr. J. Phys., 1982, vol. 27, No. 3, p. 333–338.
585
M.O.Romanyuk et al.
12. Romanyuk M.O. Temperature-and-spectral diagrams of inversion of sign of birefrin-
gence and their possible applications. // Scientific Society of T.Shevchenko in Lviv.
Physical collection, 1993, vol. 1, p. 291–303.
13. Romanyuk N.A., Kostetskii A.M. Method of measuring absolute temperature in trans-
parent isotropic media. Patent USSR, No. 742725, 1980.
14. Romanyuk N.N., Romanyuk N.A., Kostetskii A.M. Polarization- and-optical device
for reversible count of interference fringes. // Patent USSR, No. 1032329, Information
Bulletine, No. 28, 1983.
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