Contributed paper
OPTO-ELECTRONICS REVIEW 13(3), 253–257
Influence of sun radiation on results of non-contact temperature
measurements in far infrared range
H. MADURA* and M. KO£ODZIEJCZYK
Institute of Optoelectronics, Military University of Technology, 2 Kaliskiego Str., 00-908 Warsaw
Non-contact measurements of an object temperature in IR range carried out in outdoor conditions can suffer from significant
errors. An error of temperature measurement can be very high when sun radiation after reflection from an object propagates
along optical axis of a measuring device (thermovision camera, pyrometer). Radiation beams reflected from an object and
object’s radiation itself are added and a final value of temperature is higher. The paper presents results of theoretical estimations of errors of temperature measurement and their comparison with experimental results. Calculations and measurements
were made for objects of various emissivities in a spectral range of 8–9 µm.
Keywords: pyrometry, thermography, sun radiation.
1. Introduction
To make proper temperature measurement with pyrometers, emissivity of an investigated object should be known.
Most frequently, a main source of measurement errors is
improperly taken emissivity value. In some types of pyrometers, influence of object emissivity on a result of temperature measurement is significantly reduced [1]. If temperature measurements are carried out for an object illuminated with sun radiation, beams of sun radiation reflected
from an object are added and the read value of the temperature is higher than actual one. In Refs. 2 and 3, IR pyrometers are described in which sun radiation is monitored but
influence of this radiation on a result of temperature measurement was not estimated. Influence of sun radiation on a
result of temperature measurement increases for low
emissivity objects as well as for objects of low temperature.
with spectral luminance of a source for the normal direction Ln(l,T) as
L n ( l, T ) »
é
ù
1
W
M( l, T ) ê
ú.
2
p
ë cm mmsr û
(2)
Knowing geometrical relations between a radiating object and a receiver of this radiation (Fig. 1), spectral distribution of intensity of radiation reaching input aperture of a
receiver [4] can be determined
E( l, T ) = L n ( l, T )
S1 cos q 1 cos q 2 é W ù
ê
ú,
2
R2
ë cm mm û
(3)
where S1 is the area of an object’s radiating surface, R is
the distance between a radiation source and a measuring
device in cm, q1 is the angle between a normal to object
1.1. Used relations and notations
According to the Planc’s law, the dependence of spectral
distribution of black body radiation is determined as
M( l, T ) =
5
l (e
c1
c 2 lT
é W ù
ê
ú,
- 1) ë cm 2 mm û
(1)
where Plank constants c 1 = 37417.7107 ±0.0029
(Wµm4cm–2) and c2 = 14387.752 ±0.025×10–2 µmK, is the
wavelength, and T is the temperature of a black body.
Spectral distribution of black body radiation is connected
*e-mail:
[email protected]
Opto-Electron. Rev., 13, no. 3, 2005
Fig. 1. Geometrical relations between surfaces emitting and
absorbing radiation and a camera or a pyrometer.
H. Madura
253
Influence of sun radiation on results of non-contact temperature measurements in far infrared range
surface and direction of radiation propagation, q2 is the angle between optical axis of a measuring device and direction of radiation propagation.
Assuming that q2 = 0°, and substituting Eq. (2) into Eq.
(3) we have
E( l, T ) =
S cos q 1 é W ù
1
M( l, T ) 1
ê
ú.
2
p
R2
ë cm mm û
(4)
Thus, total intensity of object radiation in the spectral
range of l1–l2 wavelengths is
E=
l2
ò E(l, T )dT
l1
é W
ê
ë cm 2
ù
ú.
û
(5)
Total power irradiated from an object reaching input
aperture of the optical system S2 is given as
P0 = S 2 E [W ],
(6)
where S2 (cm2) is the area of input aperture surface of a
measuring device.
2. Sun radiation
A temperature of the Sun surface is about 5900 K. Spectral
distribution of sun radiation is the best approximated by a
black body of the temperature of 5770 K, the size of which
corresponds to the Sun’s size [5]. This body emits uniform
radiation in all directions. Total intensity of sun radiation
measured outside the earth atmosphere is called solar constant. A value of a solar constant taken in 1981 by World
Meteorological Organization (WMO) is 1367 Wm–2. The
value of solar constant accepted in the year 2000 by American Society for Testing and Materials (ASTM) is 1366.1
±0.08% Wm–2 [6]. This value has been obtained due to
many-year registration of sun radiation in the range from
120 nm to 1000 µm [7].
Fig. 2. Solar spectral irradiance outside the atmosphere proposed
by ASTM.
254
Spectral solar irradiance outside the atmosphere El,
proposed by ASTM (Fig. 2), insignificantly differs from
the distribution proposed by WMO, especially for the
waves of wavelengths above 2 µm. These distributions are
used in various simulation programs, e.g., MODTRAN,
LOWTRAN or PCMODWIN. Using these programs, intensity of sun radiation reaching the Earth surface or coefficient of atmosphere transmittance can be determined.
Because of the earth atmosphere properties, only part of
sun radiation reaches the Earth surface. Sun radiation is absorbed and scattered by atmospheric gases and aerosols. A
ratio of sun radiation intensity measured outside the earth
atmosphere to sun radiation intensity reaching the Earth
surface, for particular wavelengths, is called spectral coefficient of the earth atmosphere transmittance tE(l).
Precise determination of tE(l) is difficult because it requires consideration of many factors and parameters describing the atmosphere characteristics. The most important factors are the content and condensation rate of water
steam and influence of gases and aerosols in particular layers of the atmosphere.
The tE(l) coefficient is also influenced by temperature
and atmospheric pressure. When the value of tE(l) is determined, a thickness of the earth atmosphere should be considered depending on a position of a measuring point at the
Earth surface in respect to the Sun.
The power of sun radiation PS reaching, through the atmosphere, the object of the surface S1 can be described as
l2
PS = S1 ò t E ( l )E l dl [W ].
(7)
l1
3. Model of object radiation
In real measuring conditions, a value of radiation reaching
input aperture of an optical system of a thermovision camera depends on many factors. In majority of cases we can
only estimate them because without using special apparatus
we cannot determine them precisely.
The main factor is radiant property of the object itself
which is called the emissivity e0. In measuring practice, often emissivity is not known and using available tables there
is no certainty for its proper determination. Thus, in some
measuring conditions the object’s emissivity can be significantly different. It results from the fact that emissivity depends on such factors as, e.g., structure and ratio of surface
oxidation, the object’s temperature T0, direction of observation or spectral range for which it is determined. Inaccurate determination of emissivity value of an object is a
main reason of measurement errors.
Other factors influencing a value of radiation reaching
input aperture of optical signal of a thermovision camera
are: radiation reflected from an object surface, absorption,
dispersion, and radiant properties of the atmosphere.
Opto-Electron. Rev., 13, no. 3, 2005
© 2005 COSiW SEP, Warsaw
Contributed paper
Fig. 3. Reflection of sun radiation from scattering (a) and mirror (b)
surfaces.
Total power reaching input aperture of optical system,
for typical measuring conditions, can be written in form of
expression used in majority of FLIR systems [8]
P = e 0 t a P0 + (1 - t a ) Pa + (1 - e 0 )t a Prefl [W ], (8)
where e0 is the object emissivity, ta is the transmittance coefficient of atmosphere between an object and a camera, P0
is the power of object radiation, Pa is the power of atmosphere radiation, and Prefl is the power of radiation reflected
from an object surface.
We can distinguish two basic radiation reflections from
an object surface, i.e., scattered reflection and mirror one
(Fig. 3).
For intensively scattering surfaces, the Lambert’s cosine law is used
Prefl = PS cos a cos b [W ],
Fig. 4. Solar spectral irradiance ES,l, determined with PcModWin
program for the angle of deflection 50 of the Sun from the zenith
and Rural aerosol model and visibility of 23 km.
(9)
where PS is the total sun radiation power incident on object’s surface, a is the angle of incidence, and b is the angle of reflection.
For smooth surfaces we can take, with a good approximation, that radiation reflection is of a mirror type, i.e., Prefl
» PS.
In the calculation model, it was taken that sun radiation
reflection from a plate surface is of a mirror type. Moreover,
it was assumed that for short distances between an object
and a camera ta = 1. Thus, finally, Eq. (8) is of the form
P = e 0 P0 + (1 - e 0 ) PS [W ].
(10)
4. Estimation of measurement errors.
Simulation results
Solar irradiance reaching the Earth surface in spectral
range of 8–9 µm was determined using PcModWin program (Fig. 4).
It was calculated that for weather conditions of the following parameters:
• angle of deflection of the Sun of 50°,
• metrological visibility of 23 km,
• cloudless sky,
• ambient temperature 285 K,
• atmospheric pressure 1027 hPa,
• relative air humidity 40%,
the total sun radiation intensity on the Earth surface was
about 24 mWcm–2.
Opto-Electron. Rev., 13, no. 3, 2005
Fig. 5. Algorithm used for calculation of a relative error of object’s
temperature reading.
H. Madura
255
Influence of sun radiation on results of non-contact temperature measurements in far infrared range
Fig. 6. Calculated relative error of temperature reading of the object
emissivity e0 = 0.2 for various values of sun radiation intensity.
On the basis of mathematical description of a phenomenon of sun radiation reflection, the algorithm has been written which was used for simulations in MATLAB calculation environment. A relative error of temperature reading
has been estimated for various values of sun radiation intensity (Figs. 6 and 7).
Fig. 8. Scheme of a measuring set-up for investigations of sun
radiation influence on measurement results of object’s
temperature.
Fig. 9. Spectral emissivity of S1-S5 plates.
Fig. 7. Calculated relative error of temperature reading of the object
emissivity e0 = 0.9 for various values of sun radiation intensity.
5. Experimental results
A measuring set-up has been built to investigate sun radiation influence on an error of temperature measurement in
the field conditions (Fig. 8).
A temperature of S1-S5 metal plates having various
emissivities was measured. The plates were subsequently
situated inside a housing to have them in a field of view of
a thermovision camera. A distance between a camera’s objective and a plate was 120 cm.
Sun radiation reaches the examined plate through a
rectangular hole cut in a front wall of a housing to illuminate only a part of the investigated plate. Due to this, simultaneous measurement of a temperature of the plate’s
part reached by sun radiation (in Fig. 8 denoted with lighter
colour) and the part without sun radiation (darker colour)
was made. Sun rays, after reflection from the investigated
plate propagate along an optical axis of a thermovision
camera.
256
Fig. 10. A thermogram of S1 plate of the temperature T0 = 285 K and
a profile of temperature distribution along the marked straight line.
Opto-Electron. Rev., 13, no. 3, 2005
© 2005 COSiW SEP, Warsaw
Contributed paper
Basing on the results of experimental investigations, a
relative error of the temperature reading d, caused by reflection of sun radiation from the object’s surface, can be
determined.
Figure 12 presents comparison of experimental and calculation results. Insignificant differences between theoretical and experimental results testify on good consistence between a model and experiment. Theoretical values are little
higher than experimental ones. So, it should be supposed
that it is due to consideration of sun radiation in a model.
6. Conclusions
Fig. 11. Spectrum of radiation intensity of non illuminated and
illuminated object (S1 plate, T0 = 290 K).
In order to eliminate a heating effect of the investigated
plates because of incident sun radiation, a rectangular hole
was being opened only for measurement duration, i.e., for
about 2 s.
A temperature of the investigated plates was stated with
a heater and monitored with a thermometer.
Spectral emissivity of the plates was determined using
Specord 71 IR spectrophotometer (Fig. 9). Emissivity averaged for a given range of camera’s operation was introduced into a thermovision camera.
During experimental investigations, the thermograms
were obtained that are used for estimation of sun radiation
influence on temperature measurement results. In a
thermogram, Fig. 10, a distinct place can be seen from
which the sun rays have been reflected. A temperature
measured with a camera at this place significantly differs
from the actual object’s temperature which did not change
during a measurement.
Spectrum of the object’s own radiation and spectrum of
the object illuminated with sun radiation were determined
using SR-5000 spectroradiometer of the set-up shown in
Fig. 8. According to predictions, a value of sun radiation
after reflection from an object was added to the object’s radiation (Fig. 11).
Fig. 12. Relative error of temperature reading of the investigated
plates S3 and S4 for temperatures 285 K, 295 K, and 305 K. The
intensity of incident sun radiation ES » 24 µWcm–2.
Opto-Electron. Rev., 13, no. 3, 2005
The presented calculation and measurement results indicate
that sun radiation, even in far infrared range, can cause significant errors in temperature measurements when
thermovision cameras or pyrometers are used. It should be
taken into account that when the temperature measurements of the objects illuminated with sun radiation are
made, a measurement error increases for low-emissivity
objects and low-temperature ones. An error of temperature
measurement depends on a shape and kind of a surface of
the investigated object and a position of a pyrometer (IR
camera) in relation to a direction of propagation of main
flux of the reflected sun radiation.
Thus, new methods of temperature measurement and
new measuring devices should be find. In new measuring
devices, influence of sun radiation on the result of temperature measurement should be reduced or an user of a measuring device should be informed that the measurement is
improper (with error).
References
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(2004).
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H. Madura
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Opto-Electron. Rev., 13, no. 3, 2005
© 2005 COSiW SEP, Warsaw