Introduction
The ability of infrared thermometers to measure
temperature without coming in contact with a particular material is based on
the fact that every object emits radiant energy whose intensity is a function
of temperature. The general relationship between the radiance of a perfect emitter
with wavelength and temperature is expressed by Planck’s law, which is plotted
in figure 1.
Fig 1: Planck distribution of radiated energy from a
blackbody.
A ‘blackbody’
is a hypothetical entity, which absorbs all energy, reflects none and emits
energy with perfect efficiency. It is supposed to satisfy the ideal conditions
of:
·
Absorbing
all incident radiation regardless wavelength and direction.
·
Always
emitting the maximum possible amount of energy regardless wavelength for any
prescribed temperature.
·
Radiation
from a blackbody resembles diffusion; it is independent of direction.
A ‘graybody’ is an entity for which the emittance, reflectance and transmittance are constant for all wavelengths.
Fig 2: Radiation from a body in space.
Radiation coming from any body in space is the sum of the emitted, reflected and transmitted energies. (fig. 2). Opaque bodies do not transmit energy. The ratio of the emittance of a given graybody and the idea blackbody is called emissivity. Thus, emissivity can have the maximum value of 1.0, for the case of a blackbody, and 0.0, for the case of a perfect reflector.
Therefore, it can also be defined as:
(1)
where: 
= emissivity
=
reflectivity
In practice it is a function of both wavelength and temperature.
Infrared Measurement Theory
The three
basic modes of heat transfer are conduction, convection and radiation. Thermal
radiation can be understood as the heat that leaves an object by way of
electromagnetic radiation. Emittance is the ratio of the amount of heat
radiated by a material as compared to a black body, and it is always less than
one. Shiny, metallic materials tend to have low emittance, while matte, dark
colored materials tend to have high emittance.
Heat transfer by radiation, is described by the
Stefan-Boltzmann law:
(2)
where: 
= heat flow
rate
= emittance
of the material
= 5.67 10-8
[W/m2K4]
(Stefan-Boltzmann constant)
= temperature at the
point of
interest [oK]
= temperature of the
surroundings [oK]
Fig 3: Schematic of optics system of Inframetrics model 600
IR Scanner.
Industrial infrared thermometers usually consist of different elements, such as the collecting optics, the radiation detector and some form of indicator. For the system used, the collecting optics, consisting of a germanium window and the focusing lens, are combined with a set of electromechanical servos to perform horizontal and vertical scanning, so that the whole field of view is monitored. The scan mirrors are contained in a sealed evacuated module for increased efficiency. The detector views a thermal reference target 60 times per second and the Mercury/Cadmium/Telluride detector is cooled by liquid nitrogen to 77 oK for maximum thermal sensitivity and spatial resolution. The schematic of the optics system is shown in figure 3.
Emissivity Model
It is obvious, that the emissive capability of steel
depends on many parameters. In the present work, an effort is made to isolate
the effect of the two main factors that cause spatial and temporal variations
of emissivity, the surface condition and the temperature level.
It is assumed that the total value of emissivity is
the baseline emissivity of the material, modified by a factor depending on
temperature and another one depending on surface conditions, in this case,
color bands:
(3)
The baseline emissivity, is a handout value for the
particular material. The effect of color and temperature can be decoupled as
follows:
(4)
where: 
is the low temperature emissivity, as this
is calculated by the first set of experiments.
In the same
sense, the effect of color can be isolated as follows:
(5)
where: 
is the reference
emissivity, as this is calculated at a ‘clean’ point on the sample in the
second set of experiments and shown in figure 13.
Experimental Method
Spatial emissivity distribution
The whole idea was motivated
from the observation of the surface of beads conducted with plasma arc on 304
stainless steel plates. In the ‘as welded’ condition, they all had a similar
appearance, a series of colored zones, apparently associated with carbonization
and other microstructural transformations having taken place during and right
after the welding process. Figure 4 is a photograph of one of the as welded
samples, where the color pattern is visible.
Initially, a set of low temperature measurements was
conducted, in order to identify the spatial distribution of emissivity on the
surface of the ‘as welded’ samples. During the experiment, the samples were
heated up to 40oC in order to obtain a good resolution of the
infrared images.
Fig 5: Laboratory setup for spatial
emissivity
variation measurements.
The spatial
variation of emissivity for this particular process, plasma arc welding, is
mainly due to microstructural transformations taking place in the material
during and after the welding process, and as a result, the appearance of all
the samples is similar. Their common characteristic is the repetition of a
series of color bands, whose width varies with the welding conditions. Figure 4
is a photograph of the ‘as welded’ surface condition of the specimens. Thus,
the low temperature measurements were focused on identifying the influence of
surface color on the emissive capability of the steel. It should be noted, that
changes in surface roughness and capillary effects of the fusion zone were
incorporated in the calculations as an extra color, namely ‘black ridged’. The
laboratory setup used for the previously described experiment, is shown in
figure 4 and explained in a following paragraph.
Based on the surface appearance, the most prominent
color zones were identified by visual observation. Points belonging in these
zones were specified as data collection points. The infrared images captured on
the VHS tape, as those shown in figures 10a and 10b, were the data source. The
data processing methodology is described in full detail in the following
paragraph.
Data processing methodology:
Several parameters had to be calculated before the
actual emittance could be obtained. Those parameters were the emission level,
the relative emission level, the reference emittance, the emission ratio and
the averages.
An infrared camera,
obtains images of relative emission levels, based on a preset temperature
range. The appropriate temperature range
is chosen so that the greatest contrast in the image can be obtained without
losing any information due to the measurements being too high or too low and
therefore out of range. The emission level information was
quantitatively calculated based on the values of pixel intensity and the
temperature range set on the infrared camera according to the following
equation:
(6)
where
: 
=emission level
=minimum
temperature of the range
=maximum
temperature of the range
=pixel value
The
relative emission level was defined as follows:
(7)
where: 
= average background
emission level.
= relative emission level
The background emission level was measured with a flat, unheated sheet of aluminum foil. If the aluminum sheet is placed directly in front of the sample, then it is assumed that all surrounding emissions are reflected off the sheet and read by the camera. This is a calibration procedure that takes into account all the emissions that are surrounding the sample but not from the sample itself.
The emission ratio is a particular point’s
relative level divided by a reference point’s relative level. The reference
point is chosen to be far enough from the weld so that the surface has remained
unaffected, thus, its emittance is considered as a baseline. The reference
emittance is calculated by the use of the Stefan-Boltzmann law:
(8)
The infrared thermometer can give the value of
temperature at a point, if its emissivity is known. Therefore, if we set an
emissivity value of 1, the IR camera can provide us with a corresponding
temperature output 
:
(9)
With an additional direct temperature measurement 
on the reference
point, the previous equation can be solved for the reference emittance:
(10)
where: 
= reference
emittance
= IR camera
temperature reading on the reference point for
an emissivity value of 1
= directly
measured temperature on the reference point
=directly measured temperature of the surrounding area
After obtaining the reference emittance value, the emission ratio can be calculated as described above, by the relationship:
(11)
where : 
=
emission ratio
= relative
emission at a point
= relative emission at
the reference point
Finally, the average emittance is simply the
averaged value of all the measurements for the same colored zone for all the
samples.
(12)
where: i =
color zone number
j = sample number
k = number of measurements for zone i on sample j
Experimental Setup
Spatial emissivity measurements
In order to raise their temperature to the 40 oC
level, the samples were heated over a hot plate, and immediately placed
vertically in a stable ceramic base. The infrared camera was placed opposite
from the samples at a 9cm distance, which gave images of adequate resolution.
Fig. 6: Laboratory setup for investigating the thermal variation of
emissivity.
A direct temperature measurement was taken on the
samples with a thermocouple for calibration purposes. All the infrared camera
readings were recorded on a VHS tape for further processing.
An oven,
heated by resistance coils embedded in an open cylinder made of ceramic
insulating material, was used to heat the samples. Stainless-Steel samples were
placed on a grid-like tray in the center of the oven. Small fans were placed
along the rim of the oven to accelerate the heating of the sample by forced
convection.
A K type thermocouple was placed
in a notch cut into the metal sample, so that the temperature of the sample
could be read at any time. An Intrametrics
600 infrared (IR) camera was focused on the sample at a 58°
angle. The output from the camera was
fed to a T.V. monitor and recorded on a VHS tape. The overall setup is shown in
figure 6.
Fig.
7: Position of the samples on the grid, before
heating.
Figures 7 and 8, show the
position of the samples placed on the grid, when the grid is high, out of the
oven and when the oven is red-hot respectively.
A thick metal plate covered in a
smooth sheet of aluminum foil was placed in front of sample when taking
background measurements. Large metal tongs, slightly above the sample, held the
metal plate, at a horizontal orientation.
Each sample was placed on the
oven’s tray and slowly heated to approximately 480°C. Starting at 50°C infrared images and measurements were captured every 40°C to 60°C. When taking the infrared readings, first an
appropriate range was selected in the Infrared camera settings, in order to
obtain the best resolution for the emission levels being measured. This way the greatest contrast in the image
could be obtained without losing any information due to the measurements being
too high or too low and therefore out of range.
Fig.
8: Position of the samples inside the oven.
Once an appropriate range
was obtained VCR recording of the images was started. Within the IF camera the emittance of the sample was set equal
to 1. The camera was set to point mode, which would allow a nodal temperature
reading at a point near the thermocouple notch. Simultaneously the actual temperature of the sample was read
with the thermocouple. This
information, along with the emission level at this point, can be used to
calculate a reference emittance value for each image. Color and gray scale
infrared images were recorded as well as the range of levels for those images.
Then
a flat aluminum sheet was placed in front of the sample, as shown in figure 9,
and infrared images were recorded at its appropriate range. If the aluminum sheet is placed directly in
front of the sample, then it
is assumed that all surround emissions are reflected off the sheet and read by
the camera.
This is a
calibration procedure that takes into account all the emissions that are
surrounding the sample but not from the sample itself.
Fig. 9: Initializing the IR measurements taking into account background
radiation.
The video recorded images were transported into
computer image processing application (NIH Image 1.61) for analysis. An
example of a color infrared radiation field recorded at 350 oC is
shown in figure 10.
Fig.
10: Infrared radiation recorded at 350 oC.
Results
The emission field recorded at low temperatures is
shown in figures 11a and 11b in color and black and white respectively. The
grayscale images were used to convert the image data to temperatures.
The colors shown in figure 11a are not the actual
colors of the specimen’s surface, but they are color contours of the emission
levels for the chosen temperature range. The colormap is shown at the bottom of
the figure; red corresponds to areas emitting the most, and blue to areas that
emit less.
Those images
were post processed as described in the data post processing methodology and
the emissivity data obtained for every color band and for different samples
were averaged. The raw experimental data collected, are presented in table ….,
in the appendix.
Fig.
11a: Color
map of infrared radiation coming from
a sample close to room temperature.
Fig.
11b:
Grayscale map of infrared radiation
coming from
a sample close to room
temperature.
The variation
of emissivity over the different color bands as calculated with the previously
described methodology is plotted in figure 12.
Fig.
12: Color related variation of emissivity
This experiment
helped us define the spatial distribution of emissivity, mainly depending on
surface color and roughness. The next step was to define the temperature effect
on the emissive capability of steel.
For this case, a different laboratory setup was designed, in order to be
able to maintain the samples at high temperatures. This setup has been
described above, and is schematically shown in figure 13.
Fig. 13: Emissivity variation over a temperature range at a ‘clean’ area of
the sample.
A series of radiocity measurements were taken at
40-60 oC temperature intervals, up to the 500 oC range.
The experimental procedure has already been described in full detail. An extra measurement
was also taken at each temperature level on a ‘clean’ area of the sample that had
no original surface patterns, neither of color, nor of surface roughness.
The values of the
emittance at that point were plotted versus temperature in figure 13.
Discussion
- Actual Emissivity values as measured during experiments. (e total):
The
average (temperature) values are used in calculations related to the effect of
temperature where the color effect is not taken into account, and
the average (color) values are the means of the actual emissivity of
a particular color band over the whole
temperature
range. The calculated values are presented in table 1.
- Cold Emissivity values as measured during experiments. (e cold):
These
values are the mean emissivity values measured in low temperature, therefore,
they only include the effect of color/surface condition on the baseline
emissivity of the material as this last one is found in handbooks. The obtained
data after post-processing are summarized in table 2.
Table
2: Cold emissivity
- Reference Emissivity values as measured during experiments. (e reference):
These
values are the mean emissivity values measured at various temperatures at a
‘clean’ unaffected by process transformations point, therefore, they include
the combined effect of temperature as well as the effect of changes of
color/surface condition during the experiments, such as carbonization during
heating. These values are presented in table 3.
Table
3: Reference emissivity
·
Proposed
Model:
As analyzed in a previous paragraph, it is assumed that
the total value of emissivity is the baseline emissivity of the material,
modified by a factor depending on temperature and another one depending on
surface conditions, in this case, color bands (eq. 3):
The baseline emissivity, is a handout value for the particular material. The effect of color and temperature can be decoupled as follows (eq. 4):
where: 
is the low temperature emissivity, as this
is calculated by the first set of experiments.
The
experimental value of 
can be calculated if
we divide the values of table 1 by the values of table 2 that correspond to the
same color. The variation of the average values for all colors with temperature
is plotted in figure 14.
In the same
sense, the effect of color can be isolated as follows (eq. 5):
where: 
is the reference
emissivity, as this is calculated at a ‘clean’ point on the sample in the
second set of experiments.
Similarly, the
experimental value of 
can be calculated if
we divide the values of table 1 by the values of table 3 that correspond to the
same temperature. The variation of the average values throughout the
temperature range with color is plotted in figure 15.
Fig. 14: Color
related correction factor
Fig. 15: Temperature
related correction factor
·
Calculation
of baseline emissivity
Based
on the proposed model, we can used the equation: 
to calculate the
baseline value of emissivity and see if it is comparable with handbook values
for stainless steel. In order to do this we need to multiply the corresponding
values of (
).
Fig. 16: Experimental
estimation of baseline emissivity
The baseline
value for the different colors over the temperature range is shown in figure 15
and the mean value for all the colors is found to be 0.417. This value is in
very good accordance with handbook values. [Table of Emissivity of various
surfaces, Micron Instrument Company Inc., page 8, stainless steel 304, after
heating….]