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A method to measure temperature and emissivity
06-05-2013, 03:41 PM (This post was last modified: 12-03-2013 06:43 AM by acardoso.)
Post: #1
A method to measure temperature and emissivity
The traditional method to measure emissivity, and consequently temperature, intrinsically has two source of error, at least.

1st, we assume the electrical tape has 95% of emissivity, but we cannot be sure. Unless, we use certified tape, otherwise, like any manufacturing process, a drift around exact value is to be expected.

2nd, usually we apply the electrical tape over a less emitting surface. This means temperature on the tape will stabilize below or above, as Trefl is below or above surface temperature. Besides this, we cannot apply tape on the surface of liquid materials or over too hot surfaces, because the tape will sink or burn.

Looking for the equation

[Image: attachment.php?aid=116]

We can see

2 variables – T4 and ε
2 parameters – W and Trefl4, and
1 constant – σ.

Conditions necessary, and probably enough to guarantee the existence of a unique solution for the equation system.

[Image: attachment.php?aid=117]


After solving the system in order to T4 and ε, the solutions are

[Image: attachment.php?aid=118]


The condition (Trefl14 -Trefl24) ≠ 0 guarantees the linear independence of equations W1 and W2.
T and TreflX are expressed in Kelvin, t and tsurface in degrees Celsius.
σ= 5.670373(21) × 10−8 W m−2 K−4, tsurface = apparent temperature on the surface measured with camera set for 1 at emissivity.

To get the data to obtain the solutions, simply shoot 2 thermograms of the same scene with different Trefl.

Adverse conditions at the outside, like clean sky quickly shifting to cloudy sky and vice-versa which are a snag with other technics, are an advantage with this technic.

Formulas for LabView, Matlab, Maple

ε=-(-Trefl1^4*sigma+Trefl2^4*sigma+W1-W2)/(sigma*(Trefl1^4-Trefl2^4))
t=((W1*Trefl2^4-W2*Trefl1^4)/(-Trefl1^4*sigma+Trefl2^4*sigma+W1-W2))^(1/4)+273.15

Formulas for Excel

ε=-(-(Trefl1^4)*sigma+(Trefl2^4)*sigma+W1_-W2_)/(sigma*(Trefl1^4-Trefl2^4))
t=((W1_*Trefl2^4-W2_*Trefl1^4-W1_-W2_)/(-(Trefl1^4)*sigma+(Trefl2^4)*sigma+W1_-W2_))^(1/4)-273.15
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07-10-2013, 10:29 AM
Post: #2
RE: A method to measure temperature and emissivity
(06-05-2013 03:41 PM)acardoso Wrote:  [Image: attachment.php?aid=116]

There are some assumptions made here.

First, the assumption is emissivity is gray. In fact emissivity for most if not materials has a spectral component. This means if the average emissivity of an object in the 8 – 14 µm band is 0.95, at 3.9 µm it may be something else. I have measured paints where the emissivity drops to somewhere around 0.80 at 3.9 µm.

Second, the use of the Stefan-Boltzmann Law assumes the use of a total radiation thermometer (one with no band limits). In reality, we use instruments with band limits. In recent years some variation of the 8 – 14 µm band has become widespread.

ASTM E2758 gives a method for calculating temperature readout difference based on emissivity difference. This is based largely on work done by Peter Saunders at MSL in New Zealand. This work is contained in TG22. It uses the Sakuma-Hattori Equation for the calculation. This gives the possibility of calculating for the band limited case.

So, in the first equation, a more meaningful solution can be provided if Sakuma-Hattori is used instead of Stefan-Boltzmann.

TG22 and a companion spreadsheet can be found here:
http://msl.irl.cri.nz/training-and-resou...cal-guides

The Wikipedia entry for the Sakuma-Hattori Equation may be useful.
http://en.wikipedia.org/wiki/Sakuma%E2%8...i_equation

And here is an example of a VBA function for the SH Equation

Function TtoS(TC As Double, A As Double, B As Double, C As Double)

Const c2 As Double = 14387.752
Const T0 As Double = 273.15
Dim T As Double

T = TC + T0
TtoS = C / (Exp(c2 / (A * T + B)) - 1)

End Function
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07-11-2013, 07:25 PM
Post: #3
RE: A method to measure temperature and emissivity
A, B, C stand for?
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08-06-2013, 02:32 PM
Post: #4
RE: A method to measure temperature and emissivity
(07-11-2013 07:25 PM)acardoso Wrote:  A, B, C stand for?

A, B, and C are constants (or parameters) that are specific to a radiation thermometer (or IR thermometer or thermal imager). When trying to fit RT radiance to blackbody temperature, these three parameters are adjusted for best fit.

For work in uncertainty calculation and trying to understand the effect of a wrong emissivity setting, there are fixed values that can be used based on the RT’s spectral bandwidth (ie. an 8 – 14 um device). In TG22, Peter Saunders gives the equations to calculate these. Basically, ‘C’ is a gain factor and can be set to 1. ‘A’ relates to the effective wavelength of the RT, and ‘B’ relates to the bandwidth of the RT. The effective wavelength will generally be lower than the center wavelength of the instrument.

Frank
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08-18-2013, 10:22 AM (This post was last modified: 08-18-2013 01:21 PM by acardoso.)
Post: #5
RE: A method to measure temperature and emissivity
Same approach but using Sakuma-Hattori equation

.pdf  Sakuma-Hattori equation.pdf (Size: 39.72 KB / Downloads: 45)
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03-24-2014, 06:37 PM
Post: #6
RE: A method to measure temperature and emissivity
WOW . I going to catch up with you guys in a year or two on this one.
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10-01-2014, 05:11 AM
Post: #7
RE: A method to measure temperature and emissivity
Hi guys, this is really useful. I was wondering is there a formula to calculate the emissivity of an object that has a varying surface texture.

I was also reading that the emissivity of the material changes with temperature which makes sense, is this correct?

Many thanks for the response
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10-07-2014, 07:39 AM
Post: #8
RE: A method to measure temperature and emissivity
(10-01-2014 05:11 AM)thermographer Wrote:  Hi guys, this is really useful. I was wondering is there a formula to calculate the emissivity of an object that has a varying surface texture.

I was also reading that the emissivity of the material changes with temperature which makes sense, is this correct?

Many thanks for the response


Varying surface texture is likely to mean varying emissivity. You can either measure the emissivity at various points, or used an averaged emissivity value. The correct approach will depend on what you are trying to do.

Emissivity does change with temperature. On metals the emissivity tends to increase slowly as the temperature increases, and then it usually increases rapidly as the metal approaches melting point. On non-metals emissivity tends to decrease as the temperature increases.
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