Hi Everyone!

Please help me with my problem.
I need to calculate temperature T2 with known temperature T1, emissivity E1 and emissivty E2, (ambient temperature = Tamb and atmosphere temperature = Tatm, τ=tao).

I'm use Stefan-Boltzmann radiation law for a graybody radiator:

T2=(E1/E2)^0.25 * T1

and I have wrong results (I’m compare it with results of FLIR ThermaCam Researcher).
Inside FLIR SDK Manual I’m find this formula:

Wtot= ετ Wobj + (1 - ε) τ Wamb + (1 - τ) Watm

But I don’t understand how I can use it in my problem.
Please give some advice or some links where I can read about this.

Sorry for my bad English. I’m just a Russian student.

Artem.

The Stefan-Boltzmann equation and its "Temperature to the 4th power" is based on ALL the radiation from the shortest of wavelength to the longest.  We only look at a small part of that spectrum (8 to 12 microns?).  Then the different wavelengths get attenuated differently by lens coatings, lens materials, detector coatings etc.  Camera manufacturers used to supply curves for their cameras so you could do the type of thing you are trying.  Now that all seams to be locked up in proprietary software.

Your English seems very good to me!! 

 

Artem,

The first important thing so consider when using any of these equations is that you must use Kelvin, not degrees Celsius.

John is correct. Stefan-Boltzmann is meant to calculate the power emitted by a perfect blackbody over the entire electro-magnetic spectrum. An IR temperature measurement device only measures in a certain portion of this spectrum (with the exception of a total radiation thermometer). In the case of many handheld devices this can be 8-12um or 8-14um.

The second comment is that assuming a material to be a graybody is dangerous, since most materials do not act as graybodies. (graybody being defined as a material with constant emissivity over all wavelengths)  See http://masterweb.jpl.nasa.gov/reference/paints.htm

 If you are measuring an opaque material, τ=0. This simplifies the power equation to:

Wtot= ε Wobj + (1 - ε) Wamb

(The original equation you had came from this one by assuming (1 - ε) Wamb<< ε Wobj, assuming both Wtot1=Wtot2, and assuming Wobj=σT^4.)

The problem now is properly calculating W. Planck's Law gives us a possible solution for a single bandwidth.

L=c1/λ^5/(exp(c2/λT)-1)

To get W from this for a wideband instrument you can do one of two things. You can use a center bandwidth (say 11um for the 8-14um band) for λ. The second way is to do a numerical integration on Planck's Law over the entire bandwidth.

Either way, it is a complicated problem to solve. It may be easier to do this calculation in a spreadsheet.

Frank

Thank you for help.

This thread is interesting indeed.  Artem, I've had some similar questions recently so this thread is helping me too.  Thanks for starting it.

Frank, one question I had after reading your post was concerning the assumed value for T in Watm.  I believe Watm in this equation is referring to the transmissivity of the atmosphere instead of the object itself.  If I understand it correctly (not certain that I do),  T would normally be 1 instead of zero. Setting T to 1 would result in a multiplier of (1-1)* Watm, which would zero out Watm as you describe.  As I do much of my work with close ambient and dewpoint spread, there are times when T drops below 1 and if affects what I see.

Thanks for the excellent discussion on the partial radiation sample of the camera.  Very useful indeed.

 Cheers

-John

 

 

Using Stefan-Boltzman law for graybody should be valid so long as you are using a camera with a limited spectral response. This is a simplification that is done within the camera anyway when determining emissivity. When we calculate/estimate emissivity, the figure we end up with is a graybody equivalent, the actual emissivity may vary quite a bit between the upper an lower wavelengths, and since we dont always need the exact spectral curve this gray equivalent is more than adequate.

I suggest you post this on the flir customer help site http://flir.custhelp.com this is the best place to get answers about FLIR SDK. You should be able to post in Russian, but I suggest you post in English also.

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Bob Berry
BINDT, IRT Level 3 EL, Level 3 CV
Thermal Vision
8 Old Fair Green
Dunboyne
Co Meath
Ireland
bob@thermalvision.ie
www.thermalvision.ie