How to calculate blackbody temperature from radiance band?

In summary, the conversation is about calculating blackbody radiance in a spectral band from a given temperature, and the desire to do the reverse - calculate the temperature from a given radiance in a spectral band. The formula for this calculation is provided, along with a reference for further details. The conversation also mentions that the peak value of wavelength is related to temperature, and that the desired calculation is for a radiance over a band, not just at a single wavelength.
  • #1
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I know how to calculate blackbody radiance in a spectral band from a temperature by integrating (or summing) planks function.

How can I do the reverse? For example, I have a Radiance of 1000 W/m^2/sr in the 3-5um band, I'd like to be able to calculate 666.6K.
 
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  • #2
T=hc/{L*k *{ln{2h*c^2/(L^5*R)}+1}}
the above formula is quoted in the reference given below;
L is wavelength ,k is Boltzman constant, h and c are usual well known constant R is radiance...well i do not know details you have to search.

ref.-http://oceancolor.gsfc.nasa.gov/forum/oceancolor/topic_show.pl?tid=5478

off course the peak value of wavelength is also related with temp.
 
  • #3
I did see that, and that gives the temperature for one wavelength.

My radiance is over a band.
For example, in a BB calculator, I can put in 666.6K, over the 3-5um band, and it will give me 1000 W/m^2/sr
How do I do the reverse? I have 1000 W/m^2/sr in the 3-5um and I want to calculate the temperature
 

1. What is blackbody radiation and why is it important in calculating temperature?

Blackbody radiation is the thermal electromagnetic radiation emitted by a perfect blackbody at a given temperature. It is important in calculating temperature because it is a fundamental concept in thermodynamics and helps us understand the behavior of objects at different temperatures.

2. How do you measure radiance band to calculate blackbody temperature?

Radiance band is typically measured using specialized instruments such as spectrometers or radiometers. These instruments can measure the intensity of radiation at different wavelengths, which can then be used to calculate blackbody temperature through mathematical equations.

3. What factors can affect the accuracy of blackbody temperature calculations from radiance band?

Some factors that can affect the accuracy of blackbody temperature calculations include the emissivity of the object being measured, the distance between the object and the measuring instrument, and the temperature range being measured. Other factors such as atmospheric conditions and instrument calibration can also play a role.

4. Can blackbody temperature be calculated for non-blackbody objects?

Yes, blackbody temperature calculations can be used for non-blackbody objects as long as their emissivity is known. This is because the calculations take into account the emissivity factor, which represents how efficiently the object emits radiation compared to a perfect blackbody.

5. How is the Stefan-Boltzmann law used to calculate blackbody temperature from radiance band?

The Stefan-Boltzmann law is a fundamental equation in thermodynamics that relates the radiated power of a blackbody to its temperature. It is used in conjunction with other equations, such as Planck's law, to calculate blackbody temperature from radiance band measurements.

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