How to calculate blackbody temperature from radiance band?

AI Thread Summary
To calculate blackbody temperature from radiance in a specific spectral band, the inverse of Planck's law is utilized. The formula T=hc/{L*k *{ln{2h*c^2/(L^5*R)}+1}} allows for the determination of temperature when given radiance, where L is the wavelength, k is the Boltzmann constant, h is Planck's constant, c is the speed of light, and R is the radiance. The challenge arises when the radiance is measured over a band, rather than at a single wavelength, complicating the temperature calculation. The peak wavelength also influences temperature, but the primary concern is how to derive temperature from the total radiance across the specified band. Understanding these relationships is crucial for accurate temperature estimations from radiance data.
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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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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.
 
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
 

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