Calculate Transmission & Concentration Using Beer-Lambert Law

[nordmoon]

Let say that you use a LED and direct it through a gas. You measure the 'light' transmitted through the gas and the 'light' entering the gas to obtain the transmission.

Since the Beer–Lambert law is wavelength dependent and the LED is broadband within the region of a for example C02 band, how can you determine the transmission of this wavelength integrated light with the ultimute goal of determine the concentration of the species investigated? Beer–Lambert law states that

I/I0 = exp(kv*l) = exp(sigma*N*l)where kv (absorption coefficient) is wavelength dependent. You have calculated kv per wavelength, but since the light measured is broadband how can you 'simulate' the transmission with known kv? Sigma is the absorption cross section.

I guess the problem is that the light 'contains many wavelength (and not just one)' and that the Beer law is for one wavelength since the absorption coefficient is wavelength dependent. So how can you extract the concentration information in such arrangement? The detector sees a passband of wavelengths and each wavelength has its own extinction coefficient. Thismeans that the detector sees a summation of the effect of each individual wavelength within the passband.

I hope I made any sense.

 

[Rajini]

Hi,
concentration information can be obtained from the density and cross section [of the materials used]..these are not wavelength dependent.

 

[charng]

Thank you for your question. The Beer-Lambert law is indeed wavelength dependent, and in order to accurately determine the transmission and concentration of a gas using this law, we need to take into account the broadband nature of the LED light source.

One approach to solving this problem would be to use a spectrometer to measure the intensity of light at different wavelengths within the LED's emission spectrum. This would allow us to obtain a more accurate absorption coefficient (kv) for each individual wavelength. We could then use this information to calculate the overall transmission of the LED light through the gas by integrating the contributions from each individual wavelength.

However, this method may not be practical or feasible in some cases. Another approach would be to use a reference gas with a known concentration of the species being investigated, and measure the transmission of the LED light through this reference gas. This would provide us with a baseline for the transmission of the LED light through the gas, and we could then use this information to calculate the concentration of the species in the unknown gas sample.

In summary, the key to accurately determining the concentration of a species using the Beer-Lambert law in this setup is to take into account the broadband nature of the LED light source and to either use a spectrometer or a reference gas to obtain a more accurate absorption coefficient. I hope this helps clarify the issue. Thank you.