suppose we record a PL spectra of a dye from 350 nm to 800 nm. In X-axis the wavelength in nm and in Y-axis the intensity in arbitrary unit. Now how to calculate Jacobian? is it the direct transformation of Energy from wavelength will be put in X-axis? how to include Y-axis intensity in Jacobian calculation? as far as I came to know is f(E) = -f(lambda) hc/E^2. Suppose let's say at X-axis the wavelength is 350 nm and corresponding intensity in Y-axis is 1100. Now what / how the Jacobian calculation performed. Thank you.
Dear Animesh, as a synthetic inorganic chemist I'm absolutely not an expert in this field enough to give you a qualified answer to your interesting technical question. However, I just came across the following potentially useful article which might help you in your analysis:
Get the Basics Right: Jacobian Conversion of Wavelength and Energy Scales for Quantitative Analysis of Emission Spectra
Article Get the Basics Right: Jacobian Conversion of Wavelength and ...
Unfortunately this paper has not been posted as public full text on RG. Perhaps you can access it through your institution. I also noticed that one of the authors has an RG profile (https://www.researchgate.net/profile/Patanjali-Kambhampati). It is certainly worth a try to contact him via RG and request the full text of the paper directly from him. In my experience most authors quickly respond to such full text requests.
Good luck with your work and best wishes, Frank Edelmann
Dear Frank T. Edelmann ...Thank you for your information but even this article couldn't cover all the points. Fortunately I figured it out after going through all the mathematical part of Jacobian transformation. Thank you again.
Hello Animesh Mandal I am just following up from your question and I need to do a similar analysis with my photoluminescence spectra. My first question is: does the Jacobian transformation apply for PL spectra or just absorption spectra?
If the former is also true, could you please give me a few details on how you did this, please?
Thank you,
Cheers
Dear Hellen Nalumaga: I think the Jacobian transformation must be applied to the ordinate axis in any intensity spectrum. So, as far as I know, if you want to transform an intensity spectrum plotted as Intensity as a function of wavelength in an energy spectrum, you must substitute lambda by hc/E in the abscise axis and multiply the ordinate axis by the Jacobian Transformation factor hc/E^2. This is because the area under the curve must be preserved in both spectra. But whenever a quotient between intensities is made the transformation does not have to be applied because the transformation factor cancels out. For example, when the optical absorbance (or the optical absorption coefficient, alpha) is calculated from an optical transmission spectrum, a quotient between the intensity of the incident light and that of the transmitted one is doing. In this case, it is the absorbance (alpha) value what must be preserved during a conversion of the abscissa axis from wavelength to energy or viceversa.
But the question I have is how to calculate the average wavelength in a luminescence spectrum? Should we start from the spectrum as a function of wavelength or energy? In this case what we have is a quotient of integrals in which in the argument is the intensity function to be transformed when passing from wavelength to energy or viceversa. Someone will have an answer?
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