I remain unclear about your intent.

* Deconvolution is the process to remove a transmission function (spread) from a spectrum, generally to obtain the true spectrum independent of the instrument. Do you have a transmission function spectrum that you need to remove from the set of spectra?

* Peak fitting is the process to obtain component peaks from an envelope spectrum. In this case, the starting point is typically a first-principles definition of the peak shapes (e.g. Gaussian, Lorentz, Voigt, ...) and their parameters (e.g. position, half-width, shape factor ...). Do you have a set of first-principle definitions of peak shapes for the PL process?

I suspect that you are doing peak fitting NOT deconvolution. Spectroscopists tend to abuse the latter term (I often claim this is because deconvolution sounds more sophisticated and makes the process thereby seem "clever" compared to peak fitting). In this case, you need to have a few points completed before you start:

* First-principle definitions of your peak shapes and their key parameters (e.g. Voigt with a specific half-width and shape factor). You seem to lack this information entirely, and you probably need to research this topic further. Otherwise, you will fit the peaks to something that has no truth in the physical process, and your answers will be nonsense.

* Clean spectra (e.g. high S/N and broad backgrounds around the entire range). Your spectra have good S/N but they are cut off abruptly at the right side. This problem will limit the accuracy of the peak fitting results.

* Experience using a program to do peak fitting. Since you include Origin and MatLab in your keywords, you probably have this experience already (my recommended program for spectroscopy is Igor Pro, but that is a topic for another thread). When your questions also are asking about the best programming methods to use for peak fitting in your case ... that topic is better for off-line consultations.

In summary: Peak fitting is not a one-pass, non-interactive, black box process. You do NOT put in your spectra, push a button, and get out a truth. Instead, you put in your spectra, turn the knobs to settings that should apply for a physical process (i.e. provide peak shapes and parameters for the physical process), get out a result, and determine whether the result (the peak fit) is reliable. If it is not reliable or consistent, you start again with a different set of peak parameters and repeat the process. Your questions suggest that you have some further research to do.

I hope this helps motivate you toward a successful conclusion of your work.

Gaussian function is defined by 3 parameters: the height of the curve's peak, the position of the center of the peak and the standard deviation (the width of the "bell", https://en.wikipedia.org/wiki/Gaussian_function). Therefore you can fit your data with bell shaped peak by Gaussian. Maybe you have to add additional parameter to define a constant level of your signal.

In MATLAB you can use Curve Fitting Toolbox (http://www.mathworks.com/help/curvefit).

More convenient for this purpose is an arctangent-normal distribution of intensity in the fluorescence spectrum, the application of which is described in the following works:

https://www.researchgate.net/publication/315706188_Luminescent_transformers_of_radiation_and_description_of_the_spectra_of_fluorescence_of_dyes_by_arctangent-normal_distribution?_iepl%5BviewId%5D=Pewu0CJDt2DWUcIjYwg5LtZy&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BtargetEntityId%5D=PB%3A315706188&_iepl%5BinteractionType%5D=publicationTitle

https://www.researchgate.net/publication/252114778_Method_of_approximating_diffuse_electronic-vibrational_molecular_spectra?_iepl%5BviewId%5D=cmn5iOZHQsEtN7EPaobc9i5l&_iepl%5BprofilePublicationItemVariant%5D=default&_iepl%5Bcontexts%5D%5B0%5D=prfpi&_iepl%5BtargetEntityId%5D=PB%3A252114778&_iepl%5BinteractionType%5D=publicationTitle

Conference Paper Luminescent transformers of radiation and description of the...

Article Method of approximating diffuse electronic-vibrational molec...

Perhaps you should post a brief example of the evolution of the spectra as a function of temperature. The problem that you are trying to solve is likely otherwise only clear to specialists. Are you deconvolving (e.g. removing a transmission function) or simply peak fitting (e.g. adding component peaks to create a single envelope peak)? Do your PL peaks change in other ways (height, width, shape) as they merge in their positions?

Dear Jeffrey ,

I have attached my PL spectra with this comment. I want to deconvolute two peaks (appearing clearly at 7K) at each further temperatures. I believe it's easier for you to suggest something now.

Regards, 

Dear Vladimir and Alexander,

I will get back to you once I finish reading articles suggested by you.

Regards,

I remain unclear about your intent.

* Deconvolution is the process to remove a transmission function (spread) from a spectrum, generally to obtain the true spectrum independent of the instrument. Do you have a transmission function spectrum that you need to remove from the set of spectra?

* Peak fitting is the process to obtain component peaks from an envelope spectrum. In this case, the starting point is typically a first-principles definition of the peak shapes (e.g. Gaussian, Lorentz, Voigt, ...) and their parameters (e.g. position, half-width, shape factor ...). Do you have a set of first-principle definitions of peak shapes for the PL process?

I suspect that you are doing peak fitting NOT deconvolution. Spectroscopists tend to abuse the latter term (I often claim this is because deconvolution sounds more sophisticated and makes the process thereby seem "clever" compared to peak fitting). In this case, you need to have a few points completed before you start:

* First-principle definitions of your peak shapes and their key parameters (e.g. Voigt with a specific half-width and shape factor). You seem to lack this information entirely, and you probably need to research this topic further. Otherwise, you will fit the peaks to something that has no truth in the physical process, and your answers will be nonsense.

* Clean spectra (e.g. high S/N and broad backgrounds around the entire range). Your spectra have good S/N but they are cut off abruptly at the right side. This problem will limit the accuracy of the peak fitting results.

* Experience using a program to do peak fitting. Since you include Origin and MatLab in your keywords, you probably have this experience already (my recommended program for spectroscopy is Igor Pro, but that is a topic for another thread). When your questions also are asking about the best programming methods to use for peak fitting in your case ... that topic is better for off-line consultations.

In summary: Peak fitting is not a one-pass, non-interactive, black box process. You do NOT put in your spectra, push a button, and get out a truth. Instead, you put in your spectra, turn the knobs to settings that should apply for a physical process (i.e. provide peak shapes and parameters for the physical process), get out a result, and determine whether the result (the peak fit) is reliable. If it is not reliable or consistent, you start again with a different set of peak parameters and repeat the process. Your questions suggest that you have some further research to do.

I hope this helps motivate you toward a successful conclusion of your work.

I am not sure to understand completely the problem.

If your fit function is a bigaussian function ,with 6 parameters that all change with the temperature, the problem is a non linear one, which is a little bit more difficult.

If the positions of the maxima are the only variables, this is a linear problem which has a single solution(if it exists) given by a matrix inversion.