Several Questions:
I am measuring Time resolved Photoluminescence(TRPL) decay of nanowires using TCSPC system. The 4 exponential function( including deconvolution of IRF) fits the data better than 3 exponential functions. I need to verify that 4 exponentials are a must for fitting.
1. Is the Least square(LS) curve fitting method a good method for TRPL decay analysis ? Is the LS curve fitting method biased toward initial guess ?
2.How should I validate the 4 exponential fitting ? Does statistical F test helps ?
3. Does Laguerre polynomial based deconvolution method helps? Is it unbiased method ? Is there any available software package which will use this method to do the deconvolution ?
Any suggestions will be helpful for us i.e. papers, books, notes etc
I hardly can help you with deconvolution but want to raise another issue. Is there any physical rationale behind 4 exponential terms? The point is that any decay can be fitted with a sufficient number of exponents, but your curve may simply be non-exponential and these additional terms do not bring you any knowledge. Can you expect that your nanowires contain exactly for different populations of emitting centers?
Dear @Baichhabi, the following article discusses the issue, see the following link:
http://www.sciencedirect.com/science/article/pii/0096300379900213
A novel transform is presented which maps continuum functions (such as probability densities) into discrete sequences and permits rapid numerical calculation of convolutions, multiple convolutions, and Neumann expansions for Volterra integral equations. The transform is based on the Laguerre polynomials, associated Laguerre functions and their simple convolution properties. A second transform employs Erlang functions as elements of the basis. The limitations and advantages of the two transforms are discussed. Numerical inversion of Laplace transforms relates simply to the Erlang transform. The deconvolution of two functions, i.e., the solution of a(t) = x(t)*b(t), may also be obtained quickly in this way.
I hope that helps.
I AGREE WITH ROMAN KUBRIN, WHAT WE USUALLY SEEK FROM FITTING AN EMISSION SPECTRUM IS AN INFORMATION ABOUT THE PHYSICAL PROCESSES INVOLVED IN THE EMISSION, HENCE WE WE'D BETTER USE A MODEL WHICH TAKES INTO ACCOUNT THE PHYSICAL PARAMETERS CONNECTED TO THE PROCESSES MENTIONED ABOVE, FOR INSTANCE, FRANCK CONDON ANALYSIS MAY BE USEFUL.
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