Resolution reduction of spectroscopic data
skyrock79
Sun, 04/15/2012 - 08:59 pm
I have a set of experimental spectra (absorption vs. energy) that I want to compare with some existing standard spectra. In order to do that accurately, I have to reduce the resolution of the experimental ones to match the resolution of the standard ones (e.g., reduced the data points of experimental ones from 700 to 150). I was told i need to reduce the resolution with a Gaussian function. Can anyone tell me how to realize this in igor?
Thanks
Dimin
--Jim Prouty
Software Engineer, WaveMetrics, Inc.
April 15, 2012 at 11:21 pm - Permalink
April 16, 2012 at 05:05 am - Permalink
I would disagree with Jim here about using a smoothing operation. I suggest that you want either to deconvolve a Gaussian transmission function from your experimetal spectrum or you want to decrease the number of points in the spectrum (or both).
I suggest, the latter operation is unnecessary. You can always overlay an experimental spectrum with or on a theoretical spectrum even though they have different number of points. The interpretation of your results will be independent of this.
I suggest that deconvolution of a function from experimental data is better done by doing the inverse operation, which is to convolve a Gaussian transmission function with the theoretical spectrum. Deconvolution has multiple caveats and tricks-of-the-trade that sometimes make it seem more of an art than a science. Convolution by comparison is a recipe that you apply once you have all the ingredients in place.
So, first review the Convolve operation in Igor Pro to become familar with how it works.
Next, define the full-width-half-maximum FWHM that you expect for your transmission function of your instrument. Create a Gaussian peak centered at position ZERO having this FWHM. You would do well to make use of the relationship that peak area is proportional to height*FWHM and create a spectroscopic Gaussian peak with a height that is calculated to give an area of unity (rather than a height of unity therefore giving an area of something other than unity). The three equations for spectroscopic Gaussian peaks are given below (given in LaTeX ... parse it at the link given after it and/or view the attached PNG). The symbols A, h, w, and p are area, height, half-width (1/2 of FWHM), and position, respectively.
S_{G}(h, w, p) = h\ \exp{\left(\frac{-4\ln(2)(x - p)^2}{w^2}\right)} \hspace*{1cm} A = \sqrt{\frac{\pi}{\ln(2)}} \left(\frac{hw}{2}\right) \\
S_{G}(A, w, p) = \left(\frac{2A}{w}\sqrt{\frac{\ln(2)}{\pi}}\right) \exp\left(\frac{-4\ln(2)(x-p)^2}{w^2}\right) \hspace*{1cm} h = \sqrt{\frac{\ln(2)}{\pi}} \left(\frac{2A}{w}\right) \\
S_{G}(h, A, p) = h\ \exp\left(\frac{-2\pi\ h^2\left(x-p\right)^2}{A^2}\right) \hspace*{1cm} w = \sqrt{\frac{\ln(2)}{\pi}} \left(\frac{2A}{h}\right)
http://www.codecogs.com/latex/eqneditor.php
Now, load your theoretical spectrum and convolve it with the Gaussian transmission function wave that you created. Overlay that convolution spectrum on your experimental spectrum. Adjust the height of the convolution result as you find appropriate to match the experimental spectrum. Viola -- you have a comparison ready for interpretation.
--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville
April 16, 2012 at 11:28 am - Permalink