This discussion focuses on convoluting atomic data using a Gaussian profile with a Full Width at Half Maximum (FWHM) of 20mm. The user, Kartik, seeks assistance in processing wavelength data on the x-axis and intensity data on the y-axis. Key recommendations include sorting transitions by wavelength, creating uniformly spaced x values for smoothness, and employing a computational approach to sum contributions from Gaussian lines efficiently. The discussion emphasizes the importance of managing computational efficiency to avoid floating point errors in Excel.
PREREQUISITESData analysts, physicists, and researchers working with atomic data who need to perform convolutions for spectral analysis and improve data processing efficiency.
Kartik82 said:Hi, Can anyone please help me in convoluting atomic data. Along x-axis I have wavelength and on Y axis I have scattered intensity. I want to convolute with FWHM of 20mm.
Thanks
Kartik
Kartik82 said:Hi,
Thanks for your reply. Its Gaussian profile. As an example please see the attached one data set that I want to convolute.
Hi, X-axis is wavelength and y-axis is intensity.Quantum Defect said:X and Y are what?
Kartik82 said:Hi, X-axis is wavelength and y-axis is intensity.
Kartik
Hi,Quantum Defect said:First thing generally is to sort the transitions by wavelength/frequency however you want to do things.
You can do this in excel, but it is more efficient to write a program to do this.
If you do this in excel, you want to create a set of x values that are uniformly spaced, with a point density that is good enough to give you a smoothness that you can live with. I.e. 3 points over your FWHM is probably too coarse, but 3,000 is way to many. You decide. Populate a column vector with these values.
You can create the spectrum of Gaussian lines in a variety of ways. The simplest (but computationally inefficient way) is to add up all of the contributions for all of the lines at each X grid point.
e.g. if x = 8.0000, y = SUM(Intensity_i*(exp[-(8.0000-x_i)^2/sigma] ) Where "Intensity_i" are your y-values in your original spreadsheet, the "x_i" are the x values in your original spreadsheet, and sigma is obtained from the Gaussian that you are assuming. If the different transitions have different effective Gaussian widths, you could have a third column in your original spreadsheet. In excel, you may get a floating point error if you are too far away from the line (i.e. if x is too far away from x_i), in which case you may have to play with the limits of the sum. In a program, you could fix these with something that checks to see if x is more than 4 sigma away from the xi, and not bother to calculate the intensity if the line falls outside of this range.