Fitting K412 (quick fit) · NeXLSpectrum.jl

Quick Quantifying K412 using NeXLSpectrum VectorQuant

Fred Schamber taught me this trick for quantifying spectrum extremely quickly. It works reasonably well for a moderate number of ROIs, particularly when few of the ROIs interfere.

Use the NeXLSpectrum to load, plot, fit and report the quantification of a set of K412 spectra.

Loading NeXLSpectrum also automatically makes NeXLCore and NeXLUncertainties available.

Loading the Gadfly library adds plotting support to NeXLSpectrum.

using NeXLSpectrum              # Provides spectrum reading and fitting tools
using NeXLMatrixCorrection      # Provides `quant` to convert k-ratios to mass fraction.
using Gadfly                    # Plotting
using DataFrames, Latexify      # Tables

Read in the Spectra

path = joinpath(@__DIR__, "K412 spectra")
# Load the unknowns 
unks = map(0:4) do i
  loadspectrum(joinpath(path, "III-E K412[$i][4].msa"))
end
# Create a detector model to match the unknown spectra
det = matching(unks[1], 132.0, 10)

BasicEDS[4096 chs, 1.63032 + 9.99856⋅ch eV, 132.0 eV @ Mn K-L3, 10 ch LLD, 
[Be,Sc,Ba,Pu]]

Name	BeamEnergy	ProbeCurrent	LiveTime	RealTime	Coating	Integral	Material
III-E K412[0][all]	2e+04	1.114	235.5	286.3	nothing	8.08e+06	K412
III-E K412[1][all]	2e+04	1.114	235.4	286.2	nothing	8.077e+06	K412
III-E K412[2][all]	2e+04	1.112	235.5	286.3	nothing	8.084e+06	K412
III-E K412[3][all]	2e+04	1.11	235.4	286.3	nothing	8.087e+06	K412
III-E K412[4][all]	2e+04	1.11	235.4	286.2	nothing	8.081e+06	K412

Notice that the spectra all have 1) live-time (:LiveTime); 2) probe-current (:ProbeCurrent); 3) take-off angle (:TakeOffAngle); 4) beam energy (:BeamEnergy); and detector (:Detector) properties defined. These properties are necessary for extracting the k-ratios and estimating the composition.

unks[1][:LiveTime], unks[1][:ProbeCurrent], unks[1][:TakeOffAngle], unks[1][:BeamEnergy]

(235.48403, 1.11355, 0.6108652381980153, 20000.0)

The Unknowns

display(plot(unks..., klms=[n"O",n"Mg",n"Al",n"Si",n"Ca",n"Fe"], xmax=8.0e3))

The Reference Spectra

Build a convenient structure so it is easy to appreciate the necessary information and to splat it into filteredReference.

ffrs = references( [
  reference(n"Al", joinpath(path, "Al2O3 std.msa"), mat"Al2O3" ), #
  reference(n"Mg", joinpath(path, "MgO std.msa"), mat"MgO" ),   #
  reference(n"Fe", joinpath(path, "Fe std.msa"), mat"Fe" ),    #
  reference(n"Si", joinpath(path, "SiO2 std.msa"), mat"SiO2" ),  #
  reference(n"O", joinpath(path, "SiO2 std.msa"), mat"SiO2" ),  #
  reference(n"Ca", joinpath(path, "CaF2 std.msa"), mat"CaF2" ) 
], det)
display(plot( spectra(ffrs)..., klms= [n"O",n"Mg",n"Al",n"Si",n"Ca",n"Fe"], xmax=8.0e3))

Filter the Reference Spectra and Compute the VectorQuant Structure

vq = VectorQuant(ffrs)
plot(vq, 1:800)

Let's take a look at a residual spectrum by plotting one of the FilterFitResult objects. Perform the fit and look at the residual

res = map(unks) do unk
  fit_spectrum(unk, vq)
end
plot(res[1])

Compare this with the weighted fit

resfull = map(unks) do unk
  fit_spectrum(unk, ffrs)
end
plot(resfull[1])

Now the full data set...

Spectra	k[O K-L3 + 1 other, SiO2]	Δk[O K-L3 + 1 other, SiO2]	k[Fe L3-M5 + 13 others, Fe]	Δk[Fe L3-M5 + 13 others, Fe]	k[Mg K-L3 + 1 other, MgO]	Δk[Mg K-L3 + 1 other, MgO]	k[Al K-L3 + 3 others, Al2O3]	Δk[Al K-L3 + 3 others, Al2O3]	k[Si K-L3 + 3 others, SiO2]	Δk[Si K-L3 + 3 others, SiO2]	k[Ca K-L3 + 3 others, CaF2]	Δk[Ca K-L3 + 3 others, CaF2]	k[Fe K-L3 + 1 other, Fe]	Δk[Fe K-L3 + 1 other, Fe]	k[Fe K-M3 + 3 others, Fe]	Δk[Fe K-M3 + 3 others, Fe]
III-E K412[0][all]	0.646	0.0007025	0.04247	0.0001609	0.1473	0.0001513	0.0669	0.000103	0.3508	0.0002465	0.1922	0.0001964	0.06683	0.0001282	0.06666	0.0003453
III-E K412[1][all]	0.648	0.0007037	0.04215	0.0001603	0.1472	0.0001513	0.0667	0.0001029	0.3499	0.0002462	0.1916	0.0001961	0.06701	0.0001284	0.06714	0.0003466
III-E K412[2][all]	0.6485	0.0007045	0.04243	0.000161	0.1477	0.0001516	0.06701	0.0001032	0.351	0.0002468	0.1922	0.0001966	0.06683	0.0001283	0.06683	0.000346
III-E K412[3][all]	0.653	0.0007075	0.04192	0.0001601	0.1479	0.0001519	0.06708	0.0001033	0.3518	0.0002473	0.1926	0.000197	0.06684	0.0001284	0.06759	0.0003483
III-E K412[4][all]	0.6514	0.0007067	0.0415	0.0001593	0.1479	0.0001519	0.06722	0.0001035	0.3518	0.0002473	0.192	0.0001967	0.06687	0.0001285	0.06634	0.0003451

Spectra	k[O K-L3 + 1 other, SiO2]	Δk[O K-L3 + 1 other, SiO2]	k[Fe L3-M5 + 13 others, Fe]	Δk[Fe L3-M5 + 13 others, Fe]	k[Mg K-L3 + 1 other, MgO]	Δk[Mg K-L3 + 1 other, MgO]	k[Al K-L3 + 3 others, Al2O3]	Δk[Al K-L3 + 3 others, Al2O3]	k[Si K-L3 + 3 others, SiO2]	Δk[Si K-L3 + 3 others, SiO2]	k[Ca K-L3 + 3 others, CaF2]	Δk[Ca K-L3 + 3 others, CaF2]	k[Fe K-L3 + 1 other, Fe]	Δk[Fe K-L3 + 1 other, Fe]	k[Fe K-M3 + 3 others, Fe]	Δk[Fe K-M3 + 3 others, Fe]
III-E K412[0][all]	0.6536	0.0008101	0.04191	0.0004382	0.1476	0.0001834	0.06699	0.0001589	0.3507	0.0002889	0.1922	0.0002326	0.06683	0.0001593	0.06684	0.0006722
III-E K412[1][all]	0.6554	0.0008108	0.04156	0.0004372	0.1475	0.0001835	0.06675	0.000159	0.3499	0.0002888	0.1916	0.0002325	0.06708	0.0001595	0.06738	0.0006721
III-E K412[2][all]	0.656	0.0008124	0.04191	0.0004381	0.1479	0.0001838	0.06709	0.0001594	0.3511	0.0002896	0.1922	0.0002329	0.06688	0.0001596	0.06704	0.0006737
III-E K412[3][all]	0.6604	0.0008155	0.04146	0.000438	0.1481	0.0001841	0.06716	0.0001595	0.3519	0.00029	0.1925	0.0002333	0.06682	0.0001598	0.0678	0.0006746
III-E K412[4][all]	0.6588	0.0008149	0.04081	0.0004383	0.1482	0.0001841	0.06728	0.0001597	0.3518	0.00029	0.1922	0.0002333	0.06694	0.0001598	0.06648	0.000674

Compare the timings (full then fast)

using BenchmarkTools
@btime map(unk->fit_spectrum(unk, ffrs), unks)
@btime map(unk->fit_spectrum(unk, vq), unks)

1.422 ms (2847 allocations: 1.28 MiB)
  404.500 μs (667 allocations: 191.23 KiB)
5-element Vector{FilterFitResult{Float64}}:
 FitResult(III-E K412[0][all])
 FitResult(III-E K412[1][all])
 FitResult(III-E K412[2][all])
 FitResult(III-E K412[3][all])
 FitResult(III-E K412[4][all])