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FWHM of set of data without fitting

I need to find the full width half maximum of a set of data and I'm trying to write a function for doing that.

I'd like to do that without a proper fit of the data mainly for two reason: - I need to use it for many different shapes and I'd prefer not to change the fitting function every time - some of the data don't follow exactly any simple function. In any case, the data are quite dense so it shouldn't be a problem.

This is the solution that I found, but I'm not happy with that:

FWHMlist[list_, estimationLeft_: 1549, estimationRight_: 1551] := (
interpList = Interpolation[list, InterpolationOrder -> 1];
left = FindMinimum[Abs[interpList[x] - 0.5], {x, estimationLeft}][[
2, 1, 2]];
right = FindMinimum[Abs[interpList[x] - 0.5], {x, estimationRight}][[2, 1, 
2]];
{(right + left)/2, Abs[right - left]}
)

The problem is that for making it work nicely you need to put by hand the values of "estimationLeft" and "estimationRight" within a quite high accuracy (that can be down to 5% of the FWHM itself). Moreover, I always get this error message (twice, one for each FindMinimum), even if it finds the correct solution:

FindMinimum::lstol: The line search decreased the step size to within the tolerance specified by AccuracyGoal and PrecisionGoal but was unable to find a sufficient decrease in the function. You may need more than MachinePrecision digits of working precision to meet these tolerances.

Also, in some cases its behaviour is completely "random": sometimes it happens that I put estimationLeft=1549 and estimationRight=1551 and it finds the position of the data inverted (for example left=1551.3 and right=1549.2, while it should be the other way around) and that's why I added the Abs[] function in Abs[right - left].

I also tried with FindRoot and NSolve but none of them worked smoothly.

Here's one of the set of data I'm checking:

{{1520.22, 3.9143*10^-7}, {1520.29, 4.2235*10^-7}, {1520.35, 
  4.58852*10^-7}, {1520.41, 4.85261*10^-7}, {1520.47, 
  4.98993*10^-7}, {1520.54, 5.38451*10^-7}, {1520.6, 
  5.75251*10^-7}, {1520.66, 5.78558*10^-7}, {1520.72, 
  5.94969*10^-7}, {1520.79, 6.01124*10^-7}, {1520.85, 
  6.22937*10^-7}, {1520.91, 6.23425*10^-7}, {1520.97, 
  6.08534*10^-7}, {1521.03, 5.93284*10^-7}, {1521.1, 
  5.6918*10^-7}, {1521.16, 5.36251*10^-7}, {1521.22, 
  4.97934*10^-7}, {1521.28, 4.67186*10^-7}, {1521.35, 
  4.27334*10^-7}, {1521.41, 3.62609*10^-7}, {1521.47, 
  3.46459*10^-7}, {1521.53, 3.53876*10^-7}, {1521.59, 
  3.38124*10^-7}, {1521.66, 3.64584*10^-7}, {1521.72, 
  3.64745*10^-7}, {1521.78, 3.81447*10^-7}, {1521.84, 
  4.1051*10^-7}, {1521.91, 4.35542*10^-7}, {1521.97, 
  4.65507*10^-7}, {1522.03, 4.90923*10^-7}, {1522.09, 
  5.21076*10^-7}, {1522.15, 5.32535*10^-7}, {1522.22, 
  5.61712*10^-7}, {1522.28, 5.73446*10^-7}, {1522.34, 
  6.05857*10^-7}, {1522.4, 5.93109*10^-7}, {1522.47, 
  6.24156*10^-7}, {1522.53, 6.08723*10^-7}, {1522.59, 
  5.89722*10^-7}, {1522.65, 5.98539*10^-7}, {1522.71, 
  5.87068*10^-7}, {1522.78, 5.15607*10^-7}, {1522.84, 
  5.22349*10^-7}, {1522.9, 4.73289*10^-7}, {1522.96, 
  4.31955*10^-7}, {1523.03, 3.95917*10^-7}, {1523.09, 
  3.72316*10^-7}, {1523.15, 3.43806*10^-7}, {1523.21, 
  3.36248*10^-7}, {1523.27, 3.50636*10^-7}, {1523.34, 
  3.67204*10^-7}, {1523.4, 3.55345*10^-7}, {1523.46, 
  3.83565*10^-7}, {1523.52, 4.24807*10^-7}, {1523.59, 
  4.26466*10^-7}, {1523.65, 4.46987*10^-7}, {1523.71, 
  4.95276*10^-7}, {1523.77, 5.02934*10^-7}, {1523.83, 
  5.31009*10^-7}, {1523.9, 5.74494*10^-7}, {1523.96, 
  5.75629*10^-7}, {1524.02, 5.66701*10^-7}, {1524.08, 
  6.05141*10^-7}, {1524.15, 6.12398*10^-7}, {1524.21, 
  5.91093*10^-7}, {1524.27, 5.9609*10^-7}, {1524.33, 
  6.12125*10^-7}, {1524.39, 5.52301*10^-7}, {1524.46, 
  5.31125*10^-7}, {1524.52, 5.39433*10^-7}, {1524.58, 
  4.847*10^-7}, {1524.64, 4.42748*10^-7}, {1524.71, 
  4.20911*10^-7}, {1524.77, 3.68586*10^-7}, {1524.83, 
  3.35457*10^-7}, {1524.89, 3.77376*10^-7}, {1524.95, 
  3.55983*10^-7}, {1525.02, 3.44279*10^-7}, {1525.08, 
  3.8394*10^-7}, {1525.14, 4.00067*10^-7}, {1525.2, 
  3.99889*10^-7}, {1525.27, 4.48809*10^-7}, {1525.33, 
  4.9117*10^-7}, {1525.39, 4.76197*10^-7}, {1525.45, 
  5.16265*10^-7}, {1525.51, 5.50181*10^-7}, {1525.58, 
  5.51648*10^-7}, {1525.64, 5.80574*10^-7}, {1525.7, 
  6.00684*10^-7}, {1525.76, 5.83252*10^-7}, {1525.83, 
  6.07597*10^-7}, {1525.89, 6.05896*10^-7}, {1525.95, 
  5.63925*10^-7}, {1526.01, 5.60134*10^-7}, {1526.07, 
  5.54021*10^-7}, {1526.14, 4.83576*10^-7}, {1526.2, 
  4.60495*10^-7}, {1526.26, 4.41709*10^-7}, {1526.32, 
  3.72963*10^-7}, {1526.39, 3.55997*10^-7}, {1526.45, 
  3.62267*10^-7}, {1526.51, 3.38248*10^-7}, {1526.57, 
  3.50673*10^-7}, {1526.64, 3.8074*10^-7}, {1526.7, 
  3.83932*10^-7}, {1526.76, 3.86929*10^-7}, {1526.82, 
  4.26975*10^-7}, {1526.88, 4.51675*10^-7}, {1526.95, 
  4.71222*10^-7}, {1527.01, 4.92058*10^-7}, {1527.07, 
  5.30869*10^-7}, {1527.13, 5.2632*10^-7}, {1527.2, 
  5.63481*10^-7}, {1527.26, 5.89408*10^-7}, {1527.32, 
  5.74759*10^-7}, {1527.38, 5.82722*10^-7}, {1527.44, 
  6.12278*10^-7}, {1527.51, 5.97496*10^-7}, {1527.57, 
  5.80282*10^-7}, {1527.63, 5.90183*10^-7}, {1527.69, 
  5.67122*10^-7}, {1527.76, 5.32595*10^-7}, {1527.82, 
  5.15495*10^-7}, {1527.88, 4.81057*10^-7}, {1527.94, 
  4.40682*10^-7}, {1528., 4.09105*10^-7}, {1528.07, 
  3.77077*10^-7}, {1528.13, 3.39069*10^-7}, {1528.19, 
  3.62227*10^-7}, {1528.25, 3.87959*10^-7}, {1528.32, 
  3.62078*10^-7}, {1528.38, 3.67303*10^-7}, {1528.44, 
  4.23054*10^-7}, {1528.5, 4.16867*10^-7}, {1528.56, 
  4.23342*10^-7}, {1528.63, 4.78273*10^-7}, {1528.69, 
  5.05433*10^-7}, {1528.75, 5.12387*10^-7}, {1528.81, 
  5.43615*10^-7}, {1528.88, 5.61102*10^-7}, {1528.94, 
  5.68615*10^-7}, {1529., 5.91733*10^-7}, {1529.06, 
  6.19253*10^-7}, {1529.12, 5.88423*10^-7}, {1529.19, 
  5.99432*10^-7}, {1529.25, 6.06569*10^-7}, {1529.31, 
  5.67947*10^-7}, {1529.37, 5.47341*10^-7}, {1529.44, 
  5.25961*10^-7}, {1529.5, 5.06112*10^-7}, {1529.56, 
  4.47976*10^-7}, {1529.62, 4.25818*10^-7}, {1529.68, 
  3.84007*10^-7}, {1529.75, 3.52092*10^-7}, {1529.81, 
  3.73698*10^-7}, {1529.87, 3.52514*10^-7}, {1529.93, 
  3.77081*10^-7}, {1530., 4.00759*10^-7}, {1530.06, 
  4.00582*10^-7}, {1530.12, 4.21798*10^-7}, {1530.18, 
  4.6793*10^-7}, {1530.24, 4.77754*10^-7}, {1530.31, 
  4.99111*10^-7}, {1530.37, 5.36287*10^-7}, {1530.43, 
  5.44647*10^-7}, {1530.49, 5.64794*10^-7}, {1530.56, 
  5.84462*10^-7}, {1530.62, 5.93932*10^-7}, {1530.68, 
  5.88048*10^-7}, {1530.74, 6.12409*10^-7}, {1530.8, 
  5.84544*10^-7}, {1530.87, 5.75051*10^-7}, {1530.93, 
  5.70453*10^-7}, {1530.99, 5.3823*10^-7}, {1531.05, 
  5.09009*10^-7}, {1531.12, 4.78552*10^-7}, {1531.18, 
  4.57544*10^-7}, {1531.24, 4.14104*10^-7}, {1531.3, 
  3.7082*10^-7}, {1531.36, 3.75874*10^-7}, {1531.43, 
  3.72792*10^-7}, {1531.49, 3.6298*10^-7}, {1531.55, 
  3.84319*10^-7}, {1531.61, 3.99501*10^-7}, {1531.68, 
  3.8672*10^-7}, {1531.74, 4.34744*10^-7}, {1531.8, 
  4.49666*10^-7}, {1531.86, 4.68999*10^-7}, {1531.92, 
  5.17347*10^-7}, {1531.99, 5.18348*10^-7}, {1532.05, 
  5.39*10^-7}, {1532.11, 5.66601*10^-7}, {1532.17, 
  5.77421*10^-7}, {1532.24, 5.95685*10^-7}, {1532.3, 
  6.14646*10^-7}, {1532.36, 6.13813*10^-7}, {1532.42, 
  6.12788*10^-7}, {1532.49, 6.12889*10^-7}, {1532.55, 
  6.06748*10^-7}, {1532.61, 5.84911*10^-7}, {1532.67, 
  5.51608*10^-7}, {1532.73, 5.37742*10^-7}, {1532.8, 
  5.04793*10^-7}, {1532.86, 4.56924*10^-7}, {1532.92, 
  4.37371*10^-7}, {1532.98, 3.93941*10^-7}, {1533.05, 
  3.7887*10^-7}, {1533.11, 3.98661*10^-7}, {1533.17, 
  3.97374*10^-7}, {1533.23, 3.93975*10^-7}, {1533.29, 
  4.26558*10^-7}, {1533.36, 4.49377*10^-7}, {1533.42, 
  4.47819*10^-7}, {1533.48, 4.86029*10^-7}, {1533.54, 
  5.13083*10^-7}, {1533.61, 5.37319*10^-7}, {1533.67, 
  5.60277*10^-7}, {1533.73, 5.96615*10^-7}, {1533.79, 
  5.97419*10^-7}, {1533.85, 6.18556*10^-7}, {1533.92, 
  6.46869*10^-7}, {1533.98, 6.2984*10^-7}, {1534.04, 
  6.50267*10^-7}, {1534.1, 6.44509*10^-7}, {1534.17, 
  6.25337*10^-7}, {1534.23, 5.90752*10^-7}, {1534.29, 
  5.90374*10^-7}, {1534.35, 5.6594*10^-7}, {1534.41, 
  5.35443*10^-7}, {1534.48, 4.94193*10^-7}, {1534.54, 
  4.49487*10^-7}, {1534.6, 4.17449*10^-7}, {1534.66, 
  4.40452*10^-7}, {1534.73, 4.29065*10^-7}, {1534.79, 
  4.34901*10^-7}, {1534.85, 4.60163*10^-7}, {1534.91, 
  4.66811*10^-7}, {1534.97, 4.87345*10^-7}, {1535.04, 
  5.1991*10^-7}, {1535.1, 5.40121*10^-7}, {1535.16, 
  5.79275*10^-7}, {1535.22, 5.92716*10^-7}, {1535.29, 
  6.31406*10^-7}, {1535.35, 6.53088*10^-7}, {1535.41, 
  6.57596*10^-7}, {1535.47, 6.83577*10^-7}, {1535.53, 
  7.07946*10^-7}, {1535.6, 6.59731*10^-7}, {1535.66, 
  7.03363*10^-7}, {1535.72, 7.06889*10^-7}, {1535.78, 
  6.66386*10^-7}, {1535.85, 6.48645*10^-7}, {1535.91, 
  6.45084*10^-7}, {1535.97, 6.05684*10^-7}, {1536.03, 
  5.56335*10^-7}, {1536.09, 5.38173*10^-7}, {1536.16, 
  5.02977*10^-7}, {1536.22, 4.5372*10^-7}, {1536.28, 
  4.43375*10^-7}, {1536.34, 4.47265*10^-7}, {1536.41, 
  4.52041*10^-7}, {1536.47, 4.6251*10^-7}, {1536.53, 
  4.71308*10^-7}, {1536.59, 4.79651*10^-7}, {1536.65, 
  4.91726*10^-7}, {1536.72, 5.4149*10^-7}, {1536.78, 
  5.28421*10^-7}, {1536.84, 5.38826*10^-7}, {1536.9, 
  5.7066*10^-7}, {1536.97, 5.94345*10^-7}, {1537.03, 
  5.88357*10^-7}, {1537.09, 6.01417*10^-7}, {1537.15, 
  6.16327*10^-7}, {1537.21, 6.15539*10^-7}, {1537.28, 
  6.17448*10^-7}, {1537.34, 6.2594*10^-7}, {1537.4, 
  5.88535*10^-7}, {1537.46, 5.97005*10^-7}, {1537.53, 
  5.79931*10^-7}, {1537.59, 5.39427*10^-7}, {1537.65, 
  5.19*10^-7}, {1537.71, 5.1033*10^-7}, {1537.77, 
  4.59437*10^-7}, {1537.84, 4.14154*10^-7}, {1537.9, 
  4.0774*10^-7}, {1537.96, 4.1406*10^-7}, {1538.02, 
  3.93311*10^-7}, {1538.09, 4.22095*10^-7}, {1538.15, 
  4.28481*10^-7}, {1538.21, 4.2989*10^-7}, {1538.27, 
  4.67088*10^-7}, {1538.34, 4.9423*10^-7}, {1538.4, 
  4.96262*10^-7}, {1538.46, 5.49255*10^-7}, {1538.52, 
  5.56046*10^-7}, {1538.58, 5.76649*10^-7}, {1538.65, 
  6.0559*10^-7}, {1538.71, 6.15742*10^-7}, {1538.77, 
  6.16315*10^-7}, {1538.83, 6.51037*10^-7}, {1538.9, 
  6.36387*10^-7}, {1538.96, 6.1571*10^-7}, {1539.02, 
  6.29042*10^-7}, {1539.08, 5.99115*10^-7}, {1539.14, 
  5.64686*10^-7}, {1539.21, 5.61112*10^-7}, {1539.27, 
  5.18741*10^-7}, {1539.33, 4.82224*10^-7}, {1539.39, 
  4.56016*10^-7}, {1539.46, 4.23174*10^-7}, {1539.52, 
  4.34349*10^-7}, {1539.58, 4.40693*10^-7}, {1539.64, 
  4.29027*10^-7}, {1539.7, 4.1932*10^-7}, {1539.77, 
  4.69089*10^-7}, {1539.83, 4.78978*10^-7}, {1539.89, 
  4.87221*10^-7}, {1539.95, 5.15037*10^-7}, {1540.02, 
  5.52767*10^-7}, {1540.08, 5.54825*10^-7}, {1540.14, 
  5.89984*10^-7}, {1540.2, 6.12943*10^-7}, {1540.26, 
  6.12661*10^-7}, {1540.33, 6.38029*10^-7}, {1540.39, 
  6.47726*10^-7}, {1540.45, 6.39801*10^-7}, {1540.51, 
  6.50199*10^-7}, {1540.58, 6.53268*10^-7}, {1540.64, 
  6.48409*10^-7}, {1540.7, 5.95793*10^-7}, {1540.76, 
  6.0956*10^-7}, {1540.82, 5.8823*10^-7}, {1540.89, 
  5.48017*10^-7}, {1540.95, 5.22436*10^-7}, {1541.01, 
  5.07947*10^-7}, {1541.07, 4.5276*10^-7}, {1541.14, 
  4.42881*10^-7}, {1541.2, 4.5963*10^-7}, {1541.26, 
  4.47021*10^-7}, {1541.32, 4.46818*10^-7}, {1541.38, 
  4.84781*10^-7}, {1541.45, 4.88015*10^-7}, {1541.51, 
  4.9329*10^-7}, {1541.57, 5.41672*10^-7}, {1541.63, 
  5.55122*10^-7}, {1541.7, 5.57954*10^-7}, {1541.76, 
  6.04663*10^-7}, {1541.82, 6.22467*10^-7}, {1541.88, 
  6.24182*10^-7}, {1541.94, 6.53323*10^-7}, {1542.01, 
  6.66268*10^-7}, {1542.07, 6.61379*10^-7}, {1542.13, 
  6.88575*10^-7}, {1542.19, 6.97675*10^-7}, {1542.26, 
  6.58159*10^-7}, {1542.32, 6.66856*10^-7}, {1542.38, 
  6.51562*10^-7}, {1542.44, 6.23926*10^-7}, {1542.5, 
  5.92763*10^-7}, {1542.57, 5.81644*10^-7}, {1542.63, 
  5.19917*10^-7}, {1542.69, 5.10136*10^-7}, {1542.75, 
  5.10665*10^-7}, {1542.82, 4.92407*10^-7}, {1542.88, 
  5.20025*10^-7}, {1542.94, 5.36503*10^-7}, {1543., 
  5.39691*10^-7}, {1543.06, 5.66984*10^-7}, {1543.13, 
  5.98417*10^-7}, {1543.19, 6.06754*10^-7}, {1543.25, 
  6.59347*10^-7}, {1543.31, 6.83011*10^-7}, {1543.38, 
  7.08242*10^-7}, {1543.44, 7.58154*10^-7}, {1543.5, 
  7.65186*10^-7}, {1543.56, 7.78644*10^-7}, {1543.62, 
  8.18964*10^-7}, {1543.69, 8.38611*10^-7}, {1543.75, 
  8.32989*10^-7}, {1543.81, 8.64342*10^-7}, {1543.87, 
  8.56904*10^-7}, {1543.94, 8.57994*10^-7}, {1544., 
  8.63213*10^-7}, {1544.06, 8.72321*10^-7}, {1544.12, 
  8.46976*10^-7}, {1544.19, 8.55505*10^-7}, {1544.25, 
  8.47766*10^-7}, {1544.31, 8.37952*10^-7}, {1544.37, 
  8.70779*10^-7}, {1544.43, 9.20593*10^-7}, {1544.5, 
  9.31007*10^-7}, {1544.56, 9.74478*10^-7}, {1544.62, 
  1.03626*10^-6}, {1544.68, 1.0913*10^-6}, {1544.75, 
  1.14937*10^-6}, {1544.81, 1.23678*10^-6}, {1544.87, 
  1.31748*10^-6}, {1544.93, 1.37517*10^-6}, {1544.99, 
  1.47804*10^-6}, {1545.06, 1.55892*10^-6}, {1545.12, 
  1.63864*10^-6}, {1545.18, 1.76142*10^-6}, {1545.24, 
  1.85862*10^-6}, {1545.31, 1.96211*10^-6}, {1545.37, 
  2.09183*10^-6}, {1545.43, 2.22839*10^-6}, {1545.49, 
  2.34583*10^-6}, {1545.55, 2.51958*10^-6}, {1545.62, 
  2.67073*10^-6}, {1545.68, 2.82933*10^-6}, {1545.74, 
  3.00481*10^-6}, {1545.8, 3.22934*10^-6}, {1545.87, 
  3.43025*10^-6}, {1545.93, 3.65887*10^-6}, {1545.99, 
  3.95407*10^-6}, {1546.05, 4.26389*10^-6}, {1546.11, 
  4.60625*10^-6}, {1546.18, 4.99243*10^-6}, {1546.24, 
  5.37961*10^-6}, {1546.3, 5.8201*10^-6}, {1546.36, 
  6.34826*10^-6}, {1546.43, 6.91374*10^-6}, {1546.49, 
  7.48294*10^-6}, {1546.55, 8.16146*10^-6}, {1546.61, 
  8.93082*10^-6}, {1546.67, 9.74638*10^-6}, {1546.74, 
  0.0000106574}, {1546.8, 0.0000116214}, {1546.86, 
  0.000012724}, {1546.92, 0.0000140392}, {1546.99, 
  0.0000154451}, {1547.05, 0.0000169463}, {1547.11, 
  0.0000188481}, {1547.17, 0.0000210989}, {1547.23, 
  0.0000237694}, {1547.3, 0.0000265585}, {1547.36, 
  0.0000299197}, {1547.42, 0.0000340624}, {1547.48, 
  0.0000389017}, {1547.55, 0.00004424}, {1547.61, 
  0.00005172}, {1547.67, 0.0000616668}, {1547.73, 
  0.0000721524}, {1547.79, 0.0000868403}, {1547.86, 
  0.000104143}, {1547.92, 0.000130255}, {1547.98, 
  0.000161535}, {1548.04, 0.000199802}, {1548.11, 
  0.000252911}, {1548.17, 0.000327089}, {1548.23, 
  0.000427545}, {1548.29, 0.000557827}, {1548.35, 
  0.000746401}, {1548.42, 0.001029}, {1548.48, 0.00143916}, {1548.54, 
  0.00198357}, {1548.6, 0.00284646}, {1548.67, 0.0042478}, {1548.73, 
  0.00632993}, {1548.79, 0.00977115}, {1548.85, 0.0146819}, {1548.91, 
  0.0250958}, {1548.98, 0.0432263}, {1549.04, 0.0779823}, {1549.1, 
  0.138558}, {1549.16, 0.255334}, {1549.23, 0.466786}, {1549.29, 
  0.687991}, {1549.35, 0.84265}, {1549.41, 0.90325}, {1549.47, 
  0.907048}, {1549.54, 0.890872}, {1549.6, 0.881758}, {1549.66, 
  0.889737}, {1549.72, 0.907534}, {1549.79, 0.925909}, {1549.85, 
  0.941836}, {1549.91, 0.956288}, {1549.97, 0.962327}, {1550.04, 
  0.963002}, {1550.1, 0.964112}, {1550.16, 0.962716}, {1550.22, 
  0.957763}, {1550.28, 0.953931}, {1550.35, 0.947951}, {1550.41, 
  0.929057}, {1550.47, 0.894493}, {1550.53, 0.838966}, {1550.6, 
  0.742447}, {1550.66, 0.606328}, {1550.72, 0.448108}, {1550.78, 
  0.307077}, {1550.84, 0.193267}, {1550.91, 0.120175}, {1550.97, 
  0.072633}, {1551.03, 0.0428024}, {1551.09, 0.0262912}, {1551.16, 
  0.0167012}, {1551.22, 0.0110605}, {1551.28, 0.00736256}, {1551.34, 
  0.00485699}, {1551.4, 0.00330759}, {1551.47, 0.00232362}, {1551.53, 
  0.00164338}, {1551.59, 0.00116192}, {1551.65, 
  0.000815452}, {1551.72, 0.000612398}, {1551.78, 
  0.000458164}, {1551.84, 0.000352139}, {1551.9, 
  0.000263624}, {1551.96, 0.000205313}, {1552.03, 
  0.000159939}, {1552.09, 0.000127764}, {1552.15, 
  0.0000974857}, {1552.21, 0.0000773562}, {1552.28, 
  0.0000612388}, {1552.34, 0.000048225}, {1552.4, 
  0.0000390242}, {1552.46, 0.0000316792}, {1552.52, 
  0.0000262915}, {1552.59, 0.0000215882}, {1552.65, 
  0.0000177108}, {1552.71, 0.0000148016}, {1552.77, 
  0.0000125356}, {1552.84, 0.0000106181}, {1552.9, 
  8.86773*10^-6}, {1552.96, 7.51536*10^-6}, {1553.02, 
  6.48209*10^-6}, {1553.08, 5.59658*10^-6}, {1553.15, 
  4.79413*10^-6}, {1553.21, 4.1462*10^-6}, {1553.27, 
  3.68178*10^-6}, {1553.33, 3.25625*10^-6}, {1553.4, 
  2.85756*10^-6}, {1553.46, 2.49831*10^-6}, {1553.52, 
  2.23597*10^-6}, {1553.58, 2.01519*10^-6}, {1553.64, 
  1.76694*10^-6}, {1553.71, 1.55925*10^-6}, {1553.77, 
  1.41837*10^-6}, {1553.83, 1.26118*10^-6}, {1553.89, 
  1.14993*10^-6}, {1553.96, 1.02649*10^-6}, {1554.02, 
  9.36663*10^-7}, {1554.08, 8.94778*10^-7}, {1554.14, 
  8.47963*10^-7}, {1554.2, 7.74931*10^-7}, {1554.27, 
  7.55435*10^-7}, {1554.33, 7.47139*10^-7}, {1554.39, 
  7.06839*10^-7}, {1554.45, 7.06525*10^-7}, {1554.52, 
  7.03425*10^-7}, {1554.58, 6.87042*10^-7}, {1554.64, 
  6.80318*10^-7}, {1554.7, 6.91128*10^-7}, {1554.76, 
  6.67473*10^-7}, {1554.83, 6.61153*10^-7}, {1554.89, 
  6.75798*10^-7}, {1554.95, 6.35135*10^-7}, {1555.01, 
  6.30096*10^-7}, {1555.08, 6.46942*10^-7}, {1555.14, 
  5.84808*10^-7}, {1555.2, 5.55333*10^-7}, {1555.26, 
  5.61819*10^-7}, {1555.32, 5.04239*10^-7}, {1555.39, 
  4.70567*10^-7}, {1555.45, 4.46038*10^-7}, {1555.51, 
  4.00279*10^-7}, {1555.57, 4.06262*10^-7}, {1555.64, 
  4.07907*10^-7}, {1555.7, 3.93049*10^-7}, {1555.76, 
  4.05481*10^-7}, {1555.82, 4.21922*10^-7}, {1555.89, 
  4.28899*10^-7}, {1555.95, 4.51003*10^-7}, {1556.01, 
  4.71488*10^-7}, {1556.07, 4.83279*10^-7}, {1556.13, 
  5.10238*10^-7}, {1556.2, 5.23011*10^-7}, {1556.26, 
  5.27263*10^-7}, {1556.32, 5.45748*10^-7}, {1556.38, 
  5.62307*10^-7}, {1556.45, 5.47116*10^-7}, {1556.51, 
  5.60557*10^-7}, {1556.57, 5.60161*10^-7}, {1556.63, 
  5.32748*10^-7}, {1556.69, 5.23554*10^-7}, {1556.76, 
  5.03117*10^-7}, {1556.82, 4.57058*10^-7}, {1556.88, 
  4.5152*10^-7}, {1556.94, 4.36222*10^-7}, {1557.01, 
  3.71418*10^-7}, {1557.07, 3.59292*10^-7}, {1557.13, 
  3.8752*10^-7}, {1557.19, 3.5666*10^-7}, {1557.25, 
  3.606*10^-7}, {1557.32, 3.958*10^-7}, {1557.38, 
  3.73632*10^-7}, {1557.44, 4.03792*10^-7}, {1557.5, 
  4.19671*10^-7}, {1557.57, 4.37828*10^-7}, {1557.63, 
  4.51243*10^-7}, {1557.69, 4.84979*10^-7}, {1557.75, 
  4.9934*10^-7}, {1557.81, 4.95637*10^-7}, {1557.88, 
  5.2738*10^-7}, {1557.94, 5.23191*10^-7}, {1558., 
  5.24962*10^-7}, {1558.06, 5.47583*10^-7}, {1558.13, 
  5.35919*10^-7}, {1558.19, 5.31112*10^-7}, {1558.25, 
  5.27976*10^-7}, {1558.31, 5.00444*10^-7}, {1558.37, 
  4.78359*10^-7}, {1558.44, 4.62942*10^-7}, {1558.5, 
  4.49116*10^-7}, {1558.56, 4.05695*10^-7}, {1558.62, 
  3.81348*10^-7}, {1558.69, 3.51126*10^-7}, {1558.75, 
  3.5479*10^-7}, {1558.81, 3.75509*10^-7}, {1558.87, 
  3.68913*10^-7}, {1558.93, 3.56691*10^-7}, {1559., 
  3.88518*10^-7}, {1559.06, 4.10759*10^-7}, {1559.12, 
  4.15878*10^-7}, {1559.18, 4.31829*10^-7}, {1559.25, 
  4.66116*10^-7}, {1559.31, 4.66733*10^-7}, {1559.37, 
  4.85579*10^-7}, {1559.43, 5.14336*10^-7}, {1559.49, 
  5.06532*10^-7}, {1559.56, 5.29003*10^-7}, {1559.62, 
  5.38599*10^-7}, {1559.68, 5.34441*10^-7}, {1559.74, 
  5.257*10^-7}, {1559.81, 5.36547*10^-7}, {1559.87, 
  4.97451*10^-7}, {1559.93, 4.89881*10^-7}, {1559.99, 
  4.66134*10^-7}, {1560.05, 4.33465*10^-7}, {1560.12, 
  4.12023*10^-7}, {1560.18, 3.74186*10^-7}, {1560.24, 
  3.52459*10^-7}, {1560.3, 3.59962*10^-7}, {1560.37, 
  3.60265*10^-7}, {1560.43, 3.71048*10^-7}, {1560.49, 
  3.7938*10^-7}, {1560.55, 3.83652*10^-7}, {1560.61, 
  4.02434*10^-7}, {1560.68, 4.35622*10^-7}, {1560.74, 
  4.46141*10^-7}, {1560.8, 4.56876*10^-7}, {1560.86, 
  4.92889*10^-7}, {1560.93, 5.02818*10^-7}, {1560.99, 
  5.07472*10^-7}, {1561.05, 5.13407*10^-7}, {1561.11, 
  5.47223*10^-7}, {1561.17, 5.50261*10^-7}, {1561.24, 
  5.02213*10^-7}, {1561.3, 5.51866*10^-7}, {1561.36, 
  5.26751*10^-7}, {1561.42, 4.93767*10^-7}, {1561.49, 
  4.95485*10^-7}, {1561.55, 4.7109*10^-7}, {1561.61, 
  4.39825*10^-7}, {1561.67, 4.11854*10^-7}, {1561.74, 
  4.02752*10^-7}, {1561.8, 3.61215*10^-7}, {1561.86, 
  3.5813*10^-7}, {1561.92, 3.65193*10^-7}, {1561.98, 
  3.614*10^-7}, {1562.05, 3.66792*10^-7}, {1562.11, 
  3.86028*10^-7}, {1562.17, 3.83074*10^-7}, {1562.23, 
  4.05164*10^-7}, {1562.3, 4.41678*10^-7}, {1562.36, 
  4.45155*10^-7}, {1562.42, 4.65896*10^-7}, {1562.48, 
  4.91181*10^-7}, {1562.54, 5.03445*10^-7}, {1562.61, 
  5.07049*10^-7}, {1562.67, 5.22176*10^-7}, {1562.73, 
  5.21113*10^-7}, {1562.79, 5.30692*10^-7}, {1562.86, 
  5.39297*10^-7}, {1562.92, 5.17036*10^-7}, {1562.98, 
  5.12964*10^-7}, {1563.04, 5.09898*10^-7}, {1563.1, 
  4.796*10^-7}, {1563.17, 4.56359*10^-7}, {1563.23, 
  4.36042*10^-7}, {1563.29, 3.99088*10^-7}, {1563.35, 
  3.80347*10^-7}, {1563.42, 3.5745*10^-7}, {1563.48, 
  3.60986*10^-7}, {1563.54, 3.54648*10^-7}, {1563.6, 
  3.74047*10^-7}, {1563.66, 3.76036*10^-7}, {1563.73, 
  3.80292*10^-7}, {1563.79, 4.10273*10^-7}, {1563.85, 
  4.36294*10^-7}, {1563.91, 4.4712*10^-7}, {1563.98, 
  4.61345*10^-7}, {1564.04, 4.78653*10^-7}, {1564.1, 
  4.84456*10^-7}, {1564.16, 5.18302*10^-7}, {1564.22, 
  5.22164*10^-7}, {1564.29, 5.20212*10^-7}, {1564.35, 
  5.33134*10^-7}, {1564.41, 5.38858*10^-7}, {1564.47, 
  5.2709*10^-7}, {1564.54, 5.06943*10^-7}, {1564.6, 
  4.92774*10^-7}, {1564.66, 4.65084*10^-7}, {1564.72, 
  4.53548*10^-7}, {1564.78, 4.19295*10^-7}, {1564.85, 
  3.80935*10^-7}, {1564.91, 3.63628*10^-7}, {1564.97, 
  3.61478*10^-7}, {1565.03, 3.62205*10^-7}, {1565.1, 
  3.63325*10^-7}, {1565.16, 3.64196*10^-7}, {1565.22, 
  3.74477*10^-7}, {1565.28, 4.06607*10^-7}, {1565.34, 
  4.09479*10^-7}, {1565.41, 4.23897*10^-7}, {1565.47, 
  4.56301*10^-7}, {1565.53, 4.64998*10^-7}, {1565.59, 
  4.79293*10^-7}, {1565.66, 5.08619*10^-7}, {1565.72, 
  5.11555*10^-7}, {1565.78, 5.12805*10^-7}, {1565.84, 
  5.32302*10^-7}, {1565.9, 5.3777*10^-7}, {1565.97, 
  5.17709*10^-7}, {1566.03, 5.47141*10^-7}, {1566.09, 
  5.46472*10^-7}, {1566.15, 4.67247*10^-7}, {1566.22, 
  4.95026*10^-7}, {1566.28, 4.69605*10^-7}, {1566.34, 
  4.27756*10^-7}, {1566.4, 4.06615*10^-7}, {1566.46, 
  3.96654*10^-7}, {1566.53, 3.58181*10^-7}, {1566.59, 
  3.60586*10^-7}, {1566.65, 3.6554*10^-7}, {1566.71, 
  3.61202*10^-7}, {1566.78, 3.78514*10^-7}, {1566.84, 
  3.90038*10^-7}, {1566.9, 3.92534*10^-7}, {1566.96, 
  4.23232*10^-7}, {1567.02, 4.42563*10^-7}, {1567.09, 
  4.54717*10^-7}, {1567.15, 4.70641*10^-7}, {1567.21, 
  4.93834*10^-7}, {1567.27, 4.97927*10^-7}, {1567.34, 
  5.07608*10^-7}, {1567.4, 5.24829*10^-7}, {1567.46, 
  5.24447*10^-7}, {1567.52, 5.1717*10^-7}, {1567.59, 
  5.32684*10^-7}, {1567.65, 5.0938*10^-7}, {1567.71, 
  5.00024*10^-7}, {1567.77, 4.84666*10^-7}, {1567.83, 
  4.57878*10^-7}, {1567.9, 4.4829*10^-7}, {1567.96, 
  4.25056*10^-7}, {1568.02, 3.73932*10^-7}, {1568.08, 
  3.59996*10^-7}, {1568.15, 3.75591*10^-7}, {1568.21, 
  3.54681*10^-7}, {1568.27, 3.70144*10^-7}, {1568.33, 
  3.76103*10^-7}, {1568.39, 3.81188*10^-7}, {1568.46, 
  4.07376*10^-7}, {1568.52, 4.28222*10^-7}, {1568.58, 
  4.32461*10^-7}, {1568.64, 4.66806*10^-7}, {1568.71, 
  4.91233*10^-7}, {1568.77, 4.95157*10^-7}, {1568.83, 
  5.13491*10^-7}, {1568.89, 5.15105*10^-7}, {1568.95, 
  5.24405*10^-7}, {1569.02, 5.49872*10^-7}, {1569.08, 
  5.34437*10^-7}, {1569.14, 5.14718*10^-7}, {1569.2, 
  5.24206*10^-7}, {1569.27, 4.97602*10^-7}, {1569.33, 
  4.67481*10^-7}, {1569.39, 4.58655*10^-7}, {1569.45, 
  4.18571*10^-7}, {1569.51, 3.94378*10^-7}, {1569.58, 
  3.78642*10^-7}, {1569.64, 3.63205*10^-7}, {1569.7, 
  3.54906*10^-7}, {1569.76, 3.77561*10^-7}, {1569.83, 
  3.70489*10^-7}, {1569.89, 3.72111*10^-7}, {1569.95, 3.96338*10^-7}}

And this is the output I get:

where the red dots are the data points, the blue line is the interpolation function and the horizontal line is the FWHM (which apparently is correct, and in this case is equal to 1.46386 and centred in 1549.97.

Thanks for your help!