# Peak width of Gaussian fitting

I'm a new user of Igor, and have a question about the Gaussian peak width of the multi-peak fitting results.
I am doing photoelectron spectroscopy. The peak width defines our resolution. Usually we use FWHM as peak "width". But I saw two numbers in the fitting results. One is FWHM, the other is "Width" under "Fit function parameters". The "FWHM" is larger than "Width". My question is what is the define of this "Width".

The result is pasted here:

Peak 0 Type: Gauss

Location = 2.7105 +/- 6.1234e-06
Height = 0.88553 +/- 0.0089955
Area = 0.0011648 +/- 1.2348e-05
FWHM = 0.0012357 +/- 1.4631e-05

Fit function parameters
Location = 2.7105 +/- 6.1234e-06
Width = 0.0007421 +/- 8.7866e-06
Height = 0.88553 +/- 0.0089955
The width refers to sqrt(2) times the standard deviation. So for your numbers s.d. is 0.000525.
FWHM can be calculated from the standard deviation. Approx. 2.354*s.d. So for your numbers = 0.00123525.
yangzheng wrote:
... I am doing photoelectron spectroscopy. The peak width defines our resolution. Usually we use FWHM as peak "width".

Are you aware ...

The Gaussian peak in statistics is defined as ...

P(x) = \frac{1}{\sqrt{2\pi}\sigma}\ \exp\left[- \left(\frac{1}{2}\right)\left(\frac{x - \mu}{\sigma} \right)^2 \right]

... where P(x) is probability, \sigma is the standard deviation of the distribution, and \mu is the mean of the distribution.

The Gaussian peak in XPS/UPS is defined as ...

I(E) = h\ \exp\left(-4\ \frac{\ln(2)(E - p)^2}{w^2} \right)

... where I(E) is intensity, E is energy (BE or KE), h is peak height, p is peak position, and w is the width at half-maximum height.

The parameters of the two are defined as shown in this table.

(the LaTeX equations can be parsed from ... http://www.codecogs.com/latex/eqneditor.php)

--
J. J. Weimer
Chemistry / Chemical & Materials Engineering, UAHuntsville
For x-ray fluorescence, which is what we do, we take the width w_coef[3] and multiply by 2*sqrt(ln(2)) to get the FWHM of a peak.