# What is Fwhm: Definition and 19 Discussions

In a distribution, full width at half maximum (FWHM) is the difference between the two values of the independent variable at which the dependent variable is equal to half of its maximum value. In other words, it is the width of a spectrum curve measured between those points on the y-axis which are half the maximum amplitude.
Half width at half maximum (HWHM) is half of the FWHM if the function is symmetric.
FWHM is applied to such phenomena as the duration of pulse waveforms and the spectral width of sources used for optical communications and the resolution of spectrometers.
The term full duration at half maximum (FDHM) is preferred when the independent variable is time.
The convention of "width" meaning "half maximum" is also widely used in signal processing to define bandwidth as "width of frequency range where less than half the signal's power is attenuated", i.e., the power is at least half the maximum. In signal processing terms, this is at most −3 dB of attenuation, called "half-power point".
If the considered function is the density of a normal distribution of the form

where σ is the standard deviation and x0 is the expected value, then the relationship between FWHM and the standard deviation is
The corresponding area within this FWHM accounts to approximately 76%.
The width does not depend on the expected value x0; it is invariant under translations.
In spectroscopy half the width at half maximum (here γ), HWHM, is in common use. For example, a Lorentzian/Cauchy distribution of height 1/πγ can be defined by

Another important distribution function, related to solitons in optics, is the hyperbolic secant:

Any translating element was omitted, since it does not affect the FWHM. For this impulse we have:

where arsech is the inverse hyperbolic secant.
If the FWHM of a Gaussian function is known, then it can be integrated by simple multiplication.

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1. ### Engineering Plotting a Guassian FWHM = 1 ns

Simply plugging this into software like MATLAB will present a solid guassian distrubution. However, my doubt comes from selecting the correct sigma. t = - 10 ns to + 10 ns ##\sigma## = 0.1 ns This produces a plot like so,
2. ### The effect of instrumental broadening on FWHM in Raman peaks

I would like to know how to extract the instrumental broadening effect in Raman spectrometer using solid angle of the objectives, slit width or spectrometer length. I am calculation the FWHM in Raman peaks and I would like to know the effect of instrumental broadening on Raman line width and how...
3. ### Full Width Half Maximum of Single Coil

Homework Statement Determine the Full Width Half Maximum (FWHM) using the single coil equation and fitting parameters. The FWHM is the measure of how broad (wide) a signal is before it loses half of its intensity. In this case, its a measure of the distance spanned before the magnetic field...
4. ### How does one compute frequency bandwidth based on FWHM

In the following text the authors state: "The full width at half maximum (FWHM) we measure is about 2 km/s" and this is in the local standard of rest (LSR), ##v_{LSR}##. I have seen basic doppler shift equations to convert from these velocities to frequency (shown below in link). Although if I...
5. ### A About X-ray Photoelectron Spectroscopy

Hello, I am trying to create peak models for some XPS spectra. I have a decent intuition of the chemistry of the samples, and I obtain really good residual standard deviation values for the modeled data; however, some of the FWHM of the modeled oxidized species (C and P) on the narrow scans are...
6. ### Determine the intensity profile and fwhm for gaussian beam.

Homework Statement A beam of wavelength 600 nm has initially an intensity profile of Gaussian shape with a fwhm of 1 mm. Determine the intensity profile and fwhm 10 meter away.Homework Equations FWHM = λ/(2NA√(1 + I/Is)) The Attempt at a Solution [/B] FWHM1 = 1mm = 600 nm/(2NA√(1 + I/Is))...
7. ### Understanding FWHM in XRD Analysis of Powder Patterns

Why is FWHM taken for calculations in XRD analysis of powder pattern? I mean, why don't we take the full peak value?
8. ### Quantifying Observational Error in FWHM Measurements of Optical Signals

Hello, i have a optical signal(x is length in pixels and y is amplitude ) and i have found a number of FWHM values of peaks. The width is measured in pixels, let's say the average width of 50 peaks is 8,7 pixels, standard deviation is 0,6 and the average amplitude of peaks is 38 and standard...
9. ### X-Ray Diffraction peak width due to micro-strain

I understand that the peak-width of diffraction data increases with increasing amounts of heterogeneous, localized (AKA "micro-") strain. So, if you have a single crystal with atomic impurities in it that each create micro-strain in the lattice, you would expect the amount of peak-broadening...
10. ### What Does FWHM of a Velocity Distribution Reveal?

Hi FWHM on a velocity distribution provides me with a specific velocity. What does FWHM say about the velocity distribution, I mean, does FWHM give me the most probable velocity of the distribution or something like that? Thanks
11. ### Full Width at Half Maximum (FWHM) Interpretation

Very commonly in thin film articles/journals, I find the full width at half maximum of X-ray rocking curves associated with the quality (order) of the surface. For example, if the same material is grown on two different substrates, A and B, with FWHM values of 0.11° for A and 0.6° for B, why do...
12. ### Calculate focused spot size - Gaussian FWHM

http://www.calctool.org/CALC/phys/optics/f_NA Does anyone know how they calculate the spot size (Gaussian FWHM) at this website? For a plane wave, the focused spot size it approx=2*wavelength*f/(pi*d0) f=focal length of lens d0=collimated beam diameter before lens but how do you...
13. ### How Does FWHM Affect Spectral Resolution Calculation?

Homework Statement FWHM is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. I have this lab that requires me to calculate the limiting...
14. ### Find FWHM: Pixel Values, Gaussian Curve, Standard Deviation

Hi, I've been searching on google for minutes but couldn't find out a consistent way so far. I mean, it seems everybody has something to say about it :) My data consists of pixel values (ADU's). I am writing a script to obtain fwhm of seeing disk. By definition of the gaussian curve, i...
15. ### Sodium Iodide Detector (NaI) FWHM and applied Voltage

Hi! I have a question regarding the applied voltage on NaI(Tl) detectors, how does the voltage effect the FWHM ( energy resolution)? For example, in a HPGe detector, the higher the applied voltage ( to some extent because of the leakage current) the more electron and holes are collected...
16. ### What is the formula for calculating the FWHM of a gaussian function?

Hi, I have a gaussian of the form exp[-\frac{\pi*x^{2}}{A^2}]. I know that the FWHM=0.939A, but I cannot prove it. I Let exp[-\frac{\pi*x^{2}}{A^2}=0.5 (i.e. the half maximum part) taking natural logs I get rid of the exponential, but then which bit represents the full width?
17. ### Converting laser fwhm bandwidth in m to hz

hi, pls can someone help me with converting FWHM bandwidth of a laser from metres to hertz
18. ### XRD FWHM, debye-scherrer's formula & AFM surface morphology

Hi guys, I have an question about the correlation between grain size caculated from debye-scherrer and the AFM results for my AlN epi layer samples. From my AFM results, the trend of grain size of three samples are getting smaller( around 200-10 nm range among three samples). but the FWHM of...
19. ### FWHM of radioactive sources confusion

I am not sure if I should be using this board or the nuclear board but I chose this board because it is for class work. Anyways over the past few months I have been collecting data from radioactive sources (Th-230, Am-241, Po-210, Pu-238). Now I understand that the number of events divided by...