Full width at half maximum: Definition from Answers.com

full width at half maximum

A full width at half maximum (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.

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.

When the considered function is the normal distribution of the form

$f(x) = \frac{1}{\sigma \sqrt{2 \pi} } \exp \left[ -\frac{(x-x_0)^2}{2 \sigma^2} \right]$

where $σ$ is the standard deviation and $x 0$ can be any value (the width of the function does not depend on translation). The relationship between FWHM and the standard deviation is

$\mathrm{FWHM} = 2 \sqrt{2 \ln 2 } \; \sigma \approx 2.35482 \; \sigma.$

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

$f(x)=\operatorname{sech} \left( \frac{x}{X} \right).$

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

$\mathrm{FWHM} = 2 \; \operatorname{arsech} \left( \frac{1}{2} \right) X = 2 \ln (2 + \sqrt{3}) \; X \approx 2.633 \; X$

where arsech is the inverse hyperbolic secant.

References

This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".

	What is the width of a half Olympic pool? Read answer...
	What is half-empty and half-full? Read answer...
	What is the length and width of a rectangle whose width is one half its length and perimeter is 54cm? Read answer...

	How do you find half width at full maximum for a peakwithout being function dependent?
	What is the size a half size not full locker in middle and high schools Like width and length of inside door?
	What is the maximum temperature of exhaust gas emission of a Caterpillar Diesel Engine Model No 3512 1020kW at full load half load?

		Sci-Tech Dictionary. McGraw-Hill Dictionary of Scientific and Technical Terms. Copyright © 2003, 1994, 1989, 1984, 1978, 1976, 1974 by McGraw-Hill Companies, Inc. All rights reserved. Read more
		Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Full width at half maximum". Read more

Full width at half maximum

References

See also