Everywhere we crossing the term FWHM but what does it actually mean? what is the exact Physical significance behind it?
Can anyone clarify my difficulty?
Hi,
I think that this definition is just a convention that helps us quantify measurable physical quantaties and is relatively easier to calculate than other statistical parameters. For example, if you measure a Gaussian function, the FWHM can be calculated by just knowing the function's maximal value. This is usually easier than extracting the standard deviation of the function, which is another commonly-used statistical parameter that can define a Gaussian function.
I hope it helps,
Assaf
Hi Eliyas (and other future readers) --
There is nothing inherently superior about 'full width at half maximum' (FWHM) compared to other ways of measuring how wide something is -- 'FWHM' literally just means how wide something is when you've defined the "edge" on either side as being the point where the value has dropped to half of the maximum. It's simply convenient.
Imagine that for an object, like a wooden toy block, the edge is sharp and distinct, so it's clear where the measurement of width should begin and end. Now instead imagine a Gaussian laser pulse whose temporal shape, spectral bandwidth, and spatial profile all lack definite edges because the tails of a Gaussian remain nonzero as they decay off to infinity. In order to quantify the width of this infinite parameter, one can choose to measure from the point where the spectrum/pulse envelope/beam profile has decayed to half of its maximum value -- or one may even choose to measure from another point, such as the point at which the amplitude has decayed to 1/e. In the end, these are all simply choices to find a way to conveniently get a simple numeric representation of how wide something is.
Just for fun, I've linked to the "Full width at half maximum" Wikipedia page (where some basic info and a simple picture can be found) as well as the "Beam diameter" Wikipedia page (which explores some of the other choices people may make in defining how wide something is).
I hope this is useful for someone, ~Eric
https://en.wikipedia.org/wiki/Full_width_at_half_maximum
https://en.wikipedia.org/wiki/Beam_diameter
Dear Eliyas, FWHM is a convenient measure of the width of a function. It is easier to calculate than for example, the equivalent width of function f(x), which is defined as NIntegrate[f(x),{x,-Infinity,Infinity}]/f(0) in mathematica. But the equivalent width of a function is equal to the reciprocal of the equvalent width of its transform. Please see R. Bracewell's The Fourier transform and its applications, Chap. 8, The two damains. Regards, Shigeo.
Thank you every one. Your suggestions made some clarity in my understanding.
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