Difference between Gaussian and Airy

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A Gaussian beam profile and an Airy disk differ significantly in their energy distribution, particularly in the tails. While the central portions may appear similar, the Gaussian profile has a smooth fall-off, whereas the Airy disk exhibits ripples due to diffraction effects. This distinction is crucial for understanding various distributions, including Lorentzian, which also features significant tail energy. Mathematical descriptions and visual representations can further clarify these differences. Recognizing that "more or less the same" does not equate to "the same" is essential in this context.
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What is the difference between a Gaussian beam profile and an Airy disk? Both seem to be pretty much the same to me. An Airy disk looks like this:

res-fig2.gif


And a Gaussian beam profile looks like this:
fwhm.png


So they seem more or less the same. What is the difference between the two?
 
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You seem to be ignoring the ripples in the Airy pattern. The Gaussian falls away smoothly.

So the central portion may look the same, but the energy in the "tails" is quite different. This is an important distinction for many distributions, such as Lorentzian, which also has a lot of energy in the tails.

You should also look up the mathematical descriptions - you can find them, and more plots, on the Wolfram site.
 
"More or less the same" is not the same thing as "the same"
 
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