# Difference between Gaussian and Airy

• Choisai
Gaussian beam profile and the Airy disk. While they may have a similar appearance in their central portions, the energy distribution in their tails is quite different. This is an important distinction, especially for distributions like the Lorentzian. Additionally, there are mathematical descriptions available on the Wolfram site for those who want to learn more.
Choisai
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:

And a Gaussian beam profile looks like this:

So they seem more or less the same. What is the difference between the two?

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"

## 1. What are Gaussian and Airy distributions?

Gaussian and Airy distributions are probability distributions commonly used in statistics and physics to describe the behavior of data points. They both have a bell-shaped curve, but the shape and properties of the curves differ.

## 2. What is the main difference between Gaussian and Airy distributions?

The main difference between Gaussian and Airy distributions lies in their tails. Gaussian distributions have thinner tails, meaning that extreme values are less likely to occur. On the other hand, Airy distributions have thicker tails, making extreme values more probable.

## 3. How are Gaussian and Airy distributions used in science?

Gaussian distributions are commonly used to model natural phenomena, such as the height of individuals in a population or the amount of rainfall in a specific area. Airy distributions are often used to describe the behavior of turbulent fluids, such as air flow in pipes or ocean waves.

## 4. Can Gaussian and Airy distributions be transformed into each other?

Yes, Gaussian and Airy distributions can be transformed into each other through a mathematical process called the Fourier transform. This allows scientists to switch between the two distributions and use whichever is more appropriate for their data analysis.

## 5. Are there any real-life examples of Gaussian and Airy distributions?

Yes, both Gaussian and Airy distributions can be observed in various natural phenomena and human-made systems. For example, the distribution of IQ scores in a population follows a Gaussian distribution, while the distribution of wind speeds in a hurricane follows an Airy distribution.

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