Light Diffraction: Explaining Airy Equation

In summary, the Airy equation is a theoretical description of light diffraction that is derived from the wave equation and is used to calculate the diffraction pattern for a given aperture. This is achieved by applying the theory of Fraunhofer diffraction and using a 2D Fourier transform of the aperture function. The details of this calculation can be found in math forums or through further research.
  • #1
a-lbi
10
0
What describes Airy equation in theoretical description of light diffraction?
 
Science news on Phys.org
  • #3
Thank you for your response. I've read this article. But there are no answers for my question.

Writing more precisly. I would like to see derivation from (for instance) wave equation to get Airy equation in a light diffraction problem.
 
  • #4
To find a diffraction pattern for a given aperture, you need to apply the theory of Fraunhofer diffraction.

To do this, define an aperture function in cylindrical coordinates as follows;

a(r) = 1 for r less than or equal to a.
a(r) = 0 for r greater than a.

Where a is the radius of the aperture.

The resultant diffraction pattern is a 2D Fourier transform of this function (i.e. the Airy function). I'm sure you can find the gory details of this calculation somewhere (or maybe post in the math forums).

Claude.
 
  • #5
Thank you for your response. I can see that the problem is to get Airy equation from the two dimensional Fourier integral equation. If I have some time I will try to follow the way.
 

1. What is light diffraction?

Light diffraction is a phenomenon where light waves bend or spread as they pass through a narrow opening or around an obstacle. This causes the light to behave differently than it would in a straight path.

2. What is the Airy equation?

The Airy equation is a mathematical formula that describes the diffraction pattern of light passing through a circular aperture. It takes into account the size of the aperture and the wavelength of the light to predict the intensity of the resulting diffraction pattern.

3. How is the Airy equation derived?

The Airy equation is derived from the Huygens-Fresnel principle, which states that every point on a wavefront acts as a source of secondary waves. When these secondary waves interfere with each other, they create a diffraction pattern. By applying this principle to a circular aperture, we can derive the Airy equation.

4. What factors affect the diffraction pattern according to the Airy equation?

According to the Airy equation, the size of the aperture and the wavelength of the light are the main factors that affect the diffraction pattern. A larger aperture or a shorter wavelength will result in a narrower central peak and more intense diffraction fringes.

5. How is the Airy equation used in scientific research?

The Airy equation is used in various fields of science, such as astronomy, microscopy, and particle physics. It allows scientists to predict and analyze the diffraction patterns of light passing through different types of apertures, providing valuable insights into the nature of light and its interactions with matter.

Similar threads

  • Optics
Replies
3
Views
682
Replies
2
Views
1K
Replies
13
Views
859
Replies
3
Views
1K
Replies
15
Views
5K
Replies
10
Views
4K
Replies
1
Views
644
Replies
7
Views
4K
Replies
7
Views
6K
Back
Top