Diffraction and the Fourier Transform

Diffraction and the Fourier Transform PowerPoint PPT Presentation

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History of Diffraction. Diffraction of light was first characterized by Francesco Grimaldi, who also coined the termdiffraction in 1665. Isaac Newtoncalled itinflexionof light rays.James Gregory(16381675) observed the diffraction patterns from a bird featherthe firstdiffraction gratin

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Diffraction and the Fourier Transform

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1. Diffraction and the Fourier Transform Light bends! History of diffraction Diffraction assumptions Solution to Maxwell's Equations Fraunhofer Diffraction Some examples Youngs two-slit experiment www.physics.gatech.edu/frog/lectureswww.physics.gatech.edu/frog/lectures

2. History of Diffraction

3. Diffraction Light does not always travel in a straight line. It tends to bend around objects. This tendency is called diffraction. All waves do this, including light and acoustic waves.

4. Why its hard to see diffraction

5. Diffraction of ocean water waves

6. Diffraction of a wave by a slit Whether waves in water or electromagnetic radiation in air, passage through a slit yields a diffraction pattern that will appear more dramatic as the size of the slit approaches the wavelength of the wave.

7. Light passing by edge Diffraction by an Edge

8. Radio waves diffract around mountains.

9. Diffraction Geometry We wish to find the light electric field after a screen with a hole in it. This is a very general problem with far-reaching applications.

10. Diffraction Assumptions The best assumptions were determined by Kirchhoff (in the early 19th century): 1) Maxwell's equations 2) Inside the aperture, the field is the same as if the screen were not present. 3) Outside the aperture (in the shadow of the screen), the field is zero.

11. Huygens Principle

12. Diffraction solution The field in the observation plane, E(x,y), at a distance z from the aperture plane is a sum of spherical waves from every point within the aperture:

13. Diffraction approximations

14. More diffraction approximations Multiplying out the squares:

15. Diffraction Conventions

16. The Fraunhofer diffraction formula

17. The Uncertainty Principle in Diffraction!

18. Fraunhofer diffraction from a slit Fraunhofer Diffraction from a slit is simply the Fourier Transform of a rect function, which is a sinc function. The intensity is then sinc2.

19. Fraunhofer Diffraction from a square aperture The diffracted field is a sinc function in both x and y because the Fourier transform of a rect function is sinc. http://wpcontent.answers.com/wikipedia/en/thumb/1/1f/Square_diffraction.jpg/300px-Square_diffraction.jpghttp://wpcontent.answers.com/wikipedia/en/thumb/1/1f/Square_diffraction.jpg/300px-Square_diffraction.jpg

20. Diffraction from a Circular Aperture A circular aperture yields a diffracted Airy Pattern, which looks a lot like a sinc function, but actually involves a Bessel function.

21. Diffraction from small and large circular apertures

22. Fraunhofer diffraction from two slits

23. Diffraction from one- and two-slit screens Fraunhofer diffraction patterns

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