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#### Presentation Transcript

**1. **Diffraction and the Fourier Transform Light bends!
History of diffraction
Diffraction assumptions
Solution to Maxwell's Equations
Fraunhofer Diffraction
Some examples
Young’s 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 it’s 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