1. Circular aperture Rectangular aperture Fraunhofer Diffraction

2. Fraunhofer Diffraction pattern which you have observed in your lab for circular aperture

3. Circular aperture q R a

4. Bessel function of order m

5. I = I 0 [2 J 1 (γ) / γ] [ J 1 (γ) / γ] γ = kaq/R=k a Sin  3.83 

6. Airy disk : high irradiance circular spot

7. Diffraction from small and large circular apertures Far-field intensity pattern from a small aperture Far-field intensity pattern from a large aperture

8. With a lens of focal length F and aperture diameter D

9. Airy’s Pattern http://micro.magnet.fsu.edu/primer/java/imageformation/airydiskbasics/index.html © Molecular Expression Diffraction limit of optical microscope!

10. Diffraction limit of Camera q

11. Resolution of imaging system Just resolvedNot resolved Well resolved

12. Pinhole camera pictures Optimal pinhole sizeLarge pinhole size Too small a pinhole needs a very long exposure time

13. Two point sources cannot be resolved if their separation is less than the radius of the Airy disk. Lord Rayleigh’s Criterion

14. Central disk is surrounded by dark ring, for which According to Rayleigh’s criterion Angular limit of resolution : Limit of resolution :  l=centre to centre separation between images

15. R.P. = 1.22 λ / D D= Diameter of the telescope objective Telescope

16. Single slit – Two point sources

17. Rayleigh’s criterion and Sparrow’s criterion

18. Arbitrary Aperture  A =source strength per unit area P (X,Y,Z) R r x y z

19. Rectangular aperture

20. For rectangular aperture with width a and height b

21. http://www.kw.igs.net/~jackord/df/d1.html (Alg C) in circular aperture http://www.kw.igs.net/~jackord/df/d1.html Rectangular and triangular aperture Circular aperture Rectangular and triangular aperture

22. Circular aperture Rectangular aperture Triangular aperture Pinholes

23. Problem A 35 mm camera has a lens with a 50 mm focal length. It is used to photograph a boy of 175 cm in height., such that the image is 30 mm high. How far from the camera should the boy stand? Estimate the best resolution obtainable on the film using light of = 5000 Å, if the lens aperture is 1 cm diameter.

24. Problem Two stars have an angular separation of 1x 10 -6 radian. They both emit light of wavelengths 5770 and 5790 Å. How large a diameter of the lens in the telescope is needed to separate the images of the two stars? How large a diffraction grating is needed to separate the two wavelengths present?

25. Problem A camera lens of 60 mm focal length is accurately focused for objects at 15 m. For what aperture will diffraction blur of visible light be roughly the same as the defocus blur for a star (at  )