EOP513 Fourier Optics Assignment 4

1. Given a circular aperture 0.2 mm in diameter illuminated by a normally incident plane wave field of wavelength l = 632.8 nm. If we wish to observe a region of 50 mm in diameter in the fresnel region, how close can we be to the aperture? How far away must we be to observe fraunhofer diffraction?

2. A single slit in an opaque scren 0.10 mm wide is illuminated (in air) by plane waves from a krypton ion laser (l = 461.9 nm). If the observing screen is 1 m away, calculate the Fresnel number and determine whether the resulting pattern is far-field. Then calculate the angular width of the central maximum.

3. A narrow single slit (in air) in an opague screen is illuminated in the infrared from a He-Ne laser at 1152.2 nm, and it is found that the center of the 10^th dark band in the fraunhofer pattern lies at an angle of 6.2 degrees off the central axis. Determine the width of the slit.

   

4. A collimated beam of microwaves impinges on a metal screen that contains a long horizontal slit that is 20 cm wide. A detector moving parallel to the screen in the far-field region locates the first minimum of irradiance at an angle of 36.87 degrees above the central axis. Determine the wavelength of the radiation.

5. Use Matlab and the function fresnel to plot the Cornu spiral.

6. Use the Matlab integration function quad to calculate values for the Fresnel integral from 0.0 to 5.0 in steps of 0.5. Compare the results obtained by the function fresnel.

7. Use Matlab to plot the on-axis irradiance of a normalized slit vs. Fresnel number.

8. Use Matlab to plot the irradiance of a normalized slit for N_f = 5/2 and N_f = 2/5.

Maintained by John Loomis, last updated 8 June 2012