EOP513 Fourier Optics Assignment 5

  1. Do problems 4-1 through 4-4 from the textbook.

  2. The following approximation to the Fresnel integral function is valid for large x.

    Find an appropriate lower-limit for x (1% error). Use Matlab to plot the real and imaginary parts of the Fresnel integral and the approxmation function.

  3. Do problems 4-7, 4-9, and 4-10 as follows. Set the aperture geometry using appropriate Matlab functions. Generate an image of the input. Use Matlab to find the Fraunhofer pattern. (See fdiffract.m) Generate an image of the output. Use appropriate image scaling to show the shape of the diffraction pattern.

  4. Generate the diffraction pattern of a circular aperture (normalized radius w = 1). Use Matlab to find the Fraunhofer pattern (using method in fdiffract.m. Show both input and output images. Try to scale the image to approximate the appearance of Fig 4.10 in the textbook. Plot a radial cross-section of the output. Superimpose on this plot, the Airy pattern computed from Eq. 4-31 in the textbook (generated using somb2(x), see somb.m).

  5. Generate the diffraction pattern of a rectangular aperture (wx/wy = 2). Try to scale the image (size and irradiance) to approximate the appearance of Fig 4.8 in the textbook.

  6. Show that

  7. Generate the following aperture functions using cyl.m, rect.m, and polygon.m. Find the Fraunhofer pattern and show both your input and output images.

          


Maintained by John Loomis, last updated 9 June 2009