- Do problems 4-1 through 4-4 from the textbook.
- 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. - 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. - 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 somb^{2}(*x*), see`somb.m`). - Generate the diffraction pattern of a rectangular aperture
(
*w*= 2). Try to scale the image (size and irradiance) to approximate the appearance of Fig 4.8 in the textbook._{x}/w_{y} - Show that
- 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 *