EOP513 Fourier Optics Assignment 9

1. Do textbook problems 2.6 and 2.7

2. Use MATLAB and the Fourier-Bessel transform to demonstrate numerically that the Fourier-Bessel transform of 1/r is 1/ρ.

3. Download your class image, convert it to grayscale (see lenna and the example referenced there to see how to convert to grayscale), embed it into a 256 x 256 (or 512 x 512) array, and find its Fourier Transform. You should take the square root of the input before transforming so that an eventual inverse transform will restore the original irradiance. See Fourier transform example)

4. Use your class image to show examples of lowpass, highpass, and bandpass operations. See ( Filtering in the Frequency Domain)

5. Use one of your classmate's images and interchange the magnitude of the Fourier transform of one image with the phase of the other. You should see that the resulting inverse transform follows the phase information.

6. Multiply your image transform by 0.1 wave of uniform random phase and calculate the inverse transform. Compare side-by-side with original image. (See example)

Maintained by John Loomis, last updated 16 July 2009