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LAB 2: Recover Moire images from superimposed Fresnel zone plates

This lab requires to recover Moire images from superimposed Fresnel zone plates. Carefully read the following procedures:

1. Create Sinusoidal zone plats using the following equation:

ECE 253, Fall 2018

Fundamentals of Digital Image Processing

Department of Electrical and Computer Engineering

University of California, San Diego

f1(x, y) = 1 + 1 cos 2⇡k⇣x2 + y2⌘ 22⇣⌘

f2(x,y)=1+1cos2⇡k (xx0)2+(yy0)2 22

where x0 = y0 2 {10,20,30,40,50,60} and the coordinator of the Fresnel zone plate is depicted in Figure 1. The image f1(x, y) and f2(x, y) look like the images in Figure 2. You can freely choose the spatial frequency parameter k.

  1. Create six superimposed Fresnel zone plates:
    f(x,y)=f1(x,y)·f2(x,y)|(x0,y0) wherex0 =y0 2{10,20,30,40,50,60}. One of six superimposed images image look like the image in Figure 3
  2. Derive a spatial frequency of a Moire pattern to the superimposed image f(x,y) at each (x0,y0) using 2D-DFT. You don’t need any fancy filtering to extract a frequency of a Moire pattern. Carefully revise a lecture note to describe a spatial frequency of a Moire pattern. You only need to extract the frequency to recover a Moire image.
  3. Finally create six Moire images using the inverse 2D-DFT. One of six recovered Moire images looks like the image in Figure 4.
  4. Write the number of cycles, the number of pixels and spatial frequencies (cycles/pixel) of six Moire images. Make sure your results should match with spatial frequencies of Moire patterns in superimposed images.
  5. Write a short description of this experiment.
  6. You should submit your description, your code and the following images as a single zip file: f1(x, y), six f2(x, y) and six f(x, y) Fresnel zone plate images, and six Moire 2D-DFT (magnitude only), and six recovered Moire images. You also need to create a file including spatial frequencies of six Moire images to the x and y directions.

Programming language: Matlab

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ECEA2f5f3orSdyllabus

Figure 1: The coordinator of the Fresnel zone plate.

Figure 2: f1(x, y) and f2(x, y)|(x0,y0)

Figure 3: The superimposed image f(x, y).

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ECE 253 Syllabus

Figure 4: The recovered Moire image.

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