In Matlab, define a zero-filled 256x256 matrix named Bars by using the command, zeros. Create 2...

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In Matlab, define a zero-filled 256x256 matrix named Bars by using the command, zeros. Create 2 vertical bars, centered on the image, of width 3 and height 40 and separated from each other by 8 pixels, by setting the appropriate matrix elements to the value 1. 1. Display the image, Bars. Your matrix can be displayed as a 2D grayscale image by using the commands, imagesc and colormap. Make the image square by using the command, axis square. (10 points) 2. Pick a horizontal line through the center of the test pattern. Plot the intensity profile of this line. Label the x and y axes appropriately. (5 points) 3. To accurately reconstruct this image by sampling-ignoring edge effects-how often (for every how many pixels) must you sample (hint: Ax = 3 pixels)? What is the fundamental principle behind sampling? (5 points) Simulate the effect of scatter by creating a new image Bars_Scatter that represents the 2-dimensional convolution of Bars with the point spread function of h: Bars Scatter = Bars" h where his approximated as a 1-dimensional exponential filter that is M = 51 pixels long, normalized to unity: h() - exp(-a-1-21), 1-1..M h(i)= h() A Σh() Perform convolution in MATLAB to compute Bars_Scatter using the command, conv2 with 'same' option. 4. Choose a = 1. Using the command subplot, display on the same figure the image (Bars_Scatter) and plot of the point spread function, h. What is the FWHM of h in terms of the number of pixels? (10 points) 5. Pick the same center horizontal line as you did in Problem 2 and plot the intensity profile of this line through. Bars Scatter. Plot the original intensity profile on the same axes using the command, hold on. Specify the original and new intensity profile by using the command, legend. What happened to the intensity profile of Bars Scatter compared to Bars? (10 points) 6. Now vary the value of 'a' so that the FWHM of his greater than the separation of the bars, i.e., 8 pixels) for which the bars are not resolvable. At what approximate value of 'a' can you no longer resolve the peaks of the bars in the image? Display the new image. (10 points) 7. On another figure, in one subplot, plot the original and new intensity profiles along the center horizontal line as in Problem 5. On the same figure, in a second subplot, plot the new point spread function, h, on a different axes. (5 points) 8. What happened to the new point spread function? What will be the point spread function of an ideal system with no scatter look like? (5 points) In Matlab, define a zero-filled 256x256 matrix named Bars by using the command, zeros. Create 2 vertical bars, centered on the image, of width 3 and height 40 and separated from each other by 8 pixels, by setting the appropriate matrix elements to the value 1. 1. Display the image, Bars. Your matrix can be displayed as a 2D grayscale image by using the commands, imagesc and colormap. Make the image square by using the command, axis square. (10 points) 2. Pick a horizontal line through the center of the test pattern. Plot the intensity profile of this line. Label the x and y axes appropriately. (5 points) 3. To accurately reconstruct this image by sampling-ignoring edge effects-how often (for every how many pixels) must you sample (hint: Ax = 3 pixels)? What is the fundamental principle behind sampling? (5 points) Simulate the effect of scatter by creating a new image Bars_Scatter that represents the 2-dimensional convolution of Bars with the point spread function of h: Bars Scatter = Bars" h where his approximated as a 1-dimensional exponential filter that is M = 51 pixels long, normalized to unity: h() - exp(-a-1-21), 1-1..M h(i)= h() A Σh() Perform convolution in MATLAB to compute Bars_Scatter using the command, conv2 with 'same' option. 4. Choose a = 1. Using the command subplot, display on the same figure the image (Bars_Scatter) and plot of the point spread function, h. What is the FWHM of h in terms of the number of pixels? (10 points) 5. Pick the same center horizontal line as you did in Problem 2 and plot the intensity profile of this line through. Bars Scatter. Plot the original intensity profile on the same axes using the command, hold on. Specify the original and new intensity profile by using the command, legend. What happened to the intensity profile of Bars Scatter compared to Bars? (10 points) 6. Now vary the value of 'a' so that the FWHM of his greater than the separation of the bars, i.e., 8 pixels) for which the bars are not resolvable. At what approximate value of 'a' can you no longer resolve the peaks of the bars in the image? Display the new image. (10 points) 7. On another figure, in one subplot, plot the original and new intensity profiles along the center horizontal line as in Problem 5. On the same figure, in a second subplot, plot the new point spread function, h, on a different axes. (5 points) 8. What happened to the new point spread function? What will be the point spread function of an ideal system with no scatter look like? (5 points)

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1 Here is the code to create the Bars image and display it Bars zeros256256 Bars12832128321282012820 ... View the full answer