BIOE420 BioimagingHomework #1 (Due: 2/14/2019 in class)Note: In your solution, please be as detailed as possible. We will breakdown the pointsfor each step.Question #1 (20%):Suppose the Line spread function of an optical imaging system is: 2cos(5 ) 50( )xotherwisexl xUnit for x: cm.(a) Plot the LSF using Matlab, and determine the resolution of this imaging system inunit of
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BIOE420 Bioimaging
Homework #1 (Due: 2/14/2019 in class)
Note: In your solution, please be as detailed as possible. We will breakdown the points
for each step.
Question #1 (20%):
Suppose the Line spread function of an optical imaging system is:
2
cos(5 ) 5
0
( )
x
otherwise
x
l x
Unit for x: cm.
(a) Plot the LSF using Matlab, and determine the resolution of this imaging system in
unit of cm. Compare your results from both Matlab plots and analytical solution.
(b) Use Matlab convolution function to generate the edge spread function (ESF), and
determine the resolution using ESF. Compare with the values you obtain from (a).
Analytical Solution:
cos(5x1/2)=0.5
5(x1/2)=/3
x1/2 =/15
FWHM= 2(x1/2)==2/15= 0.4189
x = 1:.005:.995;
c1 = 0;
for i = 1:length(x)
if abs(5*x(i)) <= pi/2
psf(i) = cos(5*x(i));
else
psf(i) = 0;
end
end
plot(x,psf)
xlabel('Distance (cm)'); ylabel('Intensity');
title('Line Spread Function')
ind1 = interp1(psf(150:200),x(150:200),.5);
ind2 = interp1(psf(201:250),x(201:250),.5);
FWHM = ind2ind1
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BIOE420 Bioimaging
1 0.8 0.6 0.4 0.2 0 0.2 0.4 0.6 0.8 1
Distance (cm)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Intensity
Point Spread Function
FWHM= 0.4189
Analytical solution is identical to that of the numerical solution
%%ESF Using integration
esf = cumtrapz(x,psf);
figure;
plot(x,esf)
xlabel('Distance (cm)'); ylabel('Intensity');
title('Edge Spread Function')
normesf = esf/max(esf);
ind1 = interp1(normesf(150:250),x(150:250),.12);
ind2 = interp1(normesf(150:250),x(150:250),.88);
res = ind2ind1
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