Convolving the point sources
Now convolve your image of point 
sources with the point spread 
function, using imfilter.
(Hint: it’s usually a good idea to 
convert all your images to doubles 
before filtering them, so you may 
want to use im2double…)
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Convolving the point sources
Now convolve your image of point 
sources with the point spread 
function, using imfilter.
(Hint: it’s usually a good idea to 
convert all your images to doubles 
before filtering them, so you may 
want to use im2double…)
PD = im2double(P);
psfd= im2double(psf);
J = imfilter(PD,psfd);
imshow(J,[])
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Beating the Limit: Deconvolution
W•e’ve seen that even for an ideal optical 
system, there exist hard limits on 
performance.
I•s there any way we could cleverly get around 
these limits?
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Beating the Limit: Deconvolution
W•e’ve seen that even for an ideal optical 
system, there exist hard limits on 
performance.
I•s there any way we could cleverly get around 
these limits?
Y•es: Deconvolution!
B•asic idea: we know what a PSF looks like, so 
extrapolate backwards
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The Math
How many spots?
Open “howmany.tif” in  the 
tutorial folder.
How many spots?
Open “howmany.tif” in  the 
tutorial folder.
J = imread(‘howmany.tif’);
How many spots?
Open “howmany.tif” in  the 
tutorial folder.
J = imread(‘howmany.tif’);
Now, deconvolvethe image 
using deconvwnr, which 
performs Wiener 
deconvolutionn.
Syntax: deconvwnr(I,psf)
How many spots?
Open “howmany.tif” in  the 
tutorial folder.
J = imread(‘howmany.tif’);
Now, deconvolvethe image 
using deconvwnr, which 
performs Wiener 
deconvolutionn.
Syntax: deconvwnr(I,psf)
JD = deconvwnr(J,psf);
Least‐Squares Fitting
Fitting involves finding the curve which minimizes the sum of the squares of the offsets ("the 
residuals") of the given data points from the curve:
}
offset
x
f(x)
Included in the distributed files is D1Resids.m for 
fitting a 1D‐Gaussian to data.  Let’s try and fit one to 
a 1D intensity profile of the image “psf.tif”.
First make the intensity profile which you will fit:  I chose a horizontal slice through the middle
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