Extract the high frequencies portions

Assignment Help Simulation in MATLAB

Reference no: EM131593294 , Length: 5

In Structured Illumination Microscopy (SIM) a sinusoidal pattern (garting) is superimposed on the sample or object, in order to obtain resolution beyond the diffraction limit.

But to fully capture all the high frequencies, we need multiple images with the pattern reotated at different angles and shifted at different phases.

Then the desirable portions from each image's FFT is extract and recombined to finally obtain the super resolution image from the final reconstructed FFT as in this figure from the article by Gustafson.

1. Read the image.

2. Apply the sinusoidal pattern.

3. Rotate at different angles (and shifted at different phases if possible).

4. Extract the high frequencies portions from each image's FFT.

5. Recombine the FFTs.

6. Get the final IFFT of the image

We need to make the step of the numerical reconstruction more carefully to benefit from the structured illumination. You can basically imagine that the Fourier transform of the original image with a superposed grating structure produces two copies in the Fourier spectrum. One at a negative frequency and one at a positive frequency.

This will show approximately as two adjacent circles in the Fourier domain (with a bright dot in the middle at zero frequency, DC). You will need to select the positive (or negative) circle of frequencies only by blocking the central white dot.

You can basically select a circular region around the +1 frequency and then block all other frequencies. When calculating the inverse Fourier transform of this you should get the original image partially (corresponding to that chosen direction).

You can then repeat it at other angles and when completed full circle you have the object reconstructed(I.e. select the +1 diffraction order (and a circular region around it with a diameter slightly smaller than the distance between the 0th and +1st diffraction order.

Then rotate the grating on the object and track the same +1 diffraction order (it will move in a circle in the Fourier plane). This should give you a better reconstruction.

Attachment:- Structured Illumination Microscopy.rar

Reference no: EM131593294

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