I am in high-school and planning on basing a research essay on the topic of Fourier Optics. I was looking at the derivations behind the Fourier transform and the fact that the Fourier transform of the aperture function is the diffraction pattern in Fraunhofer diffraction.
I then starting looking into the 4f correlator and how it can be used to filter out parts of the image.
I was wondering if there would be an easy application of the 4f system that I could perform and base my essay on.
I was thinking of comparing the optical Fourier transform (analytical approach) with the fast Fourier transform (numerical approach) for a specific transparent image in which different diffraction gratings are used to filter out parts of the images.
First, I want to make sure I am understanding everything right: for optical Fourier transform I would put a masking filter (diffraction grating in my case) in the focal plane (which I would have to do a calculation to find where it is located depending on the lens) and it would filter/modify the image. Then I would take a photo of the resulting modified image.
How would I do the same process using FFT? I know I would need to take the 2d FFT of the original image to see if it produces similar results but how would I filter/modify it in the same way that was done in the 4f system with optical Fourier transform?
Also what kind of software would I need to perform the FT and is there any other way that this can be simulated using MATLAB for example?
Is what I am thinking something that is possible to do in high-school lab conditions? Or does anyone have any better ideas of an experiment that could be done regarding the 4f system (preferably something with a useful application that would make the experiment worth doing)?
Any help would be greatly appreciated.