For this activity, we investigated the properties of a 2D Fourier transform (FT) of an image. For the first part of the activity, we produced different images and obtained their FTs. As we can see from figure 1, a straight edge (i. e. square) produces a line in the FT perpendicular to the edge of the image. An annulus also produce ring in its FT and the FT of an annulus with a straight edge has broken line perpendicular to the image’s edge. The FT of a double slit is a single straight slit along the horizontal. The FT of a double pinhole along the x- axis created a series of slits of different widths and spacing.
For the second part of the activity, we simulated a sinusoid and obtained its FT. what we obtained is an image with two pinholes at the y-axis a few pixels apart.
However if we increase the frequency of the sinusoid, we can see in the FT that the pinholes moved further apart. This is because the pinholes are the spatial frequencies of the sinusoid. They are in the y-axis because the sinusoid propagates through the y-axis. The reason they move apart is that the center on the FT is equal to a DC signal or a frequency of zero. As we move further from the center, the frequency would increase so higher frequency structures can be found further from the center.
Rotating the sinusoid also causes a rotation in its FT. also like before the structures in the FT align to where the sinusoid is propagating.
If we take the FT of two superimposed sinusoids, we would obtain something like four dots in a corner of a square. I wasn’t actually expecting this since I thought that the FT would look like a cross at the center.
By superimposing another sinusoid thing get even weirder. My prediction is that upon adding another sinusoid another pair of dot would appear in the FT. Instead, there became 8 dots that are shifted from the center.
All in all it wasn’t a particularly hard activity so I would give myself an 8/10
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