Imagine you have a checkerboard pattern (below, z) that you are imaging through

Question

Imagine you have a checkerboard pattern (below, z) that you are imaging through a Fourier optics lens system (below, b). If you wanted to create a "blurred" checkerboard pattern (below, c) for artistic effect, how would you manipulate the fields in the Fourier plane? Imagine you have a checkerboard pattern (below, z) that you are imaging through a Fourier optics lens system (below, b). If you wanted to create a "blurred" checkerboard pattern (below, c) for artistic effect, how would you manipulate the fields in the Fourier plane?

Explanation / Answer

For any given image, the fourier transform formed in the fourier plane consists of lower spatial frequencies which are close to the optic axis and the higher frequencies which are farther outwards from the optic axis within the fourier plane.

The lower frequencies provide the base structure of the image whereas higher frequencies adds to the details of the image.

So, if one has to blur any image, the higher frequencies must be blocked in the fourier plane whereas the lower frequencies must be allowed to pass. This can be done using a circular aperture of a given diameter. This diameter will decide how blur the resultant image [inverse fourier] will be.

To obtain a blurred checkerboard pattern, one can use a square aperture so as to block higher frequencies.

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