More on the Fourier Transforms

Additional Properties

Anamorphism

‘Ana’ means ‘opposite’, while ‘morph’ is related to shape. Hence, the FT of an object is somewhat the opposite of the object. In simpler terms, this means that the FT of a long object will be short, and the FT of a thin object will be wide. Here are a few examples and demonstrations of this property.

Left – tall rectangular object; Right – FFT of the object, which appears like a horizontal line segment

Left – wide rectangular object; Right – FFT of the object, which appears like a vertical line segment

Note that the FT of the tall rectangle is a horizontal line segment, while the FT of the wide rectangle is a vertical line segment. Hence, an object that is long in one dimension will have an FT that is short in that dimension. Further examples are as follow:

Dots that are 10 pixels apart and the resulting Fourier Transform.

Dots 20 pixels apart and the resulting Fourier Transform.

The previous images are two dots that lie along the horizontal axis, separated by various distances. The left image have dots separated by 10 pixels, while the ones on the right are separated by 20 pixels. Note that the farther away the dots are in the image, the more narrow the fringes produced in the Fourier Transform. Hence, anamorphism!