Optical representation in the Fourier domain

In Fourier transformed images the zeroth spatial frequency is usually located at location (0, 0, 0) in a 3D image. Although this is a seemingly logical choice it is often desirable to shift the origin to the center of the image: this is the optical representation. This expression is derived from the fact that when an optical system is used to generate Fourier Transforms (any lens does this!!!), the zero frequency is on the optical axis and therefore in the center of the image.

Huygens Professional has as tool that, in addition to centering the zero frequency of an FFT for representation functions, also can be used to shift a (centered) PSF to the origin. This is useful when you want to convolve an image with a measured or computed PSF by multiplying their FFTs (see the Cookie Cutter) and transforming the result back again.

Because a centered PSF implies a shift operation from the origin to the center, the result of computing a convolution as outlined above will be a shifted image. You can prevent this from happening by applying 'To/from optic rep' prior to the convolution or use it to correct the result.