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→The OTF of an optical system with a non-rotational symmetric aberration: the figures show trefoil, not coma |
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[[File:Trefoil aberration PSF OTF and example image.svg|right|thumb|600px|When viewed through an optical system with trefoil aberration, the image of a point object will look as a three-pointed star (a). As the point-spread function is not rotational symmetric, only a two-dimensional optical transfer function can describe it well (b). The height of the surface plot indicates the absolute value and the hue indicates the complex argument of the function. A spoke target imaged by such an imaging device is shown by the simulation in (c).]]
Optical systems, and in particular [[optical aberrations]] are not always rotationally symmetric. Periodic patterns that have a different orientation can thus be imaged with different contrast even if their periodicity is the same. Optical transfer function or modulation transfer functions are thus generally two-dimensional functions. The following figures shows the two-dimensional equivalent of the ideal and the imperfect system discussed earlier,
Optical transfer functions are not always real-valued. Period patterns can be shifted by any amount, depending on the aberration in the system. This is generally the case with non-rotational-symmetric aberrations. The hue of the colors of the surface plots in the above figure indicate phase. It can be seen that, while for the rotational symmetric aberrations the phase is either 0 or π and thus the transfer function is real valued, for the non-rotational symmetric aberration the transfer function has an imaginary component and the phase varies continuously.
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