Optical transfer function: Difference between revisions

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Either [[transfer function]] specifies the response to a periodic [[sine-wave]] pattern passing through the lens system, as a function of its spatial frequency or period, and its orientation. Formally, the OTF is defined as the [[Fourier transform]] of the [[point spread function]] (PSF, that is, the [[impulse response]] of the optics, the image of a point source). As a Fourier transform, the OTF is complex-valued; but it will be real-valued in the common case of a PSF that is symmetric about its center. The MTF is formally defined as the magnitude (absolute value) of the complex OTF.

The image on the right shows the optical transfer functions for two different optical systems in panels (a) and (d). The former corresponds to the ideal, [[diffraction-limited system|diffraction-limited]], imaging system with a circular [[pupil function|pupil]]. Its transfer function decreases approximately gradually with spatial frequency until it reaches the [[diffraction-limited system|diffraction-limit]], in this case at 500 cycles per millimeter or a period of 2 μm. Since periodic features as small as this period are captured by this imaging system, it could be said that its resolution is 2 μm.<ref>The exact definition of resolution may vary and is often taken to be 1.22 times larger as defined by the [[angular resolution|Rayleigh criterion]].</ref> Panel (d) shows an optical system that is out of focus. This leads to a sharp reduction in contrast compared to the [[diffraction-limited system|diffraction-limited]] imaging system. It can be seen that the contrast is zero around 250 cycles/mm, or periods of 4 μm. This explains why the images for the out-of-focus system (e,f) are more blurry than those of the [[diffraction-limited system|diffraction-limited]] system (b,c). Note that although the out-of-focus system has very low contrast at spatial frequencies around 250 cycles/mm, the contrast at spatial frequencies near the diffraction limit of 500 cycles/mm is diffraction-limited. Close observation of the image in panel (f) shows that the spoke structure is relatively sharp for the large spoke densities near the center of the [[spoke target]].

==Definition and related concepts==