Optical transfer function: Difference between revisions

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[[File:Definitions PSF OTF MTF PhTF.svg|right|thumb|400px|Various closely related characterizations of an optical system exhibiting coma, a typical aberration that occurs off-axis. (a) The point-spread function (PSF) is the image of a point source. (b) The image of a line is referred to as the line-spread function, in this case a vertical line. The line-spread function is directly proportional to the vertical integration of the point-spread image. The optical-transfer function (OTF) is defined as the Fourier transform of the point-spread function and is thus generally a two-dimensional complex function. Typically only a one-dimensional slice is shown (c), corresponding to the Fourier transform of the line-spread function. The thick green line indicates the real part of the function, and the thin red line the imaginary part. Often only the absolute value of the complex function is shown, this allows visualization of the two-dimensional function (d); however, more commonly only the one-dimensional function is shown (e). The latter is typically normalized at the spatial frequency zero and referred to as the modulation transfer function (MTF). For completeness, the complex argument is sometimes provided as the phase transfer function (PhTF), shown in panel (f).]]

{| class="infobox wikitable"

! Dimensions !! Spatial<br />function !! Fourier<br />transform

|-

! 1D

| Line<br />-spread<br />function<br />(derivative<br />of Edge<br />edge-spread<br />function)

| 1D section of 2D optical-transfer function

|-

! 2D

| Point<br />-spread<br />function

| (2D) Optical<br />transfer<br />function

|-

! 1D3D

| 3D Point-spread function

| Line<br />spread<br />function<br />(derivative<br />of Edge<br />spread<br />function)

| Modulation<br3D />Optical-transfer<br />function

|}

Often the contrast reduction is of most interest and the translation of the pattern can be ignored. The relative contrast is given by the absolute value of the optical transfer function, a function commonly referred to as the '''modulation transfer function''' ('''MTF'''). Its values indicate how much of the object's contrast is captured in the image as a function of spatial frequency. The MTF tends to decrease with increasing spatial frequency from 1 to 0 (at the diffraction limit); however, the function is often not [[monotonic]]. On the other hand, when also the pattern translation is important, the [[complex argument]] of the optical transfer function can be depicted as a second real-valued function, commonly referred to as the '''phase transfer function''' ('''PhTF'''). The complex-valued optical transfer function can be seen as a combination of these two real-valued functions: