Optical transfer function: Difference between revisions

Revision as of 00:55, 26 February 2020

Revision as of 20:28, 10 March 2020

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==Definition and related concepts==

Since the optical transfer function<ref name=Williams2002>{{cite book |first=Charles S.|last=Williams|year=2002|title=Introduction to the Optical Transfer Function|publisher=SPIE -– The International Society for Optical Engineering|isbn=0-8194-4336-0}}</ref> (OTF) is defined as the Fourier transform of the point-spread function (PSF), it is generally speaking a [[complex number|complex-valued]] function of [[spatial frequency]]. The projection of a specific periodic pattern is represented by a complex number with absolute value and [[complex argument]] proportional to the relative contrast and translation of the projected projection, respectively.

[[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).]]

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====Edge-spread function====

The two-dimensional Fourier transform of an edge is also only non-zero on a single line, orthogonal to the edge. This function is sometimes referred to as the '''edge spread function''' (ESF).<ref>Holst, G.C. (1998). ''Testing and Evaluation of Infrared Imaging Systems'' (2nd ed.). Florida:JCD Publishing, Washington:SPIE.</ref><ref name="ElectroOpticalTestLab">{{cite web|url=http://www.electro-optical.com/html/toplevel/educationref.asp|title=Test and Measurement -– Products -– EOI|website=www.Electro-Optical.com|access-date=2 January 2018}}</ref> However, the values on this line are inversely proportional to the distance from the origin. Although the measurement images obtained with this technique illuminate a large area of the camera, this mainly benefits the accuracy at low spatial frequencies. As with the line spread function, each measurement only determines a single axes of the optical transfer function, repeated measurements are thus necessary if the optical system cannot be assumed to be rotational symmetric.

[[File:MTF knife-edge target.jpg|thumb|right|215px|In evaluating the '''ESF''', an operator defines a box area equivalent to 10%{{citation needed|date=August 2013}} of the total frame area of a '''knife-edge test target''' back-illuminated by a '''black body'''. The area is defined to encompass the edge of the target image.]]