Optical transfer function

The optical transfer function (OTF) of an optical system such as a camera, microscope, human eye, or projector specifies how different spatial frequencies are handled by the system. It is used by optical engineers to describe how the optics project light from the object or scene onto a photographic film, detector array, retina, screen, or simply the next item in the optical transmission chain. A variant, the modulation transfer function (MTF), neglects phase effects, but is equivalent to the OTF in many situations.

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 defined as the real magnitude (absolute value) of the complex OTF.

Since the optical transfer function (OTF) is defined as the Fourier transform of the point-spread function (PSF), it is generally speaking a 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.

Often the contrast reduction is of most interest and the pattern translation 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). 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:

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