Optical transfer function
![Illustration of the optical transfer function and its relation to image quality. The optical transfer function of a well-focused (a), and an out-of-focus optical imaging system without aberrations (d). As the optical transfer function of these systems is real and non-negative, the optical transfer function is equal to the modulation transfer function by definition. Images of a point source and spoke target are shown in (b,e) and (c,f), respectively.](/Images/godic/202501/31/Illustration_of_the_optical_transfer_function_and_its_relation_to_image_quality..svg5905.png")
![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).](/Images/godic/202501/31/Definitions_PSF_OTF_MTF_PhTF.svg5905.png")
![The one-dimensional optical transfer function of a diffraction limited imaging system is identical to its modulation transfer function.Spoke target imaged by a diffraction limited imaging system.Transfer function and example image of an ideal, optical-aberration-free (diffraction-limited) imaging system.](/Images/godic/202501/31/1D_diffraction_limited_optical_transfer_function..svg5905.png")
![Spoke target imaged by a diffraction limited imaging system.](/Images/godic/202501/31/Spoke_target_imaged_by_a_diffraction_limited_imaging_system..svg5905.png")
The optical transfer function (OTF) is a complex transfer function where the modulus of the function describe the modulation transfer and the argument of the function describe the phase transfer in an optical system, such as a camera, microscope, human eye, or projector, as a function of spatial frequency. It is used by optical engineers and scientists 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 transmission chain. The function specifies the translation and contrast reduction of a periodic sine pattern after passing through the lens system, as a function of its periodicity and orientation. Formally, the optical transfer function is defined as the Fourier transform of the point spread function, or impulse response of the optics, i.e. the image of a point source. When this image does not change shape upon lateral translation of the point source, the optical transfer function can be used to study the projection of arbitrary objects or scenes onto the detector or film. While figures of merit such as contrast, sensitivity, and resolution give an intuitive indication of performance, the optical transfer function provides a comprehensive and well-defined characterization of optical systems.