page_title: Ringing artifacts
section_title: Special functions
hierarchical_section_title: Ringing artifacts / Similar phenomena / Special functions
caption_attribution_description: English: A simulation of spherical aberration in an optical system with a circular, unobstructed aperture admitting a monochromatic point source. The top row is over-corrected (half a wavelength), the middle row is perfectly corrected, and the bottom row is under-corrected (half a wavelength). Going left to right, one moves from being inside focus to outside focus. The middle column is perfectly focused. Also note the equivalence of inside-focus over-correction to outside-focus under-correction. See the corresponding longitudinal sections. See also en:Image:Spherical-aberration-slice.jpg
context_page_description: In signal processing, particularly digital image processing, ringing artifacts are artifacts that appear as spurious signals near sharp transitions in a signal. Visually, they appear as bands or "ghosts" near edges; audibly, they appear as "echos" near transients, particularly sounds from percussion instruments; most noticeable are the pre-echos. The term "ringing" is because the output signal oscillates at a fading rate around a sharp transition in the input, similar to a bell after being struck. As with other artifacts, their minimization is a criterion in filter design.
context_section_description: Many special functions exhibit oscillatory decay, and thus convolving with such a function yields ringing in the output; one may consider these ringing, or restrict the term to unintended artifacts in frequency domain signal processing.
  Fraunhofer diffraction yields the Airy disk as point spread function, which has a ringing pattern.
  The Bessel function of the first kind,  which is related to the Airy function, exhibits such decay.
  In cameras, a combination of defocus and spherical aberration can yield circular artifacts ("ring" patterns). However, the pattern of these artifacts need not be similar to ringing (as discussed on this page) – they may exhibit oscillatory decay (circles of decreasing intensity), or other intensity patterns, such as a single bright band.
caption: Combinations of defocus and spherical aberration exhibit ring artifacts.
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