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| {{Redirects here|Defocus|the intentional use of defocusing|shallow focus}}
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| [[Image:Bokeh Example.jpg|thumb|A photograph of [[Christmas lights]] with significant defocus aberration.]]
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| {{Optical aberration}}
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| In [[optics]], '''defocus''' is the [[aberration in optical systems|aberration]] in which an image is simply out of [[focus (optics)|focus]]. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Optically, defocus refers to a [[Translation (physics)|translation]] along the [[optical axis]] away from the plane or surface of best focus. In general, defocus reduces the sharpness and [[contrast (vision)|contrast]] of the [[image]]. What should be sharp, high-contrast edges in a scene become gradual transitions. Fine detail in the scene is blurred or even becomes invisible. Nearly all image-forming optical devices incorporate some form of focus adjustment to minimize defocus and maximize image quality.
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| The degree of image blurring for a given amount of focus shift depends inversely on the lens [[f-number]]. Low f-numbers, such as {{f/|1.4|}} to {{f/}}2.8, are very sensitive to defocus and have very shallow [[depth of focus|depths of focus]]. High f-numbers, in the {{f/}}16 to {{f/}}32 range, are highly tolerant of defocus, and consequently have large depths of focus. The limiting case in f-number is the [[pinhole camera]], operating at perhaps {{f/}}100 to {{f/}}1000, in which case all objects are in focus almost regardless of their distance from the pinhole [[aperture]]. The penalty for achieving this extreme depth of focus is very dim illumination at the imaging [[Photographic film|film]] or [[Image sensor|sensor]], limited resolution due to [[diffraction]], and very long [[exposure time]], which introduces the potential for image degradation due to [[motion blur]].
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| The amount of allowable defocus is related to the [[Optical resolution|resolution]] of the imaging medium. A lower-resolution imaging chip or film is more tolerant of defocus and other aberrations. To take full advantage of a higher resolution medium, defocus and other aberrations must be minimized.
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| Defocus is modeled in [[Zernike polynomial]] format as <math>a(2 \rho^2-1)</math>, where <math>a</math> is the defocus coefficient in [[wavelength]]s of light. This corresponds to the [[parabola]]-shaped [[optical path difference]] between two spherical [[wavefront]]s that are [[tangent]] at their [[surface vertex|vertices]] and have different [[radius of curvature (optics)|radii of curvature]].
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| For some applications, such as [[phase contrast]] [[electron microscopy]], defocused images can contain useful information. Multiple images recorded with various values of defocus can be used to examine how the intensity of the electron wave varies in three dimensional space, and from this information the phase of the wave can be inferred. This is the basis of non-interferometric [[phase retrieval]]. Examples of phase retrieval algorithms that utilise defocused images include the [[Gerchberg–Saxton algorithm]] and various methods based on the [[transport of intensity equation]].
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| == See also ==
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| * [[Bokeh]]
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| ==References==
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| {{commonscat|Blurred images}}
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| *Smith, Warren J., ''Modern Optical Engineering'', McGraw–Hill, 2000, Chapter 11, ISBN 0-07-136360-2
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| [[Category:Optics]]
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| [[Category:Geometrical optics]]
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