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Inoptics,defocus is theaberration in which an image is simply out offocus. This aberration is familiar to anyone who has used a camera, videocamera, microscope, telescope, or binoculars. Optically, defocus refers to atranslation of the focus along theoptical axis away from the detection surface. In general, defocus reduces thesharpness andcontrast of theimage. 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.
The degree of image blurring for a given amount of focus shift depends inversely on the lensf-number. Low f-numbers, such asf/1.4 tof/2.8, are very sensitive to defocus and have very shallowdepths of focus. High f-numbers, in thef/16 tof/32 range, are highly tolerant of defocus, and consequently have large depths of focus. The limiting case in f-number is thepinhole camera, operating at perhapsf/100 tof/1000, in which case all objects are in focus almost regardless of their distance from the pinholeaperture. The penalty for achieving this extreme depth of focus is very dim illumination at the imagingfilm orsensor, limited resolution due todiffraction, and very longexposure time, which introduces the potential for image degradation due tomotion blur.
The amount of allowable defocus is related to theresolution 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.
Defocus is modeled inZernike polynomial format as, where is the defocus coefficient inwavelengths of light. This corresponds to theparabola-shapedoptical path difference between two sphericalwavefronts that aretangent at theirvertices and have differentradii of curvature.
For some applications, such asphase contrastelectron 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-interferometricphase retrieval. Examples of phase retrieval algorithms that use defocused images include theGerchberg–Saxton algorithm and various methods based on thetransport-of-intensity equation.
In casual conversation, the termblur can be used to describe any reduction in vision. However, in a clinical setting blurry vision means the subjective experience or perception of optical defocus within theeye, calledrefractive error. Blur may appear differently depending on the amount and type of refractive error. The following are some examples of blurred images that may result from refractive errors:
The extent of blurry vision can be assessed by measuringvisual acuity with aneye chart. Blurry vision is often corrected by focusing light on the retina withcorrective lenses. These corrections sometimes have unwanted effects including magnification or reduction, distortion, color fringes, and altered depth perception. During an eye exam, the patient's acuity is measured without correction, with their current correction, and afterrefraction. This allows theoptometrist orophthalmologist ("eye doctor") to determine the extent refractive errors play in limiting the quality of the patient's vision. ASnellen acuity of 6/6 or 20/20, or as decimal value 1.0, is considered to be sharp vision for an average human (young adults may have nearly twice that value). Best-corrected acuity lower than that is an indication that there is another limitation to vision beyond the correction of refractive error.
Optical defocus can result from incorrect corrective lenses or insufficientaccommodation, as, e.g., inpresbyopia from the aging eye. As said above, light rays from a point source are then not focused to a single point on the retina but are distributed in a little disk of light, called theblur disk. Its size depends on pupil size and amount of defocus, and is calculated by the equation
(d = diameter in degrees visual angle,p = pupil size in mm,D = defocus in diopters).[1]
Inlinear systems theory, the point image (i.e. the blur disk) is referred to as thepoint spread function (PSF). The retinal image is given by theconvolution of the in-focus image with the PSF.
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