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Diffraction-limited system
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===Digital photography=== In a digital camera, diffraction effects interact with the effects of the regular pixel grid. The combined effect of the different parts of an optical system is determined by the [[convolution]] of the [[point spread function]]s (PSF). The point spread function of a diffraction limited circular-aperture lens is simply the [[Airy disk]]. The point spread function of the camera, otherwise called the instrument response function (IRF) can be approximated by a rectangle function, with a width equivalent to the pixel pitch. A more complete derivation of the modulation transfer function (derived from the PSF) of image sensors is given by Fliegel.<ref>{{cite journal|last1=Fliegel|first1=Karel|title=Modeling and Measurement of Image Sensor Characteristics|journal=Radioengineering|date=December 2004|volume=13|issue=4|url=http://www.radioeng.cz/fulltexts/2004/04_04_27_34.pdf}}</ref> Whatever the exact instrument response function, it is largely independent of the f-number of the lens. Thus at different f-numbers a camera may operate in three different regimes, as follows: # In the case where the spread of the IRF is small with respect to the spread of the diffraction PSF, in which case the system may be said to be essentially diffraction limited (so long as the lens itself is diffraction limited). # In the case where the spread of the diffraction PSF is small with respect to the IRF, in which case the system is instrument limited. # In the case where the spread of the PSF and IRF are similar, in which case both impact the available resolution of the system. The spread of the diffraction-limited PSF is approximated by the diameter of the first null of the [[Airy disk]], :<math> d/2 = 1.22 \lambda N,\, </math><ref>{{cite book | last=Goodman | first=Joseph W. | chapter= 4.4.2 Example of Fraunhofer Diffraction Patterns for Circular Aperture | title=Introduction to Fourier Optics | publisher=Roberts and Company Publishers | publication-place=Englewood, Colorado | date=2005 | isbn=0-9747077-2-4}}</ref> where <math>\lambda</math> is the wavelength of the light and <math>N</math> is the [[f-number]] of the imaging optics, i.e., <math> 2 NA \rightarrow (2.44N)^{-1} </math> in the Abbe diffraction limit formula. For instance, for an f/8 lens (<math>N=8</math> and <math>NA\approx2.5%</math> ) and for green light (<math>\lambda_g=</math> 0.5 μm wavelength) light, the focusing spot diameter will be d = 9.76 μm or 19.5<math>\lambda_g</math>. This is similar to the pixel size for the majority of commercially available 'full frame' (43mm sensor diagonal) cameras and so these will operate in regime 3 for f-numbers around 8 (few lenses are close to diffraction limited at f-numbers smaller than 8). Cameras with smaller sensors will tend to have smaller pixels, but their lenses will be designed for use at smaller f-numbers and it is likely that they will also operate in regime 3 for those f-numbers for which their lenses are diffraction limited.
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