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The diffraction theory of point spread functions was first studied by [[George Biddell Airy|Airy]] in the nineteenth century. He developed an expression for the point spread function amplitude and intensity of a perfect instrument, free of aberrations (the so-called [[Airy disc]]). The theory of aberrated point spread functions close to the optimum focal plane was studied by [[Frits Zernike|Zernike]] and Nijboer in the 1930–40s. A central role in their analysis is played by Zernike's [[Zernike polynomials|circle polynomials]] that allow an efficient representation of the aberrations of any optical system with rotational symmetry. Recent analytic results have made it possible to extend Nijboer and Zernike's approach for point spread function evaluation to a large volume around the optimum focal point. This extended Nijboer-Zernike (ENZ) theory allows studying the imperfect imaging of three-dimensional objects in [[confocal microscopy]] or astronomy under non-ideal imaging conditions. The ENZ-theory has also been applied to the characterization of optical instruments with respect to their aberration by measuring the through-focus intensity distribution and solving an appropriate [[inverse problem]].
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=== Microscopy ===
[[File:63x 1.4NA Confocal Point Spread Function 2+3D.png|thumb|An example of an experimentally derived point spread function from a confocal microscope using a 63x 1.4NA oil objective. It was generated using Huygens Professional deconvolution software. Shown are views in xz, xy, yz and a 3D representation.]]
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