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]].
