History and Methods
The diffraction theory of point-spread functions was first studied by 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 the Dutch physicists Fritz Zernike and Nijboer in the 1930–40s. A central role in their analysis is played by Zernike’s 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 is instrumental in 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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