Rayleigh and other resolution criteria

Abstract

The Rayleigh resolution criterion, which states that two objects are just resolved when the maximum in the focal plane of one Airy pattern falls on the first minimum of the other, is described in nearly all optics books. The minimum between the two maxima is said to be 0.81 of the peak intensity. This value actually holds only for slit images such as are formed in spectroscopy or Fabry-Perot interferometry. For point sources such as stars, the minimum is 0.74, for example. Although mathematically elegant, the Rayleigh resolution is exceeded experimentally for some low-scatter optical systems, a result which has given rise to the less pessimistic Abbe and Sparrow criteria. On the other hand, if significant near-angle scattering exists and this background is not suppressed electronically, Rayleigh resolution may be unobtainable even for perfectly figured optical systems. As a working standard, the concept of diffraction-limited optics based on the Rayleigh criterion is thus useful provided that the values are not taken too seriously.