ABSTRACT
The Gaussian region in terms of the degrees of terms in a power series which are to be neglected can be amplified by considering the physical magnitudes of the terms neglected. Lord Rayleigh suggested in 1880 that a pencil could be regarded as substantially aberration-free if the wavefront were within a quarter of a wavelength of a true sphere, since then the light disturbances arriving at the focus would all reinforce each other in phase; this is the so-called Rayleigh quarter-wavelength rule. Thus, one may say that physically the higher order terms which are neglected in the Gaussian approximation ought to amount to less than a quarter of a wavelength, or, in other words, the Gaussian region is the region so close to the axis that within it all deviations of wavefronts and refracting surfaces from true spherical shape are less than a quarter wavelength.
