At the focal point (E =o, n = o) all the secondary waves agree in phase, and the intensity is easily expressed, whatever be the form of the aperture.
So long as there is no sensible discrepancy of phase there can be no sensible diminution of brightness as compared with that to be found at the focal point itself.
The function of a lens in forming an image is to compensate by its variable thickness the differences of phase which would otherwise exist between secondary waves arriving at the focal point from various parts of the aperture.
E is then the co-ordinate relatively to 0 of any focal point 0' for which the retardation is R; and the required result is obtained by simply integrating (5) with respect to from - cc to +oo.
It is evident that the effect at the focal point is the obliteration of the first and other spectra of odd order, so that as regards the spectrum of the first order we may consider that the two beams interfere.