788 Mr. F. Twyman on an Interj erometer 



of the lens for which we require to find the aberration 

 according to geometrical optics. This operation amounts 

 in effect to fitting our reference sphere to various points of 

 the wave surface given by the lens, and is immediately 

 translatable into the desired terms. 



If the aberration of wave-front amounts, however, only to 

 one or two bands or less, the nomenclature and methods of 

 geometrical optics fail to afford us any idea of the distribution 

 of light in the neighbourhood of the focus of the lens. We 

 must then use the methods of the wave theory of light. The 

 question has been mathematically treated by various investi- 

 gators who have, of course, all assumed as available in the 

 form of a mathematical expression (or have calculated for 

 various specific cases) the aberration of wave-front. For 

 instance, to take a recent example, Dr. Silberstein* deter- 

 mined the light distribution round the focus of a lens having 

 aberration, first obtaining an expression for the aberration of 

 wave-front, and then using it to determine the distribution 

 of light intensity. 



So far as the author is aware, no one has yet attempted to 

 determine the distribution of light intensity around the 

 focus of an existing lens from experimental data obtained 

 from the lens itself. The following method would appear 

 to be practical, and to afford results accurate to a fair degree 

 of approximation. It is an application of the method of 

 Cornu's spiral. Fig. 13 represents an interferogram as seen 

 on one of the lens interferometers described, the thick lines 

 representing dark bands. All these interferograms may of 

 course be considered as maps, showing the relative phase in 

 which the disturbance passing through various parts of the lens 

 reaches the surface or the centre of the reference spheie. I 

 have marked one of the dark bands 0. The next dark band will 



therefore be correctly marked — , since we are considering 



single passage through the lens only, while the interferogram 

 is obtained by double transmission. Having obtained a photo- 

 graph of this appearance one enlarges it to such a convenient 

 size that a number of fractional phase lines can be inter- 

 polated, as has been done by the lines of medium thickness 

 marked 0, OItt, 0'2tt, 0'37t, &c. Finer lines again have 

 been drawn intermediately to the others. 



* " Light Distribution round the Focus of a Lens at Various xlper- 

 tures," L. Silberstein, Phil. Mag. xxxv. (Jan. 1918). The paper gives a 

 brief resume of earlier work in this direction. See also the interesting 

 paper by Conrady on Star Discs (Monthly Notices, R. A. S. June 1919), 

 as a further example of the more recent work. 



