462 ON METHODS FOR DETECTING SMALL OPTICAL RETARDATIONS, [415
values of 0/0 are chosen which make (I + 0/0) TT integral. The calculations recorded in Table I refer in the first instance to the values of
.......... ............ (18)
TABLE I.
— — 7T,
= + 7T.
<Pie (IB) (18)2
o-oooo 3-704 13-72
0-2732 3-475 12-08 ;
0-5000 2-979 8-87
0-5915 ' 2-721 7-40 ;
0-9099 1-707 2-91
1-0000 1-418 2-01
1-2282 0-758 0-57
1-5465 0-115 o-oi
2-0000 -0-177 0-03
It will be seen that, in spite of bhe fact that nine-tenths of the whole light passes, the definition of- what should be the edge of the field at 0 = 9 is very bad. Also that the illumination at 0t=0 is greater than what it would be (-7T2) if the second screening were abolished altogether (± % = oo ).
So far we have dealt only with cases where the second aperture is symmetrically situated with respect to the geometrical focus. This restriction we will now dispense wibh, considering first the case where £j = 0 and £2(= f) is positive and of arbitrary value. The coefficient of sin T in (7) becomes simply
....................(19)
0) £J assume infinite
e+* .w
In the coefficient of cos I7, Ci {(# + 0)|ri}, Ci {(9 values, but by (15) we see that
Ci((0 + 0)£}-d {(0-0)fc}-log so that the coefficient of cos T is
.(21)
The intensity I at angle 0 is represented by the sum of the squares of (19) and (21). When 0 = 0 at the centre of the field of view, I = 4 (Si 0£)2, but at the edges for which it suffices to suppose 0 = + 0, a modification is called for, since Ci {(0 - 0) £} must then be replaced by 7 + log | (6 - 0) ||. Under these circumstances the coefficient of cos T becomes
and
/={Si(20£)}2+{7 + log(20£)-Ci(20£)}*.............(22)(1870).osely what is actually the distribution of light between the central and lateral bands in the diffraction pattern formed at the plane of the second aperture. By (5) the intensity oi light at f is proportional to £~2 sin2 6% or, if we write r) for 6%, to ?7~2 sin2 77, The whole light between 0 and 97 is thus represented by