positions for u03b1 and u03b2 resulting from evaluation of equations 13 and 14 generally do not fall onto actually measured data for this reason the complementary fans must be obtained through interpolation for this purpose one proceeds as follows be the characteristic quantities of a complementary beam p n t m t q t c 1 to be calculated index t target and let equ21 and equ22 be the characteristic quantities of a direct beam p n m q c 1 from which the complementary beam p n t m t q t c 1 is to be calculated from 13 and 14 with the arbitrary stipulation am k am there results equ23 and equ24 this first yields non integers n and m the complementary beam p n t m t q t 1 is now to be produced by means of interpolation from adjacent n n m m beams with integral n and m e g through bilinear interpolation between the adjacent beams the z focus position of a direct beam in the spiral with slope slope d u03b1 dz sbsp f results as for a complementary beam one obtains equ25 wherein t q is the angle of inclination of a beam against a plane perpendicular to the z axis known as the cone angle the following holds equ26.