Tham khảo tài liệu 'modern developments in x-ray and neutron optics episode 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 20 F. Schafers The direction cosines are transformed correspondingly 0 S Dx 9 Dz x o s Is ls cos x - ms sin x and finally ms ls sin x cos 9 ms cos x cos 9 nS J ls sinxsin 9 ms cosxsin 9 In the new coordinate system the ray is described by x y I t z 1 ls ms S Misalignment A six-dimensional misalignment of an optical element can be taken into account three translations of the coordinate system by ỗx 5y and 5z and three rotations by the misorientation angles 5x x-y plane ỖỰ x-z plane and ỗ ộ y-z plane . Since the rotations are not commutative the coordinate system is first rotated by these angles in the given order and then translated. For the outgoing ray to be described in the non-misaligned system the coordinate system is backtransformed in reverse order . Thus the optical axis remains unaffected by the misalignment. Second-Order Surfaces Optical elements are described by the general equation for second-order surfaces F x y z anx2 a22y2 a33Z2 2ai2xy 2a13xz 2 13 2a23yz 2a14x 2a24y 2a34z a44 0. This description refers to a right-handed coordinate system attached to the centre of the mirror with its surface in x-z plane and y-axis points to the normal . This coordinate system is used for the optical elements COne CYlinder and SP_here. Note that for the elements EL-lipsoid and PA-raboloid a coordinate system is used which again is attached to the centre of the mirror with x-axis on the surface but the z-axis is parallel to the symmetry axis of this element for an easier description in terms of the aj parameters see Figs. and . The ajj-values of Table are given for this system. Thus the rotation angle of the coordinate system from source to element is here 9 a EL and 29 PA respectively 9 being the grazing incidence angle and a the tangent angle on the ellipse. 21 2 The BESSY Raytrace Program RAY Fig. . Ellipsoid definitions and coordinate systems Fig. . Paraboloid Definitions and coordinate systems The individual .
