ESM
[B._Beckhoff,_et_al.]_Handbook_of_Practical_X-Ray_(b-ok.org).pdf

X ray optics 167 6 8 10 12 14 10 3 10 4 sige 220 si

Info icon This preview shows pages 188–191. Sign up to view the full content.

X-Ray Optics 167 6 8 10 12 14 10 3 10 4 SiGe (220) Si (220) Si (111) (a) Energy resolution E/ E Energy (keV) 6 8 10 12 14 3.5 4.0 4.5 5.0 5.5 6.0 (b) Spectral Intensity gain Energy (eV) Fig. 3.55. Energy resolution ( a ) and spectral flux enhancement ( b ) of the graded SiGe monochromator in comparison with double Si (220) monochromator crystals were also reported [168, 169]. The idea of a focusing device on the basis of a laterally graded asymmetric crystal was published [167]. 3.5 Focusing Diffraction Optics A. Erko 3.5.1 Zone Plates Zone Plate as an Imaging System The principles of 3-D diffraction focusing optics can be described using the simple scheme of a transmission zone plate shown in Fig. 3.56.
Image of page 188

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

168 A. Erko R 2 Source plane Focal plane r n t Cross-section of on-axes ZP R n 2 R n 1 A 2 A 1 r n Zone plate Fig. 3.56. Three-dimensional zone-structure of an “on-axis” transmission zone plate. The volume cross-section of the ellipsoids of revolution (left) is represented perpendicular to optical axis projection (right) Shown here is an interference pattern produced upon the interaction of two spherical waves irradiated in points A 1 and A 2 . Each rotational ellipsoid in Fig. 3.56 corresponds to a surface of equal phase, according to the fundamental property of an ellipsoid: the equal sum of the paths R 1 + R 2 for each point of the ellipsoidal surface. In Fig. 3.56 the path difference for the different surfaces corresponds to phase shift, π , of nλ/ 2. A cross-section of this system of ellipsoids perpendicular to the optical axis represents a zone plate. A real zone plate has a finite thickness, which increases with X-ray energy. Therefore, according to Fig. 3.56 a zone plate is a 3-D object with an ellipsoidal shape of the outer zones. Each zone is a volume section of equal phase surfaces, which lie on rotational ellipsoids. If point A 1 is at infinity, the rotational ellipsoid degenerates into rotational paraboloid. Any scattering point C on a given ellipsoid surface forms the same wave phase at observation in point A 2 if point A 1 is a radiation source. The phase difference between the ellipsoidal surfaces is chosen to be π , so the optical path difference: ( R n 1 + R n 2 ) ( R 01 + R 02 ) = 2 , (3.104) where ( R 01 + R 02 ) is the distance between A 1 and A 2 along the axis. If rays penetrate the screen at appropriate points one can obtain an on- axis Fresnel zone plate. In this case only those regions of the screen are opened that contribute to the image of point A 2 with the same phase sign. This is a transparent Fresnel zone plate, characterized by the Fresnel zone radii r n and thickness t . The Fresnel n -zone radius is determined by the equation: r n = nR 01 R 02 λ R 01 + R 02 , (3.105)
Image of page 189
X-Ray Optics 169 where n is the zone number. Here R 1 and R 2 are the corresponding distances from the screen to radiation source and the image. Using the thin lens formula (1 /R 01 ) + (1 /R 02 ) = 1 /F , (3.105) gs written as: r n = Fnλ (3.106) with F denoting the focal distance.
Image of page 190

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 191
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '14
  • MichaelDudley

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern