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

# Zone plate aberrations the aberrations of optical

• Notes
• 898

This preview shows pages 190–192. Sign up to view the full content.

Zone Plate Aberrations The aberrations of optical elements are conventionally analysed in terms of L : the optical path difference: L = R 2 1 + r 2 n + R 2 2 + r 2 n R 2 1 + R 2 2 . (3.107) These aberrations become noticeable when the term ∆ L is comparable with λ/ 4. (a) Spherical aberrations: For the regular zone plate constructed in accordance with (3.105), the term responsible for the spherical aberration is: 1 8 n 2 λ 2 1 R 3 1 + R 3 2 R 1 + R 2 < λ 4 . (3.108) One finds that the spherical aberration is a maximum for R 1 = 2 F , i.e., for the unit magnification. The maximum zone number N is limited by the value of: N < 8 F 3 λ . (3.109) (b) Chromatic aberrations Since the focal length of a zone plate is a function of wavelength, the chro- matic aberrations are very strong. In some schemes of X-ray microscopes [170] holographically made zone plates in combination with pinhole in focal plane are used as the monochromators. Chromatic aberration is significant for: L = 2 ± λ 4 . (3.110) The maximum number of zones for which chromatic aberration can still be neglected is given by: N < λ λ . (3.111) This equation is also valid for the calculation of an energy resolution when the pinhole of the diffraction-limited size β is used in a focal plane. (c) Off-axis aberrations These aberrations arise due to off-axis source position or ellipticity in zone- plate structure. If the primary beam is parallel and α is a beam incidence

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

170 A. Erko angle (angle to the optical axes), then the optical pass difference will have aberration terms, as: L = r 3 n α 4 F 2 3 r 2 n a 2 4 F + 2 . (3.112) Using (3.112), one can estimate tolerance on zone plate orientation for the definite resolution in microprobe application. The first term in (3.112) is responsible for the coma aberration and second for the astigmatism and field curvature. Applying the λ/ 4 criteria for the above mentioned equation, one can write alignment requirements. In case of a zone plate with a number of zones N > 100, coma is the main aberration: -coma: α < N 1 . 5 F λ . (3.113) In case of a zone plate with a number of zones N < 100, astigmatism and field curvature are the main aberrations: -astigmatism and field curvature: α 1 3 N . (3.114) In comparison with a conventional lens a zone plate forms a distortion- free image. Another technological requirement to the optics designed for high- resolution image transmission is that it should be free of wave-front phase distortions caused by zone plate surface roughness and refraction index ﬂuc- tuations within the medium. The approximate maximum value of the surface roughness could be roughly estimated by equation: ς < 0 . 1 t opt . (3.115) For example, the surface distortions for transparent silicon zone plates can practically reach ς = 0 . 1–0.3 µ m without affecting the image quality substantially.
This is the end of the preview. Sign up to access the rest of the document.
• Spring '14
• MichaelDudley

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern