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

In fig 362 is shown an angular spectrum calculated by

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In Fig. 3.62 is shown an angular spectrum calculated by the RAY program for the zone plate parameters listed in Table 3.6. - 300 - 200 - 100 0 100 200 300 10 - 2 10 - 1 10 0 First order spectra in image plane (slit limited) Diffraction on a ZP 5 th order 3 rd order 1 st order Relative angular flux density (rays/mrad) Angle (mrad) Fig. 3.62. The angular spectrum, calculated just behind a ZP (solid line) and in the focal plane limited by a slit of 10 µ m (dashed line)
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X-Ray Optics 179 The ray-trace program RAY for a zone plate was used for the development of a practical method for measurements of zone plate parameters: efficiency and resolution. In Fig. 3.62 is shown an angular spectrum of the rays, dif- fracted on a zone plate and calculated just behind an optical element. One can evidently see different angular regions, responsible for focusing in different diffraction orders: +1; +3; +5. These spectra can be used for direct measure- ments of a zone plate resolution and efficiency. With the help of the Fast Fourier Transform program this spatial frequency spectrum can be converted into an intensity distribution in a focal plane of a zone plate. Our calculations show identical results obtained by Fourier transformation of the spectra and ray-tracing. The parameters measured by this method are free from experi- mental errors, arising from the source size and quality of the optics, placed in front of a zone plate. A parallel beam, spatially filtered through a pinhole can be used as a source in this experiment. 3.5.2 Reflection Zone Plate and Bragg–Fresnel Optics Reflection Zone Plate Principle Here the possibility of using a reflection zone plate is discussed. This consists of a reflector with an elliptical phase-shifting Fresnel structure on the surface (Fig. 3.63). A Bragg reflector on a crystal or multilayer structure or a total Bragg angle Sagittal diffraction Meridional diffraction Axis direction Focal plane t opt Fig. 3.63. Diffraction on the meridional ( a ) and sagittal ( b ) directions for reflection zone plates with optimum thickness t opt
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180 A. Erko external reflector on a super-polished surface can be used as reflective sub- strate. The optical path, l, of the beam in the phase-shifting material must be the same for both reflection zone plates and transmission zone plates. Con- sequently, the zone thickness required to give the optimum phase shift for reflection zone plates is smaller than for transmission zone plates since the radiation passes twice through the zone material at an angle. Unlike for the previously reported Bragg–Fresnel lenses [177] the Fresnel structure is evaporated or sputtered onto the surface of a reflector. The struc- ture is approximated by the formulae: x n + cos θ B 2 ν sin θ B 2 + y 2 n sin 2 θ B = Fnλ sin 2 θ B (3.129) with ν = R 1 /R 2 + 1 R 1 /R 2 1 , (3.130) where x n and y n are the coordinates of the n th elliptical zone on the surface, θ B is the Bragg or grazing incidence angle, F is the focal distance and R 1 and R 2 are the source to lens and source to image distances respectively.
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