X-Ray Optics Calculator

• Refractive Optics
Main Formulae
• Refraction Index decrement
• Compound Refractive Lens (cylindrical)
• Compound Refractive Lens (parabolical)
• Planar Parabolic Refractive Lens
• Planar Kinoform Refractive Lens

Refractive Optics

Definition

• Wavelength λ
• Focus distance f
• Real part of decrement of refraction index δ
• Imaginary part of decrement of refraction index β

Refraction Index Decrement

The Refraction Index Decrement and related parameters are calculated from the atomic scattering factors and Compton and Rayleigh cross-sections.

First part of the atomic scattering data is given on a uniform logarithmic mesh with 500+ points from 0.01 keV to 30 keV. The atomic scattering factors are based upon experimental measurements of the atomic photoabsorption cross section. The absorption measurements provide values for the imaginary part of the atomic scattering factor. The real part, which describes the dispersion of radiation as it interacts with matter, is calculated from the absorption measurements using the Kramers-Kronig integral relations.
Source: http://henke.lbl.gov/optical_constants/
B. L. Henke, E. M. Gullikson, and J. C. Davis, Atomic Data and Nuclear Data Tables Vol. 54 No. 2, 181-343 (July 1993).

The atomic scattering factors for energies above 30 keV up to 10 MeV are taken from data set calculated by Lynn Kissel. The original data is available from
    http://www-phys.llnl.gov/V_Div/scattering/elastic.html
These data are computed for neutral atoms, only, entirely within a local relativistic self-consistent potential with the Slater local-exchange coefficient and Latter tail. For a detailed discussion of the underlying validity of the information contained in these directories see, for example:
Validity of Form-Factor, Modified-Form-Factor and Anomalous-Scattering-Factor Approximations in Elastic Scattering Calculations, by Lynn Kissel, B. Zhou, S. C. Roy, S. K. Sen Gupta and R. H. Pratt, Acta Crystallographica Vol. A51, 271-288 (1995).

Another data set of atomic scattering factors is taken from tabulated data calculated by Christopher T. Chantler. The original data is available from
    https://physics.nist.gov/PhysRefData/FFast/html/form.html
Herein, the primary interactions of x-rays with isolated atoms from Z = 1 (hydrogen) to Z = 92 (uranium) are described and computed within a self-consistent Dirac-Hartree-Fock framework. This has general application across the range of energy from 1-10 eV to 400-1000 keV, with some limitations as the low- and high-energy extremes are approached. For a detailed discussion of the underlying validity of the information contained in these directories see, for example:
C. T. Chantler, Theoretical form factor, attenuation and scattering tabulation for Z=1-92 from E=1-10 eV to E=0.4-1.0 MeV, J. Phys. Chem. Ref. Data 24 (1995), 71-643.

Compton and Rayleigh cross-sections data has been extracted from the file raycomin.f of the library by Brennan and Cowan
S. Brennan and P.L. Cowan, Rev. Sci. Instrum. 63,1, 850 1992
The file raycomin.f is available by ftp from the authors from http://www-ssrl.slac.stanford.edu/absorb.html

Compound Refractive Lens (cylindrical)

Compound Refractive Lens (parabolical)

Planar Parabolic Refractive Lens

Planar Kinoform Refractive Lens