Compound Refractive Lens Parameters


Redefine the conditions by the values you need.
Distance sourse-to-lens [m]:   Source size [mkm]:  
Energy of X-rays [keV]:   Wall between holes [mkm]:  
Radius of holes [mkm]:   Number of holes in array:  
Roughness teeth height [mkm]:  

Press button of the lens material to obtain the CRL parameters:



Focal length in [m] =   Aperture in [mkm] =  
Focal distance in [m] =   Slit-effect parameter =  
Focus for point source in [mkm] =   Gain for point source =  
Focus for real source in [mkm] =   Gain for real source =  
Real Gain for rough surfaces =   Lens length in [mm] =  

            Refractive index is n = 1 + (- + i )*10-8
            Chemical formula:
            Relation: Compton / Photoabsorption =

How these are calculated

Calculation is based on the results of works:
    Nature, 1996, vol.384, p.49;
    Applied Optics, 1998, vol.37, No.4, p.653
as well as on some additional (unpublished) analysis.

Let us introduce a notation:

  rs - source-to-lens distanse,
  ws - width of source (source size),
  E - energy of X-rays,
  R - radius of holes,
  d - wall thickness between holes,
  N - number of holes in array,
  h - total height of teeth due to roughness of all surfaces of holes.
  n = 1 - D + iB - refractive index (D - decrement),
  L = 12.397 / E - wavelength of X-rays,
  M = 12.567 B / L - absorption coefficient

The parameters are calculated using the formulas:

  Focal length - F = R / (2ND),
  Focal distance - rf = F / ( 1 - F/rs ),
                Aperture due to circular form - Ac = 2R (4LF / R 2 )1/4,
                Aperture due to arsorption - Aa = 2R (2 / MRN )1/2,
  Slit effect parameter - pse = Ac / Aa,
  Aperture is approximated as - A = min( Ac, Aa ),
  Focus for point source - wfp = Lrf / A,
                Source size projection - wsp = ws rf / rs,
  Gain for point sourse - G = ( A / wfp )( 1 + rf / rs ) exp( -MNd ) X,
              where   X = 1   if   pse < 1   else   X = 0.7854,
  Gain for real sourse - g = G / C   if   C > 1,   where   C = ( wsp / wfp ) X,
              here   X = 0.886   if   pse < 1   else   X = 1.111,
  Real gain for rough surfaces - gr = g exp( -( 0.507 hDE )2 ),
  Focus for real source - wfr = wfp + wsp.

The estimations contain maximum error when the slit effect parameter is close to unity as well as the projection of source size is close to focus width for a point source.
The decrement of refractive index D is calculated taking into account only Rayleigh scattering. The index of absorption B is calculated taking into account Photoelectric absorption and Compton scattering. The energy dependence of cross section for these processes for different chemical elements was calculated using Log-Log polynomial approximation taken from the book: Handbook of X-Ray Spectrometry, Methods and Techniques, edited by E. Van Grieken & Andrjei A. Marcowicz, Marcel Dekker, Inc., New York, Basel, Hong Kong.

created: November, 1998;   modified: September, 2000;