# 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as well as on some additional (unpublished) analysis.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,
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;