[ Identification | Description | Input parameters | Links ]

# The `Lens` Component

Refractive lens with absorption, incoherent scattering and surface imperfection.

## Identification

- Site:
- Author: C. Monzat/E. Farhi/S. Desert/G. Euzen
- Origin: ILL/LLB
- Date: 2009

## Description

    Refractive Lens with absorption, incoherent scattering and surface imperfection.
    Geometry may be:
    spherical (use r1 and r2 to specify radius of curvature),
    planar    (use phiy1 and phiy2 to specify rotation angle of plane w.r.t beam)
    parabolic (use focus1 and focus2 as optical focal length).

    Optionally, you can specify the 'geometry' parameter as a OFF/PLY file name.
    The complex geometry option handles any closed non-convex polyhedra.
    It computes the intersection points of the neutron ray with the object
    transparently, so that it can be used like a regular sample object.
    It supports the PLY, OFF and NOFF file format but not COFF (colored faces).
    Such files may be generated from XYZ data using:
    qhull < coordinates.xyz Qx Qv Tv o > geomview.off
    or
    powercrust coordinates.xyz
    and viewed with geomview or java -jar jroff.jar (see below).

    The lens cross-section is seen as a 2*radius disk from the beam Z axis, except
    when a 'geometry' file is given.
    Usually, you should stack more than one of these to get a significant effect
    on the neutron beam, so-called 'compound refractive lens'.

    The focal length for N lenses with focal 'f' is f/N, where f=R/(1-n)
    and R = r/2   for a spherical lens with curvature radius 'r'
    R = focus for a parabolic lens with focal of the parabola
    and n = sqrt(1-(lambda*lambda*rho*bc/PI)) with
    bc  = sqrt(fabs(sigma_coh)*100/4/PI)*1e-5
    rho = density*6.02214179*1e23*1e-24/weight

    Common materials: Should have high coherent, and low incoherent and absorption cross sections
    Be:            density=1.85,  weight=9.0121, sigma_coh=7.63,  sigma_inc=0.0018,sigma_abs=0.0076
    Pb:            density=11.115,weight=207.2,  sigma_coh=11.115,sigma_inc=0.003, sigma_abs=0.171
    Pb206:                                     sigma_coh=10.68, sigma_inc=0    , sigma_abs=0.03
    Pb208:                                     sigma_coh=11.34, sigma_inc=0    , sigma_abs=0.00048
    Zr:            density=6.52,  weight=91.224, sigma_coh=6.44,  sigma_inc=0.02,  sigma_abs=0.185
    Zr90:                                      sigma_coh=5.1,   sigma_inc=0    , sigma_abs=0.011
    Zr94:                                      sigma_coh=8.4,   sigma_inc=0    , sigma_abs=0.05
    Bi:            density=9.78,  weight=208.98, sigma_coh=9.148, sigma_inc=0.0084,sigma_abs=0.0338
    Mg:            density=1.738, weight=24.3,   sigma_coh=3.631, sigma_inc=0.08,  sigma_abs=0.063
    MgF2:          density=3.148, weight=62.3018,sigma_coh=11.74, sigma_inc=0.0816,sigma_abs=0.0822
    diamond:       density=3.52,  weight=12.01,  sigma_coh=5.551, sigma_inc=0.001, sigma_abs=0.0035
    Quartz/silica: density=2.53,  weight=60.08,  sigma_coh=10.625,sigma_inc=0.0056,sigma_abs=0.1714
    Si:            density=2.329, weight=28.0855,sigma_coh=2.1633,sigma_inc=0.004, sigma_abs=0.171
    Al:            density=2.7,   weight=26.98,  sigma_coh=1.495, sigma_inc=0.0082,sigma_abs=0.231
    perfluoropolymer(PTFE/Teflon/CF2):
    density=2.2,   weight=50.007, sigma_coh=13.584,sigma_inc=0.0026,sigma_abs=0.0227
    Organic molecules with C,O,H,F

    Example: Lens(r1=0.025,r2=0.025, thickness=0.001,radius=0.0150)

    %BUGS
    parabolic shape is not fully validated yet, but should do still...

## Input parameters

Parameters in boldface are required; the others are optional.

Name | Unit | Description | Default |
r1 | m | radius of the first circle describing the lens. r>0 means concave face, r<0 means convex, r=0 means plane | 0 |
r2 | m | radius of the second circle describing the lens r>0 means concave face, r<0 means convex, r=0 means plane | 0 |
focus1 | m | focal of the first parabola describing the lens | 0 |
focus2 | m | focal of the second parabola describing the lens | 0 |
phiy1 | deg | angle of plane1 (r1=0) around y vertical axis | 0 |
phiy2 | deg | angle of plane2 (r2=0) around y vertical axis | 0 |
thickness | m | thickness of the lens between its two surfaces | 0.001 |
radius | m | radius of the lens section, e.g. beam size. | 0.015 |
sigma_coh | barn | coherent cross section | 11.74 |
sigma_inc | barn | incoherent cross section | 0.0816 |
sigma_abs | barn | thermal absorption cross section | 0.0822 |
density | g/cm3 | density of the material for the lens | 3.148 |
weight | g/mol | molar mass of the material | 62.3018 |
p_interact | 1 | MC Probability for scattering the ray; otherwise transmit | 0.1 |
focus_aw | deg | vertical angle to forward focus after scattering | 10 |
focus_ah | deg | horizontal angle to forward focus after scattering | 10 |
RMS | Angs | root mean square roughness of the surface | 0 |
geometry | str | Name of an Object File Format (OFF) or PLY file for complex geometry. The OFF/PLY file may be generated from XYZ coordinates using qhull/powercrust | 0 |

AT ( | , | , |  | ) RELATIVE |  |
ROTATED ( | , | , |  | ) RELATIVE |

## Links

- Source code for `Lens.comp`.
- M. L. Goldberger et al, Phys. Rev. 71, 294 - 310 (1947)
- Sears V.F. Neutron optics. An introduction to the theory of neutron optical phenomena and their applications. Oxford University Press, 1989.
- H. Park et al. Measured operationnal neutron energies of compound refractive lenses. Nuclear Instruments and Methods B, 251:507-511, 2006.
- J. Feinstein and R. H. Pantell. Characteristics of the thick, compound refractive lens. Applied Optics, 42 No. 4:719-723, 2001.
- Geomview and Object File Format (OFF)
- Java version of Geomview (display only) jroff.jar
- qhull
- powercrust

[ Identification | Description | Input parameters | Links ]