Synchrotron Radiation Workshop Software Tool for SR Wavefront Calculations

1
Synchrotron Radiation Workshop Software Tool
for SR Wavefront Calculations

• O. Chubar (SOLEIL), P. Elleaume (ESRF)

2
Topics

• Introduction
• Motivation
• Codes with Similar Functions
• Synchrotron Radiation Calculations
• Approaches Retarded Potentials for Spontaneous
  Emission,
• Fourier Optics for Wavefront Propagation
• Examples
• Possible Evolution

3
Motivation

• Fast computation of Synchrotron Radiation emitted
  by relativistic electrons in Magnetic Fields of
  arbitrary configuration
• Wavefront Propagation

4
Computer Codes with Similar Functions
SR(/UR) Spontaneous Emission
URGENT by R. Walker et. al. (ELETTRA,
) RADIA/Wingz by P. Elleaume et. al. (ESRF) B2E
by P. Elleaume et. al. (ESRF) XOP by S. del Rio
(ESRF), R. Dejus (APS) WAVE by U. Flechsig, J.
Bahrdt (BESSY) SRW by O.C., P. Elleaume
(ESRF/SOLEIL) SPECTRA by T. Tanaka, H. Kitamura
(SPring-8)
Ray-Tracing / Wavefront Propagation
Geometrical Optics
SHADOW (Univ. Wisconsin) XOP by S. del Rio
(ESRF), R. Dejus (APS) RAY by A. Erko et. al.
(BESSY) Optical design code by T. Moreno
(SOLEIL) Commercial packages CODE V, OSLO,
ZEMAX,
Wave (/ Physical) Optics
PHASE by J. Bahrdt (BESSY) SRW by O.C., P.
Elleaume (ESRF/SOLEIL) Commercial packages
MICROWAVE Studio, ZEMAX,
5
Spontaneous Emission by Relativistic Electron in
Free Space
Lienard-Wiechert Potentials for One Electron
(Gaussian CGS)
?
Electric Field in Frequency Domain (exact
expression, valid in the Near- and in the Far
Field !)
(?)
I.M.Ternov used this approach in Far Field
approximation
J.D.Jackson
The equivalence of the two expressions can be
shown by integration by parts
Phase Expansion (valid in Near Field)
6
Incoherent and Coherent Spontaneous Emission
Electron Dynamics
? Initial Conditions
Spectral Photon Flux per unit Surface emitted by
the whole Electron Beam
Common Approximation for CSR Thin Electron
Beam
For Gaussian Longitudinal Bunch Profile
is Gaussian, the 6-fold integration can be done
analytically (!)
However, if
? Efficient method for CSR computation taking
into account 6D phase space distribution of
electrons
7
Self-Amplified Spontaneous Emission Described by
Paraxial FEL Equations Approximation of slowly
varying amplitude of the Radiation Field
Particles dynamics in undulator and radiation
fields (averaged over many periods)
W.B.Colson J.B.Murphy C.Pellegrini E.Saldin E.Bess
onov et. al.
Paraxial wave equation with current
Solving this system gives electric field at the
FEL exit
8
Fully-Coherent Wavefront Propagation
Kirchhoff Integral Theorem applied to SR
Valid at large observation angles Is applicable
to complicated cases of diffraction inside vacuum
chamber
Huygens-Fresnel Principle
Fourier Optics
Free Space (between parallel planes
perpendicular to optical axis)
Assumption of small angles
Thin Optical Element
Stationary Phase Method (or Improved
Ray-Tracing)
Thick Optical Element
9
Partially-Coherent Wavefront Propagation
Intensity Averaging of the Propagated
One-Electron Wavefronts
Convolution is valid in many cases -
projection geometry - focusing by a thin
lens - diffraction on one slit (/pinhole) -
Propagation of the Mutual Intensity
K.-J. Kim
Mutual Intensity
Wigner Distribution (or mathematical Brightness)
10
SRW Examples Convetntional Bending Magnet SR
Intensity Distribution in transverse plane close
to the source
Intensity Distributions at various Polarizations

• E 2.5 GeV B 1.56 T (? ? 5.3 m)
• I 500 mA
• ? 10 ?m r ? 0.7 m

11
SRW Examples Undulator Radiation
On-Axis Energy Spectrum
Undulator
?u 35 mm
K 2.2
Spectral Flux / Surface
E-beam
E 6 GeV
?x eff / R 16.2 ?r
?z eff / R 3.96 ?r
?E / E 10-3
R 30 m
Spectral Flux / Surface (vertical cuts)
12
SRW Examples HU256 Spectral Flux in a
Quasi-Periodic Mode (SOLEIL)
Vertical Magnetic Field Modulation Bmin 0.88
B0, Bmax 1.10 B0 (one mod. coefficient per
period)
Spectral Flux through a Finite Aperture
Bn(s)
(F2 F3)/F1 0.14
(F2 F3)/F1 0.08
Flux compared to Periodic Mode F1 q-p 0.70
F1 p
(F2 F3)/F1 0.16
(F2 F3)/F1 0.10
0.5 Bn(s)
(F2 F3)/F1 0.22
(F2 F3)/F1 0.21
0.25 Bn(s)
13
SRW Examples Maximal Spectral Flux of SOLEIL
Undulators
Spectral Flux optimized vs Currents in Coils (or
Magnetic Gap and Shift) for each Photon Energy
HU640 (EM)
HU256 (EM)
HU80 (PPM APPLE-II)
U20 (Hybrid, in-vacuum)
14
SRW Examples Useful Flux and Power at Fixed
Absorber SOLEIL HU-80, Medium-size section,
Linear Horizontal Polar. Mode, Gap 15 mm
15
FS Slice Separation at SLS Angular Horizontal
Scheme
Electron Trajectory and Photon Absorbers
Method of A.Zholents and M.Zolotorev Separation
scheme G.Ingold et. al.
Radiator Undulator U19 (in-vacuum)
E-Beam, Modulation
?Emax? 21.5 MeV
E0 2.44 GeV Is.b. 2 mA ?b 12 ps
fL 1 kHz ?L 21 fs
Intensity Distributions in the Median Plane 15.7
m from Radiator Finite-Emittance Electron Beam
G.Ingold
SRW
16
FS Slice Separation Using SOLEIL Native
Lattice Hard X-Rays Slit-Based Spatial
Horizontal Separation Scheme
E-Beam, Modulation
Hard X-Ray Radiator Undulator U20
?Emax?14 MeV (pessimistic) fL 10 kHz ?L 50 fs
E0 2.75 GeV Is.b. 10 mA ?b 24 ps
T. Moreno M. Idir
1st Slit
U20
15 m
2 m
Slit Dimensions 0.5 mm x 0.5 mm xc 2.4 mm
Intensity in Transverse Planes After Slit(s)
Cuts by Median Plane
? 6.93 keV
2x107 ph/s/0.1bw
17
FS Slice Separation Using SOLEIL Native
Lattice Soft X-Rays Mixed Angular-Spatial
Horizontal Separation Scheme
E-Beam, Modulation
Soft X-Ray Radiator Undulator HU80
(Apple-II)
?Emax? 20 MeV
E0 2.75 GeV Is.b. 10 mA ?b 24 ps
fL 10 kHz ?L 50 fs
Slit, Mirror
Plane of 11 Imaging
10 m
HU80 Centered at 1.35 m from the Middle of
Straight Sect.
Slit Dimensions 2 mm x 1 mm Slit
Position xc 2.5 mm
Intensity in Transverse Plane Before Mirror
Intensity in the Plane of 11 Imaging
? 415 eV
Linear- Horizontal Polarization
18
Obtaining short x-ray pulse from a long
electron bunch
A. Zholents et. al., LBNL
RF deflecting cavity
RF deflecting cavity
Electron trajectory
X-ray compression in asymmetric-cut crystals
?l
Collimating mirror
Radiation from tail electrons
Undulator
Radiation from head electrons
Input x-ray pulse gtgt diffraction limited size and
natural beamsize
19
CSR from Electron Bunch with Large Vertical Size
Spectral Flux of Bending Magnet CSR through Fixed
Aperture 120 mm h. x 60 mm v. _at_ 3 m from
tangential source point
? 100 ?m, ?e y 25 ?m
E 2.75 GeV B 1.72 T I 1 mA Ne ? 7.3 x
109 ?b 30 ?m (??)
? 100 ?m, ?e y 4 mm
Bending Magnet CSR Intensity Profiles (? 100
?m, 3 m from tangential source point)
Horizontal Polarization
Vertical Polarization
20
SRW Examples Focusing the Undulator Radiation
21
SRW ExamplesPeculiarities of Undulator
Radiation Wavefronts (I)
Planar Undulator, Odd Harmonics E 6 GeV K
2.2 38 x 42 mm ? 2.36 keV ( fundamental) 1
1 imaging 30 m from middle of Undulator to Thin
Lens Phase Correction
22
SRW ExamplesPeculiarities of Undulator
Radiation Wavefronts (II)
Planar Undulator, Even Harmonics E 6 GeV K
2.2 38 x 42 mm ? 4.775 keV (2-nd harmonic) 1
1 imaging 30 m from middle of Undulator to
Thin Lens Phase Correction
23
SRW ExamplesPeculiarities of Undulator
Radiation Wavefronts (III)
Helical Undulator, Harmonics n gt 1 E 6 GeV Bx
max Bz max 0.3 T 28 x 52 mm ? 4.20 keV
(2-nd harmonic) 1 1 imaging 30 m from middle
of Undulator to Thin Lens Phase Correction
24
SRW Examples Phase Corrections for Bending
Magnet SR (I)
Intensity Distributions
Phase Correction
Horizontal Polarization
E 2.5 GeV B 1.6 T ? 40 eV 5 m from source
Vertical Polarization
Analytical Approximation
25
SRW Examples Phase Corrections for Bending
Magnet SR (II) Intensity in the Image Plane
E 2.5 GeV B 1.56 T ? 40 eV 1 1
imaging 5 m from Source Point to Thin Lens
Without Phase Correction
With Phase Correction
Horizontal Intensity Cut
Horizontal Polarization
Vertical Polarization
Vertical Intensity Cut
26
GENESIS SRW Example SASE (and possibly HGHG)
and Wavefront Propagation
Test steady-state simulations for X-FEL

• E 25 GeV
• 20 ?m
• 1.0 ?r
• ?u 48.5 mm
• B0 0.93 T
• Lu tot 120 m

? ? 1 Å
27
SRW Examples X-Ray Focusing Using a Zone Plate
Zone Plate or Ideal Lens
A 200 ?m, F 0.966 m Au, 2.9 ?m
? 12 keV
50 m from Source
0.325 m (?F/3)
0.74 m
0.985 m (?F)
Zone Plate
Ideal Lens
28
SRW Examples PSF Computation for Parabolic
X-Ray CRL
A.Snigirev, B.Lengeler et. al., 1998
? 6.9 ?106
? 8.9 keV
Latten 0.106 mm
N 1
F 13.6 m
?FWHM 7.3 ?m
? 1. ?106
? 23 keV
Latten 1.89 mm
N 7
F 13.1 m
?FWHM 4.1 ?m
29
SRW Examples Fresnel Diffraction of Partially
Coherent X-Rays
A.Snigirev et. al.
? 11 keV
Slits (100 x100 ?m2)
Detector (YAG microscopeCCD)
Mirror
Undulator (38 x 42 mm)
Si (111)
rs 37.6 m
rd 5.5 m
30
SRW Examples Interference of Partially Coherent
X-Rays
A.Snigirev et. al.
? 11 keV
Detector (YAG microscopeCCD)
B fiber (d 100 ?m)
Mirror
Undulator (38 x 42 mm)
rs 40.6 m
Si (111)
rd 5.5 m
31
SRW Examples Beam Imaging Using Linear
Horizontal SR Polarization Component
Simplified Optical Scheme (Top View)
A.Hofman, F.Meot, NIM Vol.203, 483 (1982)
SR Intensity Distribution in the Image Plane
(Horizontal Polarization)
Vertical Cut Zoomed
Vertical Cut
E 2.75 GeV, I 500 mA ? 500 nm Optical
Magnification 1 (for simplicity of
simulation) Vert. Angular Aperture 12 mr Hor.
Angular Aperture 6 mr (not optimized)
Horizontal Cut
RMS Vertical Size of the E-Beam and the Spot
red curve filament e-beam (?e z 0), blue ?e z
18.3 ?m, black ?e z 23.3 ?m
(expected), green ?e z 28.3 ?m,
?tot z ?r z ? 27 ?m ?tot z ? 33 ?m ?tot z ? 36
?m ?tot z ? 39 ?m
?
RMS Horizontal Size of the E-Beam and the Spot
red curve filament e-beam (?e x 0), black ?e
x 86 ?m (expected),
?tot z ?r z ? 32 ?m ?tot z ? 93 ?m
32
SRW Examples Beam Imaging Using Linear Vertical
SR Polarization Component
Simplified Optical Scheme (Top View)
Å.Andersson, M.Eriksson and O.Chubar, Proc.
EPAC-96, p.1689
SR Intensity Distribution in the Image Plane
(Vertical Polarization)
Vertical Cut
Vertical Cut Zoomed
E 2.75 GeV, I 500 mA ? 500 nm Optical
Magnification 1 (for simplicity of
simulation) Vert. Angular Aperture 12 mr Hor.
Angular Aperture 6 mr (not optimized)
RMS Vertical Size of the E-Beam and the Intensity
Fluctuation in the Fringes
red curve filament e-beam (?e z 0), blue ?e z
18.3 ?m, black ?e z 23.3 ?m
(expected), green ?e z 28.3 ?m,
Imin/Imax ? 0 (lt 10-3) Imin/Imax ?
0.36 Imin/Imax ? 0.56 Imin/Imax ? 0.73
33
SRW Examples Beam Imaging Using Simple
Double-Slit Interferometer
Simplified Optical Scheme (Side View)
T.Mitsuhashi, Proc. PAC-97, p.766.
SR Intensity Distribution in the Image Plane
(Horizontal Polarization Component)
Vertical Cut Zoomed
Vertical Cut
E 2.75 GeV, I 500 mA, ? 500 nm Distance
from Source to Slits 5 m Optical Magnification
1 (for simplicity of simulation) Vertical
Distance between Slits 30 mm (not optimized)
red filament e-beam (?e z 0), blue ?e z
18.3 ?m, black ?e z 23.3 ?m, green ?e z
28.3 ?m,
Imin/Imax ? 0 (lt 10-3) Imin/Imax ?
0.59 Imin/Imax ? 0.78 Imin/Imax ? 0.88 (no
fringes)
SR Intensity Distribution in the Image Plane
(Vertical Polarization Component)
Vertical Cut
Vertical Cut Zoomed
red filament e-beam (?e z 0), blue ?e z
18.3 ?m, black ?e z 23.3 ?m, green ?e z
28.3 ?m,
Imin/Imax ? 0 (lt 10-5) Imin/Imax ?
0.67 Imin/Imax ? 0.88 Imin/Imax ? 0.99 (no
fringes)
34
SRW Examples Estimation of the Apparent
Brightness
Lens
Real Aperture
Plane of 11 Imaging
?x ?x ?y ?y
R. Bosch using SRW
R
R
Spectral Flux
Apparent Spectral Brightness
Intensity at the Waist (SOLEIL, ?10 ?m, hor.
ap. 87 mr)
35
Spontaneous Emission from Edges of Bending
Magnets
First observed and treated
in electron synchrotrons
in proton synchrotrons
R.Bossart et. al., CERN, 1979
M.Nikitin et. al., Tomsk, 1979
R.Coisson, 1977 - 79
E.Bessonov, 1983
Yu.Bashmakov, 1986
N.Smolyakov, 1983
IR Applications
Y.-L.Mathis and P.Roy at LURE (1995), ANKA
(2000) R.Bosch, T.May at SRC Wisconsin (1995)
Intensity Distribution
E 2.5 GeV Bmax 1.56 T L 6 m ? 10 ?m
36
ER at ESRF

• SRW Calculations and Measurements at new ESRF IR
  Beamline
• (K.Scheidt, J.Susini, P.Dumas, F.Polack, Dec.
  2004)
• 500 nm, r 6.2 m from downstream bending
  magnet edge
• Scale 13 mm (hor.) x 9 mm (vert.)

37
SRW Examples IR ER Emission at Different
Wavelengths (SOLEIL)
Magnetic Field (Medium-Size Straight Section)
Spectral Flux through Finite Aperture 66.2 mr (
61 mr 5.2 mr) Hor. x 18 mr Vert
Spectral Flux / Surface
Distance from BM edge 1.27 m
Horizontal Cuts (Median Plane)
38
SRW Examples IR Extraction Scheme at SMIS
Beamline
M1 Flat Slotted
M2 Toroid Rt? 6 m, Rs? 2.26 m fx? 1.6 m, fz? 2.1
m
M3 Toroid Rt? 10 m, Rs? 3.08 m fx? 3.54 m, fz?
2.18 m
W1 Diamond D 20 mm
M5
BM
M4 Flat
Aperture
1.35 m
0.6 m
7.53 m
2.29 m
1.7 m
3 m
Flux 1.67 x 1014 Phot/s/0.1bw
Flux 1.35 x 1014 Phot/s/0.1bw
Intensity Distributions at 10 ?m Wavelength
Intensity Profiles
Optical scheme F. Polack, P. Dumas
39
SRW Examples Intensity Distributions of the
Focused Edge Radiation Near the Waist in
Presence of Aberrations
M1
W1
M2
M3
W2
e-
BM
0.23 m
0.58 m
1.46 m
3.5 m
1.75 m
Measurements _at_ ANKA IR
Y.-L.Mathis, B. Gasharova
SRW Simulations
40
SRW Implementation

• ? Kernel
• - The SRW Kernel is a shared (/ static) library
  written in ANSI C
• - Development is done using MS Visual Studio IDE
  on Windows
• - The source is also compiled for Mac OS X using
  CodeWarrior or gcc
• ? Front-End
• - IGOR Pro (WaveMetrics) commercial (however,
  relatively low-cost) graphing/viewing package
  with integrated powerful script language
• ? Platforms
• - Windows
• - Mac OS

41
Planned Developments in SRW

• ? Emission / Sources
• - Treatment of 6D phase space distribution of
  electrons at computation of incoherent and
  coherent spontaneous emission
• - Improvement of the efficiency and accuracy of
  high-K undulator / wiggler calculations
• ? Wavefront Propagation
• - Improvement of the free-space propagator for
  wide wavefronts
• - Implementation of a library of thick optical
  elements (mirrors, gratings, )
• - Elements of X-ray dynamical crystal diffraction
  and scattering
• - 3D tracking / viewing of optical layouts
• ? Inter-Operation with Other Codes
• - Integration of GENESIS 1.3 (for SASE / HGHG
  simulation)
• - Interfacing of multi-parametric optimizing
  libraries (GSL, EO, ) to the same front-end /
  scripting environment
• - Export / import of data structures to / from
  other codes
• ? New Interfaces
• - Cross-platform (Windows / Linux / Mac OS)
  graphical front-end with Python as scripting
  environment

42
Acknowledgements

• ? J.-L. Laclare, J.-M. Filhol, D. Raoux
• ? P. Dumas, G. Williams, P. Roy, Y.-L.Mathis
• ? M. Bowler, R. Bosch
• ? A. Snigirev, I. Snigireva, V. Kohn, N.
  Smolyakov
• ? All Users of SRW and RADIA

43
(No Transcript)
44
SOLEIL and ArcEnCiel Requirements for Modeling
of Coherent Radiation

• ? SOLEIL
• ? IR and UV beamline optimization
• ? Simulation of diffractive and refractive
  optical elements for soft and hard X-rays
• ? Specific experimental techniques
• - micro-focusing
• - phase-contrast diffraction-enhanced imaging
  and tomography
• - short pulses project(s)
• - diagnostics of the source and beamline
  characterization
• ? ArcEnCiel (the 4th generation SOLEIL partner
  project)
• ? Wavefront propagation calculations for HGHG /
  harmonic generation in gases
• ? Studies of coherence degradation in the
  resulting wavefront
• ? Beamline optimization
• ? Experimental techniques

45
Comparison SRW Wavefront Propagation /
Geometrical Ray-Tracing SOLEIL SMIS IR
Beamline (I)
Initial Wave Front
l10 mm
SRW Simulations by P. Dumas
Ray-Tracing Simulations by B. Lagarde
46
Comparison Geometrical Ray-Tracing / SRW
Wavefront Propagation SOLEIL SMIS IR Beamline
(II)
At Toroidal Mirror M2
At Toroidal Mirror M3
47
Comparison Geometrical Ray-Tracing / SRW
Wavefront Propagation SOLEIL SMIS IR Beamline
(III)
Near the First Focus
At CVD Diamond Window
48
Comparison Geometrical Ray-Tracing / SRW
Wavefront Propagation SOLEIL SMIS IR Beamline
(IV)
At Flat Mirror M6
At Flat Mirror M7
49
ER at ESRF
G.Mulhaupt, C.Denise, 1995 P.Elleaume, K.Scheidt,
1998
Measurements at ID4 ? 450 nm, r 8.2 m from
downstream bending magnet edge
1 mm
50
ER Based Electron Beam Emittance Diagnostics
Measurements at Siberia-1 (Kurchatov Inst., 1994)
E 450 MeV, ? 560 nm, r 5.47 m
?x eff /r 0.70 ? 0.06 mr
?y eff /r 0.154 ? 0.014 mr
51
Spontaneous SR Emission by Relativistic Charged
Particles in Free Space
Lienard-Wiechert potentials for one particle
(Gaussian CGS)
?
Exact expression, valid in the Near and in the
Far Field (!)
Ternov used this approach for Far Field
Phase expansion
Spectral-angular distribution of energy emitted
by many particles

• Incoherent part of SE

• Coherent part of SE

52
Wave Front Propagation
Kirchhoff Integral Theorem applied to SR
Valid at large observation angles Is applicable
to complicated cases of diffraction inside vacuum
chamber
Fourier Optics
Free Space (Huygens-Fresnel Principle)
Optical Elements
Assumption of small angles
Partial Coherence
Averaging of the propagated Intensity
Alternative method propagation of Mutual
Intensity / Wigner Distribution
K.-J. Kim
53
ER (/TR) Approximate Analytical Formulae
L
z
P(x,y,z)
A
e-
x
z
B
Numerical Illustrations
y
Far Field
8

10
11
6
10
11

4
10
11

One BM Edge (A)
11
2

10
x
,
mm
-7.5
-5
-2.5
2.5
5
7.5
10
Two BM Edges (B)
Near Field
One BM Edge (A)
10
6

10
10
5

10
10
4

10
3
10
10

2
10
10

10
Two BM Edges (B)
1

10
x
,
mm
-40
-20
20
40
54
Broadband SR Spectrum as Observed at Different
Angles
Spectral Flux through Finite Aperture 10 mr H x
10 mr V (30 mm x 30 mm at 3 m from the source)

• L 10 m
• r ? 3 m

Collection from central part of BM
E 6 GeV Bmax 0.85 T I 200 mA
Collection from BM edges (aperture centered on
the straight section axis)
55
SRW Examples Wave Front Propagation IR ER
Source Characterization (1 1 Imaging Scheme)
Wavefront at the Lens
SR part
ER part
Intensity in the Image Plane
Intensity Cuts by the Median Plane
?S 0 cm
red from full aperture black from ER
part blue from SR part
? 10 ?m S 1.27 m
?S 20 cm
?S 60 cm
56
CSR from Electron Bunch with Large Vertical Size
(II)
Bending Magnet CSR Intensity Distributions (3 m
from tangential source point)
?e y 4 mm
?e y 25 ?m
Different Vertical Size of E-Beam
E 2.75 GeV B 1.72 T I 1 mA Ne ? 7.3 x
109 ?b 30 ?m (??) ? 100 ?m
Intensity Distributions in the Plane of 1 1
Imaging
Cut by Horizontal Median Plane
Cut by Vertical Median Plane
?e y 25 ?m
?e y 4 mm
57
CSR from Electron Bunch with Large Vertical Size
(III)
Spectral Flux of Coherent Edge Radiation through
Fixed Aperture 120 mm h. x 60 mm v. _at_ 3 m from
downstream magnet edge
E 2.75 GeV Bmax 1.72 T Lstr. sect. 12.4
m I 1 mA Ne ? 7.3 x 109 ?b 30 ?m (??)
Intensity Distributions of Coherent Edge
Radiation ? 100 ?m, 3 m from downstream magnet
edge
?e y 25 ?m
?e y 4 mm
?e y 8 mm
58
Radia, SRW Now and in the Future
Currently
RADIA (3D magnetostatics)
SRW, B2E (SR SE, phys. optics)
interfaced to
interfaced to
Mathematica (WolframResearch)
Igor Pro (Wavemetrics)
Solving Direct Problems, Addressing Inverse
Problems by iterations
In the Future
Gen. Optimizer (multi-param. minimiz., regularizat
ion of ill-posed problems, )
RADIA (3D magnetostatics, proc. magnetic
measurements)
SRW (SR SE, SASE(?), physical optics, dyn.
crystal diffraction, )
DLLs / shared libraries, interfaced to

• Igor Pro (WaveMetrics)
• Python (free)

Solving Inverse Problems related to IDs, Magnets,
SR, User Experiments