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The BESSY RAYTRACE PROGRAM
to calculate (not only)
SYNCHROTRON RADIATION BEAMLINES
Franz Schäfers (HZB-BESSY)
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2The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Speicherring
Undulator
Vorspiegel
Refokussier-Spiegel
Monochromator
Spiegel Gitter
Eintritts-Spalt
Austritts-Spalt
ExperimentDetektor
e-
Experimentier- steuerung
Datenerfassung
Monochromator-steuerung
Probe
e
e
e-
e-
HISTORY1984 FORTRAN-VMS/PDP-111989 VMS / VAX1990 Surface profiles1993 Stokes formalism1994 Crystal optics1995 Helical Undulators1996 VMS / Alpha2000 Multilayers2002 PC-Windows / LINUX2003 Pathlength2005 Wavefront2006 Expert‘s Optics2008 Zoneplates2008 Spinger Vol. 137…
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50 BESSY beamlinesfrom IR to hard x-rays
~100 copies worldwide
3The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
• Imaging / focusing properties of optical systems• create rays within a source volume• trace them through optical elements• display geometric distribution at the focus
•Design tool for (SR-) beamlines• dipole radiation (bending magnets)• 3G Wiggler/Undulator beamlines, 4G FEL’s• general optical applications• predict performance under realistic conditions• specify requirements of optical elements before order
• RAY, REFLEC• user-friendly• easy to learn• easy accessible• every day use• minimum file handling• online graphic• quick response to new demands
Bendable cylindrical mirror
aperture
179.45 ° Crystal 1
Crystal 2
<0.5 mrad
Bendable cylindrical mirror
11.4 m 25.4 m 28 m
focus
Wiggler Source
0 m 39.5m
1606 mm
1533 mm
1400 mm
Side view
aperturesplane grating
sphericalmirror
exit II
( R=10.3m)
1200 l/mm3600 l/mm
13847
16452
18452
horizontalvertical
24258
± 150 mm
exit I
σ +
σ −
0
23681
5806
5229
distance to source [mm]
15 mrad
BESSY II
What is raytracing?Intro
4The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
photon sourceWAVE / URGENT / SMUT
raytracingRAY
gratingsEFFI
FEMANSYS / ProE
optical elementsREFLEC
-0.05 0.00 0.05 0.10
-0.1
0.0
0.1
0 5000
-0.1
0.0
0.1
-0.05 0.00 0.05 0.100
2000
4000
y (m
m)
u41-162-0p7-40-ray1. image at : 755.00 mmN/s/0.1A/ 0.0mrad/ 0.1000%BW .1360D+16Transmission: 44.889 % 112222( 112222) out of 250000N
max/mm2: 0.6915D+18
S1: 1.000 S2: 0.000 S3: 0.000
x (mm)
Inte
nsity
Intensity
Width(x): 0.0472 mmCenter : 0.014 mm
Width(y): 0.0819 mmCenter : -0.002 mm
spot patternspatial distributiontemperature distribution
JOB 38 UE522003/09/29 08.25
Distribution in pinhole
hori. position (mm)
vert. position (mm)
phot
ons/
s/m
m2 /B
W
E = 396eV
-1.5-1
-0.50
0.51
1.5
-1-0.75
-0.5-0.250
0.250.5
0.751
200
400
600
800
1000
x 10 12
grating efficiency
0.2 0.4 0.6 0.80.2
0.4
0.6
0.8
1.0
cff
blaz
e an
gle
(°)
0.0
0.2
0.4
0.6
grat
ing
effic
ienc
y
BESSY optics software tools
talk M. Scheer
talk J. Bahrdt/ PHASE
Intro
5The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
• A RAY is described by 12 parameters• geometric coordinates (x,y,z)• emission angle (l, m, n)• energy (hv)• polarisation (S0, S1, S2, S3)• time (pathlength) (t)
• The RAY starts in a SOURCE-volumewith defined emission characteristics
• The RAY is modified by OPTICAL ELEMENTSacc. to laws of geometry and optics
• transmitting - slits, foils (abs.)• reflecting - mirrors (refl.)• dispersing - gratings, zoneplates (eff.)• diffracting - crystals (refl.)
• All parameters of the RAY can be visualisedat the Source, Optics and Image Planes
αβ2Θ
1. OPTICAL ELEMENT
IMAGEPLANE
xs
ys
zsχψϕ xM
zM
yM
yI
xI
zI
SOURCE
What is a ray?
3 m
. .
Intro
6The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
1E-3 0.01 0.1 1 10 100
Photon Energy (keV)
CROMER (Z=2-92) f1, f2
HENKE (Z=1-92) f1, f2
MOLECULES (Al2O3, SiC, SiO2…) n, k
PALIK (Al, Au, C, Cr, Cu, Ir, Ni, Os, Pt, Si,…) n, k
OPTICAL DATA TABLES
STRUCTURE FACTORS fo, fH, fHCZinkblendeHexagonalBeryl
Calculation of
• Reflectivity• Efficiency• Transmission• Rocking curves• Photon Flux• Resolving power• Polarisation
EUV VUV XUV soft X hard XVIS UV
Intro
7The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Basic law of RAY:§1: ALL RAYS HAVE EQUAL PROBABILITY = INTENSITY
• Probability distribution- start coordinates x, y, z- emission angles ϕ, ψ- energy, time…
• Advantages - easy- few rays enough for realistic simulation
(within given statistics)- no systematic errors (only statistical)
0.0
0.2
0.4
0.6
0.8
1.0
3σ2σ1σ0-1σ-2σ-3σ
+1 σ = 68.3 %FWHM = 76.0 %+2 σ = 95.4 %+3 σ = 99.7 %
Gaussiandistributionfunction
+1 σ
FWHM
(2.35 σ)
w(x)=exp(-x2/2σ2)
Prob
abilit
y w
(x)
x
1. get random number ran10 < ran1 < 1
2. scale variable, e.g. x x = (ran1 - 0.5) δx-δx/2 < x < δx/2
3. probability for this x value w(x) = exp(-x2/2σ2)
Applicable to ANY probability function
• Example: Gaussian intensity profile
• Systematic generation or…
• Statistical generation of rays within the source
4. get random number ran20 < ran2 > 1
5. ACCEPT x ONLY IF w(x) - ran2 > 0
6. if not, goto 1
+/- 3σx
Raytrace
8The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
• Statistical treatment of an ensemble of raysCollective effects (Interference, diffraction…)
§2: ALL RAYS ARE INDEPENDENT, but…(Particles and Waves)
• Diffraction on slits (P~ (sin v/v)) • Zoneplate diffraction (A. Erko)
• Reflectity losses / angle / energy (Rocking curves)
-100 -80 -60 -40 -20 0 20 40 60 80 100-100
-80
-60
-40
-20
0
20
40
60
80
100
KRGF
µm
µm
40 80 120 160 200
100
RAY
40 80 120 160 200
40
80
120
160
200
µm
88 90 92 94 96 98 1000.0
0.2
0.4
0.6
0.8
1.0
102 rays 0.1 sec
Ray
s / c
hann
el (n
orm
.)
Photon energy (eV)
88 90 92 94 96 98 1000.0
0.2
0.4
0.6
0.8
1.0
103 rays 1 sec
Ray
s / c
hann
el (n
orm
.)
Photon energy (eV)88 90 92 94 96 98 100
0.0
0.2
0.4
0.6
0.8
1.0
104 rays 5 sec
Ray
s / c
hann
el (n
orm
.)
Photon energy (eV)
Mo/Si N=50d=6.75 nm
88 90 92 94 96 98 1000.0
0.2
0.4
0.6
0.8
1.0
105 rays 45 sec
Ray
s / c
hann
el (n
orm
.)
Photon energy (eV)
Mo/Si N=50d=6.75 nm
Raytrace
88 90 92 94 96 98 1000.0
0.2
0.4
0.6
0.8
1.0
106 rays 420 sec
Ray
s / c
hann
el (n
orm
.)
Photon energy (eV)
Mo/Si N=50d=6.75 nm
9The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
SOURCES
DI_pole WI_ggler
PO_int PI_xel CI_rcle
2.
• Realistic simulation of source intensity, volume and emission• Input by file: create your own source ((helical) undulator…)• SR sources: polarisation included
electron beam emittance effectsdetuning effects (orbit change, misalignment)
SS txx αrrr
+=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
ψϕψ
ψϕα
coscossin
cossin
S
S
S
S
nml
r
10The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
0222222
),,(
44342414
231312
233
222
211
=++++++++
+++=
=
azayaxayzaxzaxya
zayaxazyxF
2nd, 3rd order surfaces
PM_plane m.
CY_linder (x,z)
SP_here
EL_lipsoid
PA_raboloid (circ., ell.)
TO_roid
ET_elliptical toroid
0232
223
231
213
221
212
=++
+++
+++
yzbzyb
xzbzxb
xybyxb
DI_aboloid
CO_ne
EO_expert‘s optic
Raytrace
11The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Textbook raytracing
)(13,2,1
zzml
nyx
yx
II
I −⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛=⎟⎟
⎠
⎞⎜⎜⎝
⎛
Data Evaluation, Storage, Display
Start with a new ray in the source…
2.
nr
Find the intersection point xM, yM, zM
Find the local normal vector
Find the direction of outgoing ray
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
++=
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
=
z
y
x
zyxz
y
x
fff
fffnnn
n222
1r
nn rrorr )(2 112 ααα ⋅−=
Ff ∇=r
Attach next optical elementor find intersection with
Image Plane
)( 1αr
)( 2αr
(Include slope errors, surface profile)
12)()()(~ MqzzxM xzTDDx rr⋅= χθ
Raytrace
12The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Features of optical elements
• Miscellaneous: Misalignment
Spacer dB
Absorber dA
T
RIO
ES
EP
θ
XMi
ZMi
YMi
χ
ψφ
α
θ Θ−α
Increasing d
Lattice Planes
X-ray Source
• (Multilayer-) Coatings on Optics
• Special monochromator mounts:SX700 plane grating PGMSpherical grating SGM
Varied Line Spacing-(VLS-) gratingsLaterally graded crystals, -multilayers
• Rectangular, circular shape or rings (capillaries)
Measured, calc. surface profiles
βα
PM
PG (SG)
Raytrace
13The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
0 20 40 60 80 100 120 140
-70
-60
-50
-40
-30
-20
-10
0
100 eV
135 eV
75 eV
3rd order
conical diffraction
3000 l/mm 75/100/135 eV 2θ=160o
2nd order
1st order
Y Po
sitio
n (m
m)
X Position (mm)
0 order
-10 0 10 20-40
-30
-20
-10
0
10
20
30
40
-4
-3
-2
-1
2
3
100 eV75 eV
135 eV
Y Po
sitio
n (m
m)
X Position (mm)
100 l/mm 75/100/135 eV 2θ=160o
100 eV75 eV
135 eV
0
1
4
Reflection Gratings (plane, spherical, toroidal)
kλ=d(sinα +sinβ)( )
⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
−
−−+=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛
11
211
21
21
1
2
2
2
anannm
l
nml
( )37
265
34
2320 4324321/1 xbxbxbzbzbzbnnd ++++++⋅==
VLS-Grating:
3 21
-2-1
0
m=
α β1-1 0
-2 2
3m=-3
=)( 2αr
dkl/1=α
Raytrace
14The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
KMCKMC--1 1 beamlinebeamline performanceperformance
2 4 6 8 10 12 14108
109
1010
1011
1012
RAY
Pt LIII
Pt LII
Energy (keV)
Pho
ton
Flux
/ 10
0 m
A
Si (111)
Pt LI
Examples
11540 11800 12978 28098 35273distance to source (mm)
0
distance between elements (mm)15120 717512978
179.2 °
328
side view
crystal 1
crystal 2
<0.5 mrad
<0.2 mrad
2 4 6 8 10 12
0.1
1
10
Si (555)
Si (444)Si (333)
InSb (111)
Si (111)Si (311)
Si (422)
Res
olut
ion
(eV)
Energy (keV)2 4 6 8 10 12
0.1
1
10
Si (555)
Si (444)Si (333)
InSb (111)
Si (111)Si (311)
Si (422)
Res
olut
ion
(eV)
Energy (keV)
(HAX)PES better than calc.
15The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Stigmatic Imaging of an astigmatic sourceDiaboloid - optics
slope error (σ) 0.5 μm x 0.2 μrad
IDL-Animation(Thomas Zeschke, BESSY)
(Convert toroid to spherical wavefront)
5 times higherflux densit
y
Examples
16The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Diaboloid - opticsExamples
17The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
Time Evolution of beams -controlling the pulse shape & broadening
zqzzyyxxpl oldoldold −−+−+−= ))()()(( 222
plλπϕ 2
=cplt =
Path length
Phase Travel time
Confining illuminated grating length: pulse length unchanged
-60 -40 -20 0 20 40 600
200
400
600
800
1000
1200
30 μm
Ray
s / c
hann
el
Time (fs)
100 fs
Source GratingFocus
Examples
18The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
zqzzyyxxpl oldoldold −−+−+−= ))()()(( 222
plλπϕ 2
=cplt =
Path length
Phase Travel time
Wavefronts, Coherence
InterferencePhaseGeometric Intensity
2ji
jeI ϕ∑=
Coherent illumination of toroid, 10:1, θ=2.5o
=
• Similar to “real” wavefront codes: PHASE, SRW• Phasespace, time, energy, polarisation:
Identify sections of equal phase: Coherence
Outlook
19The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
• The program has NO intelligence - even after 25 years of programming
YOU ARE THE EXPERT – NOT RAY !!!
LIMITATIONS / WARNINGSConclusions
• The program will NOT give any ideas for the kind of beamline you want to have
• Nor does it have any idea of good experiments at a beamline
• The program performs only what was programmed -The results are valid only within the mathematical or physical model implemented
• The program may still have errors (it has - definitely!!)
• The designer may have made typing errors in the input menue
• The designer may have misunderstand the program’s language or a result
20The BESSY raytrace program RAYF. SchaefersRAY @ SMEXOS Feb. 24.-25. 2009
ProgrammingProgramming
Josef Josef FeldhausFeldhaus (Start)(Start)
Michael Michael KrumreyKrumrey (CR)(CR)
K.J.S. K.J.S. SawhneySawhney (EPU)(EPU)
Dirk Dirk AbramsohnAbramsohn (PC)(PC)
ShahinShahin SahraeiSahraei (RZP)(RZP)
AdvertisementAdvertisement
William William PeatmanPeatman((““Gratings, Mirrors and SlitsGratings, Mirrors and Slits””))
Alexei Alexei ErkoErko, , MouradMourad IdirIdir et et al.(edal.(ed.).)((““Modern DevelopmentsModern Developments…”…”))
UsersUsers
BESSY optics groupBESSY optics groupWorldwide usageWorldwide usage
Acknowledgements Acknowledgements
Special features Special features implementationimplementation
Alexei Alexei ErkoErko ((……))
Rolf Rolf FollathFollath (time)(time)
GerdGerd ReichardtReichardt (GR)(GR)
Fred Fred SenfSenf (CO)(CO)
Thomas Thomas ZeschkeZeschke ((IDL,Diab.,PhaseIDL,Diab.,Phase))