coherence measurements at p04 petr skopintsev p04 users meeting, 13.06.2014 collaboration between:...
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![Page 1: Coherence measurements at P04 Petr Skopintsev P04 Users Meeting, 13.06.2014 Collaboration between: Jens Viefhaus (P04 – Beam line) Axel Rosenhahn (Analytical](https://reader036.vdocuments.net/reader036/viewer/2022081419/5697bfc71a28abf838ca7de7/html5/thumbnails/1.jpg)
Coherence measurements at P04
Petr SkopintsevP04 Users Meeting, 13.06.2014
Collaboration between:Jens Viefhaus (P04 – Beam line)Axel Rosenhahn (Analytical Chemistry Group, Ruhr-University Bochum)Ivan Vartanyants (Coherent Imaging Group)
DESY, Hamburg, Germany
NRC “Kurchatov Institute”, Moscow, Russia
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Petr Skopintsev | Coherence measurements at P04 | 13.06.2014 | Page 2
Outline
>Theory of spatial coherence measurements
>First P04 experiment Comparison of NRAs and Double Pinholes
>Second P04 experiment Additional investigation with NRAs
>Summary
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Spatial coherence
Intensity Сoherence Factor
Degree of spatial coherence
𝟎≤𝜁 ≤𝟏Incoherentfield
Coherentfield
𝐼 (𝒓 )=Г (𝒓 ,𝒓 ) 𝛾 (𝒓 𝟏 ,𝒓𝟐 )=Г (𝒓𝟏 ,𝒓 𝟐)
√𝐼 (𝒓𝟏 ) 𝐼 (𝒓 𝟐 )
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Young’s Experiment
Fourier transform of I(q)
𝐼 (𝑞 )=𝐼 𝐴 (𝑞) (𝟏+¿𝛾12∨𝐜𝐨𝐬 (𝒒 ∙𝒅+𝛼12))
~𝐼 (𝑥)=𝑻 (𝒙 )+¿𝛾12∨
¿2
[𝑒𝑖𝛼12𝑻 (𝒙−𝒅 )+¿+𝑒− 𝑖𝛼12𝑻 (𝒙−𝒅 ) ] ¿
Double pinholes diffractionintensity distribution I(q)
IncoherentCoherentPart. coherent
, , ,
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Young’s Experiment
Modulus of complex degree of spatial coherence is a function of distance between slits:
|
J.W. Goodman, Statistical optics
Δx-Δx Δx
𝐶0=𝐼 1+ 𝐼2
𝛾12
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Petr Skopintsev | Coherence measurements at P04 | 13.06.2014 | Page 6
Young’s Experiment
Modulus of complex degree of spatial coherence is a function of distance between slits:
|
J.W. Goodman, Statistical optics
Δx-Δx Δx
𝐶0=𝐼 1+ 𝐼2
𝛾12
𝒍𝒄
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10 points10 peaks
𝐶𝑖𝑗=¿𝛾 𝑖𝑗∨√ 𝐼𝑖 𝐼 𝑗
, 1 experiment with 5 slits =
10 experiments with 2 slits
Non-Redundant Array of Slits
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P04 beamline (PETRA III) experiment
Undulator tuned to400 eVA
B Exit slit openings: 40 µm and 230 µm
* Vacuum chamber constructed by Hans Peter Oepen group (Hamburg University)
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Data: Typical Intensity Scans
NRA
Double pinholes
Detector plane Fourier Transform
NRA
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Data: Typical Intensity Scans
NRA
Double pinholes
Detector plane Fourier Transform
NRA
400 eV
800 eV
800 eV
400 eV
Second harmonics(monochromator)
R
2R
2R
R
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Data: Typical Intensity Scans
NRA
Double pinholes
Detector plane Fourier Transform
NRA
400 eV
800 eV
800 eV
400 eV
Second harmonics(monochromator)
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Data: Typical Intensity ScansN
RA
Do
ub
le
pin
ho
les
Detector plane Fourier Transform
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Data: Beam Profile Scans
FWHM=42± 2 µm
µmµm
FWHM=11± 1 µm
Exit slit 230 µmExit slit 40 µm
• Performed on double pinholes separated by 15 µm• FWHM found with double Gauss functions fits
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Results: NRA & D.P. are identical
Exit Slit width 40 µm Exit Slit width 230 µm
Double pinholes data pointsNRA data pointsE = 400 eV
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P04 beamline experiment
C Exit slit cut out 396.5, 400 and 403 eV fraction of the beam
Beam defining slit opening variedD
* Vacuum chamber constructed by Hans Peter Oepen group (Hamburg University)
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Beam defining slit variation
Exit Slit width 230 µmE = 396.5 eV, 400 eV, 403 eV
𝜻=𝟎 .𝟎𝟓÷𝟎 .𝟖 𝜻=𝟎 .𝟏𝟐÷𝟎 .𝟏𝟒 𝜻=𝟎 .𝟐𝟒÷𝟎 .𝟐𝟓
Features of coherence dependence on beam defining slit opening observed
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Second experiment at P04
Aim – measure spatial coherence prior to ptychography experiment
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Second experiment at P04
1. 50 μm2. 100 μm3. 200 μm
500 eVa. Horizontalb. Vertical
NRA orientationExit slit openingUndulator energy
* HORST chamber constructed by Axel Rosenhahn group (Ruhr-University Bochum)
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P04 diffraction patterns
Typical diffraction image Fourier transform
Area for further analysis
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P04 Vertical coherence
Exit slit:
Bea
m
prof
ileC
oher
ence
FWHM = 29.5 μmFWHM = 12.6 μmFWHM = 7 μm
lc = 4.2 μm
lc = 2.4 μm
lc = 7.5 μm ζ = 0.37
50 μm 100 μm 200 μm
ζ = 0.10ζ = 0.73
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P04 Horizontal coherence
FWHM estimated as 100 μm
lc = 12.4 μm
lc = 12.4 μm lc = 12.5 μm ζ = 0.14 ζ = 0.14ζ = 0.15C
oher
ence
Exit slit: 50 μm 100 μm 200 μm
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PETRA III vs BESSY II
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Conclusions
1. NRA allows to measure full spatial coherence function in one exposure
2. Results with NRAs and double pinholes are identical
3. NRA method works especially well with large beams
4. This approach can be effectively used prior to any
coherent imaging experiment
5. May be useful for measuring single pulse coherence
properties of FELs
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Thanks to
Thank you for your attention!
DESY:A. SingerO.Y. GorobtsovD. DzhigaevA. ShabalinO.M. YefanovM. RoseR.P. KurtaI.A. Vartanyants
Bochum:T. Senkbeil A. Buck T. Gorniak A. Rosenhahn
Uni. Hamburg:J. BachB. BeyersdorffR. FrömterH.P. Oepen
DESY:L. Glaser
L. MüllerS. SchleitzerG. Grübel
SLAC:A. SakdinawatJ. Viefhaus
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S1. Temporal coherence
𝐸∆𝐸
≈ 1000
𝑙𝑡 ≈ λ𝐸
∆𝐸=3.1𝜇𝑚
15𝜇𝑚
𝟖𝟎𝒄𝒎
𝟔𝟐𝒎𝒎
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S2. Two-dimensional NRA
Image taken from Gonzalez, A. I. & Meja, Y. (2011). J. Opt. Soc. Am. A, 28(6), 1107-1113
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S3. Non-uniformity of coherence
0 7.5 15-15 -7.5
0
7.5
15
-15
-7.5
15-15 0 7.5-7.5𝑟1
𝑟2
𝑟1
Г (𝒓 𝟏 ,𝒓𝟐 )
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S3. Non-uniformity of coherence
0 7.5 15-15 -7.5
0
7.5
15
-15
-7.5
50 μm
100 μm
200 μm𝑟1
𝑟2Г (𝒓 𝟏 ,𝒓𝟐 )
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S4. More data on coherence
400 eV396.5 eV 403 eV
𝑫𝒆𝒔=4.7 mm
𝜻=𝟎 .𝟎𝟓÷𝟎 .𝟖 𝜻=𝟎 .𝟏𝟐÷𝟎 .𝟏𝟒 𝜻=𝟎 .𝟐𝟒÷𝟎 .𝟐𝟓
𝑫𝒆𝒔=1 .7 mm 𝑫𝒆𝒔=0 . 8 mmEnergy: