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Coherence measurements at P04
Petr Skopintsev P04 Users Meeting, DESY, Hamburg, Germany NRC “Kurchatov Institute”, Moscow, Russia Collaboration between: Jens Viefhaus (P04 – Beam line) Axel Rosenhahn (Analytical Chemistry Group, Ruhr-University Bochum) Ivan Vartanyants (Coherent Imaging Group)
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Theory of spatial coherence measurements
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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Mutual coherence function Degree of spatial coherence
Г 𝒓 𝟏 , 𝒓 𝟐 = 𝐸 𝒓 𝟏 , 𝐸 ∗ ( 𝒓 𝟐 ) Intensity Сoherence Factor 𝛾 𝒓 𝟏 , 𝒓 𝟐 = Г 𝒓 𝟏 , 𝒓 𝟐 𝐼 𝒓 𝟏 𝐼 𝒓 𝟐 𝐼 𝒓 =Г 𝒓,𝒓 Degree of spatial coherence 𝜁= Г 𝒓 𝟏 , 𝒓 𝟐 2 𝑑 𝒓 𝟏 𝑑 𝒓 𝟐 𝐼 𝒓 𝟏 𝑑 𝒓 𝟏 𝐼 𝒓 𝟐 𝑑 𝒓 𝟐 Time domain removed for simplicity 𝟎≤𝜁≤𝟏 Incoherent field Coherent field
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intensity distribution I(q)
Young’s Experiment 𝐼 𝑞 = 𝐼 𝐴 𝑞 𝟏+ |𝛾 12 |𝐜𝐨𝐬(𝒒∙𝒅+ 𝛼 12 ) 𝐼 (𝑥)=𝑻 𝒙 + | 𝛾 12 | 2 𝑒 𝑖 𝛼 12 𝑻 𝒙−𝒅 + + 𝑒 −𝑖 𝛼 12 𝑻 𝒙−𝒅 Incoherent Coherent Part. coherent 𝑪 𝟎 , 𝑪 𝟎 , 𝑪 𝟎 , 𝑪 𝟏𝟐 𝑪 𝟏𝟐 =𝟎 𝑪 𝟏𝟐 𝑪 𝟏𝟐 =𝟎 Double pinholes diffraction intensity distribution I(q) Fourier transform of I(q)
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𝛾 12 Young’s Experiment Δx
𝐶 0 = 𝐼 1 + 𝐼 2 𝛾 12 𝐶 21 = | 𝛾 12 | 𝐼 1 𝐼 2 𝐶 12 = | 𝛾 12 | 𝐼 1 𝐼 2 Δx -Δx Δx Modulus of complex degree of spatial coherence is a function of distance between slits: | 𝛾 12 |≡|𝛾 ∆𝑥 | J.W. Goodman, Statistical optics
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𝛾 12 𝒄𝒐𝒉𝒆𝒓𝒆𝒏𝒄𝒆 𝒍𝒆𝒏𝒈𝒕𝒉 𝒍 𝒄 Young’s Experiment Δx
𝐶 0 = 𝐼 1 + 𝐼 2 𝒄𝒐𝒉𝒆𝒓𝒆𝒏𝒄𝒆 𝒍𝒆𝒏𝒈𝒕𝒉 𝒍 𝒄 𝛾 12 𝐶 21 = | 𝛾 12 | 𝐼 1 𝐼 2 𝐶 12 = | 𝛾 12 | 𝐼 1 𝐼 2 Δx -Δx Δx Modulus of complex degree of spatial coherence is a function of distance between slits: | 𝛾 12 |≡|𝛾 ∆𝑥 | J.W. Goodman, Statistical optics
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Non-Redundant Array of Slits
10 peaks 10 points 𝐶 0 = 𝑖=1 𝑛=10 𝐼 𝑖 , 1 experiment with 5 slits = 10 experiments with 2 slits 𝐶 𝑖𝑗 =| 𝛾 𝑖𝑗 | 𝐼 𝑖 𝐼 𝑗
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P04 beamline (PETRA III) experiment
Undulator tuned to 400 eV 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 NRA Double pinholes Detector plane Fourier Transform
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Data: Typical Intensity Scans
2R R NRA NRA Second harmonics (monochromator) 800 eV 2R Double pinholes 400 eV R 400 eV 800 eV Detector plane Fourier Transform
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Data: Typical Intensity Scans
NRA NRA Second harmonics (monochromator) 800 eV Double pinholes 400 eV 400 eV 800 eV Detector plane Fourier Transform
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Data: Typical Intensity Scans
NRA Double pinholes Detector plane Fourier Transform
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Data: Beam Profile Scans
Performed on double pinholes separated by 15 µm FWHM found with double Gauss functions fits Exit slit 40 µm Exit slit 230 µm 15 µm 15 µm FWHM=11±1µm FWHM=42±2 µm
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Results: NRA & D.P. are identical
E = 400 eV Double pinholes data points NRA data points Exit Slit width 40 µm Exit Slit width 230 µm
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D C P04 beamline experiment Beam defining slit opening varied
Exit slit cut out 396.5, 400 and 403 eV fraction of the beam * Vacuum chamber constructed by Hans Peter Oepen group (Hamburg University)
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Beam defining slit variation
E = eV, 400 eV, 403 eV Exit Slit width 230 µm 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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Aim – measure spatial coherence prior to ptychography experiment
Second experiment at P04 Aim – measure spatial coherence prior to ptychography experiment
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Second experiment at P04 Undulator energy Exit slit opening
NRA orientation 1. 50 μm μm μm a. Horizontal b. Vertical 500 eV * HORST chamber constructed by Axel Rosenhahn group (Ruhr-University Bochum)
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P04 diffraction patterns
Typical diffraction image Fourier transform How can we achieve nm-scale resolution? Why phase images are of interest? Area for further analysis
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50 μm 100 μm 200 μm P04 Vertical coherence Beam profile Coherence
Exit slit: 50 μm 100 μm 200 μm Beam profile FWHM = 7 μm FWHM = 12.6 μm FWHM = 29.5 μm lc = 7.5 μm lc = 4.2 μm lc = 2.4 μm ζ = 0.73 ζ = 0.37 ζ = 0.10 Coherence
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P04 Horizontal coherence
Exit slit: 50 μm 100 μm 200 μm Coherence lc = 12.5 μm lc = 12.4 μm lc = 12.4 μm ζ = 0.14 ζ = 0.14 ζ = 0.15 FWHM estimated as 100 μm
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PETRA III vs BESSY II
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Conclusions NRA allows to measure full spatial coherence function in one exposure Results with NRAs and double pinholes are identical NRA method works especially well with large beams This approach can be effectively used prior to any coherent imaging experiment May be useful for measuring single pulse coherence properties of FELs
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Thank you for your attention!
Thanks to DESY: A. Singer O.Y. Gorobtsov D. Dzhigaev A. Shabalin O.M. Yefanov M. Rose R.P. Kurta I.A. Vartanyants SLAC: A. Sakdinawat J. Viefhaus DESY: L. Glaser L. Müller S. Schleitzer G. Grübel Uni. Hamburg: J. Bach B. Beyersdorff R. Frömter H.P. Oepen Bochum: T. Senkbeil A. Buck T. Gorniak A. Rosenhahn Thank you for your attention!
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𝟔𝟐𝒎𝒎 𝟖𝟎 𝒄𝒎 S1. Temporal coherence 𝑙 𝑡 ≈λ 𝐸 ∆𝐸 =3.1 𝜇𝑚 𝐸 ∆𝐸 ≈1000
𝒍 𝒕 (3.1 𝜇𝑚)>∆𝑳 (0.6 𝜇𝑚) 𝟔𝟐𝒎𝒎 15 𝜇𝑚 ∆𝑳=𝟎.𝟔 𝝁𝒎 𝟖𝟎 𝒄𝒎
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S2. Two-dimensional NRA Image taken from Gonzalez, A. I. & Meja, Y. (2011). J. Opt. Soc. Am. A, 28(6),
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S3. Non-uniformity of coherence
𝑟 2 Г 𝒓 𝟏 , 𝒓 𝟐 15 7.5 -7.5 -15 𝑟 1 -15 -7.5 7.5 15 𝑟 1 -15 -7.5 7.5 15
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S3. Non-uniformity of coherence
𝑟 2 Г 𝒓 𝟏 , 𝒓 𝟐 50 μm 15 7.5 100 μm -7.5 -15 200 μm -15 -7.5 7.5 15 𝑟 1
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S4. More data on coherence
Energy: 396.5 eV 400 eV 403 eV 𝑫 𝒆𝒔 =4.7 mm 𝑫 𝒆𝒔 =1.7 mm 𝑫 𝒆𝒔 =0.8 mm 𝒍 𝒄𝒐𝒉 =𝟏.𝟗 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟐.𝟑 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟑.𝟎 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟒.𝟒 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟒.𝟓 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟒.𝟗 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟗.𝟎 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟗.𝟒 𝝁𝒎 𝒍 𝒄𝒐𝒉 =𝟗.𝟓 𝝁𝒎 𝜻=𝟎.𝟎𝟓÷𝟎.𝟖 𝜻=𝟎.𝟏𝟐÷𝟎.𝟏𝟒 𝜻=𝟎.𝟐𝟒÷𝟎.𝟐𝟓
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