Coherent Diffraction Imaging with Nano- and Microbeams
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1 Diffraction Imaging with Nano- and Microbeams Why does lensless need? Mark A Pfeifer Cornell High Energy Synchrotron Source Cornell University Ithaca, NY map322@cornell.edu XLD 2011 June 28, 2011
2 Outline diffraction and why it will never work for x-rays. diffraction - how it works. Can you really use a lens for that? Why should I use phasing algorithms when I have a lens? Putting it all together.
3 Some thoughts by Sayre Some implications of a theorem due to Shannon (Nyquist frequency)
4 Some thoughts by Sayre
5 Fourier intensity measurements and the autocorrelation density amplitude
6 Fourier intensity measurements and the autocorrelation density intensity
7 Fourier intensity measurements and the autocorrelation autocorrelation intensity
8 Fourier intensity measurements and the autocorrelation autocorrelation intensity If only intensity measured, sampling requirement doubled. In greater than one dimension, autocorrelation uniquely determines original function.
9 Wavefront reconstruction e : Gerchberg and Saxton - Optik 1971, 1972 intensity measurements in exit plane and far field alternately enforced known intensities, kept phase estimates, propagated with FFT algorithm equivalent to steepest descents visible light: Fienup finite source size, positivity, and measured far-field correct for atmospheric disturbances diagnose aberration in Hubble s main mirror explored range of algorithms with degrees of feedback
10 Born and Wolf Born and Wolf, Principles of Optics: In the method of wave-front reconstruction, a background is artificially added. There are no conditions to be satisfied regarding symmetry or even periodicity. On the other hand this method is not suitable for X-ray analysis owing to the practical impossibility of producing a strong coherent background.
11 Born and Wolf Born and Wolf, Principles of Optics: In the method of wave-front reconstruction, a background is artificially added. There are no conditions to be satisfied regarding symmetry or even periodicity. On the other hand this method is not suitable for X-ray analysis owingtothepractical impossibility of producing a strong coherent background.
12 Coherence Rotating anode L T = λd 2s = 0.14nm 2m 2 1mm =70nm fractional coherence 2 14
13 Coherence Rotating anode L T = λd 2s = 0.14nm 2m 2 1mm =70nm fractional coherence 2 14 APS undulator A fractional coherence ph/s/0.1%
14 Coherence Rotating anode L T = λd 2s = 0.14nm 2m 2 1mm =70nm fractional coherence 2 14 APS undulator A fractional coherence ph/s/0.1% ERL helical mode delta fractional coherence ph/s/0.1%
15 First X-ray demonstration Miao JOSA SEM VLM Diffraction CDI
16 CDI moves into 3D and biology Au decorated Si3N4 pyramids Chapman, JOSA Yeast cells Shapiro PNAS Pb crystals - strain mapping Pfeifer, Nature 2006.
17 A nice flow chart showing how CDI works
18 A nice flow chart showing how CDI works
19 A nice flow chart showing how CDI works
20 A nice flow chart showing how CDI works F
21 A nice flow chart showing how CDI works F
22 A nice flow chart showing how CDI works F F 1
23 A nice flow chart showing how CDI works F F 1
24 A nice flow chart showing how CDI works F time passes F 1
25 Missing information
26 Fresnel CDI Geometry
27 Fresnel CDI Illumination far field from Fresnel zone plate diffraction from Au test pattern
28 Fresnel CDI Illumination far field from Fresnel zone plate diffraction from Au test pattern
29 Fresnel CDI Illumination Harry Quiney, Nature Physics Complex wave field reconstructed in region of focus. Only need far-field intensity pattern and knowledge of focal length.
30 Fresnel CDI Sample Results Brian Abbey APL Interconnect from circuit board Garth Williams Cytometry Malaria infected red blood Cell comparison of light microscopy, SEM and FCDI
31 Ptychography Rodenburg PRL Collect diffraction patterns from overlapping regions Thibault Science Focused Beam recovered
32 Ptychography Au star test pattern measured at APS 2-ID-B with MMPAD
33 Ptychography Au star test pattern measured at APS 2-ID-B with MMPAD
34 Ptychography Au star test pattern measured at APS 2-ID-B with MMPAD
35 Ptychography Au star test pattern measured at APS 2-ID-B with MMPAD
36 Signal to noise Garth Williams Acta Crys A Effect of Poisson noise in diffraction pattern similar to Poisson noise in image.
37 Signal to noise Andreas Schropp and Christian G Schroer NJP resolution for isolated feature same (or better) than same feature as part of larger sample
38 X-ray microscopy comparison TXM FCDI ptychography NA efficiency mode contrast λ 2Δr e lens e det full field absorption, phase sin ( ) Nλ 4a e det full-field absorption, phase sin ( ) Nλ 4a e det scanning abs., phase, fluorescence, photoelectrons
39 X-ray microscopy comparison TXM FCDI ptychography NA efficiency mode contrast λ 2Δr =0.01 e lens e det full field absorption, phase sin ( ) Nλ 4a =0.5 edet full-field absorption, phase sin ( ) Nλ 4a =0.5 edet scanning abs., phase, fluorescence, photoelectrons assuming λ =0.1nm wavelength Δr =5nm finest zone width in zone plate N = 1000 number of rows/columns in area detector a =50nm size
40 Multi-modal diffraction Fresnel CDI Full field variable zoom No fast scanning Dosing more even take multiple exposures of same illuminated area and cross correlate no partially overlapping Ptychography X-ray fluorescence Photoelectrons Potential for z-scanning instead of tomography (poorer resolution)
41 Strain mapping within polycrystalline film Diff. aperture diffraction. Wang, Micron Matt Miller Group Marcus Newton Nature Mat 2010.
42 Multi-energy Bragg CDI ki Q kf
43 Multi-energy Bragg CDI Q ki kf
44 Single shot three dimensional of 3D strain Consider a detector at a distance l from a sample, centered about a Bragg peak, G, at an energy E. Measurements made over values p x, p y,and δe E. q = k o l p x ˆq x + ( k o l p y δe E G cos θ) ˆq y + δe E G sin θˆq z For 5nm resolution of 500nm particle at detector distance l =2m, and energy E =6keV, require: pixels of (100μm) 2 480eV range at 2.4keV resolution If an appropriate energy discriminating detector were possible, then a full three dimensional mapping of the strain a nanocrystal could be made in situ in a single measurement, with no scanning. If three detectors could be located at three Bragg peaks (i.e. three {200} peaks when the incident beam is co-axial with the {111}, then a three dimensional mapping of three different strain projections could be made in real time.
45 Summary STXM without phase retrieval is throwing away information. diffraction will be able to stay ahead of purely lens based - but high efficiency help. Fresnel CDI and ptychography have same basic geometry and optics, and can recover your focal spot complex wave field. Efficiency of optic (or optical system) and detector as important as source properties.
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Optical Diffraction and Interference using Single Photon Counting
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Models of Light The wave model: The ray model: The photon model:
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