Today s Outline - April 17, C. Segre (IIT) PHYS Spring 2018 April 17, / 22

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1 Today s Outline - April 17, 2018 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

2 Today s Outline - April 17, 2018 Diffraction enhanced imaging C. Segre (IIT) PHYS Spring 2018 April 17, / 22

3 Today s Outline - April 17, 2018 Diffraction enhanced imaging Grating interferometry C. Segre (IIT) PHYS Spring 2018 April 17, / 22

4 Today s Outline - April 17, 2018 Diffraction enhanced imaging Grating interferometry Coherent diffraction imaging C. Segre (IIT) PHYS Spring 2018 April 17, / 22

5 Today s Outline - April 17, 2018 Diffraction enhanced imaging Grating interferometry Coherent diffraction imaging Holography C. Segre (IIT) PHYS Spring 2018 April 17, / 22

6 Today s Outline - April 17, 2018 Diffraction enhanced imaging Grating interferometry Coherent diffraction imaging Holography Imaging research C. Segre (IIT) PHYS Spring 2018 April 17, / 22

7 Today s Outline - April 17, 2018 Diffraction enhanced imaging Grating interferometry Coherent diffraction imaging Holography Imaging research Final Exam information Wednesday, May 2, 2018, 10:30-12:30, Room 213 SB C. Segre (IIT) PHYS Spring 2018 April 17, / 22

8 Diffraction Enhanced Imaging Oltulu et al., Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging, J. Phys. D: Appl. Phys. 36, 2152 (2003). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

9 Diffraction Enhanced Imaging DEI is an imaging method which was developed in in the late 1990 s at Illinois Tech. Oltulu et al., Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging, J. Phys. D: Appl. Phys. 36, 2152 (2003). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

10 Diffraction Enhanced Imaging DEI is an imaging method which was developed in in the late 1990 s at Illinois Tech. it relies on an analyzer crystal to separate the various components of an image measured normally by simple radiography Oltulu et al., Extraction of extinction, refraction and absorption properties in diffraction enhanced imaging, J. Phys. D: Appl. Phys. 36, 2152 (2003). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

11 Diffraction Enhanced Imaging C. Segre (IIT) PHYS Spring 2018 April 17, / 22

12 Diffraction Enhanced Imaging Taking multiple images instead of just 2 permits the extraction of additional information C. Segre (IIT) PHYS Spring 2018 April 17, / 22

13 Diffraction Enhanced Imaging Taking multiple images instead of just 2 permits the extraction of additional information analyzer rocking curves taken at three pixel locations show typical effects of different interactions with sample C. Segre (IIT) PHYS Spring 2018 April 17, / 22

14 Diffraction Enhanced Imaging A. reference region with no sample Taking multiple images instead of just 2 permits the extraction of additional information analyzer rocking curves taken at three pixel locations show typical effects of different interactions with sample C. Segre (IIT) PHYS Spring 2018 April 17, / 22

15 Diffraction Enhanced Imaging A. reference region with no sample B. refraction and some absorption effects Taking multiple images instead of just 2 permits the extraction of additional information analyzer rocking curves taken at three pixel locations show typical effects of different interactions with sample C. Segre (IIT) PHYS Spring 2018 April 17, / 22

16 Diffraction Enhanced Imaging A. reference region with no sample B. refraction and some absorption effects C. scattering effects dominate Taking multiple images instead of just 2 permits the extraction of additional information analyzer rocking curves taken at three pixel locations show typical effects of different interactions with sample C. Segre (IIT) PHYS Spring 2018 April 17, / 22

17 Diffraction Enhanced Imaging C. Segre (IIT) PHYS Spring 2018 April 17, / 22

18 Grating interferometry Full field phase imaging can be achieved using an interferometric technique C. Segre (IIT) PHYS Spring 2018 April 17, / 22

19 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave C. Segre (IIT) PHYS Spring 2018 April 17, / 22

20 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

21 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously C. Segre (IIT) PHYS Spring 2018 April 17, / 22

22 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously ψ x e ik2 xz/(2k) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

23 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

24 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

25 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously the repeat distance, called the Talbot distance, is given by d T = 2p 2 1 /λ ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

26 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously the repeat distance, called the Talbot distance, is given by d T = 2p 2 1 /λ for p 1 = 1µm and λ = 1Å we have a Talbot distance, d T = 20mm ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

27 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously the repeat distance, called the Talbot distance, is given by d T = 2p 2 1 /λ for p 1 = 1µm and λ = 1Å we have a Talbot distance, d T = 20mm ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) for an absorption grating C. Segre (IIT) PHYS Spring 2018 April 17, / 22

28 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously the repeat distance, called the Talbot distance, is given by d T = 2p 2 1 /λ for p 1 = 1µm and λ = 1Å we have a Talbot distance, d T = 20mm ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) for a partial phase grating the pattern of transmission may be repeated at rational fractions of d T C. Segre (IIT) PHYS Spring 2018 April 17, / 22

29 Grating interferometry Full field phase imaging can be achieved using an interferometric technique Talbot effect: vertical grating illuminated by a plane wave for a vertical grating of period p 1 illuminated by a wavelength λ the transverse wave number is k x = 2π/p 1 propagating the wave downstream as described previously the repeat distance, called the Talbot distance, is given by d T = 2p 2 1 /λ for p 1 = 1µm and λ = 1Å we have a Talbot distance, d T = 20mm ψ x e ik2 xz/(2k) e i(2π/p 1) 2 z/(2k) e i2πλz/(2p2 1 ) for a full π phase grating the lateral period is doubled the pattern of transmission may be repeated at rational fractions of d T C. Segre (IIT) PHYS Spring 2018 April 17, / 22

30 Talbot Interferometer The Talbot interferometer consists of two gratings, a phase grating of lateral period p 1 (G1) and an absorption grating of lateral period p 1 /2 (G2) which in combination, measure the distortion of the phase field due to the sample C. Segre (IIT) PHYS Spring 2018 April 17, / 22

31 Talbot Interferometer The Talbot interferometer consists of two gratings, a phase grating of lateral period p 1 (G1) and an absorption grating of lateral period p 1 /2 (G2) which in combination, measure the distortion of the phase field due to the sample when measuring, G1 if held fixed and G2 is scanned laterally over a full period p 1 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

32 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating p 1 I I Detector Pixel x g C. Segre (IIT) PHYS Spring 2018 April 17, / 22

33 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating p 1 I as the absorption grating, (G2) is moved laterally, the pink triangles show the ideal intensity observed at the detector as a function of x g I Detector Pixel x g C. Segre (IIT) PHYS Spring 2018 April 17, / 22

34 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating p 1 I as the absorption grating, (G2) is moved laterally, the pink triangles show the ideal intensity observed at the detector as a function of x g I Detector Pixel x g C. Segre (IIT) PHYS Spring 2018 April 17, / 22

35 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating p 1 I I x g Detector Pixel as the absorption grating, (G2) is moved laterally, the pink triangles show the ideal intensity observed at the detector as a function of x g the real intensity is more sinusoidal because of finite beam size C. Segre (IIT) PHYS Spring 2018 April 17, / 22

36 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating I I p 1 Detector Pixel x g as the absorption grating, (G2) is moved laterally, the pink triangles show the ideal intensity observed at the detector as a function of x g the real intensity is more sinusoidal because of finite beam size when the sample is in place the intensity is reduced and shifted by refraction to the blue blocks and curve C. Segre (IIT) PHYS Spring 2018 April 17, / 22

37 Talbot interferometer operation With no sample in place, the pink blocks are the intensity at d = p1 2 /8λ downstream from a φ = π grating I I p 1 Detector Pixel three positions of the absorption grating are all that is needed to obtain the information to produce absorption, dark field and phase contrast images x g as the absorption grating, (G2) is moved laterally, the pink triangles show the ideal intensity observed at the detector as a function of x g the real intensity is more sinusoidal because of finite beam size when the sample is in place the intensity is reduced and shifted by refraction to the blue blocks and curve C. Segre (IIT) PHYS Spring 2018 April 17, / 22

38 Visibility We can define the visibility function as C. Segre (IIT) PHYS Spring 2018 April 17, / 22

39 Visibility We can define the visibility function as V = I max I min I max + I min C. Segre (IIT) PHYS Spring 2018 April 17, / 22

40 Visibility We can define the visibility function as p 1 I V = I max I min I max + I min for the ideal intensity V 1 I Detector Pixel x g C. Segre (IIT) PHYS Spring 2018 April 17, / 22

41 Visibility We can define the visibility function as p 1 I V = I max I min I max + I min I Detector Pixel x g for the ideal intensity V 1 but for small Gaussian smearing, σ p 1 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

42 Visibility We can define the visibility function as p 1 I V = I max I min I max + I min I Detector Pixel x g for the ideal intensity V 1 but for small Gaussian smearing, σ p 1 V 1 8 2π σ p 1 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

43 Visibility We can define the visibility function as p 1 I V = I max I min I max + I min I Detector Pixel with the sample in place, the visibility is necessarily smaller due to absorption x g for the ideal intensity V 1 but for small Gaussian smearing, σ p 1 V 1 8 2π σ p 1 C. Segre (IIT) PHYS Spring 2018 April 17, / 22

44 Grating interferometry Plastic containers filled with water (left) and powdered sugar (right). (a) absorption image, (b) phase contrast image, (d) dark field image. C. Segre (IIT) PHYS Spring 2018 April 17, / 22

45 Grating interferometry Plastic containers filled with water (left) and powdered sugar (right). (a) absorption image, (b) phase contrast image, (d) dark field image. visibility of zero leads to the speckling in (b) as can be seen from the red line in (c) C. Segre (IIT) PHYS Spring 2018 April 17, / 22

46 Grating interferometry The different contrasts are easily seen in the image of a chicken wing C. Segre (IIT) PHYS Spring 2018 April 17, / 22

47 Grating interferometry The different contrasts are easily seen in the image of a chicken wing the absorption contrast (left) is most like a conventional radiograph C. Segre (IIT) PHYS Spring 2018 April 17, / 22

48 Grating interferometry The different contrasts are easily seen in the image of a chicken wing the absorption contrast (left) is most like a conventional radiograph the phase contrast (right) is sensitive to changes in angle of the surface and buried interfaces C. Segre (IIT) PHYS Spring 2018 April 17, / 22

49 Grating interferometry The different contrasts are easily seen in the image of a chicken wing the absorption contrast (left) is most like a conventional radiograph the phase contrast (right) is sensitive to changes in angle of the surface and buried interfaces the dark field image lights up where there is a a large amount of scattering C. Segre (IIT) PHYS Spring 2018 April 17, / 22

50 Tomography with a Talbot interferometer The Talbot interferometer may be used for tomography as well Phase imaging with an x-ray Talbot interferometer, A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattora, JCPDS-International Centre for Diffraction Data, (2006). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

51 Tomography with a Talbot interferometer The Talbot interferometer may be used for tomography as well Phase imaging with an x-ray Talbot interferometer, A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattora, JCPDS-International Centre for Diffraction Data, (2006). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

52 Tomography with a Talbot interferometer The Talbot interferometer may be used for tomography as well the sample is rotated and the phase data is recorded in the usual way Phase imaging with an x-ray Talbot interferometer, A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattora, JCPDS-International Centre for Diffraction Data, (2006). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

53 Tomography with a Talbot interferometer The Talbot interferometer may be used for tomography as well the sample is rotated and the phase data is recorded in the usual way 3D reconstruction was performed on a cancerous rabbit liver Phase imaging with an x-ray Talbot interferometer, A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattora, JCPDS-International Centre for Diffraction Data, (2006). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

54 Tomography with a Talbot interferometer The Talbot interferometer may be used for tomography as well the sample is rotated and the phase data is recorded in the usual way 3D reconstruction was performed on a cancerous rabbit liver then a mouse tail with cartilage and bone Phase imaging with an x-ray Talbot interferometer, A. Momose, W. Yashiro, Y. Takeda, Y. Suzuki, and T. Hattora, JCPDS-International Centre for Diffraction Data, (2006). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

55 SAXS from a sphere For incoherent beam, illuminating a small particle (a sphere), we have the typical small angle pattern which shows broad features described in a previous chapter C. Segre (IIT) PHYS Spring 2018 April 17, / 22

56 SAXS from a sphere For incoherent beam, illuminating a small particle (a sphere), we have the typical small angle pattern which shows broad features described in a previous chapter C. Segre (IIT) PHYS Spring 2018 April 17, / 22

57 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains C. Segre (IIT) PHYS Spring 2018 April 17, / 22

58 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains C. Segre (IIT) PHYS Spring 2018 April 17, / 22

59 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains on the left is the speckle pattern given by the interference of the coherent beam with the seven spheres, C. Segre (IIT) PHYS Spring 2018 April 17, / 22

60 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains on the left is the speckle pattern given by the interference of the coherent beam with the seven spheres, on the right is the full pattern including the SAXS from individual spheres C. Segre (IIT) PHYS Spring 2018 April 17, / 22

61 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains on the left is the speckle pattern given by the interference of the coherent beam with the seven spheres, on the right is the full pattern including the SAXS from individual spheres the speckle changes with a different arrangement of spheres C. Segre (IIT) PHYS Spring 2018 April 17, / 22

62 Coherent Scattering from Multiple Spheres If the beam has coherence at least on the order of the size of the arrangement of the seven spheres shown, one obtains T= 295K T=145K on the left is the speckle pattern given by the interference of the coherent beam with the seven spheres, on the right is the full pattern including the SAXS from individual spheres the speckle changes with a different arrangement of spheres this can be seen when the speckle appears below a glass transition at 145K C. Segre (IIT) PHYS Spring 2018 April 17, / 22

63 Oversampling and image C. Segre (IIT) PHYS Spring 2018 April 17, / 22

64 Iterative Reconstruction start with experimental data and a randomly generated phase C. Segre (IIT) PHYS Spring 2018 April 17, / 22

65 Iterative Reconstruction start with experimental data and a randomly generated phase intermediate step shows partial phase retrieval but distorted scattering pattern C. Segre (IIT) PHYS Spring 2018 April 17, / 22

66 Iterative Reconstruction start with experimental data and a randomly generated phase intermediate step shows partial phase retrieval but distorted scattering pattern convergence to reconstructed phase, scattering and real space image C. Segre (IIT) PHYS Spring 2018 April 17, / 22

67 Gold nanoparticle imaging by CXI C. Segre (IIT) PHYS Spring 2018 April 17, / 22

68 Gold nanoparticle imaging by CXI C. Segre (IIT) PHYS Spring 2018 April 17, / 22

69 Lattice dynamics by CXI C. Segre (IIT) PHYS Spring 2018 April 17, / 22

70 Lattice dynamics by CXI Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals, J.N. Clark, et al., Science 341, (2013). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

71 Lattice dynamics by CXI Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals, J.N. Clark, et al., Science 341, (2013). C. Segre (IIT) PHYS Spring 2018 April 17, / 22

72 Lattice dynamics by CXI Ultrafast three-dimensional imaging of lattice dynamics in individual gold nanocrystals, J.N. Clark, et al., Science 341, (2013). C. Segre (IIT) PHYS Spring 2018 April 17, / 22