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2. Focusing Microscopy Object placed close to secondary source: => strong magnification The smaller the focus, the sharper the image! Spectroscopy, tomography large depth of field scanning beam over sample (diffraction, SAXS, XAS, fluorescence…) 1 Small focus requires 1. small source 2. long distance L1 source-lens 3. small focal length and large effective aperture of lens 2 a. FOCUSING with rotationally parabolic Be lenses ( R = 1500µm) Image of the ID18 source at ESRF Intensity 600000 39 CRLs no CRLs 400000 15 m 200000 14.4125eV 39 Be lenses R = 1500µm 0.55 mm 0 -1.0 -0.5 0.0 0.5 Vertical position 100000 39 CRLs no CRLs 80000 (A. Chumakov ESRF) 60000 Intensity f = 11.718m geometric aperture: 2.5mm 1.0 239 m 40000 20000 1.57 mm 0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 Horizontall position 1.0 1.5 2.0 3 Intensity profile in the horizontal: ID18 well fitted by a Gaussian with 239 µm FWHM (very low background in the wings) 4 b. Focusing with Be lens at energies as low as 2keV ID12 at ESRF (A. Rogalev) gain in intensity on sample at 2 keV: factor 500 compared to situation without lens! 5 c. Prefocusing with linear lenses R = 200 to 1000µm, Be, Al and Ni length 2.5 mm * collecting more intensity * for making spot on sample more circular (on storage rings) 6 SEM image of linear Be lens (R=500µm) 7 Focusing with 2 independent linear lenses in cross-geometry • Ratio of horizontal to vertical source size in storage rings: 20 and more =>elongated spot on sample • Generation of more circular spot size by astigmatic imaging of source via 2 independent linear lenses in cross geometry • Example: experiment at DIAMOND Light Source by A. Snigirev et al with 1D Be from RXOPTICS 8 Astigmatic focusing with 2 crossed, linear Be lenses HR X-ray CCD 12 keV Si-111 1D Be Vert 1D Be Hor B16 4m 1.4 m 44 m from source 7.5 m 7.5 m Vertical N=17 R=300µm L2 ~ 4m Horizontal N=17 R=200µm N=15 R=300µm L2 ~ 1.4m Crossed gain: 1200 9 Astigmatic-Cross focusing with 2 linear Be CRLs Astigmatic focusing with 2 crossed, linear Be lenses I & A Snigirev, I. Dolbnya, K. Sawhney Collaboration with Optics Group at DIAMOND Profile: 7.5 µm Vertical focusing: Be CRL N = 17, R = 300 m L2 = ~ 4 m Intensity, arb. un. FWHM Horizontal focusing: Be CRL N = 17 R = 200 m N = 15 R = 300 m L2 = ~ 1.4 m 30000 25000 Gain = 1200 1D and 2D Fourier transform 15000 10000 20000 15000 10000 5000 5000 0 0 0 Porous 7.5 µm FWHM horizontal focusing vertical focusing 25000 20000 horizontal Intensity, arb. un. 30000 vertical Si; 2.5 m pitch Distance, microns In front of horizontal CRL 10 20 30 40 10 20 30 Distance, microns 40 50 3. Coherent flux * diffraction of individual large molecules, nanoparticles * speckle spectroscopy Illuminated area on sample must be smaller than the lateral coherence area at the sample position. Then all monochromatic photons are undistinguishable, i.e. they are in the same mode! * coherent photon flux is a property of the brillance B of the source and of the degree of monochromaticity * the coherent flux can at best be conserved, it cannot be increased by a focusing optic. Fc B 2 11 Example: ID13 at ESRF Be lens: R = 50µm, N = 162, f = 205.9mm, Deff = 295µm, dtr = 42nm L1 = 100m, L2 = 206.3mm geometric image of source S S L2 L1 S‘ geom (nm) S‘ incl diffr (nm) FWHM S (µm) horizontal 120 248 251 vertical 20 41 59 diffraction limited in the vertical ! 12 Example: low-betha undulator at ESRF 1. Be lenses, 17 keV, N = 162, f = 205.9mm, dtr = 42nm L1 = 100 m, L2 = 0.2063 m 2. horizontal Source size FWHM 120µm vertical 20µm Geometric image FWHM 248 nm 41nm Image is diffraction limited in the vertical: => coherent illumination in the vertical Not so in the horizontal! 13 3. remedy for horizontal direction * insert a linear lens (prefocussing lens) which focuses only in the horizontal * the secondary source S‘ must have a lateral coherence length at the postion of lens 2 which is equal to the effective aperture of lens2. S S‘ Prefocusing lens 50m Lens 2 50m 14 Prefocusing lens Be linear: R = 500µm, N = 55, f = 3.854m, Deff = 1048µm Image S‘ at b1 = 4.168m behind horizontal lens lateral (horizontal) coherence length at position of lens 2: 295µm this is equal to Deff of lens 2: only the coherent flux passes through lens 2, the rest is peeled off. gain in flux (compared to no prefocusing): about factor 10. 15 Coherent Imaging (Ptychography) (see talk by F. Seiboth, C. Schroer) * illuminate sample coherently in a small spot by means of Be-lenses * Scan this microfocus over sample with overlaping neighboring scans * take a diffraction image on each position * overlap of images allows for reconstruction of the object when each spot is illuminated coherently Our Be lenses preserve coherence well enough to give a resolution which is 10 times better than the spot size! 16 MANY THANKS To my former students, Anatoly and Irina Snigirev from ESRF Christian Schroer and collaborators from TU Dresden for many years of efficient and pleasant collaboration 17