1 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…)

2 Small focus requires 1. small source 2. long distance L 1 source-lens 3. small focal length and large effective aperture of lens

3 a. FOCUSING with rotationally parabolic Be lenses ( R = 1500µm) Image of the ID18 source at ESRF eV 39 Be lenses R = 1500µm f = m geometric aperture: 2.5mm (A. Chumakov ESRF)

4 Intensity profile in the horizontal: ID18 well fitted by a Gaussian with 239 µm FWHM (very low background in the wings)

5 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!

6 c. Prefocusing with linear lenses Be, Al and Ni R = 200 to 1000µm, length 2.5 mm * collecting more intensity * for making spot on sample more circular (on storage rings)

7 SEM image of linear Be lens (R=500µm)

8 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

9 B16 Si keV HR X-ray CCD 4 m 44 m from source 1D Be Vert 1D Be Hor 1.4 m 7.5  m Astigmatic focusing with 2 crossed, linear Be lenses Vertical Horizontal Crossed N=17 R=300µm N=17 R=200µm gain: 1200 L2 ~ 4m N=15 R=300µm L2 ~ 1.4m

Vertical focusing: Be CRL N = 17, R = 300  m L 2 = ~ 4 m Horizontal focusing: Be CRL N = 17R = 200  m N = 15R = 300  m L 2 = ~ 1.4 m Gain = 1200 Porous Si; 2.5  m pitch In front of horizontal CRL Astigmatic-Cross focusing with 2 linear Be CRLs 1D and 2D Fourier transform Profile: vertical horizontal 7.5 µm FWHM 7.5 µm FWHM Astigmatic focusing with 2 crossed, linear Be lenses I & A Snigirev, I. Dolbnya, K. Sawhney Collaboration with Optics Group at DIAMOND

11 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.

12 Example: ID13 at ESRF Be lens: R = 50µm, N = 162, f = 205.9mm, D eff = 295µm, d tr = 42nm L 1 = 100m, L 2 = 206.3mm geometric image of source FWHM S (µm) S‘ geom (nm) S‘ incl diffr (nm) horizontal vertical diffraction limited in the vertical !

13 Example: low-betha undulator at ESRF 1. Be lenses, 17 keV, N = 162, f = 205.9mm, d tr = 42nm L 1 = 100 m, L 2 = m 2. Source size FWHM Geometric image FWHM horizontal 120µm 248 nm vertical 20µm 41nm Image is diffraction limited in the vertical: => coherent illumination in the vertical Not so in the horizontal!

14 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 Lens 2 50m

15 Prefocusing lens Be linear: R = 500µm, N = 55, f = 3.854m, D eff = 1048µm Image S‘ at b 1 = 4.168m behind horizontal lens lateral (horizontal) coherence length at position of lens 2: 295µm this is equal to D eff 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.

16 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!

17 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