Spatial resolution. Spatial resolution

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1 11/05/00 Refraction Compound refractive lenses (concave) Snigirev et al, NATURE 199 patents: Tomie 1995 x-rays: n = 1 - δ - i β < 1 Chromatic lenses Prod.: Aachen, D need of concave and parabolic lenses f=r 0 /(δ) l = 1/(ρ*[µ/ρ]) lens transmission: T(y) = exp(-y /fδl) for d=0 Gaussian with σ = sqrt(fδl) resolution [nm] 10 8 Li CRL No: R 0 and N are free R=0.5λsqrt[R 0 /(Nlδ )] 1 R = λ Pt capillary R exp =7 x 55 1 kev for mini-lens in Si (Schroer et al, APL 005) 8 8 photon energy [ev] 1

2 11/05/00 Schroer et al (PRL 005): Better focus adiabatically to R=.7 7. kev R exp not yet (production D?) Schroer et al (PRL 005): Better lighten the lens with Fresnel s lighthouse lens strategy and focus adiabatically to R=.1 7. kev R exp not yet (production D?) What to do? Lighten a refractive lens by removing all material, which retards the field by multiples of π

3 11/05/00 Fresnel (kinoform)) lenses How to reduce absorption in CRL s? CRL B. Lengeler et al Clessidra A tiny plastic x-ray x lens (1D)! hair May 00 3

4 11/05/00 A tiny plastic x-ray x lens! Jark et al, JSR 00 Effective aperture similar to CRL s. f=1 m... m for λ=0.15 nm Exp. focus.8 µm! At ELETTRA 15x intensity gain in one dimension in 30 µm spot! Click to edit. mm Master subtitle style High resolution radiograph A tiny plastic x-ray x lens (D)! Two-dimensional focus behind crossed lenses CCD image: May 00 lens shadow focus, gain 5x size 50 x 80 µm

5 11/05/00 other Fresnel (kinoform)) lenses a b c d e No limit for R! Decreases with feature size! R exp 0. µm (1D with c) a) Aristov et al, APL000 b) Snigireva et al, NIM001 c) Evans-Lutterodt, OE003 d) ANKA, Karlsruhe, 005 e) Cederstroem, JSR 005 Diffraction Bragg-Fresnel reflection zone-plate Michette et al, Opt. Commun, 005 Combine diffraction of different order 5

6 11/05/00 resolution [nm] R = λ Pt capillary Li CRL photon energy [ev] Once more multilayer coating R ult x 30 kev R exp not yet Some problems: Spatial coherence Diffraction limited spot size is obtained with spatially coherent incident radiation A = lens aperture Q = source distance S (A/Q) = λ ===> Q=SA/λ e.g. S=30 µm, A=1 mm, λ =0.15 nm: Q=00 m!! S= 30 µm, A=0.0 mm, λ=0.15 nm: Q= m!! Is your aperture spatially coherently illuminated? Is your demagnification of order of 10,000?

7 11/05/00 Some problems: Depth of focus Let s go back Schroer et al, PRL 005 f<1 7. kev! assume NA=10 mrad=0.01 then f µm for s 0 nm f 100 µm for s 1000 nm Attenuation length l in Au/Si l = 1/00 7. kev l =.5/10 10 kev l = 0.0/ kev Scanning or imaging? Some problems: spot size? Classical knife-edge test CRL: C.G. Schroer et al, APL 87, 1103 (005) Fluorescence from test pattern A.C. Thomson et al, Proc. SPIE 15, 1 (000) 100 Fit to integrated data 0. µm Click to edit Master 0 subtitle style 1.0 µm R from knife-edge (fwhm) KB mirror: 1.0 µm zone-plate: 0. µm rel. transmission [%] Simulation:.0 µm experiment: KB mirrors zoneplate dot diameter [microns] 7

8 11/05/00 Summary: l Simpler optics may bring us ideally to R - nm (capillaries, waveguides, tilted Laue lenses, adiabatic CRL s) l More sophisticated objects are capable of R 1- nm (ideal Laue lenses, adiabatic kinoform refractive lenses, Bragg-Fresnel reflection zone-plates) l Is R λ possible? l An X-ray waveguide could provide already R 5- nm (but only 1D, no further recent efforts) l Fresnel zone-plates have R 0 nm (better in imaging) l Many other systems could arrive at about R 30-5 nm X-ray Zoom lens: Do-It It-Yourself! 1 many n>1: in the visible β θ = (1-n)/tanβ n<1: x-rays B. Cederström, R. N. Cahn, M. Danielsson, M. Lundqvist, D. R. Nygren: Focusing x-rays with old LP s Nature 0, 951 (000) Click to edit Master θsubtitle style d d g/n L g g y x 1 3 N 8

9 11/05/00 Get it almost for free 0 µm 1 mm Sawtooth comb milled into PLEXIGLASS in ELETTRA workshop [Marco De Gregorio, Gilio Sandrin] For geometrical optics it is a lens with parabolic transmission function, i.e. an approximation of CRL Test it at home x-ray tube (35 kv white) 0.0 mm x mm alligator lens in PMMA 50 teeth over 50 mm vert. acc mm for 1 kev opening 0. mm ( µm pitch) Si(Li) detector behind 0.01 mm slit expected beam size: without lens: 0.3 mm with lens: 0.0 mm 90 mm 90 mm With an average transmission of 0.85 in the effective aperture an intensity gain of g = 0.85 * 0.3/0.0 =.3 is expected 9

10 11/05/00 Results (1D) You get gain! Jark, X-ray spectrom. 00 experiment g/n =.0 µm Open/close the alligator mouth (lens): a) tunable large bandpass x-ray monochromator! b) tunable beam collimator d d g/n θ L y Click gto edit Master subtitle style g x gain gain 0 ray-tracing perfect comb defect comb Lens 30tuning photon energy [kev] experiment g/n = 1.3 µm ray-tracing perfect comb defect comb 1 3 N D with crossed pair photon energy [kev] Reflection vertically focusing elliptical mirror parabola: y l v Appendix: in more detail = b x (x'',y'') r' v l h r' h horiz. foc. ellip. mirror Crossed mirror pair (Kirkpatrick-Baez system) image Click to edit y Master subtitle style (x',y') x l Ideally elliptical mirrors needed l approximate as parabola y=(bx) 1/, y/ x =0.5 (b/x) 1/ l for x=x : y/ x (x ) = Φ crit l then b=(φ crit ) x and at x=x : y/ x (x ) = Φ crit (x /x ) 1/ l deflection angle is y/ x l and convergence angle in focus (h,v),f = NA = Φ crit [1-(x /x ) 1/ ] l Mirror size parameter: q=l/r= x -x /r 10

11 11/05/00 Reflection l NA = Φ crit (1 q ) + q l mirrors just touch with q h = l h /r h = l v /r v = q v = q r h q r h = r v q r v we put r v = m r h : then q = (m-1)/(m+1) l at ELETTRA m=5: q = 1.33 h,f = v,f = 1.1 Φ crit = NA l more realistic NA = Φ crit In more detail Crossed mirror pair (Kirkpatrick-Baez system) vertically focusing elliptical mirror l v r' v l h r' h horiz. foc. ellip. mirror image OPERATIONAL example: ESRF (bendable flat mirror): f=95 mm and l=90 mm NA = 0.8 Φ crit R = λ/(0.8 sqrt(δ)) = R prac = 5 * R single bounce capillary exp: Φ =. mrad at 0.5 kev 11