it s refraction, it s diffraction, it s a kinoform lens - new concepts in focusing x-rays detlef smilgies chess

Transcription

1 it s refraction, it s diffraction, it s a kinoform lens - new concepts in focusing x-rays detlef smilgies chess

2 what is a lens? incoherent source > geometric optics > refraction Snell s law > lensmaker equation 1/f = (n-1) (1/R 1 + 1/R 2 ) coherent source > wave optics > refraction > phase shift along optical paths an ideal lens converts a plane wave into a spherical wave preserving the coherence

3 transmission optics for x-rays (all values for 10 kev photons) refraction is small: Re(n)=1-δ with δ= refractive power: f=r/2 (n-1) = R/2δ absorption is high: absorption lengths 1µm 10µm complex refractive index: n=1-δ+iβ figure of merit: β/δ = 10-5 (Li,Be) 10-3 (C,Al,Si) 10-1 (Au,Pt,W) dilemma: smaller f > smaller R more flux > larger aperture > larger R

4 lens-like focusing devices refractive limit diffractive limit compound refractive lens f=r/2nδ Fresnel zone plate

5 diffractive optics: Fresnel zones plane wave λ circles of constant phase shift from point P P comment by Don Bilderback: if you replace the opaque sections by a transparent phase-shifting material to get a phase shift of Φ=π, you get a phase zone plate with an efficiency close to 100% if only partial waves contributing positive amplitudes at P are allowed to interfere: constructive interference > we converted a plane wave coherently into a spherical wave

6 limitations compound refractive lens small focusing power: multiple lenses needed small aperture Fresnel diffractive lens smallest feature size limits focal spot size limits also aperture x-ray transmission through absorber: E >20 kev

7 kinoform lenses Ken Evans-Lutterodt, BNL works if phase difference air to silicon equals 2π how to enhance aperture while reducing absorption in refractive lens

8 phase difference wave in air: exp(i k x) wave in silicon: exp(i n k x) n = 1-δ, δ = 3x10-6 for 1 Å radiation calculation: Φ = k x n k x = δ k x = 2π δ/λ x numbers: Φ=2π means x = λ/δ = 30 µm -> we can use multiples of 30 µm, if needed

9 general implication for refractive lenses: maximum phase error we have seen: x=30 µm yields 2π phase shift preserving wave front in multiple lens arrays: -> total phase shift < π/10 -> total roughness < 1.5 µm compound lens: -> for 100 lenses and random roughness σ: σ tot = sqrt(100) σ = 10 σ -> max roughness of single lens surface: 0.15 µm while diameter is typically 1 mm!

10 the Brookhaven lens Ken Evans-Lutterodt & coworkers single lens: 13 kev (X13B) f=15 cm aperture: 100µmV x 10µmH focal size achieved -> 1µm FWHM theoretical limit: -> 0.2 µm FWHM Ken Evans-Lutterodt et al.: Single-element elliptical hard x-ray micro-optics, Optics Express (2003) 11,

11 added: the Russian lens Aristov et al. (thanks for the ref. to Alexander Kazimirov) Aristov et al., APL 77, 4058 (2000).

12 Karlsruhe/ESRF collaboration Nazmov/Snigirev focal spot 55 kev and 2m, gain 15 V. Nazmov et al: Kinoform X-ray lens creation in polymer materials by deep X-ray lithography, Nuclear Instruments and Methods in Physics Research B 217 (2004)

13 variations on a theme Werner Jark et al., ELLETRA

14 another approach: discrete approximation of a refractive lens Cederström and coworkers jaw-type lens

15 the Elletra project Werner Jark & coworkers Werner Jark et al.: Focusing X-rays with simple arrays of prismlike structures, J. Synchrotron Rad. (2004). 11,

16 the Elletra project Werner Jark & coworkers aperture 0.5mm, depth 0.4mm, f=2m spot size 2.8µm, period 20.4µm. gain 8keV resist thickness 1mm, etched to 0.4mm

17 the Swedish concept Björn Cederström & coworkers Björn Cederström et al.: Generalized prism-array lenses for hard X-rays, J. Synchrotron Rad. (2005). 12,

18 the Swedish concept Björn Cederström & coworkers Intensity in focal plane measured with knife-edge scan. E = 13.4 kev, F = 55 cm, intensity gain = 39, FWHM = 1.4 mm, the fraction of power in the central peak is 41%.

19 summary refractive-diffractive optics

20 take-home messages lots of recent developments in refractive/diffractive optics various approaches to overcome the 1/f versus aperture dilemma in one or a few lenses evolution of concepts from Fresnel s classic kinoform lens to generalized prism arrays