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Diffractive optical elements for differential interference contrast x-ray microscopy

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Abstract

In this paper we introduce phase diffractive optical elements (DOEs) that beside simple focusing, can perform new optical functions in the range of x-rays. In particular, the intensity of the wavefront can be distributed with almost complete freedom. We calculated and fabricated high resolution DOEs that can focus a monochromatic x-ray beam into multiple spots displaced in a single or two planes along the optical axis or can shape the beam into a desired continuous geometrical pattern. The possibility to introduce a specified phase shift between the generated spots, which can increase the image contrast, is demonstrated by preliminary results obtained from computer simulations and experiments performed in visible light. The functionality of the DOEs has been tested successfully in full-field differential interference contrast (DIC) x-ray microscopy at the ID21 beamline of the European Synchrotron Radiation Facility (ESRF) operated at 4 keV photon energy.

©2003 Optical Society of America

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Figures (10)

Fig. 1.
Fig. 1. (a) The phase function of a one dimensional object described in 250 pixels; (b) Intensity distributions obtained with the same shear Δx=2 but different bias values: Δθ=0 - first line, Δθ=π/4 - second line, and Δθ=3π/4 - third line; for clarity, the second line is offset by -2 and the third by -4
Fig. 2.
Fig. 2. DOEs producing the same beam shearing (1 mm) but different bias: a) Δθ=0, b) Δθ=π
Fig 3.
Fig 3. The phase distributions along the x axis obtained in the focal plane for the DOEs depicted in Fig. 2; (a) the phase difference between the two points pointed out by circles is Δθ=0 (b) the phase difference between the two points pointed out by circles is Δθ=π
Fig.4.
Fig.4. The experimental interference patterns obtained after the focal plane of the DOEs; the left pattern corresponding to the DOE with the bias Δθ=0 is shifted with half of a fringe with respect to the right pattern which corresponds to the DOE with bias retardation is Δθ=π
Fig. 5.
Fig. 5. Optical functions and details of two phase DOEs to generate two spots (shear Δx=200 nm, bias Δθ=0) in the same focal plane at z=50 mm from the DOE (a), and two axial spots separated by 1 mm along the optical axis at z1=49.5 mm and z2=50.5 mm from the DOE (b)
Fig. 6.
Fig. 6. SEM pictures showing an overview (a) of the DOE that generates two spots and details of the outermost area (b) whose resolution is 100 nm
Fig. 7.
Fig. 7. Optical setup of the full-field imaging microscope
Fig. 8.
Fig. 8. Images obtained for PMMA square shaped and ring shaped test patterns obtained in transmission x-ray microscopy by using standard ZP - (a),(d) and phase DOEs for DIC - (b), (c), (e), and (f) (see the text for the description of the images).
Fig. 9.
Fig. 9. Imaging of an array of yeast cells in full field DIC with a two axial spot phase DOE as objective
Fig. 10.
Fig. 10. X-ray beam shaping: magnified logo OK! image on CCD the detector

Equations (9)

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i ( x , y ) = f ( x 0 , y 0 ) h ( x x 0 , y y 0 ) d x 0 d y 0 2
h ( x , y ) = 0.5 δ ( x Δx 2 , y ) exp ( jΔθ ) + 0.5 δ ( x + Δx 2 , y ) exp ( jΔθ )
i ( x , y ) = ct sin 2 ( ϕ ( x Δx 2 ) ϕ ( x + Δx 2 ) + Δθ )
i ( x , y ) = ct sin 2 ( Δx ϕ ( x , y ) x + Δθ )
W out ( x , y , 0 ) = t ( x , y ) W in ( x , y , 0 )
W in ( x , y ) = W out ( x , y )
Φ ( x , y ) = { arg [ W out ( x , y , 0 ) ] arg [ W in ( x , y , 0 ) ] } 2 π
W in ( x e , y e , 0 ) = s a s cos ψ s , e exp j k r s , e r s , e , W out ( x e , y e , 0 ) = g a g cos ψ g , e exp j ( k r g , e + φ g ) r g , e
d ( x , y ) = Φ ( x , y ) λ 2 π δ ( λ )
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