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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References

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    [CrossRef]
  2. G. Schneider, �??Cryo X-ray microscopy with high spatial resolution in amplitude and phase contrast,�?? Ultramicroscopy 75, 85-104 (1998).
    [CrossRef] [PubMed]
  3. G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, B. Niemann, �??Phase-contrast X-ray microscopy studies,�?? Optik 97, 181-182 (1994).
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    [CrossRef]
  5. E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barrertt, �??High efficiency multilevel zone plates for keV X-rays,�?? Nature 40, 895-898 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  20. E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, T. Wilhein, and J. Susini, �??Design and fabrication of new optics for X-ray microscopy and material science,�?? J. Phys. IV France 104, 177-183 (2003).
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AIP Conf. Proc. (1)

J. Susini, R. Barret, B. Kaulich, S. Oestreich, and M. Salomé, �??The X-ray microscopy facility at the ESRF: A status report,�?? AIP Conf. Proc. 507, 19-26 (2000).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

T. Wilhein, B. Kaulich, E. Di Fabrizio, F. Romanato, S. Cabrini, and J. Susini, �??Differential interference contrast X-ray microscopy with submicron resolution,�?? Appl. Phys. Lett. 78, 2082-2084 (2001).
[CrossRef]

J. Appl. Phys. (1)

C. Jacobsen, M. R. Howells, �??A technique for projection x-ray lithography using computer-generated holograms,�?? J. Appl. Phys. 71, 2993-3001 (1992).
[CrossRef]

J. of Microscopy (1)

P. J. McMahon, E.D. Barone-Nugent, B.E. Allman, and K.A. Nugent, �??Quantitative phase-amplitude microscopy II: differential interference contrast imaging for biological TEM,�?? J. of Microscopy 206, 204-208 (2002).
[CrossRef]

J. Opt. Soc. Am A (1)

B. Kaulich, T. Wilhein, E. Di Fabrizio, F. Romanato, M. Altissimo, S. Cabrini, B. Fayard, and J. Susini, �??Differential interference contrast X-ray microscopy with twin zone plates,�?? J. Opt. Soc. Am A 19, 797-806 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

C. Preza, D.L. Snyder, J.A. Conchello, �??Theoretical development and experimental evaluation of imaging models for differential-interference-contrast microscopy,�?? J. Opt. Soc. Am. 16, 2185-2199 (1999).
[CrossRef]

J. Phys. IV France (1)

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, T. Wilhein, and J. Susini, �??Design and fabrication of new optics for X-ray microscopy and material science,�?? J. Phys. IV France 104, 177-183 (2003).
[CrossRef]

Microelectronic Eng. (1)

D. Cojoc, E Di Fabrizio, L. Businaro, S.Cabrini, F. Romanato, L. Vaccari, M. Altissimo, �??Design and fabrication of diffractive optical elements for optical tweezer arrays by means of e-beam lithography,�?? Microelectronic Eng. 61-62, 963-969 (2002).
[CrossRef]

Nature (1)

E. Di Fabrizio, F. Romanato, M. Gentili, S. Cabrini, B. Kaulich, J. Susini, R. Barrertt, �??High efficiency multilevel zone plates for keV X-rays,�?? Nature 40, 895-898 (1999).
[CrossRef]

Opt. Commun. (1)

A.A Firsov, A.A. Svintsov, S.I. Zaitsev, A. Erko, A, V.V. Aristov, �??The first synthetic X-ray hologram: results,�?? Opt. Commun 202, 55-59 (2002).
[CrossRef]

Optik (1)

G. Schmahl, D. Rudolph, G. Schneider, P. Guttmann, B. Niemann, �??Phase-contrast X-ray microscopy studies,�?? Optik 97, 181-182 (1994).

Physica (1)

F. Zernike, �??Phase contrast, a new method for the microscopic observation of transparent objects,�?? Physica 9, 686-698, (1942).
[CrossRef]

Rev. Metall. (1)

G. Normarski, and A.R. Weill, �??Application à la métallographie des methods interférentielles à deux ondes polarisées ,�?? Rev. Metall. 2, 121-128 (1955).

SPIE Proc. (1)

E. Di Fabrizio, D. Cojoc, S. Cabrini, B. Kaulich, T. Wilhein, J. Susini, �??Novel diffractive optics for x-ray beam shaping,�?? SPIE Proc. 4783, 105-114 (2002).
[CrossRef]

Surf. Sci. (1)

P. Facci, D. Alliata, L. Andolfi, B. Schnyder, R. Koetz, "Formation and characterization of protein monolayers on oxygen-exposing surfaces by multiple-step self-chemisorption," Surf. Sci. 504C, 282-292 (2002).
[CrossRef]

Ultramicroscopy (1)

G. Schneider, �??Cryo X-ray microscopy with high spatial resolution in amplitude and phase contrast,�?? Ultramicroscopy 75, 85-104 (1998).
[CrossRef] [PubMed]

Other (3)

D. Attwood, Soft x-rays and extreme ultraviolet radiation; principles and applications, (Cambridge University Press, 1999).
[CrossRef]

A. G. Michette, Optical Systems for Soft X-rays, (Plenum Press, New York, 1986).
[CrossRef]

Applied Optics Research, �??GLAD 4.5 Theoretical Description,�?? 4.1-5.15 (AOR 1997).

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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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