A compound refractive lens for focusing high-energy X-rays

Snigirev, A.; Kohn, V. G.; Snigireva, I.; Lengeler, B.

doi:10.1038/384049a0

Cited by 1,018 publications

(583 citation statements)

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“…The introduction of compound refractive lenses (CRLs) (Snigirev et al, 1996;Vaughan et al, 2011) has extended fullfield X-ray microscopy to X-ray energies above 15 keV (Lengeler et al, 1999). With a numerical aperture of order 1 mrad, CRL-based objectives are well matched to the high brilliance of synchrotron beams.…”

Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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The fractional Fourier transform (FrFT) is introduced as a tool for numerical simulations of X-ray wavefront propagation. By removing the strict sampling requirements encountered in typical Fourier optics, simulations using the FrFT can be carried out with much decreased detail, allowing, for example, on-line simulation during experiments. Moreover, the additive index property of the FrFT allows the propagation through multiple optical components to be simulated in a single step, which is particularly useful for compound refractive lenses (CRLs). It is shown that it is possible to model the attenuation from the entire CRL using one or two effective apertures without loss of accuracy, greatly accelerating simulations involving CRLs. To demonstrate the applicability and accuracy of the FrFT, the imaging resolution of a CRL-based imaging system is estimated, and the FrFT approach is shown to be significantly more precise than comparable approaches using geometrical optics. Secondly, it is shown that extensive FrFT simulations of complex systems involving coherence and/or non-monochromatic sources can be carried out in minutes. Specifically, the chromatic aberrations as a function of source bandwidth are estimated, and it is found that the geometric optics greatly overestimates the aberration for energy bandwidths of around 1%.

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Section: Introductionmentioning

confidence: 99%

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

Pedersen

Simons

Detlefs

et al. 2018

J Synchrotron Radiat

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“…9 for photon energies >10 keV the lens aperture ε almost matches the size of the beam cone at ELETTRA bending magnets Figure 10 shows the transmission functions obtained from ray-tracing calculations for such a lens for different photon energies in the range 8-18 keV. With one exception (dotted curve), the calculations were made with an absorbing wire of diameter 1.1Y 0 [for Y 0 see Eqn (12)] on the optical axis positioned in front of the lens. Such a device will efficiently block photons of higher photon energy, which pass the lens essentially without deviation, and it will therefore significantly reduce the tails.…”

Section: Resultsmentioning

confidence: 99%

A simple x‐ray monochromator based on an alligator lens

Jark

2004

X-Ray Spectrometry

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Alligator lenses, i.e. two inclined arrays of sawteeth or prisms, which face each other, can focus x-rays with photon energies >4 keV. The inclination angle can be changed easily, and thus either the focal length for fixed photon energy or the photon energy in a fixed slit position can be varied. The material distribution in this condition is approximately parabolic along the teeth axis, hence it is of the shape required for aberration-free focusing at a given photon energy. As the refractive index varies significantly with photon energy in the x-ray range, these lenses suffer from chromatic aberrations, if illuminated with white x-rays. In combination with a slit such a lens can therefore be used as an easily insertable inline monochromator. In this work, a simple universal function for the dependence of the transmission on the photon energy was derived for this application. The required tolerances for the shape of the sawteeth are found to be compatible with standard workshop machining procedures. A laboratory-made lens of Plexiglas is shown to increase the flux density in a laboratory setup by a factor of 3, i.e. 50% of the expected result for a perfect lens. The discrepancy can be consistently ascribed to macroscopic defects of the sawteeth tips. Expectations for the performance of these lenses as monochromators at synchrotron radiation sources are presented. A single Be alligator lens is expected to provide tuning between at least 8 keV and 20 keV photon energy with a bandpass of 6%, sufficient for XRF and SAXS experiments. Consequently, such a lens pair is all that is needed for building simple synchrotron radiation beamlines for special x-ray experiments.

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“…Nevertheless we would like to mention that for normal incidence transmission optics, the phase shift is proportional to the thickness of the material of the optical component. This effect is used for the manufacture of zone plates and refractive lenses for X-rays [9]. Therefore, one of the most straightforward implementations of the phase correction derived by eq.…”

Section: Formal Methods To Compute Phase Correctionmentioning

confidence: 99%

Phase analysis and focusing of synchrotron radiation

Chubar

Elleaume

Snigirev

1999

Nuclear Instruments and Methods in Physics Research Section A:

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High accuracy calculations of synchrotron radiation (SR) emitted by a relativistic electron show that the phase of the frequency domain electric field of SR differs from the phase of radiation of a virtual point source. These differences may result in the reduction of focusing efficiency of diffraction-limited SR, if the focusing is performed by conventional optical components optimised for point sources. We show that by applying a phase correction locally, one may transform the phase of SR electric field at a desired polarisation to that of a point source. Such corrections are computed for undulator radiation (planar and helical) and bending magnet radiation (central part and edges). The focusing of the corrected SR wavefront can result in the increase of peak intensity in the focused spot up to several times compared to the focusing without correction. For non-diffraction-limited radiation, the effect of the phase corrections is reduced. Due to this reason, the use of the proposed phase corrections in existing electron storage rings is essentially of interest in the photon energy range from infrared to VUV. All numerical calculations discussed in the paper were performed by means of the computer code SRW 2 . PACS: 41.60.Ap (synchrotron radiation); 42.25.-p (wave optics); 42.30.Va (image forming and processing).

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A compound refractive lens for focusing high-energy X-rays

Cited by 1,018 publications

References 4 publications

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

The fractional Fourier transform as a simulation tool for lens-based X-ray microscopy

A simple x‐ray monochromator based on an alligator lens

Phase analysis and focusing of synchrotron radiation

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