Influence of crystal surface roughness on the angular spread of x-ray diffracted beam

Hrdá, J.; Hrdý, J.; Hignette, O.; Hoszowska, J.

doi:10.1117/12.505553

Cited by 3 publications

(4 citation statements)

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“…This approach is obviously justified when the size of the unevenness structures is much larger than the wavelength. Nevertheless, as was shown in [9] and will be shown later, this theoretical model, together with the surface profile measurement (e.g. by alpha-step) can predict the spread of the diffracted beam.…”

Section: Introductionmentioning

confidence: 69%

“…Then the integration was performed over all these deviations by using MATLAB and by taking into account the distribution function. In [9] all calculations were performed for white impinging beam with the divergence of 10 µrad × 10 µrad and for the diffraction on a Si(111) single crystal. It was shown that when the diffracted beam forms small angle with the surface (e.g.…”

Section: Calculation and Measurement Of The Spread Of Diffracted Beammentioning

confidence: 99%

“…The experimental arrangement is shown in figure 2. The crystals were the same as in [9], i.e. silicon single crystals with the asymmetry angle α = 11.25˚.…”

Section: Calculation and Measurement Of The Spread Of Diffracted Beammentioning

confidence: 99%

“…Crystals are the same as in the previous experiment [9] but the diffraction surfaces are re-etched (crystal which is only etched) and re-polished (MC polished crystal). Now the surface structure after etching is more pronounced (which, at the same time, somewhat complicates the comparison with the previous experiment [9]). Figure 3 shows the photographs of both diffracting surfaces.…”

Section: A224mentioning

confidence: 99%

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Influence of the crystal-surface unevenness on the angular spread of an x-ray diffracted beam

Hrdá¹,

Potlovskiy²,

Hrdý³

et al. 2005

J. Phys. D: Appl. Phys.

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One of the factors influencing the focus size in diffractive–refractive optics is the quality of diffracting surface. If the surface is uneven, as it is when the silicon crystal surface is only etched, then the diffraction at each point of the surface is a combination of an asymmetric and inclined diffraction (general asymmetric diffraction). This somewhat deviates and spreads the diffracted beam. The integration over the surface hit by an incident beam gives the angular spread of the diffracted beam. It is shown theoretically that in some cases (highly asymmetric, highly inclined cut) the etched surface may create the spread of the diffracted beam such that it causes a significant broadening of the focus. In this case a mechanical–chemical polishing is necessary. This has been verified by us earlier in a preliminary experiment with synchrotron radiation. In this work the new experiment with the same crystals is performed using double crystal (+, −) arrangement and a laboratory x-ray source (CuKα radiation). We compared two samples; one of them is mechanically–chemically (MC) polished and thus the diffracting surface is almost perfect; the other is only etched. This experiment allows a better comparison of the result with the theory. The difference between the measured rocking curve widths for the etched and MC polished crystals (10″) roughly agrees with theory (7″), which supports the correctness of the theoretical approach.

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Section: Introductionmentioning

confidence: 69%

Section: Calculation and Measurement Of The Spread Of Diffracted Beammentioning

confidence: 99%

“…The experimental arrangement is shown in figure 2. The crystals were the same as in [9], i.e. silicon single crystals with the asymmetry angle α = 11.25˚.…”

Section: Calculation and Measurement Of The Spread Of Diffracted Beammentioning

confidence: 99%

Section: A224mentioning

confidence: 99%

See 2 more Smart Citations

Influence of the crystal-surface unevenness on the angular spread of an x-ray diffracted beam

Hrdá¹,

Potlovskiy²,

Hrdý³

et al. 2005

J. Phys. D: Appl. Phys.

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Aberrations of diffractive–refractive optics: Bragg-case sagittal focusing of multiple parabolic elements

Hrdý¹,

Kuběna²,

Mikulı́k³

2005

J. Phys. D: Appl. Phys.

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The diffractive–refractive optical device consisting of four crystals in (+, −, −, +) setting with longitudinal parabolic grooves has a geometrical aberration which influences the achievable focus size. This aberration is discussed analytically by using a new, more precise formula for the calculation of focusing distance, which respects the finite distance between optical elements. The calculation of the intensity distribution surrounding the focus is illustrated by a ray-tracing method based on the dynamical theory of diffraction. It demonstrates an achievable focus size. Finally we discuss that this aberration may be suppressed by the slight narrowing of the groove profile. In particular, the parameter a in the equation of parabola has to slightly grow with x. A practical application may require an ultra-precise fabrication of the grooves.

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Diffractive–refractive optics: low-aberration Bragg-case focusing by precise parabolic surfaces

Oberta

Mikulı́k

Kittler

et al. 2009

J Synchrotron Radiat

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Based on analytical formulae calculations and ray-tracing simulations a low-aberration focal spot with a high demagnification ratio was predicted for a diffractive-refractive crystal optics device with parabolic surfaces. Two Si(111) crystals with two precise parabolic-shaped grooves have been prepared and arranged in a dispersive position (+,-,-,+) with high asymmetry. Experimental testing of the device at beamline BM05 at the ESRF provided a focal spot size of 38.25 microm at a focal distance of 1.4 m for 7.31 keV. This is the first experiment with a parabolic-shaped groove; all previous experiments were performed with circular grooves which introduced extreme aberration broadening of the focal spot. The calculated and simulated focal size was 10.8 microm at a distance of 1.1 m at 7.31 keV. It is assumed that the difference between the measured and calculated/simulated focal spot size and focal distance is due to insufficient surface quality and to alignment imperfection.

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Influence of crystal surface roughness on the angular spread of x-ray diffracted beam

Cited by 3 publications

References 0 publications

Influence of the crystal-surface unevenness on the angular spread of an x-ray diffracted beam

Influence of the crystal-surface unevenness on the angular spread of an x-ray diffracted beam

Aberrations of diffractive–refractive optics: Bragg-case sagittal focusing of multiple parabolic elements

Diffractive–refractive optics: low-aberration Bragg-case focusing by precise parabolic surfaces

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