Diffractive Refractive Optics Research Articles

Diffractive-refractive optics: Focus size of sagittally focusing X-ray monochromator

A sagittally focusing X-ray crystal monochromator based on diffractive–refractive optics is a four-crystal (+,−,−,+) monochromator with parabolic longitudinal grooves on the crystals surface. Such a monochromator is simultaneously able of focusing and monochromatizing a white beam. The focusing was experimentally proved in earlier papers but the size of the focus was always larger than expected. This discrepancy has not been properly discussed. Such a discussion is presented in this paper.

Diffractive–refractive optics: X-ray focusing splitter

The sagittally focusing X-ray crystal monochromator based on diffractive–refractive optics (IDL—inclined diffraction lens) is the Bartel monochromator with longitudinal parabolic grooves fabricated to its diffraction surface. It is proposed to modify the groove profile in such a way that it will be composed of two laterally displaced parabolic surfaces. This kind of monochromator generates two, slightly laterally displaced focused beams. The pulses prolongation by this kind of optics is also discussed.

Computational imaging using lightweight diffractive-refractive optics.

Diffractive optical elements (DOE) show great promise for imaging optics that are thinner and more lightweight than conventional refractive lenses while preserving their light efficiency. Unfortunately, severe spectral dispersion currently limits the use of DOEs in consumer-level lens design. In this article, we jointly design lightweight diffractive-refractive optics and post-processing algorithms to enable imaging under white light illumination. Using the Fresnel lens as a general platform, we show three phase-plate designs, including a super-thin stacked plate design, a diffractive-refractive-hybrid lens, and a phase coded-aperture lens. Combined with cross-channel deconvolution algorithm, both spherical and chromatic aberrations are corrected. Experimental results indicate that using our computational imaging approach, diffractive-refractive optics is an alternative candidate to build light efficient and thin optics for white light imaging.

X-ray beam splitting design for concurrent imaging at hard X-ray FELs and synchrotron facilities

A new configuration of diffractive–refractive optics for beam splitting is investigated. The set-up can be applied to perform imaging with two beams simultaneously. It brings advantages toward dynamic studies using image guided diffraction or fluorescence spectroscopy. The optimal energy range of operation for the beam-splitter is between 7keV and 24keV, reaching best efficiency at an energy of 10keV. Due to the long focusing distances (several tens of meters) created by the diffractive–refractive optics and the higher refraction efficiency in the softer energy range, the presented set-ups are ideal for hard X-ray FEL sources.

X-ray collimation by crystals with precise parabolic holes based on diffractive–refractive optics

Two crystals with precise parabolic holes were used to demonstrate sagittal beam collimation by means of a diffractive-refractive double-crystal monochromator. A new approach is introduced and beam collimation is demonstrated. Two Si(333) crystals with an asymmetry angle of α = 15° were prepared and arranged in a dispersive position (+,-,-,+). Based on theoretical calculations, this double-crystal set-up should provide tunable beam collimation within an energy range of 6.3-18.8 keV (Θ(B) = 71-18.4°). An experiment study was performed on BM05 at ESRF. Using 8.97 keV energy, the beam profile at various distances was measured. The experimental results are in good agreement with theoretical predictions. Owing to insufficient harmonic suppression, the collimated (333) beam was overlapped by horizontally diverging (444) and (555) beams.

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

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.

Diffractive-refractive optics: X-ray collimator

Diffractive-refractive optics are x-ray focusing monochromators based on the diffraction on profiled crystal surface. Diffraction on longitudinal parabolic groove machined in crystal surface forms a sagittaly focused synchrotron radiation beam. Such kind of monochromator may be realized as a crystal with parabolic hole, where the beam is diffracted on the inner wall of the hole. Two such asymmetrically cut crystals set into antiparallel position, creating a dispersive (+,-,-,+) arrangement, form a sagittaly focusing x-ray monochromator which should be practically aberration-free. The focusing properties of such kind of monochromator are discussed in detail and it is shown for the first time that it can be used not only for focusing but also for creating highly parallel monochromatic beam in the broad region of the Bragg angles. This device with parabolic hole has not been tested experimentally yet.

Diffractive–refractive optics in the Laue case: first experiment

The possibility of sagittally focusing synchrotron radiation using an asymmetric Laue crystal with profiled surfaces has been experimentally demonstrated for the first time. The sample was a Si single crystal with two parallel cylindrical holes of diameter 8 mm. The axes of the holes formed an angle of 7.95 degrees with the (111) diffracting planes and were arranged vertically with respect to the diffracting planes. 15.35 keV synchrotron radiation was diffracted in the space between the holes. The minimum thickness of this Laue crystal was 0.5 mm. The diffracted beam formed an angle of 0.55 degrees with the exit surface. The experiment was performed at beamline BM05 at the ESRF. The length of the beamline was not sufficiently long to detect the focus, but the experiment clearly showed that the diffracted beam was sagittally convergent.

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

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.

Aberrations of Bragg-case diffractive-refractive optics (sagittal focusing)

Aberrations of Bragg-case diffractive-refractive optics (sagittal focusing)

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

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.

Diffractive refractive optics: the possibility of sagittal focusing in Laue-case diffraction.

The sagittal deviation of a Laue-diffracted X-ray beam caused by the inclination of an exit crystal surface with respect to an entrance crystal surface has been studied both theoretically and experimentally. The use of this effect for sagittal focusing of X-ray synchrotron radiation diffracted by a Laue crystal is suggested. The focusing is based on the refraction effect due to the parabolic profile of an exit or/and entrance surface. The crystal is not bent. In order to achieve a reasonable focusing distance, the crystal should be cut asymmetrically. The experiment was performed at beamline BM5 at the ESRF.

Diffractive-refractive optics for high energy astronomy

In a companion paper diffractive-refractive optics components such as Fresnel Zone Plates and their derivatives have been proposed as a basis for telescope systems for X-ray and gamma-ray astronomy with high sensitivity and superb angular resolution. A wide family of configurations is possible and the first paper concentrated on simple systems for gamma-ray energies. The main problems arise from the very long focal lengths involved (~10 6 km) and from chromatic aberration in the focussing system. Ideas are presented here that could in some circumstances allow the focal length to be reduced by many orders of magnitude. In addition it is shown how lenses which are to first order achromatic might be constructed. Finally, the possibility of using similar optical components for X-ray and gamma-ray interferometry is discussed.