Modelling phase imperfections in compound refractive lenses

Celestre, Rafael; Berujon, Sébastien; Roth, Thomas; Río, Manuel Sánchez del; Barrett, R.

doi:10.1107/s1600577519017235

Cited by 13 publications

(14 citation statements)

References 58 publications

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“…Zernike polynomial fitting is a useful tool in diagnosing visible optics wave aberrations over a circular or annular aperture. Zernike polynomials expansion is used over the wavefront error map in quantifying optics aberrations present in X-ray optics (Celestre et al, 2020;Seiboth et al, 2016;Zhou et al, 2018). An imperfect optics produces blurred images of a source, and the performance improvement of optics by aberration compensation schemes can be expressed in terms of reduction in the coefficient of classical primary (Seidel) optics aberrations closely represented by low-order Zernike polynomials.…”

Section: Introductionmentioning

confidence: 99%

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures

Dhamgaye

Laundy

Baldock

et al. 2020

J Synchrotron Radiat

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A refractive phase corrector optics is proposed for the compensation of fabrication error of X-ray optical elements. Here, at-wavelength wavefront measurements of the focused X-ray beam by knife-edge imaging technique, the design of a three-dimensional corrector plate, its fabrication by 3D printing, and use of a corrector to compensate for X-ray lens figure errors are presented. A rotationally invariant corrector was manufactured in the polymer IP-STM using additive manufacturing based on the two-photon polymerization technique. The fabricated corrector was characterized at the B16 Test beamline, Diamond Light Source, UK, showing a reduction in r.m.s. wavefront error of a Be compound refractive Lens (CRL) by a factor of six. The r.m.s. wavefront error is a figure of merit for the wavefront quality but, for X-ray lenses, with significant X-ray absorption, a form of the r.m.s. error with weighting proportional to the transmitted X-ray intensity has been proposed. The knife-edge imaging wavefront-sensing technique was adapted to measure rotationally variant wavefront errors from two different sets of Be CRL consisting of 98 and 24 lenses. The optical aberrations were then quantified using a Zernike polynomial expansion of the 2D wavefront error. The compensation by a rotationally invariant corrector plate was partial as the Be CRL wavefront error distribution was found to vary with polar angle indicating the presence of non-spherical aberration terms. A wavefront correction plate with rotationally anisotropic thickness is proposed to compensate for anisotropy in order to achieve good focusing by CRLs at beamlines operating at diffraction-limited storage rings.

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Section: Introductionmentioning

confidence: 99%

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures

Dhamgaye

Laundy

Baldock

et al. 2020

J Synchrotron Radiat

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“…However, by translating the phase plate along the optical axis by a certain distance, one can compensate these effects and the phase plate can correct over a broad energy range . Instead of measuring the wavefield for a specific lens combination, one can also pursue the approach to characterize the thickness profile of individual lens elements (Celestre et al, 2020). This allows to numerically calculate any lens stack from the measured single lenses at arbitrary photon energies and to retrieve the potential wavefront deformation of this lens configuration numerically.…”

Section: Refractive Phase Platesmentioning

confidence: 99%

Hard X-ray wavefront correction via refractive phase plates made by additive and subtractive fabrication techniques

Seiboth

Brückner

Kahnt

et al. 2020

J Synchrotron Radiat

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Modern subtractive and additive manufacturing techniques present new avenues for X-ray optics with complex shapes and patterns. Refractive phase plates acting as glasses for X-ray optics have been fabricated, and spherical aberration in refractive X-ray lenses made from beryllium has been successfully corrected. A diamond phase plate made by femtosecond laser ablation was found to improve the Strehl ratio of a lens stack with a numerical aperture (NA) of 0.88 × 10−3 at 8.2 keV from 0.1 to 0.7. A polymer phase plate made by additive printing achieved an increase in the Strehl ratio of a lens stack at 35 keV with NA of 0.18 × 10−3 from 0.15 to 0.89, demonstrating diffraction-limited nanofocusing at high X-ray energies.

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“…6, the single lens model, accounts for the absorption (first exponential) and phase shift (second exponential) from a single X-ray lenslet. Stacked lenses can be simulated either by a single-lens-equivalent representation or by using multi-slice-like techniques, where the X-ray beam is propagated using free-space propagators in between the optical elements [ 15 ].…”

Section: The Ideal Crlmentioning

confidence: 99%

“…a model that could parametrise all sources of deviations from the parabolic shape. To circumvent that and to accurately model phase imperfection in compound refractive lenses, metrology data can also be used for optically imperfect X-ray lenses [ 15,35 ]. Fig.…”

Section: Metrology Datamentioning

confidence: 99%

“…8 shows three examples of lens figure errors from (a)-(c) a commercial pressed Beryllium lens, (d)-(f) an in-house pressed Aluminium lens and a (g)-(h) in-development laser-ablated Diamond lens from a commercial partner. The figure errors were measured with at-wavelength metrology and can be directly plugged into simulations as they describe the accumulated errors in projection approximation of both front and back focusing surfaces [ 15,36,37 ]. The effect on a coherent X-ray of optical imperfections from metrology data is shown in Fig.…”

Section: Metrology Datamentioning

confidence: 99%

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Recent developments in X-ray lens modelling with SRW

Celestre

Chubar

Roth

et al. 2020

Advances in Computational Methods for X-Ray Optics V

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The advent of 4 th generation high-energy synchrotron facilities (ESRF-EBS and the planned APS-U, PETRA-IV and SPring-8 II) and free-electron lasers (Eu-XFEL and LCLS-II) allied with the recent demonstration of highquality free-form refractive optics for beam shaping and optical correction have revived interest in compound refractive lenses (CRLs) as optics for beam transport, probe formation in X-ray micro-and nano-analysis as well as for imaging applications. Ideal CRLs have long been made available in the 'Synchrotron Radiation Workshop' (SRW), however, the current context requires more sophisticated modelling of X-ray lenses. In this work, we revisit the already implemented wave-optics model for an ideal X-ray lens in the projection approximation and propose modifications to it as to allow more degrees of freedom to both the front and back surfaces independently, which enables to reproduce misalignments and manufacturing errors commonly found in X-ray lenses. For the cases where simply tilting and transversely offsetting the parabolic sections of a CRL is not enough, we present the possibility of generating the figure errors by using Zernike and Legendre polynomials or directly adding metrology data to the lenses. We present the effects of each new degree of freedom by calculating their impact on point spread function and the beam caustics.

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Modelling phase imperfections in compound refractive lenses

Cited by 13 publications

References 58 publications

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures

Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures

Hard X-ray wavefront correction via refractive phase plates made by additive and subtractive fabrication techniques

Recent developments in X-ray lens modelling with SRW

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