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

Abstract

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.

Polished diamond X-ray lenses

“…The spherical aberrations of the diamond lenses, here accentuated by post-polishing, are also commonly found in commercial Be lenses as presented in Figs. 8 and 9 (bottom row) and extensively reported (Celestre et al, 2020a;Dhamgaye et al, 2020;Seiboth et al, 2020). The reason here is not a polishing process but imperfections in the plastic-forming process used for the lens manufacture or in the manufacturing of the paraboloidal punches on a lathe.…”

“…9 (middle). This is particularly amenable to reduction of the wavefront aberrations via the use of azimuthally symmetric refractive phase plates (Seiboth et al, 2020;Dhamgaye et al, 2020). Fig.…”

Precise wavefront characterization of x-ray optical elements using a laboratory source

“…Alternatively, if the wavefront aberrations are small enough they can be corrected using a phase plate. In the Xray regime, phase correcting elements have been successfully implemented to improve wavefronts of compound refractive lenses [42][43][44] and Kirkpatrick-Baez focusing mirrors [45,46]. The same principle can be used to reduce phase aberrations in MLLs.…”

“…X-ray phase correctors often utilize refraction and can be manufactured using additive or subtractive approaches [47]. A subtractive approach was demonstrated using laser ablation [48] while additive correctors can be made by 3D printing [42][43][44]. The advantage of 3D printing is the high degree of control of the printing parameters and the freedom to print almost any arbitrary shape.…”

Alvarez varifocal X-ray lens

“…In the case of Kirkpatrick-Baez (KB) mirror systems [9] which consist of two elliptical mirrors, independently focusing in horizontal and vertical directions, astigmatism can occur due to a mispositioning of either mirror along the optical axis or by an error in the setting of the pitch angle of either mirror. In the case of compound X-ray refractive lens (CRL), astigmatism may be introduced by the fabrication process causing error in the lens thickness, mispositioning of individual lenses from the axis, or angular misalignment of the stack of lenses [10]. Defocus aberration can be corrected by translating the sample to the correct focal plane but in practice, this may be difficult due to the constraints of complex sample environments.…”