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

MetadataDetails
Publication Date2020-10-19
JournalJournal of Synchrotron Radiation
AuthorsVishal Dhamgaye, David Laundy, Sara J. Baldock, Thomas Moxham, Kawal Sawhney
InstitutionsRaja Ramanna Centre for Advanced Technology, Diamond Light Source
Citations16
AnalysisFull AI Review Included

This research details the successful use of a custom-designed, 3D printed refractive phase plate to compensate for fabrication-induced wavefront errors in Beryllium Compound Refractive Lenses (Be CRLs).

  • Core Achievement: A rotationally invariant polymer corrector plate, fabricated via two-photon polymerization, reduced the Root Mean Square (RMS) wavefront error of a 98-lens Be CRL stack (CRL1) by a factor of six.
  • Performance Metric: RMS wavefront error decreased from 14.4 pm (before correction) to 2.4 pm (after correction).
  • Focus Improvement: The correction significantly improved the focused beam profile, reducing the vertical focus size (FWHM) from 2.3 ”m to 0.9 ”m.
  • Methodology: Wavefront errors were measured at-wavelength using an adapted knife-edge imaging technique, allowing for the quantification of 2D rotationally variant error maps.
  • Aberration Correction: The rotationally invariant corrector successfully compensated for lower- and higher-order spherical aberrations (Zernike terms Z11, Z22, Z37, etc.).
  • Future Direction: The study identified significant remaining non-spherical aberrations (astigmatism, coma) and proposed the design of a rotationally anisotropic (variant) corrector plate to achieve near-perfect, diffraction-limited focusing (RMS error < 0.07λ).
ParameterValueUnitContext
RMS Wavefront Error (Before Correction)14.4pmBe CRL1 (98 lenses), average error
RMS Wavefront Error (After Correction)2.4pmBe CRL1 (98 lenses), measured
RMS Wavefront Error Reduction84%Achieved by rotationally invariant corrector
Vertical Focus Size (Before Correction)2.3”mFWHM, aberrated focus
Vertical Focus Size (After Correction)0.9”mFWHM, corrected focus
Corrector MaterialIP-S Polymer-Manufactured via two-photon polymerization
Corrector Surface Finish~20nmSuitable for normal-incidence X-ray optics
Corrector Transmission~99%Measured at 15 keV
X-ray Energy (Characterization)15keVMonochromatic beam, Si(111)
CRL1 Lens Count98-Be bi-concave parabolic lenses
CRL Radius of Curvature (R)200”mAt the apex of the Be lenses
Optical Path Difference (OPD) per 10 ”m IP-S11.74pmCalculated phase advance
Target RMS Error (Proposed Anisotropic Corrector)< 0.07λ-Goal for full aberration compensation

The experiment involved three primary stages: wavefront sensing, corrector design and fabrication, and performance validation.

  • Setup: Performed at the Diamond Light Source B16 Test beamline using a Si(111) double-crystal monochromator (15 keV).
  • Technique Adaptation: The knife-edge imaging wavefront-sensing technique was adapted to measure full 2D rotationally variant wavefront errors. This involved rotating the knife-edge at various polar angles (e.g., 45°, 90°, 270°) to scan the intensity across the focal plane.
  • Data Processing: The measured 2D wavefront error maps were fitted using Zernike polynomial expansion (Noll notation) up to order n = 16 to quantify specific aberrations (e.g., spherical aberration Z11, astigmatism Z5/Z6).
  • Design Input: An average, rotationally invariant wavefront error profile was calculated from the polar-angle-resolved measurements to serve as the design basis for the first corrector plate.
  • Design Conversion: The required optical path length difference (Δw) was converted into a physical thickness profile (t) for the IP-S polymer, based on the refractive decrement (ÎŽ) of the material.
  • 3D Printing: Fabrication utilized a Nanoscribe Photonic Professional GT2 system employing the two-photon polymerization technique.
  • Process Parameters: IP-S resist was drop-cast onto ITO-coated glass. Printing was done in dip-in lithography mode using a femtosecond Ti-sapphire laser (800 nm) focused by a 25x objective.
  • Development: The patterned resist was developed in PGMEA for 20 min, rinsed in IPA, and dried using N2-enriched air.
  • Alignment: The 3D printed corrector was placed upstream of the Be CRLs and precisely aligned laterally to the lens optical axis to minimize the measured RMS wavefront error.
  • Focus Measurement: Focus profiles were measured before and after correction in both vertical and horizontal directions to quantify the reduction in FWHM focus size.
  • Error Quantification: The RMS wavefront error was calculated using a modified formula that weights the error by the transmitted X-ray intensity, providing a figure of merit relevant for X-ray lenses with significant absorption.
  • Anisotropic Proposal: Based on the remaining uncorrected astigmatism and coma terms, a design for a second, rotationally variant corrector plate was proposed to achieve complete compensation.

The technology developed for high-precision wavefront correction using 3D printed optics is critical for advanced X-ray science and micro-fabrication industries.

  • Synchrotron and XFEL Facilities: Essential for achieving diffraction-limited focusing at fourth-generation light sources (DLSRs and XFELs), maximizing flux density for experiments like coherent diffraction imaging and spectroscopy.
  • High-Resolution X-ray Microscopy: Enables the creation of pseudo-perfect X-ray lenses, improving the resolution and image quality of nano-focusing microscopes used in materials science and biology.
  • Custom Micro-Optics Manufacturing: The use of two-photon polymerization (Nanoscribe) allows for the rapid, high-precision fabrication of arbitrary 3D refractive structures, useful for custom X-ray optical elements (e.g., phase plates, diffractive optics, and specialized lenses).
  • In-Situ Optics Metrology: The adapted knife-edge imaging technique provides a robust, at-wavelength method for quality control and diagnosis of fabrication errors in mass-produced X-ray optics (e.g., Be, Al, or Si lenses).
  • Adaptive X-ray Optics: The framework supports the development of complex, rotationally anisotropic correctors needed to compensate for non-spherical aberrations in high-numerical aperture X-ray systems.
View Original 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-S TM 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.