Correction of the X-ray wavefront from compound refractive lenses using 3D printed refractive structures
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2020-10-19 |
| Journal | Journal of Synchrotron Radiation |
| Authors | Vishal Dhamgaye, David Laundy, Sara J. Baldock, Thomas Moxham, Kawal Sawhney |
| Institutions | Raja Ramanna Centre for Advanced Technology, Diamond Light Source |
| Citations | 16 |
| Analysis | Full AI Review Included |
Executive Summary
Section titled âExecutive SummaryâThis 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).
Technical Specifications
Section titled âTechnical Specificationsâ| Parameter | Value | Unit | Context |
|---|---|---|---|
| RMS Wavefront Error (Before Correction) | 14.4 | pm | Be CRL1 (98 lenses), average error |
| RMS Wavefront Error (After Correction) | 2.4 | pm | Be CRL1 (98 lenses), measured |
| RMS Wavefront Error Reduction | 84 | % | Achieved by rotationally invariant corrector |
| Vertical Focus Size (Before Correction) | 2.3 | ”m | FWHM, aberrated focus |
| Vertical Focus Size (After Correction) | 0.9 | ”m | FWHM, corrected focus |
| Corrector Material | IP-S Polymer | - | Manufactured via two-photon polymerization |
| Corrector Surface Finish | ~20 | nm | Suitable for normal-incidence X-ray optics |
| Corrector Transmission | ~99 | % | Measured at 15 keV |
| X-ray Energy (Characterization) | 15 | keV | Monochromatic beam, Si(111) |
| CRL1 Lens Count | 98 | - | Be bi-concave parabolic lenses |
| CRL Radius of Curvature (R) | 200 | ”m | At the apex of the Be lenses |
| Optical Path Difference (OPD) per 10 ”m IP-S | 11.74 | pm | Calculated phase advance |
| Target RMS Error (Proposed Anisotropic Corrector) | < 0.07λ | - | Goal for full aberration compensation |
Key Methodologies
Section titled âKey MethodologiesâThe experiment involved three primary stages: wavefront sensing, corrector design and fabrication, and performance validation.
1. Wavefront Sensing and Diagnosis
Section titled â1. Wavefront Sensing and Diagnosisâ- 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.
2. Corrector Plate Fabrication
Section titled â2. Corrector Plate Fabricationâ- Design Conversion: The required optical path length difference (Îw) 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.
3. Performance Validation
Section titled â3. Performance Validationâ- 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.
Commercial Applications
Section titled âCommercial ApplicationsâThe 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.