Focusing performance of hard X-ray single Kinoform lens
At a Glance
Section titled âAt a Glanceâ| Metadata | Details |
|---|---|
| Publication Date | 2015-01-01 |
| Journal | Acta Physica Sinica |
| Authors | Zhi Chen, Liang Xu, Rongchang Chen, Du Guo-Hao, Biao Deng |
| Citations | 2 |
| Analysis | Full AI Review Included |
Technical Documentation & Analysis: Hard X-ray Kinoform Lenses
Section titled âTechnical Documentation & Analysis: Hard X-ray Kinoform LensesâExecutive Summary
Section titled âExecutive SummaryâThis analysis confirms the critical role of high-purity diamond in achieving state-of-the-art hard X-ray focusing performance using single Kinoform lenses. The key findings and value proposition for 6CCVD clients are summarized below:
- Material Superiority: Single Crystal Diamond (SCD) is validated as the optimal material, providing significantly smaller focal spots and higher intensity gain compared to Silicon (Si) and Aluminum (Al) across the 10-60 keV range.
- Nanoscale Focusing Achieved: The optimized Kinoform lens successfully focuses 30 keV hard X-rays down to an exceptional 14 nm lateral beam size (FWHM).
- High Intensity Gain: The optimized design yields an intensity gain of 40,500x (four orders of magnitude), crucial for high-throughput X-ray nano-microscopy and spectroscopy.
- High Transmittance: The lens maintains a high transmittance of 31%, exceeding the required 30% threshold for effective operation.
- Simplified Optics: The single Kinoform lens design offers a high-efficiency alternative to complex Compound Refractive Lenses (CRLs), simplifying alignment and reducing system footprint.
- Optimized Geometry: The final design parameters include a 1 mm aperture, 786.2 mm focal length, and a critical 636 nm vertex radius of curvature.
Technical Specifications
Section titled âTechnical SpecificationsâThe following hard data points were extracted from the optimized design parameters for the 30 keV hard X-ray single Kinoform lens:
| Parameter | Value | Unit | Context |
|---|---|---|---|
| Optimal Material | Diamond (SCD) | N/A | Selected for lowest absorption and highest refractive index contrast. |
| Design Photon Energy (E) | 30 | keV | Target energy for hard X-ray applications. |
| Lateral Beam Size (FWHM) | 14 | nm | Achieved focal spot size. |
| Axial Beam Size (FWHM) / Focal Depth | 62 | ”m | Depth of focus at optimal performance. |
| Intensity Gain (I/Io) | 40,500 | N/A | Four orders of magnitude increase. |
| Transmittance (T) | 31 | % | Optimized light throughput. |
| Lens Aperture (A) | 1 | mm | Geometric aperture size. |
| Focal Length (f) | 786.2 | mm | Optimized focal distance. |
| Vertex Radius of Curvature (R) | 636 | nm | Critical parameter for final optimization. |
| Number of Steps (N) | 39 | N/A | Optimized for reduced fabrication complexity while maintaining performance. |
Key Methodologies
Section titled âKey MethodologiesâThe research utilized a rigorous physical optics approach combined with computational modeling to optimize the Kinoform lens design:
- Physical Model Derivation: Established the X-ray single Kinoform lens focusing model based on Fermatâs principle, X-ray diffraction theory, and Fourier optics.
- Boundary Curve Solution: Derived the exact solution for the refractive boundary curve, confirming its elliptical shape, which dictates the maximum numerical aperture (NAmax).
- Complex Transmittance Function: Developed the complex amplitude transmittance function (TKL) incorporating both phase shift (refraction) and amplitude decay (absorption) within the lens material.
- Iterative Diffraction Calculation: Employed the Fast Fourier Transform (FFT) algorithm to compute the iterative diffraction integral, determining the complex wave amplitude and resulting light intensity distribution.
- Systematic Parameter Study: Conducted comprehensive simulations analyzing the impact of four critical variables on focusing performance:
- Material (Diamond, Si, Al).
- Photon Energy (10 keV to 60 keV).
- Number of Steps (N).
- Vertex Radius of Curvature (R).
6CCVD Solutions & Capabilities
Section titled â6CCVD Solutions & CapabilitiesâThis research highlights the necessity of high-quality, low-absorption diamond material for next-generation hard X-ray optics. 6CCVD is uniquely positioned to supply the foundational materials and precision services required to replicate and advance this work.
Applicable Materials
Section titled âApplicable MaterialsâThe study conclusively proves that Optical Grade Single Crystal Diamond (SCD) is the material of choice due to its superior refractive properties and minimal absorption coefficient (ÎČ) in the hard X-ray regime.
| 6CCVD Material Recommendation | Application Context |
|---|---|
| Optical Grade SCD Wafers | Required for achieving the highest intensity gain and smallest FWHM (14 nm) focusing spot, as demonstrated in the paper. |
| SCD Substrates (0.1 ”m - 500 ”m) | Provides the necessary thickness control for precise step height fabrication (L2Ï) and minimizes bulk absorption losses. |
Customization Potential
Section titled âCustomization PotentialâThe fabrication of Kinoform lenses requires ultra-precise micro-structuring (lithography and etching) on a highly polished, defect-free substrate. 6CCVD provides the necessary foundation and advanced processing capabilities:
- Precision Polishing: Achieving the required optical performance demands extremely low surface roughness. 6CCVD guarantees Ra < 1 nm on SCD surfaces, minimizing scattering that would degrade the 14 nm focal spot.
- Custom Dimensions: While the paper used a 1 mm aperture, 6CCVD can supply SCD wafers in custom dimensions, or large-area PCD plates up to 125 mm, suitable for developing large-scale or arrayed X-ray optics.
- Metalization Services: Although not explicitly used in this specific Kinoform design, 6CCVD offers in-house metalization (Au, Pt, Ti, W, etc.) for integration with mounting structures or for creating hybrid diffractive/refractive elements.
Engineering Support
Section titled âEngineering SupportâThe optimization process detailed in this paperâbalancing step number (N), vertex radius (R), and material propertiesâis complex. 6CCVDâs in-house PhD team can assist with material selection for similar X-ray Nanoprobe and Synchrotron Optics projects. We provide consultation on:
- Optimizing SCD thickness and orientation for specific photon energy ranges (e.g., 10 keV to 60 keV).
- Specifying surface quality requirements (Ra) necessary to maintain high coherence and minimize spherical aberration.
- Designing custom substrate geometries for integration into complex beamlines.
For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.
View Original Abstract
Nowadays, X-ray nanoprobe plays an important role in many research fields, ranging from materials science to geophysics and environmental science, to biophysics and protein crystallography. Refractive lenses, mirrors, and Laue lenses, can all focus X-rays into a spot with a size of less than 50 nm. To design a refractive lens at fixed wavelengths, absorption in the lens material can be significantly reduced by removing 2Ïup phase-shifting regions. This permits short focal length devices to be fabricated with small radii of curvatures at the lens apex. This feature allows one to obtain a high efficiency X-ray focusing. The reduced absorption loss also enables optics with a larger aperture, and hence improving the resolution for focusing. Since the single Kinoform lens can focus hard X-ray into a spot on a nanoscale efficiently, it has very important application prospect in X-ray nano-microscopy and nano-spectroscopy. We present a theoretical analysis of optical properties of the single Kinoform lens. Using Fermatâs principle of least time, an exact solution of the single Kinoform lens figure is derived. The X-ray diffraction theory is reviewed. The complex amplitude transmittance function of the X-ray single Kinoform lens is derived. According to Fourier optics and optical diffraction theory, we set up the physical model of X-ray single Kinoform lens focusing. Employing this physical model, we study how the focusing performance of hard X-ray single Kinoform lens is influenced by the material, the photon energy, the number of steps and the vertex radius of curvature. We find that diamond single Kinoform lens can achieve a smaller focusing beam size with higher intensity gain than Al and Si single Kinoform lens. The single Kinoform lens designed at a certain photon energy can also focus other photon energies with different lateral beam sizes, axial beam sizes, intensity gains and focusing distances. The numbers of steps of a single Kinoform lens can be lessened with the thickness of step increasing, while the single Kinoform lens keeps good focusing performance. To improve the focusing performance further, reducing the vertex radius of curvature is proposed. Following these rules, a single Kinoform lens is optimally designed to focus 30 keV hard X-ray down to a lateral size of 14 nm (full-width at half-maximum, FWHM) and an axial size of 62 ÎŒm (FWHM) with an intensity gain of four orders of magnitude and transmittance of 30%.