Structural Investigation of Single Specimens with a Femtosecond X-Ray Laser: Routes to Signal-to-Noise Ratio Enhancement

Chulho Jung, Daewoong Nam, Junha Hwang, Daeho Sung, Dohyung Cho, Heemin Lee, Sangsoo Kim, Kensuke Tono, Makina Yabashi, Tetsuya Ishikawa, Do Young Noh, and Changyong Song

Phys. Rev. Applied 13, 064045 – Published 18 June 2020

Abstract

Interest in atomic scale structures of individual specimens has invigorated developments of high-resolution probes, which include single-particle imaging using x-ray free-electron lasers (XFELs). The demonstrated spatial resolution, however, remains at tens of nanometers with difficulty in collecting diffraction signals at high frequency distinguished from noises. As such, various resolution-enhancement methods have been introduced, but few experimental verifications are available. Here, by carrying out XFEL single-pulse diffraction experiments, we explicitly unveil the dependence of SNRs on incident x-ray flux, data averaging, or multiparticle interference. We further propose a data-accumulation method of resolution-shell averaging as a robust scheme to improve the SNR. This study establishes a roadmap with which high-resolution XFEL single-pulse experiments can be contrived.

Received 27 February 2020
Revised 1 May 2020
Accepted 1 June 2020

DOI:https://doi.org/10.1103/PhysRevApplied.13.064045

Physics Subject Headings (PhySH)

Metrology Nanocrystals Structural properties

Free-electron lasers Nanostructures X-ray lasers

Femtosecond laser irradiation X-ray diffraction

Condensed Matter, Materials & Applied PhysicsInterdisciplinary PhysicsGeneral Physics

Authors & Affiliations

Chulho Jung^1,†, Daewoong Nam ^2,†, Junha Hwang^1,†, Daeho Sung¹, Dohyung Cho¹, Heemin Lee¹, Sangsoo Kim², Kensuke Tono ³, Makina Yabashi⁴, Tetsuya Ishikawa⁴, Do Young Noh⁵, and Changyong Song ^1,*

¹Department of Physics, Pohang University and Science and Technology, Pohang 37673, Korea
²Pohang Accelerator Laboratory, Pohang 37673, Korea
³Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan
⁴RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan
⁵Department of Physics and Photon Science, Gwangju Institute of Science and Technology, Gwangju 61005, Korea

^*cysong@postech.ac.kr
^†These authors contributed equally to this work.

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 13, Iss. 6 — June 2020

Subject Areas

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
XFEL single-pulse diffraction and signal-to-noise analysis. (a) Single-pulse coherent diffraction pattern from a single $Au$ nanoparticle. The diffraction signal extends to 0.54 nm⁻¹ (broken white line). (b) Radial intensity is displayed with the solid line from the fit to the x-ray scattering factor of an ideal sphere. The maximum diffraction angle is read when the signal deviates from the expected fringe pattern. (c) Reconstructed image of the diffraction pattern in (a). (d) Image resolution is estimated by calculating the phase-retrieval transfer function (PRTF) to read 0.45 nm⁻¹ as the maximum resolution. The scale bar in the image indicates 100 nm.
Reuse & Permissions
Figure 2
Resolution and XFEL photon flux. Resolutions from XFEL single-pulse diffractions are obtained for different x-ray photon fluxes. The two solid lines display the power-law dependence of d⁻¹ ∼ I^α with α = 1/3 (green) and 1/4 (blue) as guides to eyes. Most of the measured data are located within the two exponents. The dashed line in orange indicates the maximum resolution available for the detector limited by the detector size.
Reuse & Permissions
Figure 3
Resolution and accumulation of single-pulse diffraction patterns. (a) Improvement in the resolution is achieved by adding a number of single-pulse diffraction patterns. Resolutions for single-pulse patterns are shown with the improvement finally achieved showing 4, 9, and 11% increases after adding four, seven, and ten patterns, respectively. The shaded line in sky blue shows the expected resolution enhancement for comparable flux increase. (b) Reduction in the resolution is observed with more single-pulse diffraction patterns, when the patterns with different resolutions are added. (c) Radial intensity shows that the resolution decreases by adding more patterns with poor resolution, corresponding to case in (b). The resolution increases slightly (in red) from a single pattern (in black), but eventually decreases (in blue).
Reuse & Permissions
Figure 4
Resolution-shell averaging for the SNR enhancement. (a) Simulated single-pulse diffraction pattern with the employed image as an inset. Noises are added. (b) Single-pulse data are classified for the total intensity collected from each pattern. Random hitting of specimens within the Gaussian x-ray beam profile is assumed. (c) Averaged diffraction patterns in a weaker intensity group (upper panel) compared with the strongest intensity group (lower panel) of the histogram in (b). (d) Resolution shell of the data from the weak intensity group is determined when the data deviate from the strongest intensity group (broken line with arrow). Inset shows final resolution shell. The line plot is obtained for the white-colored range in the inset. (e) Ideal calculated diffraction pattern without noise. (f) Average data without considering the resolution shell. (g) Averaged data following the resolution-shell averaging method. Insets in (e)–(g) show enlarged images of the boxed region clearly evidencing the enhanced SNR in (g) following the resolution-shell averaging scheme.
Reuse & Permissions
Figure 5
Multiparticle interference with the anisotropic signal enhancement for SNR improvement. (a)–(c) Numerical simulations of the multiparticle diffractions. Diffraction pattern is shown in the left panel and its angle-dependent signal strength in the region (between white dashed lines) is displayed on the right panel. Strong anisotropy reflects on the distribution of the specimens contributed by the interference scattering. Insets in the diffraction patterns (a)–(c) display the distribution of the specimens used for the numerical simulations. (d)–(f) Experimental data from multiparticle diffraction of two (d) and three nanoparticles in linear (e) and triangular arrangement (f). Images shown in the insets (d)–(f) are obtained from the phase retrieval of the experimental diffraction patterns. The color-map scale bars show the intensity scale, and we use different color-map schemes for simulation (a)–(c) distinguished from experimental results (d)–(f).
Reuse & Permissions

Physical Review Applied