Attentional Ptycho-Tomography (APT) for three-dimensional nanoscale X-ray imaging with minimal data acquisition and computation time

TL;DR

Attentional Ptycho-Tomography (APT) is presented, an approach to drastically reduce the amount of angular scanning, and thus the total acquisition time, and thus the total acquisition time to be applicable to other branches of nanoscale imaging.

Abstract

Noninvasive X-ray imaging of nanoscale three-dimensional objects, e.g. integrated circuits (ICs), generally requires two types of scanning: ptychographic, which is translational and returns estimates of complex electromagnetic field through ICs; and tomographic scanning, which collects complex field projections from multiple angles. Here, we present Attentional Ptycho-Tomography (APT), an approach trained to provide accurate reconstructions of ICs despite incomplete measurements, using a dramatically reduced amount of angular scanning. Training process includes regularizing priors based on typical IC patterns and the physics of X-ray propagation. We demonstrate that APT with 12-time reduced angles achieves fidelity comparable to the gold standard with the original set of angles. With the same set of reduced angles, APT also outperforms baseline reconstruction methods. In our experiments, APT achieves 108-time aggregate reduction in data acquisition and computation without compromising quality. We expect our physics-assisted machine learning framework could also be applied to other branches of nanoscale imaging.

Figures (7)

• Figure 1: X-ray ptycho-tomography and the implementation of APT.(a) Brief schematic of X-ray ptycho-tomography geometry with translational scanning of synchrotron X-rays (ptycho-scans) and symmetric angular scanning of the IC sample with uniform angular increment (tomo-scans). (b) Gold standard uses $349$ tomo-scans within the angular range of $\pm 70.4^\circ$, but our machine learning framework (APT) uses fewer tomo-scans optimized through two steps. (c) Diffraction intensities are pre-processed with an approximate inverse operator to generate the Approximant (and more details can be found in Methods and Supplementary Materials.) One of two non-overlapping portions of the Approximant is used for training with a negative Pearson correlation coefficient (NPCC) as the training loss function, where network weights are updated over several training epochs. For testing, best trained weights are loaded and fixed to generate outputs over the test volume ($4.48\times 93.2\times 3.92\:\mu\text{m}^3$).
• Figure 2: Optimizing the number of tomo-scans - qualitative view. Qualitative comparison from a parameter sweep over the number of tomo-scans ($N$) at two different depths: (a)$z = 0.364\:\mu\text{m}$ and (b)$y = 0.532\:\mu\text{m}$. The figure shows APT reconstructions with different $N$ over the test volume ($4.48\times 93.2\times 3.92\:\mu\text{m}^3$).
• Figure 3: Optimizing the number of tomo-scans - quantitative view.(a) Quantitative comparison from a parameter sweep over the number of tomo-scans ($N$) with four different quantitative metrics. (b) The number of tomo-scans that optimally compromise the performance ($N^*$) is $28.89$ in average, where APT reduces the data acquisition and computation time by a factor of $85$.
• Figure 4: Optimizing the number of angular range - qualitative view. Qualitative comparison from a parameter sweep over the angular scanning range at two different depths: (a)$z = 1.092\:\mu\text{m}$ and (b)$y=4.186\:\mu\text{m}$. The figure shows APT reconstructions over the test volume ($4.48\times 93.2\times 3.92\:\mu\text{m}^3$).
• Figure 5: Optimizing number of angular range - quantitative view.(a) Quantitative comparison from a parameter sweep over the angular scanning range at $N = N^*\:(= 29)$. (b) The total angular range that optimally compromise the performance ($\theta^*$) is $\theta^* = \pm 16.93^\circ$ in average. APT decreases the time for whole process by $108$ times.