Guided progressive reconstructive imaging: a new quantization-based framework for low-dose, high-throughput and real-time analytical ptychography

TL;DR

The paper tackles the bottleneck of real-time, low-dose ptychography by introducing Guided Progressive Reconstructive Imaging (GPRI), a quantization-based framework that treats scattering events one-by-one and builds the image from a precomputed library of kernel-limited guide functions. By mapping per-count contributions to a Wigner-distribution deconvolution (WDD) like process, GPRI achieves linear scaling with the number of events and supports live feedback, high dose efficiency, and larger fields of view compared to conventional dense-frame workflows. Key contributions include the formal derivation of count-wise guide functions for WDD (and extensions to SBI/iCoM), demonstration on simulated sparse data showing dose-effective reconstruction down to ~10 e−/Ų, and a discussion of real-time, cross-discipline applicability. The work signals a significant shift toward accessible, reproducible, low-dose ptychography with potential impact across electron, X-ray, and optical coherence imaging, enabling immediate results and broader adoption of high-throughput, high-sensitivity imaging techniques.

Abstract

By profiting from recent developments in detector technologies, making it possible to access a stream of detection events with few-ns time resolutions, a new ptychographic workflow is established. This methodological framework, referred to as guided progressive reconstructive imaging, relies on a quantization-based description of the acquired intensity, through an elementary derivation. Established direct phase retrieval solutions, such as the Wigner distribution deconvolution approach, can then be adapted to a continuous treatment of received counts, with no need for a dense data representation. Consequently, the result is obtained in the form of a progressively improving estimate, while providing immediate user feedback thanks to a remarkable processing speed, able to surpass the acquisition bandwidth. This fast measurement is enabled by the cumulative usage of a pre-calculated library of kernel-limited guide functions, compiling count-wise contributions as a function of the triggered detector pixel. Hence, the reconstruction offers the same advantages of direct phase retrieval methods, in particular a high dose-efficiency and the absence of complex convergence dynamics, with much less stringent restrictions on the field of view than is typical in current alternatives. Its implementation is also significantly more straightforward and flexible. Overall, this work constitutes a major evolution in the state-of-the-art, facilitating repeatable and low-dose experiments with high accessibility, and being applicable to electron-based imaging, X-ray diffraction and optical microscopy.

Figures (4)

• Figure 1: Illustration of a STEM-based scattering experiment and its usage within a basic GPRI process. An electron wave travels from the focal plane $\vec{q}_0$ to the specimen plane $\vec{r}_0$, and propagates to the far-field $\vec{q}$ before collapsing. The resulting detection event leads to a specific contribution to the reconstructed specimen. It is obtained by selection of $G^{Pty}_{\vec{q}}\left(\vec{r}\right)$ within a library, and addition around the current scan position $\vec{r}_s$.
• Figure 2: Illustration of the practical processing in GPRI. The kernel-limited guide function is used to update the few pixels of the reconstruction window that are found around the considered scan position $\vec{r}_s$. The reconstruction grid may be finer than the scan grid, and the ratio of the scan step over its pixel size is required to be an integer to permit straightforward selection of the updated pixels. Both the kernel size and the frequency cutoff in the measurement of $\gamma \, T^{WDD}\left(\vec{r}\right)$ are user-defined.
• Figure 3: Depiction of a library $G^{WDD}_{\vec{q}}\left(\vec{r}\right)$ along $\vec{r}$, for a few indicated values of $\vec{q}\,=\,\left[\,q_x\,;\,0\,\right]$, equal to fractions of the aperture radius $q_A$. No MTF is included in the calculation, hence the use of the scattering vector dimension directly. For each case, both the imaginary and real parts of the guide function are shown, alongside their Fourier transform amplitude. An exception is the case of a), i.e. for $\parallel\vec{q}\parallel\,=\,0\,\text{nm}^{-1}$, where the imaginary part is found below numerical precision. The real-space extent shown covers a radius equal to $8\,\delta r_{Abbe}$ and frequency space is diffraction-limited. Colorbars reflect numerical, and unitless, values taken by the guide functions. The Wiener filter parameter was $\epsilon\,=\,10^{-6}$.
• Figure 4: Results of GPRI-based WDD imaging, employing simulated scattering pattern. The concerned specimen is a poliovirus, illuminated under an acceleration voltage of 200 kV and a convergence half-angle $\alpha\,=\,2\,\text{mrad}$. Calculations are done for a variety of average numbers of electrons per pattern $N_{e^-}$, and corresponding doses given in $e^-/\text{\AA}^2$. For each case, the position-dependent measurement of the projected potential $\mu^{WDD}\left(\vec{r}\right)$ is displayed alongside the square root of its Fourier transform's amplitude $\sqrt{\mid\tilde{\mu}^{WDD}\left(\vec{Q}\right)\mid}$. The colorbars reflect values of projected potential, in V$\cdot$nm.