Optimizing probes for multi-beam ptychography

TL;DR

Multi-beam ptychography (MBP) increases imaging throughput by using multiple coherent beams, but robust reconstruction becomes harder as beam count grows. The authors propose a framework evaluating probe sets by separability, uniformity, and fabrication feasibility, and compare four probe strategies (Zernike, Hadamard-based binary phase, experimental phase plates, and spiral phase) through simulations with a synthetic, spectrally uniform object. Hadamard-based probes emerge as the most robust and scalable option, offering strong separability, uniform SBP performance, and practical fabrication advantages; spirals are competitive but scale less efficiently, while Zernike and phase plates lag in reliability and scalability. These findings provide concrete design criteria for robust, high-throughput MBP in coherent X-ray and EUV imaging, guiding future exploration of orthogonal bases and fabrication methods.

Abstract

Multi-beam ptychography (MBP) offers a scalable solution to improve the throughput of state-of-the-art ptychography by increasing the number of coherent beams that illuminate the sample simultaneously. However, increasing the number of beams in ptychography makes ptychographical reconstructions more challenging and less robust. It has been demonstrated that MBP reconstructions can be made more robust by using well-structured and mutually separable probes. Here, we present a quantitative framework to assess probe sets based on separability, uniformity, and fabrication feasibility. We show that Hadamard-based binary phase masks consistently outperform Zernike polynomials, experimentally feasible phase plates, and spiral phase masks across varying scan densities. While spiral masks yield comparable resolution, they scale less efficiently due to increased structural complexity. Our results establish practical criteria for evaluating and designing structured probes to enable more robust and scalable implementation of MBP in high-throughput coherent X-ray and EUV imaging.

Figures (9)

• Figure 1: Representative examples of four distinct wavefront modulation designs used for probe generation. The left panels show the phase distributions of the corresponding pupil functions, while the right panels display the resulting probe amplitudes after propagating to the sample. The effective probe radius, defined as the radius enclosing 90% of the total intensity, is quantified by cumulative intensity analysis, indicated by the white circles and annotated with the corresponding radius values in pixels.
• Figure 2: Illustration of the synthetic test object used for probe performance evaluation. Phase map and amplitude map generated using independent Perlin noise fields with identical spectral content, but different seeds for the random number generator. Four randomly selected subregions (labeled a-d) are marked on the maps. Below are the spectral magnitudes (in logarithmic scale) of these subregions and their corresponding radial power spectra.
• Figure 3: Obtained average reconstruction quality and standard deviation as a function of number of scan points per area, for 16 different sub-regions of the same object using a single representative probe from the Hadamard-like set.
• Figure 4: Representative examples of probes generated using square-aperture Zernike polynomials. Left: pupil function phase maps. Right: resulting probe amplitudes after propagation to the object plane. Each probe is overlaid with a white circle indicating the effective radius enclosing 90% of the total intensity.
• Figure 5: Representative examples of probes generated using Hadamard-like binary phase modulations. Left: pupil function phase maps. Right: resulting probe amplitudes after propagation to the object plane. Each probe is overlaid with a white circle indicating the effective radius enclosing 90% of the total intensity.