Streaming Parallax Ptychography for Dose-Efficient Diffractive Imaging

Imaging beam-sensitive materials, including metal-organic frameworks and biological proteins, requires dose-efficient strategies that maximize information per scattered electron. Direct ptychographic methods in 4D-STEM are particularly attractive in this context because they avoid iterative refinement and provide quantitative phase contrast at low dose. However, practical implementation for in-situ parameter tuning and dose minimization requires reconstruction algorithms that operate at or near acquisition speed. We present a unified framework for direct ptychography that reveals a deep connection to parallax imaging and enables real-time streaming reconstruction [1-2]. Under the weak-phase approximation, the diffraction intensity separates into a linear object term modulated by a probe-dependent kernel Γ(q,k). Conventional estimators such as single-sideband ptychography (SSB), Wigner distribution deconvolution (WDD), and optimum bright-field (OBF) [3-5], invert this kernel by looping over spatial frequencies q, but require aberration-dependent normalizations and, in real-space implementations, the precomputation of convolution kernels whose bandwidth scales with the aberration gradient magnitude [6]. Reordering the inversion as a loop over bright-field detector frequencies k, reveals a simpler structure. To leading order in aberration phase, the kernel reduces to a phase ramp in spatial frequency, corresponding to a lateral shift in real space (see Figure 1). Each bright-field frequency therefore contributes a shifted view of the object, which is the essence of parallax imaging [1-2]. Formulated in real-space, the reconstruction kernel amounts to either a shifted delta function, corresponding to pure parallax [7], or a single detector-independent real-space filter for phase-flipped parallax. This formulation also provides two distinct computational advantages. First, for pure parallax no convolution is required, and reconstruction reduces to direct indexing and accumulation operations. For phase-flipped parallax only a single real-space kernel is required that is independent of detector pixel, eliminating the need to precompute and store a four-dimensional library of aberration-dependent kernels Γ(q,k) [5-6]. This substantially reduces both memory footprint and sensitivity to live aberration tuning. Second, the same detector-loop formulation enables efficient scan up sampling by Fourier tiling of the virtual bright-field images prior to accumulation. Because aberration-induced shifts are generally subpixel, this procedure naturally extends to both parallax and direct ptychographic inversion, enabling recovery of spatial frequencies beyond the native scan sampling without iterative refinement [1-2]. Together, these features enable true streaming reconstruction during acquisition. For each probe position, bright-field intensities are accumulated directly into the reconstruction buffer via integer or subpixel shifts, with computational cost scaling with the number of bright-field pixels rather than with full Fourier transforms per scan position [8]. This speed enables live optimization of defocus, scan rotation, and scan step size, facilitating adaptive acquisition strategies that minimize dose while preserving spatial frequency transfer up to twice the convergence semiangle (see Figure 2). We have implemented these detector-loop kernels in the streaming-capable LiberTEM-live framework as LiberTEM-parallax [9] and deployed them as a containerized operator within the user-friendly interactEM environment [10], enabling real-time reconstruction directly at the microscope. We demonstrate how streaming parallax ptychography provides immediate feedback during 4D-STEM experiments on beam-sensitive materials, guiding parameter selection and preventing over-exposure [11]. Parallax imaging as an approximation to single sideband ptychography for simulated apoferritin. Streaming pure and phase-flipped parallax reconstructions for simulated apoferritin protein.