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Coded x-ray diffraction imaging (CXRDI) is an emerging computational imaging approach that aims to solve the phase retrieval problem in x-ray crystallography based on the intensity measurements of encoded diffraction patterns. Boolean coding masks (BCMs) with complementary structures have been used to modulate the diffraction pattern in CXRDI. However, the optimal spatial distribution of BCMs still remains an open problem to be studied in depth. Based on the spectral initialization criterion, we provide a theoretical proof for the premise that the optimal complementary BCMs should obey the blue noise distribution in the sense of mathematical expectation. In addition, the benefits of the blue noise coding strategy are assessed by a set of simulations, where better reconstruction quality is observed compared to the random BCMs and other complementary BCMs.

 

Abstract Earth’s habitability is closely tied to its late-stage accretion, during which impactors delivered the majority of life-essential volatiles. However, the nature of these final building blocks remains poorly constrained. Nickel (Ni) can be a useful tracer in characterizing this accretion as most Ni in the bulk silicate Earth (BSE) comes from the late-stage impactors. Here, we apply Ni stable isotope analysis to a large number of meteorites and terrestrial rocks, and find that the BSE has a lighter Ni isotopic composition compared to chondrites. Using first-principles calculations based on density functional theory, we show that core-mantle differentiation cannot produce the observed light Ni isotopic composition of the BSE. Rather, the sub-chondritic Ni isotopic signature was established during Earth’s late-stage accretion, probably through the Moon-forming giant impact. We propose that a highly reduced sulfide-rich, Mercury-like body, whose mantle is characterized by light Ni isotopic composition, collided with and merged into the proto-Earth during the Moon-forming giant impact, producing the sub-chondritic Ni isotopic signature of the BSE, while delivering sulfur and probably other volatiles to the Earth.