No abstract

Holographic reconstruction is troubled by the phase-conjugate wave front arising from Hermitian symmetry of the complex field. The so-called twin image obfuscates the reconstruction in solving the inverse problem. Here we quantitatively reveal how and how much the twin image affects the reconstruction and propose a compressive sensing (CS) approach to reconstruct a hologram completely free from the twin image. Using the canonical basis, the incoherence condition of CS is naturally satisfied by the Fourier transformation associated with wave propagation. With the propagation kernel function related to the distance, the object wave diffracts into a sharp pattern while the phase-conjugate wave diffracts into a diffuse pattern. An iterative algorithm using a total variation sparsity constraint could filter out the diffuse conjugated signal and overcome the inherent physical symmetry of holographic reconstruction. The feasibility is verified by simulation and experimental results, as well as a comparative study to an existing phase retrieval method.

Crystal phase engineering of noble-metal-based alloy nanomaterials paves a new way to the rational synthesis of high-performance catalysts for various applications. However, the controlled preparation of noble-metal-based alloy nanomaterials with unconventional crystal phases still remains a great challenge due to their thermodynamically unstable nature. Herein, we develop a robust and general seeded method to synthesize PdCu alloy nanomaterials with unconventional hexagonal close-packed (hcp, 2H type) phase and also tunable Cu contents. Moreover, galvanic replacement of Cu by Pt can be further conducted to prepare unconventional trimetallic 2H-PdCuPt nanomaterials. Impressively, 2H-Pd67Cu33 nanoparticles possess a high mass activity of 0.87 A mg–1 Pd at 0.9 V (vs reversible hydrogen electrode (RHE)) in electrochemical oxygen reduction reaction (ORR) under alkaline condition, which is 2.5 times that of the conventional face-centered cubic (fcc) Pd69Cu31 counterpart, revealing the important role of crystal phase on determining the ORR performance. After the incorporation of Pt, the obtained 2H-Pd71Cu22Pt7 catalyst shows a significantly enhanced mass activity of 1.92 A mg–1 Pd+Pt at 0.9 V (vs RHE), which is 19.2 and 8.7 times those of commercial Pt/C and Pd/C, placing it among the best reported Pd-based ORR electrocatalysts under alkaline conditions.