Photoemission orbital tomography (POT) from photoelectron momentum maps (PMMs) is a powerful technique that visualizes the shape of the molecular orbitals (MOs) of molecular films. For further utilization of POT, a simple and low-cost method of POT is highly required. Here, we propose a new POT method based on the PhaseLift algorithm (PhaseLift POT). This method utilizes a lifting procedure to convert the PMM, which is a second-order polynomial of MO coefficients, into a first-order polynomial of the lifted MO coefficients and further relaxes the equality constraint for a given PMM. We also established a method to improve the accuracy of phase retrieval from the noisy PMM data by using sparsity for MO coefficients (sparse PhaseLift POT). These methods make it possible to reconstruct the three-dimensional MOs, including phases of the wave function, directly from a single experimental PMM. This method can also precisely determine the adsorption-induced molecular deformations with an accuracy of 0.05 [Å]. Furthermore, the robust sparse PhaseLift POT is robust against unavoidable noise in the experimental PMMs due to the relaxation of the matching condition for a given PMM. Therefore, this will be an innovative tool for POT, especially for analyzing the dynamics of the molecules during the chemical reaction and excitation processes.

中文翻译：

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使用鲁棒稀疏相升的光电发射轨道断层扫描

光电子动量图 (PMM) 的光发射轨道断层扫描 (POT) 是一种强大的技术，可以可视化分子膜分子轨道 (MO) 的形状。为了进一步利用POT，非常需要一种简单且低成本的POT方法。在这里，我们提出了一种基于PhaseLift算法的新POT方法（PhaseLift POT）。该方法利用提升过程将作为MO系数的二阶多项式的PMM转换为提升的MO系数的一阶多项式，并进一步放宽给定PMM的等式约束。我们还建立了一种通过使用 MO 系数的稀疏性（稀疏 PhaseLift POT）来提高从噪声 PMM 数据中检索相位的准确性的方法。这些方法使得可以直接从单个实验 PMM 重建三维 MO，包括波函数的相位。该方法还可以精确测定吸附引起的分子变形，精度可达 0.05 [Å]。此外，由于给定 PMM 的匹配条件放宽，鲁棒稀疏 PhaseLift POT 对于实验 PMM 中不可避免的噪声具有鲁棒性。因此，这将是 POT 的一个创新工具，特别是用于分析化学反应和激发过程中分子的动力学。