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In the coherent diffraction imaging (CDI) techniques, a key point is to reconstruct the complex-valued object from the far-field intensity measurements, i.e., solving the phase retrieval problem. However, due to this ill-posed problem, traditional phase retrieval algorithms often encounter some problems associated with the iteration convergence. In this work, complementary phase modulations (CPM) are introduced to generate different far-field intensity measurements. The namely CPM-based method aims to find out the global optimal solution by imposing multi-dimensional constraints, including the diverse intensity images at the Fourier plane and the CPM at the object plane. It is proved by the numerical simulations and the optical experiments that the convergence speed and the recovery accuracy could be greatly improved. Furthermore, the shifting complementary phase modulations (SCPM)-based method is proposed by introducing more CPMs. The reconstruction performance is further improved even when the phase range is larger, and the support constraints are not required. In addition, the SCPM-based method is more robust to the Poisson noise. With the outstanding reconstruction performance, the CPM-based methods may be helpful to phase imaging in the application of visible-light microscopy and X-ray imaging.

Azulene is a prototypical molecule with an anomalous fluorescence from the second excited electronic state, thus violating Kasha's rule, and with an emission spectrum that cannot be understood within the Condon approximation. To better understand photophysics and spectroscopy of azulene and other non-conventional molecules, we develop a systematic, general, and efficient computational approach combining semiclassical dynamics of nuclei with ab initio electronic structure. First, to analyze the nonadiabatic effects, we complement the standard population dynamics by a rigorous measure of adiabaticity, estimated with the multiple-surface dephasing representation. Second, we propose a new semiclassical method for simulating non-Condon spectra, which combines the extended thawed Gaussian approximation with the efficient single-Hessian approach. S$_{1} \leftarrow$ S$_0$ and S$_{2} \leftarrow$ S$_0$ absorption and S$_{2} \rightarrow$ S$_0$ emission spectra of azulene, recorded in a new set of experiments, agree very well with our calculations. We find that accuracy of the evaluated spectra requires the treatment of anharmonicity, Herzberg--Teller, and mode-mixing effects., Added Fig. 1 and Eq. (5), modified figure captions. Last 15 pages contain the Supporting Information

Lithium-zinc ferrite hollow microspheres (LiZn FHMs) containing special surface crystals were synthesized by self-reactive quenching technology. The samples were heat-treated at 1200 °C and held for 4 h. The influence of the heat-treatment on LiZn FHMs was studied. The results show that the surface of hollow microspheres is smooth without heat-treatment. The phase components are Fe2O3, Fe3O4, Li0.435Zn0.195Fe2.37O4, and Li0.5Fe2.5O4. The minimum reflectivity is −13.5 dB, and the corresponding frequency is 7.5 GHz. The effective absorption band lower than −10 dB is 6.2–8.5 GHz, and the bandwidth is 2.3 GHz. After heat-treatment, crystals on the surface of hollow microspheres grow significantly. Multiple-shape micro-nano crystals containing triangular, polygonal, and irregular crystal are generated. However, the phase composition does not change. The real part of the permittivity (e′), the imaginary part of permittivity (e″), the real part of permeability (μ′), and the imaginary part of permeability (μ″) all increase, and the microwave absorption properties at low frequency are significantly increased, with the absorption peak moving to a lower frequency range. The minimum reflectivity is −26.5 dB, and the corresponding frequency changes to 3.4 GHz. The effective absorption band is 2.6–4 GHz, and the bandwidth is 1.4 GHz.

The phase retrieval problem, usually known as reconstructing an estimate of phase object from its diffraction intensity patterns, exists widely in the optical imaging field. In this paper, a deep convolutional neural network (CNN) framework is developed to accomplish the phase reconstruction given a single-shot Fourier measurement, without the requirement of prior knowledge (like nonnegativity and support constraints) or time-consuming iterations. A receptive field and input enhance learning-based design principle is applied to establish the neural network architecture. And a new loss function that combines the structural similarity (SSIM) index and the mean square error (MSE) is taken to further improve the network training. Quantitative (the average SSIM and relative MSE are ~ 0.9900 and 0.0012, respectively) and qualitative (SSIM, ranging from 0.87 to 0.95) phase reconstructions are achieved in the numerical simulation and experiment, respectively. Once the proposed network is well trained, it is convenient for the users to perform the phase reconstruction at a remarkably fast speed (~ 0.425 s). Moreover, our network is considerably robust to different noises and could be trained to additionally function as a denoiser in the phase retrieval process. In practice, the proposed method is able to build an accurate propagation model of the practical imaging system, and significantly enhance and improve the spatial resolution. With the great convenience and high accuracy of phase recovery, the proposed deep CNN framework may be helpful to solve the phase retrieval problem in Fourier imaging systems, like coherent diffraction imaging (CDI), X-ray imaging, and imaging through diffusers, etc.

In this paper, we propose an analytical phase retrieval approach applying only phase modulations in the region isolated from the object to be measured. This approach employs a series of intensity-only measurements and can accurately and conveniently achieve phase recovery in the range of [0, 2π) once a reference phase is calibrated in advance. To improve the robustness of the algorithm, this paper yields an over-determined method (OM) by extending the phase modulation procedure from 3 steps into n steps. The algorithm's exact phase retrieval ability, the influence of key parameters’ disturbance on solving precision, and the theory of robustness improvement are all verified through numerical simulations. It is noteworthy mentioning that the robustness enhancement method performs well–improving the phase retrieval accuracy efficiently. Also, an experiment is undertaken and the results are satisfactory, demonstrating the core of our approach and showing the capability of OM.