Chiral objects are abundant in nature, and although the enantiomers have almost identical physical properties apart from their handedness, they can exhibit significantly different chemical properties and biological functions. This underscores the importance of sorting chiral substances. In this Letter, we demonstrate that chirality-sorting optical force pairs can be inversely generated in a tightly focused Gaussian beam by tailoring the input polarization state. We provide a detailed method for constructing the polarization state of the incident light to create the desired chiral optical field that generates the chirality-sorting optical force pairs. These force pairs precisely trap two opposite enantiomers at distinct predetermined positions within the same equilibrium plane, enabling their simultaneous identification and separation. Notably, the trapping positions and separation distances can be freely adjusted by altering the incident polarization parameters.@en

In the theory of partial coherence, coherence singularities can occur in the spectral degree of coherence (SDOC): in case the fields at two different points are completely uncorrelated, the phase of the SDOC is undefined. For a partially coherent vortex beam, the detection of coherence singularities is linked to the measurement of topological charge, whose magnitude equals the number of ring dislocations in its far field amplitude. However, the phase distribution of coherence singularities is rarely mentioned in the literature and the amplitude distribution can hardly reflect the sign of topological charge. In this letter, we present a phase-analysis method for measuring the coherence singularities by introducing a movable perturbation at a certain point in an illumination window of a finite size. Using the proposed method, we measure experimentally the coherence singularities of a partially coherent vortex beam in the focal plane. From the results, the magnitude and sign of the topological charge can be determined simultaneously from the phase distribution of the coherence singularities. Our results can find application in information transmission.

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We propose and experimentally demonstrate a noniterative diffractive imaging method for reconstructing the complex-valued transmission function of an object illuminated by spatially partially coherent light from the far-field diffraction pattern. Our method is based on a pinhole array mask, which is specially designed such that the correlation function in the mask plane can be obtained directly by inverse Fourier transforming the diffraction pattern. Compared to the traditional iterative diffractive imaging methods using spatially partially coherent illumination, our method is noniterative and robust to the degradation of the spatial coherence of the illumination. In addition to diffractive imaging, the proposed method can also be applied to spatial coherence property characterization, e.g., free-space optical communication and optical coherence singularity measurement.

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The complete characterization of spatial coherence is extremely di cult because the mutual coherence function (MCF) is a complex-valued function of four independent Cartesian coordinates. This di culty limits the ability to control and to optimize the spatial coherence in a broad range of key applications. Here we propose an e cient and robust scheme for measuring the complete MCF of an arbitrary partially coherent beam using self-referencing holography, which does not require any prior knowledge or making any assumptions about the MCF. We further apply our method to lensless di ractive imaging, and experimentally demonstrate the reconstruction of a phase object under spatially partially coherent illumination. This application is particularly useful for imaging at short wavelengths, where the illumination sources lack spatial coherence and no high-quality imaging optics are available.

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