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Rotation is a common motional form in nature, existing from atoms and molecules, industrial turbines to astronomical objects. However, it still lacks an efficient and reliable method for real-time image processing of a fast-rotating object. Since the Fourier spectrum of a rotating object changes rapidly, the traditional Fourier transform (FT) techniques become extremely complicated and time consuming. Here, we propose a Laguerre-Gaussian (LG) transform to analyze the rotating object with LG-mode basis. The rotation operation provides a feasible way to acquire LG spectrum, which is similar to the function of lens in FT. Particularly, the obtained LG spectrum does not change even the object working at a high rotating speed. By analyzing the LG spectrum, one can perform image processing such as reconstruction, edge enhancement, and pattern replication. Such LG transform provides an efficient and convenient way to real-time monitor and analyze a fast-rotating object in scientific research and industry.
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Laguerre-Gaussian (LG) beam has orbital angular momentum (OAM). A particle trapped in an LG beam will rotate about the beam axis, due to the transfer of OAM. The rotation of the particle is usually in the same direction as that of the beam OAM. However, we discovere that when the LG beam is strongly focused, the rotation of the particle and the beam OAM might be in the opposite direction. This anomalous effect is caused by the negative torque on the particle exerted by the focused LG beam, which is similar to the optical pulling force in the linear case. We calculated the scattering force distribution of a micro-particle trapped in an optical tweezers formed by the strongly focused LG beam, and showed that there exist stable trajectories of the particle that controlled by the negative torque. We proposed several necessary conditions for observing the counter-intuitive trajectories. Our work reveals that the strongly trapped micro-particle exhibits diversity of motion patterns.
It has previously been shown theoretically that the exchange of linear momentum between the light field in an optical cavity and a vibrating end mirror can entangle the electromagnetic field with the vibrational motion of that mirror. In this paper we consider the rotational analog of this situation and show that radiation torque can similarly entangle a Laguerre-Gaussian cavity mode with a rotating end mirror. We examine the mirror-field entanglement as a function of ambient temperature, radiation detuning and orbital angular momentum carried by the cavity mode.
We found that small perturbations of the optical vortex core in the Laguerre-Gaussian (LG) beams generate a fine structure of the Hermite-Gauss (HG) mode spectrum. Such perturbations can be easily simulated by weak variations of amplitudes and phases of the HG modes in the expansion of the LG beam field. We also theoretically substantiated and experimentally implemented a method for measuring the topological charge of LG beams with an arbitrary number of ring dislocations. Theoretical discussion and experimental studies were accompanied by simple examples of estimating the orbital angular momentum and the topological charge of perturbed LG beams.
Vast geographical distances in Africa are a leading cause for the so-called digital divide due to the high cost of installing fibre. Free-Space Optical (FSO) communications offer a convenient and higher bandwidth alternative to point-to-point radio microwave links, with the possibility of re-purposing existing infrastructure. Unfortunately, the range of high bandwidth FSO remains limited. While there has been extensive research into an optimal mode set for FSO to achieve maximum data throughput by mode division multiplexing, there has been relatively little work investigating optical modes to improve the resilience of FSO links. Here we experimentally show that a carefully chosen subset of Hermite-Gaussian modes is more resilient to atmospheric turbulence than similar Laguerre-Gauss beams, theoretically resulting in a 167% theoretical increase of propagation distance at a mode dependent loss of 50%.
The Montage image mosaic engine has found wide applicability in astronomy research, integration into processing environments, and is an examplar application for the development of advanced cyber-infrastructure. It is written in C to provide performance and portability. Linking C/C++ libraries to the Python kernel at run time as binary extensions allows them to run under Python at compiled speeds and enables users to take advantage of all the functionality in Python. We have built Python binary extensions of the 59 ANSI-C modules that make up version 5 of the Montage toolkit. This has involved a turning the code into a C library, with driver code fully separated to reproduce the calling sequence of the command-line tools; and then adding Python and C linkage code with the Cython library, which acts as a bridge between general C libraries and the Python interface. We will demonstrate how to use these Python binary extensions to perform image processing, including reprojecting and resampling images, rectifying background emission to a common level, creation of image mosaics that preserve the calibration and astrometric fidelity of the input images, creating visualizations with an adaptive stretch algorithm, processing HEALPix images, and analyzing and managing image metadata.
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