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Register a new userAn optimal transport model for imaging in atmospheric turbulence
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We describe a new model for image propagation through open air in the presence of changes in the index of refraction (e.g. due to turbulence) using the theory of optimal transport. We describe the relationship between photon density, or image intensity, and the phase of the traveling wave and, together with a least action principle, suggest a method for approximately recovering the solution of the photon flow. By linking atmospheric propagation solutions to optimal transport, we provide a physics-based (as opposed to phenomenological) model for predicting turbulence-induced changes to sequences of images. Simulated and real data are utilized to validate and compare the model to other existing methods typically used to model this type of data. Given its superior performance in describing experimental data, the new model suggests new algorithms for a variety of atmospheric imaging applications.
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Correlated imaging through atmospheric turbulence is studied, and the analytical expressions describing turbulence effects on image resolution are derived. Compared with direct imaging, correlated imaging can reduce the influence of turbulence to a certain extent and reconstruct high-resolution images. The result is backed up by numerical simulations, in which turbulence-induced phase perturbations are simulated by random phase screens inserting propagation paths.
A laser beam propagating to a remote target through atmospheric turbulence acquires intensity fluctuations. If the target is cooperative and provides a coherent return beam, the phase measured near the beam transmitter and adaptive optics can, in principle, correct these fluctuations. Generally, however, the target is uncooperative. In this case, we show that an incoherent return from the target can be used instead. Using the principle of reciprocity, we derive a novel relation between the field at the target and the reflected field at a detector. We simulate an adaptive optics system that utilizes this relation to focus a beam through atmospheric turbulence onto the incoherent surface.
We provide a survey of recent results on model calibration by Optimal Transport. We present the general framework and then discuss the calibration of local, and local-stochastic, volatility models to European options, the joint VIX/SPX calibration problem as well as calibration to some path-dependent options. We explain the numerical algorithms and present examples both on synthetic and market data.
Vector beams are inhomogeneously polarized optical fields with nonseparable, quantum-like correlations between their polarisation and spatial components, and hold tremendous promise for classical and quantum communication across various channels, e.g. the atmosphere, underwater, and in optical fibre. Here we show that by exploiting their quantum-like features by virtue of the nonseparability of the field, the decay of both the polarisation and spatial components can be studied in tandem. In particular, we invoke the principle of channel state duality to show that the degree of nonseparability of any vector mode is purely determined by that of a maximally nonseparable one, which we confirm using orbital angular momentum (OAM) as an example for topological charges of l = 1 and l = 10 in a turbulent atmosphere. A consequence is that the well-known cylindrical vector vortex beams are sufficient to predict the behaviour of all vector OAM states through the channel, and find that the rate of decay in vector quality decreases with increasing OAM value, even though the spread in OAM is opposite, increasing with OAM. Our approach offers a fast and easy probe of noisy channels, while at the same time revealing the power of quantum tools applied to classical light.
A Lagrangian flow network is constructed for the atmospheric blocking of eastern Europe and western Russia in summer 2010. We compute the most probable paths followed by fluid particles which reveal the {it Omega}-block skeleton of the event. A hierarchy of sets of highly probable paths is introduced to describe transport pathways when the most probable path alone is not representative enough. These sets of paths have the shape of narrow coherent tubes flowing close to the most probable one. Thus, even when the most probable path is not very significant in terms of its probability, it still identifies the geometry of the transport pathways.
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