When an optical beam propagates through a turbulent medium such as the atmosphere or ocean, the beam will become distorted. It is then natural to seek the best or optimal beam that is distorted least, under some metric such as intensity or scintillation. We seek to maximize the light intensity at the receiver using the paraxial wave equation with weak-fluctuation as the model. In contrast to classical results that typically confine original laser beams to be from a special class, we allow the beam to be general, which leads to an eigenvalue problem of a large-sized matrix with each entry being a multi-dimensional integral. This is an expensive and sometimes infeasible computational task in many practically reasonable settings. To overcome this expense, in a change from past calculations of optimal beams, we transform the calculation from physical space to Fourier space. Since the structure of the turbulence is commonly described in Fourier space, the computational cost is significantly reduced. This also allows us to incorporate some optional turbulence assumptions, such as homogeneous-statistics assumption, small-length-scale cutoff assumption, and Markov assumption, to further reduce the dimension of the numerical integral. The proposed methods provide a computational strategy that is numerically feasible, and results are demonstrated in several numerical examples. These results provide further evidence that special beams can be defined to have beam divergence that is small.
more »
« less
Scintillation minimization versus intensity maximization in optimal beams
In free-space optical communications and other applications, it is desirable to design optical beams that have reduced or even minimal scintillation. However, the optimization problem for minimizing scintillation is challenging, and few optimal solutions have been found. Here we investigate the general optimization problem of minimizing scintillation and formulate it as a convex optimization problem. An analytical solution is found and demonstrates that a beam that minimizes scintillation is incoherent light (i.e., spatially uncorrelated). Furthermore, numerical solutions show that beams minimizing scintillation give very low intensity at the receiver. To counteract this effect, we study a new convex cost function that balances both scintillation and intensity. We show through numerical experiments that the minimizers of this cost function reduce scintillation while preserving a significantly higher level of intensity at the receiver.
more »
« less
- Award ID(s):
- 1750488
- PAR ID:
- 10521389
- Publisher / Repository:
- Optica
- Date Published:
- Journal Name:
- Optics Letters
- Volume:
- 48
- Issue:
- 15
- ISSN:
- 0146-9592
- Page Range / eLocation ID:
- 3865
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
null (Ed.)We frame the collision avoidance problem of multi-agent autonomous vehicle systems into an online convex optimization problem of minimizing certain aggregate cost over the time horizon. We then propose a distributed real-time collision avoidance algorithm based on the online gradient algorithm for solving the resulting online convex optimization problem. We characterize the performance of the algorithm with respect to a static offline optimization, and show that, by choosing proper stepsizes, the upper bound on the performance gap scales sublinearly in time. The numerical experiment shows that the proposed algorithm can achieve better collision avoidance performance than the existing Optimal Reciprocal Collision Avoidance (ORCA) algorithm, due to less aggressive velocity updates that can better prevent the collision in the long run.more » « less
-
We consider the problem of subset selection in the online setting, where data arrive incrementally. Instead of storing and running subset selection on the entire dataset, we propose an incremental subset selection framework that, at each time instant, uses the previously selected set of representatives and the new batch of data in order to update the set of representatives. We cast the problem as an integer bi- nary optimization minimizing the encoding cost of the data via representatives regularized by the number of selected items. As the proposed optimization is, in general, NP-hard and non-convex, we study a greedy approach based on un- constrained submodular optimization and also propose an efficient convex relaxation. We show that, under appropriate conditions, the solution of our proposed convex algorithm achieves the global optimal solution of the non-convex problem. Our results also address the conventional problem of subset selection in the offline setting, as a special case. By extensive experiments on the problem of video summarization, we demonstrate that our proposed online subset selection algorithms perform well on real data, capturing diverse representative events in videos, while they obtain objective function values close to the offline setting.more » « less
-
We consider the problem of subset selection in the online setting, where data arrive incrementally. Instead of storing and running subset selection on the entire dataset, we propose an incremental subset selection framework that, at each time instant, uses the previously selected set of representatives and the new batch of data in order to update the set of representatives. We cast the problem as an integer binary optimization minimizing the encoding cost of the data via representatives regularized by the number of selected items. As the proposed optimization is, in general, NP-hard and non-convex, we study a greedy approach based on unconstrained submodular optimization and also propose an efficient convex relaxation. We show that, under appropriate conditions, the solution of our proposed convex algorithm achieves the global optimal solution of the non-convex problem. Our results also address the conventional problem of subset selection in the offline setting, as a special case. By extensive experiments on the problem of video summarization, we demonstrate that our proposed online subset selection algorithms perform well on real data, capturing diverse representative events in videos, while they obtain objective function values close to the offline setting.more » « less
-
This paper proposes a set of novel optimization algorithms for solving a class of convex optimization problems with time-varying streaming cost functions. We develop an approach to track the optimal solution with a bounded error. Unlike prior work, our algorithm is executed only by using the first-order derivatives of the cost function, which makes it computationally efficient for optimization with time-varying cost function. We compare our algorithms to the gradient descent algorithm and show why gradient descent is not an effective solution for optimization problems with time-varying cost. Several examples, including solving a model predictive control problem cast as a convex optimization problem with a streaming time-varying cost function, demonstrate our results.more » « less
An official website of the United States government

