240 research outputs found
The Green-function transform and wave propagation
Fourier methods well known in signal processing are applied to
three-dimensional wave propagation problems. The Fourier transform of the Green
function, when written explicitly in terms of a real-valued spatial frequency,
consists of homogeneous and inhomogeneous components. Both parts are necessary
to result in a pure out-going wave that satisfies causality. The homogeneous
component consists only of propagating waves, but the inhomogeneous component
contains both evanescent and propagating terms. Thus we make a distinction
between inhomogenous waves and evanescent waves. The evanescent component is
completely contained in the region of the inhomogeneous component outside the
k-space sphere. Further, propagating waves in the Weyl expansion contain both
homogeneous and inhomogeneous components. The connection between the Whittaker
and Weyl expansions is discussed. A list of relevant spherically symmetric
Fourier transforms is given
Pupil filters for generation of light sheets.
Pupil filters for cylindrical (two-dimensional) focusing with extended depth of field are investigated. An important application is in generating light sheets with uniform intensity. Filters for spherical (three-dimensional) focusing with a flat axial intensity, coupled with weak side lobes are also discussed
Polarized focused vortex beams: half-order phase vortices.
A theoretical treatment is presented for the focusing of polarized vortex beams, including the generation of Bessel beams. A combination of a phase vortex with arbitrary topological charge, and a polarization vortex of arbitrary order is considered. Results are given for both paraxial and high NA systems. Conditions for the presence of non-zero on-axis intensity are given. An interesting observation is that half-order phase vortices can exist, without the existence of any phase discontinuity. The behavior of Bessel beams with half-order phase vortices is investigated
Equivalent of the point spread function for partially coherent imaging
Angularly diverse or partially coherent illumination is widely used for optical, x-ray, and electron microscopy. A long-standing challenge in developing new partially coherent approaches is that the nonlinear image formation model does not allow physical intuition into how the imaging and illumination pupils impact contrast and resolution. We report a phase-space model, the phase-space imaging kernel, for partially coherent systems that describes image formation in terms of a convolution and is analogous to the point spread function model for coherent imaging. We simulate phase-space imaging kernels for brightfield and differential interference contrast (DIC) microscopes to explain a seemingly paradoxical experimental result that the DIC image of a point depends on the coherence of the illumination. We discuss interpretation of the spatial and spatial-frequency marginals of the kernel. We expect this intuitive model and simulations to facilitate design of novel computational schemes for phase imaging and optical lithography
Improved expressions for performance parameters for complex filters
Improved expressions are given for the performance parameters for transverse and axial gains for complex pupil filters. These expressions can be used to predict the behavior of filters that give a small axial shift in the focal intensity maximum and also predict the changes in gain for different observation planes
Parallel Bayesian Optimization of Agent-based Transportation Simulation
MATSim (Multi-Agent Transport Simulation Toolkit) is an open source
large-scale agent-based transportation planning project applied to various
areas like road transport, public transport, freight transport, regional
evacuation, etc. BEAM (Behavior, Energy, Autonomy, and Mobility) framework
extends MATSim to enable powerful and scalable analysis of urban transportation
systems. The agents from the BEAM simulation exhibit 'mode choice' behavior
based on multinomial logit model. In our study, we consider eight mode choices
viz. bike, car, walk, ride hail, driving to transit, walking to transit, ride
hail to transit, and ride hail pooling. The 'alternative specific constants'
for each mode choice are critical hyperparameters in a configuration file
related to a particular scenario under experimentation. We use the
'Urbansim-10k' BEAM scenario (with 10,000 population size) for all our
experiments. Since these hyperparameters affect the simulation in complex ways,
manual calibration methods are time consuming. We present a parallel Bayesian
optimization method with early stopping rule to achieve fast convergence for
the given multi-in-multi-out problem to its optimal configurations. Our model
is based on an open source HpBandSter package. This approach combines hierarchy
of several 1D Kernel Density Estimators (KDE) with a cheap evaluator
(Hyperband, a single multidimensional KDE). Our model has also incorporated
extrapolation based early stopping rule. With our model, we could achieve a 25%
L1 norm for a large-scale BEAM simulation in fully autonomous manner. To the
best of our knowledge, our work is the first of its kind applied to large-scale
multi-agent transportation simulations. This work can be useful for surrogate
modeling of scenarios with very large populations.Comment: LOD'2022 (Nature Springer Computer Science Proceedings - LNCS
- …