This paper extends a recent fast method for simulating optical propagation through random media like atmospheric turbulence. The previously published method simulates arbitrary sources propagating through two phase screens to an observation plane using a semi-analytic technique. The new advancement in this paper covers specific cases of sources with a known, closed-form solution for the non-turbulent field as a function of propagation distance. With the closed-form expressions, the authors did additional analytic evaluation, which leaves even less numerical work for the computer. This reduces the computation further than treating the source as arbitrary. Further, this semi-analytic method has been extended to propagate the wave through a simple optical system to an image plane. The specific cases of off-axis planar and spherical waves can be used to simulate a collection of point spread functions (PSFs) that are partially correlated across the field of view. Subsequently, these PSFs can be used with an extended scene’s reflectance array to synthesize an incoherent, anisoplanatic image.
Split-step wave-optical simulations are useful for studying optical propagation through random media like at- mospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semi-analytic approach to evaluating the Fresnel diffraction integral with a phase screen in the source plane, which is a key building block in split-step simulations. Compared to the standard angular-spectrum approach using the fast Fourier transform, the semi-analytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points are evaluated or when many time steps are used, the semi-analytic method computes faster than the angular-spectrum method.
Beams with structured phase and beams with partial spatial coherence have both been considered for a variety of applications for many years, and it would seem natural to combine their advantageous properties. However, there is a conceptual difficulty in doing so because partially coherent beams lack a definite phase, which would seem to rule out a direct synthesis. Nevertheless, research over the past decade has clarified the relationship between phase singularities of coherent fields and correlation singularities of two-point correlation functions, showing that coherent vortices survive the disruption of spatial coherence. In this presentation we discuss a number of theoretical models of what we refer to as “partially coherent vortex beams,” considering their relative merits.
The recently introduced class of Multi-Gaussian Schell-model [MGSM] beams is investigated via simulations and experiments with regards to its intensity fluctuations on propagation in atmospheric turbulence. The results indicate that the scintillation index of the MGSM beam is reduced for high values of the summation index, in agreement with previous theoretical results.
We introduce the concept of pseudo-Bessel correlated beams and investigate their scintillation properties on
propagation through turbulence. In weak turbulence the scintillation index of pseudo-Bessel correlated beams
is formulated by using the Rytov approximation. The study of scintillation is extended to strong turbulence by
numeric simulations. It is shown that by choosing an appropriate coherence parameter, pseudo-Bessel correlated
beams have lower scintillation than comparable fully coherent beams in both weak and strong turbulence.
The scintillation properties of Airy beam arrays in atmospheric turbulence are investigated. Similar to their
propagation in free space, the average propagation paths of Airy beams are also parabolic in turbulence. By
utilizing this self-bending property, the constituent Airy beamlets propagate through relatively independent
regions of turbulence and fully overlap at the on-axis detector. Through numeric simulations, it is shown that
the scintillation of Airy beam array is significantly reduced compared to a single Airy beam.
The propagation of vortex beams as an information carrier for free-space laser communications has been proposed
as a method for propagating through weak and strong atmospheric turbulence. This paper shows simulations of
vortex charge conservation through turbulence and an analysis of the results. We also show an experimental
demonstration of the generation of optical vortices with both integral and fractional charge using a segmented
deformable mirror.
A simplified analytic model is employed to demonstrate how surface plasmons propagating between the slits
in Young's interference experiment can modulate the spatial coherence of the light field radiated by the two
slits. The model is verified by comparison with results from rigorous numerical simulations. Our simulations
reveal that the coherence can indeed be enhanced or suppressed, depending on the distance between the slits.
Extending our analysis to a three-slit geometry, the effect on the degree of modulation when another slit is placed
between the two slits is investigated. It is found that, compared to the two-slit case, the center slit serves not
only as a barrier that can reduce the modulation, but can also act to enhance the amount of modulation. These
results are promising for the development of novel "coherence converting" devices with suitable metallic arrays
of subwavelength apertures.
Optical singularities serve as scientific landmarks in the topological landscape of light patterns. These curious
features exhibit conservation properties and unique diffraction patterns that are finding increasing importance
in many branches of modern optics. Caustics are singularities in ray optics that are markedly different from
those in wave optics owing to the inclusion of phase and polarization in the latter case. Optical vortices and
polarization singularities are examples of singular patterns in electromagnetic fields. There is some evidence that
single photons can also exhibit singular attributes. This talk will describe examples of both naturally occurring
and man-made optical singularities, how they may be put to use, and future directions in this field.
Studies of phase singularities in wavefields typically consider only monochromatic or deterministic wavefields.
When the wavefield is partially coherent, field singularities are not well defined and one must turn instead to the
study of singularities of correlation functions. It has been demonstrated by a number of researchers that there is
an intimate link between correlation singularities and the field singularities of the corresponding fully coherent
field. Here we investigate this connection further by theoretically constructing fields which contain both field
and correlation singularities.
The evolution of the scintillation and topological charge of coherent vortex beams in turbulence is analyzed.
Although such beams typically have inferior scintillation properties when compared with a comparable Gaussian
beam, the topological charge of the vortex beam shows significant stability. The possibility of using such beams
in optical communications is discussed.
Optical coherence theory traditionally deals with the properties of randomly fluctuating fields over long time
averages. For certain applications (such as optical communications) and special beam classes (such as vortex
beams), however, the averaging process can obscure important physical aspects of the field behavior. We demonstrate
a new method of simulating partially coherent fields of nearly arbitrary spatial and temporal coherence.
Over sufficiently long time intervals, these simulations produce the expected average properties. The results are
used to gain insight into the propagation properties of partially coherent fields through atmospheric turbulence.
The combination of the angular spectrum representation (in space-frequency domain) and of the Rytov
perturbation theory is applied for description of the second-order statistical properties of arbitrary (coherent and
partially coherent) stochastic fields (whether scalar or electromagnetic) which propagate in turbulent atmosphere.
The analysis is restricted to weak regime of atmospheric fluctuations. We first introduce the new method for scalar
fields and derive expressions for the cross-spectral density function, from which the spectral and the coherence
properties of the propagating fields can be determined. Next we extend the new technique to electromagnetic
domain, i.e. we derive expressions for the elements of the 2x2 cross-spectral density matrix of the electric
field from which its spectral, coherence and polarization properties can then be found. We illustrate the new
method by applying it to propagation of several model beams through the atmosphere. In particular, we consider
Gaussian beam, Bessel beam, Gaussian Schell-model beam in their scalar or electromagnetic versions. We find
that the results obtained on the basis of the new theory are in good agreement with those obtained earlier by
standard techniques.
Diffraction tomography (DT) is an established imaging technique for reconstructing the complex-valued refractive index distribution of a weakly scattering 3D sample. Due to experimental difficulties associated with the direct measurement of the phase of an optical wavefield, the effectiveness of DT for optical imaging applications
has been limited. A theory of intensity diffraction tomography (I-DT) has been proposed to circumvent this phase retrieval problem. In this work, we review the features of I-DT reconstruction theory that are relevant to optical microscopy. Computer-simulation studies are conducted to investigate the performance of reconstruction
algorithms for a proposed I-DT microscope. The effects of data noise are assessed, and statistically optimal reconstruction strategies that employ multiple detector planes are proposed.
In this work we investigate the phase-contrast tomography reconstruction problem assuming an incident (paraxial) spherical-wave. Starting from linearized inverse scattering theory, we develop an intensity diffraction tomography (I-DT) reconstruction algorithm that is relevant to scanning geometries that have a fixed source-to-object distance. This reconstruction algorithm accounts for first-order scattering effects introduced by the object and provides a
relationship between the intensity measurements made on two parallel detector planes and the desired complex refractive index distribution. A preliminary numerical investigation of the developed
reconstruction algorithm is presented.
In this work, we examine the application of intensity diffraction tomography (I-DT) for imaging three-dimensional (3D) phase objects. We develop and investigate two algorithms for reconstructing phase objects that utilize only half of the measurements that would be needed to reconstruct a complex-valued object function. Each reconstruction algorithm reconstructs the phase object by use of different sets of intensity measurements. We demonstrate that the numerical and noise propagation properties of the two reconstruction algorithms differ considerably.
A reconstruction theory for intensity diffraction tomography (I-DT) has been proposed that permits for the reconstruction of a weakly-scattering object without explicity knowledge of phase information. In this work, we examine the noise properties of I-DT. An explicit expression for the variance of the estimated object function as a function of spatial frequency is derived and employed for understanding the noise properties of images reconstruction in I-DT. It is demonstrated analytically and numerically that the noise properties of I-DT are significantly different from those of conventional diffraction tomography (DT).
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