The human eye is a complex optical system with multiple elements. It is aspheric, nonsymmetric, and time dependent; yet, overall it has incredible performance. There have been various instruments developed over the years to measure and then to guide treatment to correct for ocular aberrations. As the development of these instruments (and treatments) has progressed, we have sought to correct more difficult cases, which may be more aberrated, time-dependent, or difficult in some other way. To this end, we have developed a new dynamic aberrometer that expands the boundaries of measurement capability with the aim of measuring and treating more difficult cases. This aberrometer has been designed that incorporates high-resolution Shack–Hartmann wavefront sensing, full gradient (spot) corneal topography, dynamic acquisition, and a subjective digital refractometer. This instrument is designed to measure extremely high aberrations and to provide information for treatment in multiple modalities. A small clinical study was conducted with subjects ranging from 23 to 64 years old to evaluate the effectiveness of the dynamic analysis at selecting a refraction. Examples are presented for measurements with keratoconus, irregular corneas, and tear-film irregularity. In the clinical study, young subjects showed an overall +0.27 D reduction in instrument induced myopia using dynamic measurement compared to a snapshot. The instrument has a large dynamic range for measuring subjects with keratoconus and other aberrated corneal conditions. The new instrument is effective at providing information needed for treatment in multiple modalities. The subjective digital refractometer corrects the fixation target for the objectively measured low-order aberrations (defocus and astigmatism). This provides immediate subjective feedback on the objective refraction and, with the ability to manually adjust the refraction parameters, the ability to compare objective and subjective refractions in the same setting.
For the laser beam propagation through strong and deep turbulence, a discrepancy between the wave optics simulation and existing theoretical predication has been reported. In this paper, from the perspective of short-exposure and long-exposure point spread functions and optical transfer functions, the instantaneous speckle profiles that accurately reflect turbulence features and diffraction effect are generated. their statistical behaviors, from average short exposure beam sizes, on-axis scintillation indices and to the corresponding probability density functions, are carefully examined and favorably compared with their analytical counterparts. We believe this work will be helpful in a better understanding of the optical properties of deep turbulence and wave optics simulation and bridging the gap between them.
It is known that certain geometrical-optics predictions often agree well with optical turbulence field observations even though theoretical constraints for ignoring diffraction may be violated. Geometrical optics assumptions can simplify analyses, and ray optics can significantly reduce simulation computation time. Here, an investigation into angle-of-arrival fluctuations is presented involving wave optics and geometrical (ray) optics computer simulations of a plane wave of visible light propagating through a turbulent refractive-index field. The simulation and Rytov-based theory results for the variances of aperture-filtered angle-of-arrival fluctuations generally agree well for weak scattering (Rytov variance, σR2≲0.2), but for increasing Rytov variance, the simulation results demonstrate a positive slope that can be significantly shallower than that predicted by the theory. For weak-to-moderate scattering regimes (σR2≲2.67), a comparison of the ray and wave results show they match for aperture diameters greater than about two Fresnel lengths. This result is consistent with a previous theoretical analysis by Cheon and Muschinski. For the strongest scattering case studied (σR2=26.7), the wave and ray simulations match for aperture diameters greater than about 10 Fresnel lengths. For smaller apertures, we attribute the disparity between the wave and ray simulation results to a Fresnel filtering effect.
The analysis of optical propagation through both deterministic and stochastic refractive-index fields may be substantially
simplified if diffraction effects can be neglected. With regard to simplification, it is known that certain geometricaloptics
predictions often agree well with field observations but it is not always clear why this is so. Here, a new
investigation of this issue is presented involving wave optics and geometrical (ray) optics computer simulations of a
beam of visible light propagating through fully turbulent, homogeneous and isotropic refractive-index fields. We
compare the computationally simulated, aperture-averaged angle-of-arrival variances (for aperture diameters ranging
from 0.5 to 13 Fresnel lengths) with theoretical predictions based on the Rytov theory.
In an experimental setting where new sensing techniques are being developed and the source/medium/system parameters
are in a constant state of change, a flexible radiometric prediction tool can be essential for experimental design and
analysis. The Spectral Signature Sensing (SSS) analysis and visualization software development is a user-friendly
analytic tool that is designed for radiometric analysis and modeling of radiant optical energy from a source to a detection
system. Transmission through the atmosphere is computed with MODTRAN and the code features multiple-source
options and a flexible set of parameters for the detector. It also provides a Google Earth display function to visualize the
simulation scenario. In this paper a summary is presented of the radiometric calculations applied in this modeling tool.
The essential components and the main features are briefly described including the system-component inputs, other
options such as save and load inputs, and the resulting spectral plots and radiometric output.
The Compressive Line Sensing (CLS) active imaging system has been demonstrated to be effective in scattering mediums, such as coastal turbid water, fog and mist, through simulations and test tank experiments. The CLS prototype hardware consists of a CW laser, a DMD, a photomultiplier tube, and a data acquisition instrument. CLS employs whiskbroom imaging formation that is compatible with traditional survey platforms. The sensing model adopts the distributed compressive sensing theoretical framework that exploits both intra-signal sparsity and highly correlated nature of adjacent areas in a natural scene. During sensing operation, the laser illuminates the spatial light modulator DMD to generate a series of 1D binary sensing pattern from a codebook to “encode” current target line segment. A single element detector PMT acquires target reflections as encoder output. The target can then be recovered using the encoder output and a predicted on-target codebook that reflects the environmental interference of original codebook entries. In this work, we investigated the effectiveness of the CLS imaging system in a turbulence environment. Turbulence poses challenges in many atmospheric and underwater surveillance applications. A series of experiments were conducted in the Naval Research Lab’s optical turbulence test facility with the imaging path subjected to various turbulence intensities. The total-variation minimization sparsifying basis was used in imaging reconstruction. The preliminary experimental results showed that the current imaging system was able to recover target information under various turbulence strengths. The challenges of acquiring data through strong turbulence environment and future enhancements of the system will be discussed.
A significant improvement to the recently introduced complex screen (CS) method for generating partially coherent Schell-model sources is presented. The method, called the modified phase screen (MPS) technique, applies a deterministic amplitude and the phase portion of a CS to an initially coherent light source using a single phase-only spatial light modulator. The MPS technique, unlike the CS approach from which it is derived, does not produce a fully developed speckle pattern in the source plane, and therefore converges faster and more uniformly to the desired partially coherent source. The analytical development of the MPS method is presented. Experimental results of a Bessel-Gaussian-correlated Schell-model source, generated using the CS and MPS approaches, are compared to demonstrate the validity and utility of the MPS technique.
Optical polarimetry is an approach that shows promise for refractive index estimation from scattering off a target’s surface, which is task of pivotal importance for remote sensing and computer graphics applications. However, the estimation often relies on a microfacet polarimetric bidirectional reflectance distribution function (pBRDF) that is limited to specular targets involving single surface scattering. In this paper, we develop an analytic model for the degree of polarization (DOP) reflected from a rough surface that includes a multiplicative factor for the effect of diffuse scattering. Evaluation of the model indicates that diffuse scattering can significantly affect the DOP values, and the biased DOP values can further lead to inaccurate estimation of the surface refractive index.
We conduct an initial experimental study of implementing partially coherent beams with super-Gaussian far-field intensity distributions with the help of a reflection-type spatial light modulator. Using a recently proposed random screen approach for any Schell model type of beam, various super-Gaussian far-field intensity patterns are generated, although with an expected diffraction limited core (bright spot) in the center of each pattern. It is demonstrated that the experimental results agree well with the theoretical predictions. Our work is beneficial for creating and implementing exotic beams in various applications and can be useful for improving link performance in free-space optical communications.
KEYWORDS: Scalable video coding, Optical simulations, Global system for mobile communications, Beam propagation method, Wave propagation, Computer simulations, Transmittance, Gaussian beams, Atmospheric propagation, Coherence (optics)
In this work we propose a numerical wave optics approach for simulating the propagation of a beam with spatially varying coherence properties. The concept involves the development of a random screen with spatially varying correlation (SVC) properties that is implemented in the source plane. Three scenarios with different SVC effects are presented and a large sequence of screen realizations is applied and the intensity results after propagation are averaged to yield the partially coherent result. This approach allows the propagation characteristics of a wide range of beam types to be evaluated. The simulation results demonstrate that beams with SVC properties can obtain unusual intensity distribution, which might not be achieved with more conventional beams such as the Gaussian Schell-model beam.
A prototype infrared (IR) acousto-optic tunable filter (AOTF)-based point spectrometer has been designed for examining and analyzing potential biological samples collected in situ from the planets or other solar system objects. The reflectance spectrometer operates at a wavelength range of 1.6 to 3.6 μm, which is diagnostic of minerals and organics, and inspects a 1-mm sized spot on the sample. The tuning component is the AOTF that has been utilized in a variety of spectral detection applications. The instrument’s specification and design approach including the selected components is described. The data acquisition system, the electronic components, and their interconnections are presented. The instrument’s radiometric performance is examined and described by a noise equivalent reflectance value of 0.13% that is obtained from the laboratory measurements. The device has been demonstrated by measuring the reflectance spectra for a variety of geological samples and comparing the results with the United States Geological Survey data.
We extend the theory of beam wander for propagation through atmospheric turbulence to the case of a focused partially coherent beam (PCB). In addition to investigating the beam wander expression, we restate expressions for the beam size, long- and short-time average beam intensity profile, and the on-axis scintillation index of tracked and untracked beams. A wave optics simulation is implemented and the numerical results are compared with corresponding analytic results. The cases examined involve turbulence strengths ranging from Cn2 = 10−16 to 10−14 m−2/3 and for various horizontal paths ranging from 1 to 10 km. Although the extended analytic theory stems from a study of coherent beams, the simulation results show good agreement with the analytical results for PCBs in fluctuation regimes ranging from weak to intermediate.
KEYWORDS: Turbulence, Scintillation, Receivers, Optical simulations, Atmospheric propagation, Wave propagation, Beam propagation method, Solids, Global system for mobile communications, Transmitters
The propagation of partially coherent vortex beams through atmospheric turbulence in weak-to-strong fluctuation
regimes is investigated. Irradiance profiles from wave optics simulations and analytical theory compare favorably for a
variety of link parameters. Simulation results indicate that partially coherent vortex beams can reduce scintillation index
values relative to comparable classic Gaussian Schell model beams when turbulence conditions are mediate to strong.
However, the overall propagation performance of partially coherent vortex beams, as measured by the metric Δ, tends to
be poorer than classic Gaussian Schell model beams because of larger inherent beam spread.
KEYWORDS: Laser systems engineering, Signal to noise ratio, Statistical analysis, Error analysis, Atmospheric turbulence, Satellites, Optical alignment, Transmitters, Monte Carlo methods, Laser optics
Laser pointing systems for small targets are mainly confronted with two pointing errors, jitter and boresight,
arising due to atmospheric turbulence, mechanical vibrations and errors in optical alignment. Knowledge of these
parameters provides information about the quality of the pointing and tracking system. In the past, several
techniques have been investigated to estimate these parameters from returned laser signals. These include the
key ratio technique, the chi-squared method and the maximum likelihood (ML) estimation technique. These
techniques have been studied in the literature for Gaussian irradiance profiles. In particular, the ML estimation
technique has been found to provide excellent results. In this paper, we extend the ML estimation technique from
Gaussian profiles to near-Gaussian irradiance profiles. Our results show that the modified estimator performs
much better than a direct application of the original ML estimator.
We recently proposed a metric that incorporates scintillation reduction and beam spread for
evaluating the performance of a partially coherent laser beam propagating through atmospheric
turbulence. The metric was evaluated relative to other measures such as probability of fade and
number of fades and it was verified that the metric can be used to find the parameters for optimal or
near-optimal beam performance. In this work, we review the performance metric and develop
analytical expressions as a function of the source beam curvature F0 and other link parameters. The
behavior of the metric as a function of F0 is investigated for different link scenarios. A wave
(physical) optics simulation is also implemented and its results compare favorably with the analytical
results.
In this work, the propagations of unpolarized and polarized beams are modeled using wave optics
simulations. The second-order correlation properties and the degree of polarization were examined
for various scenarios. Our results are consistent with a theoretical analysis available in the literature.
The average intensity profiles in the receiver plane show excellent consistence with the theory. The
on-axis scintillation indices are investigated and we find that when source transverse correlation
distance is much smaller than the atmospheric correlation distance, then the unpolarized beam
reduces the normalized intensity fluctuation up to a factor of two.
KEYWORDS: Turbulence, Scintillation, Wave propagation, Free space optics, Beam propagation method, Global system for mobile communications, Optical engineering, Optical simulations, Signal to noise ratio, Solids
A performance metric is described that can be used to determine the parameters of a partially coherent beam for near-optimal performance of a free-space optical link. The metric is defined as the mean received irradiance minus the standard deviation of the irradiance, and maximizing balances the effects of beam spread and scintillation. An analytic form of is developed for a Gaussian Schell-model beam, where the optimization parameter is the transverse coherence length. Comparisons of the metric performance are made with the more conventional probability-of-fade metric. The metric is applied to determine the characteristics of the optimized coherence length as a function of a variety of link parameters and scenarios. In general, the optimized coherence length tends to decrease with increasing turbulence strength and propagation distance but increases with wavelength, although the behavior of specific scenarios can vary.
The use of multiple, mutually incoherent beams for a laser link through turbulence can reduce the effects of scintillation
at the receiver. A recent approach involving an array of parallel propagating beams in a circle pattern has been presented
in the literature and studied to determine the best beam spacing for the lowest scintillation effects. This approach has the
disadvantage of reduced irradiance at the receiver as the beam separation increases. To remove this constraint, we
present a modified approach where the multiple beams are individually aimed at the receiver. A wave (physical) optics
simulation was applied to study the performances of 2-, 3-, 4-, and 5-beam transmitter sources. The mean irradiances I
and scintillation indices σI2 are examined for some specific link geometries and fluctuation strengths and the results are
compared with those of the original method. For evaluation, we also employ a recently proposed performance metric
that incorporates both I and σI2 to indicate the near-optimal beam separation for the cases studied. Finally, we examine
the probability of fade for our selected cases the modified approach has improved performance.
A brief review is provided of the current state of the concepts, analytic theory and simulation capabilities related to
the propagation of spatially partially coherent beams through turbulence. A spatially, partially coherent beam can
reduce scintillation at the receiver and provide better free space optical link performance.
A fiber bundle arrangement has been proposed in the literature to produce a partially spatially coherent beam. The
bundle contains fibers of random lengths and the source has limited temporal coherence. The analytical expression for
the autocorrelation function of the bundle pupil is derived, which defines the behavior of the beam as it propagates.
Simulation results are used to verify the analytic theory. The far-field irradiance pattern for the bundle arrangement is
addressed analytically and through wave optics simulation. Averaging the irradiance pattern for a number of simulation
realizations was shown to converge to the analytic result. The process of averaging over a small band of source
wavelengths is developed and is shown to result in a spatially partially coherent beam. Simulation results again
compared favorably with the analytic theory.
The nematic liquid crystal variable retarder is a useful device for examining the polarization properties of optical components and material samples as well as for remote sensing applications. The response of the retarder to oblique ray angles is important in applications requiring a finite field of view such as imaging polarimetry. Mueller matrices that describe the response to incident angle are developed in two ways using an extended Jones matrix approach and through an alteration of a standard Stokes Mueller matrix for a retarder. Comparisons of the model results with lab measurements show good agreement, although with some differences due to varying assumptions in the models and nonideal aspects of the actual variable retarder. We provide analytical models that can be applied relatively easily to examine the effects of oblique angles in systems using liquid crystal variable retarders.
A performance metric is proposed as a general measure for optimizing the transverse coherence length lc of a partial
spatially coherent beam for a given communication scenario. The expression is essentially the mean intensity minus the
standard deviation of the intensity and we seek to maximize this quantity. It is preliminarily verified by the probability
of fade with log-normal distribution model under the weak turbulence condition. We also examine it as a function of lc
using wave optics simulations and compared these results with the relationships predicted by analytic theory under weak
to medium-strong turbulence conditions. Our results verify there exists a unique coherence length that can optimize the
receiver beam quality. After calculating the probability of fades of the optimal partially coherent beam and the fully
coherent beam and comparing them with the wave optics simulation results, good agreement was observed.
KEYWORDS: Receivers, Scintillation, Atmospheric propagation, Turbulence, Wave propagation, Optical simulations, Global system for mobile communications, Beam propagation method, Transmitters, Free space optics
It is known that partially (spatial) coherent beams can reduce the effects of scintillation in a free space optical link. However, practical implementations of this type of beam are still under investigation. In this work we apply a wave optics model to analyze the propagation through turbulence of a coherent beam and a particular version of a pseudo-partially coherent beam. The beam we study is created with a sequence of five Gaussian random phase screens for each atmospheric realization. We examine the average intensity profiles, the scintillation index and aperture averaging factor for a horizontal propagation scenario. We find this pseudo-partially coherent beam behaves much like a Gaussian Schell-model beam.
KEYWORDS: Atmospheric propagation, Optical simulations, Scintillation, Beam propagation method, Turbulence, Atmospheric turbulence, Global system for mobile communications, Wave propagation, Free space optics, Computer simulations
We describe a numerical, wave optics approach for simulating the propagation of a partially coherent beam. The approach requires the application of a succession of phase screens at the transmit end of the link and the summation of the resulting intensity profiles at the receiving end. To test the approach, a phase screen formulation for a Gaussian Schell-model beam was derived using a Gaussian random phase screen where its parameters are related to a form of the spatial coherence function for the transmittance. The numerical model was applied to several cases of propagation through vacuum and atmospheric turbulence and the resulting average beam intensity profile is shown to be nearly identical to the profile predicted by analytical results for the Gaussian Schell-model beam. Finally, the scintillation index of a coherent beam was investigated and the numerical result was found to generally follow the theoretical result, especially for source sizes that are relatively small or relatively larger. The model developed in this paper can be applied to analysis and design of free space optical laser links that utilize various partially coherent beams.
An analytic mathematical model is developed for a Liquid Crystal Variable Retarder (LCVR) based on an extended Jones matrix representation. The model is used to determine the polarimetric response of the LCVR to rays of non-normal incidence. The model shows reasonable agreement with laboratory measurements of a LCVR for both linear and circular input polarizations at arbitrary incident angles. The model is also applied to a two-LCVR imaging polarimeter system that is capable of measuring the full Stokes parameters of a scene. It is shown that the LCVR response can have a significant effect on the recovered Stokes values for non-normal incidence, which is important for determining the polarimetric performance of such a system over an extended field-of-view.
KEYWORDS: Liquid crystals, Mathematical modeling, Molecules, Wave plates, Polarization, Polarizers, Power meters, Systems modeling, Refraction, Chemical elements
We examine the effect of incident angle on the Liquid Crystal Variable Retarder (LCVR) and develop a Mueller matrix formulation for the LCVR that is a function of incident angle and applied voltage. By comparing the model with laboratory measurements for both linear and circular input polarization, we show that the mathematical model provides a credible representation of a real LCVR. The model can be used to determine the field angle effects of LCVRs in complex optical polarization systems.
Thermal capture and emission processes of Sn-related DX centers in AlxGa1-xAs (x equals 0.26) were measured by a constant capacitance voltage transient in various temperatures. By employing a Laplace defect spectroscopic method, the non-exponential transients were decomposed into several discrete exponential components. The results shown that more exponential components appeared int he small emission rate region as capture period increased. This indicates that electrons preferentially fill shallow energy levels due to their lower capture barriers. Discrete exponential components of the capture process were identified and four of their barriers were preliminarily measured to be about 0.14, 0.15, 0.16, and 0.17 eV, respectively.
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