Estimation of modified Zernike coefficients from turbulence-degraded multispectral imagery using deep learning.

We investigate how wavelength diversity affects the performance of a deep-learning model that predicts the modified Zernike coefficients of turbulence-induced wavefront error from multispectral images. The ability to perform accurate predictions of the coefficients from images collected in turbulent conditions has potential applications in image restoration. The source images for this work were a point object and extended objects taken from a character-based dataset, and a wavelength-dependent simulation was developed that applies the effects of isoplanatic atmospheric turbulence to the images. The simulation utilizes a phase screen resampling technique to emulate the simultaneous collection of each band of a multispectral image through the same turbulence realization. Simulated image data were generated for the point and extended objects at various turbulence levels, and a deep neural network architecture based on AlexNet was used to predict the modified Zernike coefficients. Mean squared error results demonstrate a significant improvement in predicting modified Zernike coefficients for both the point object and extended objects as the number of spectral bands is increased. However, the improvement with the number of bands was limited when using extended objects with additive noise.

Estimation of non-uniform motion blur using a patch-based regression convolutional neural network.

The non-uniform blur of atmospheric turbulence can be modeled as a superposition of linear motion blur kernels at a patch level. We propose a regression convolutional neural network (CNN) to predict angle and length of a linear motion blur kernel for varying sized patches. We analyze the robustness of the network for different patch sizes and the performance of the network in regions where the characteristics of the blur are transitioning. Alternating patch sizes per epoch in training, we find coefficient of determination scores across a range of patch sizes of R 2>0.78 for length and R 2>0.94 for angle prediction. We find that blur predictions in regions overlapping two blur characteristics transition between the two characteristics as overlap changes. These results validate the use of such a network for prediction of non-uniform blur characteristics at a patch level.

Deep learning estimation of modified Zernike coefficients and recovery of point spread functions in turbulence.

Recovering the turbulence-degraded point spread function from a single intensity image is important for a variety of imaging applications. Here, a deep learning model based on a convolutional neural network is applied to intensity images to predict a modified set of Zernike polynomial coefficients corresponding to wavefront aberrations in the pupil due to turbulence. The modified set assigns an absolute value to coefficients of even radial orders due to a sign ambiguity associated with this problem and is shown to be sufficient for specifying the intensity point spread function. Simulated image data of a point object and simple extended objects over a range of turbulence and detection noise levels are created for the learning model. The MSE results for the learning model show that the best prediction is found when observing a point object, but it is possible to recover a useful set of modified Zernike coefficients from an extended object image that is subject to detection noise and turbulence.

Low-wavenumber compensation with Zernike tilt for non-Kolmogorov turbulence phase screens.

The fast-Fourier-transform-based filtering method for phase screen generation remains popular for numerical simulation of optical propagation through turbulence; however, these screens inherently underrepresent the spectral density at low wavenumbers. Here, the "Z-tilt" approach is explored to augment the spectral density at low wavenumbers by adding a random phase tilt, which is derived from the wavefront phase statistics of a Zernike polynomial basis. This approach is computationally efficient and can be applied to any statistically homogeneous and isotropic refractive index field. An analytic result is provided for the von Kármán spectrum with finite outer scale. In a quantitative comparison with phase screens compensated for using a common subharmonic approach, the Z-tilt method shows the best agreement with the analytical structure function when the outer scale is greater than about three times the screen dimension. For outer scales of the order of the screen dimension, the subharmonic and a modified Z-tilt method give the most accurate results. A propagation simulation demonstrates that the aperture-averaged angle-of-arrival variance is accurately predicted using the Z-tilt method.

Modeling solar eclipse shadow bands using wave optics simulation through distributed turbulence.

Thin, wavy ribbons of light known as "shadow bands" can be seen moving and undulating on the ground just preceding and following the occurrence of a total solar eclipse. Using the scattering scintillation theory, Codona [Astron. Astrophys.164, 415 (1986)AAEJAF0004-6361] presented theoretical investigations that explain recorded features of shadow bands and suggest the turbulence mainly responsible for the bands is within the bottom 2-3 km of the atmosphere. This paper proposes an approach to model the shadow band phenomena using a numerical wave optics simulation. The simulation approach employs numerical wave optics techniques to model a crescent-shape source, propagation of component plane waves through turbulence phase screens, and observation of the light at the ground. The simulation produces intensity patterns with structures and evolution that are consistent with actual shadow band observations and Codona's theory. The contribution of the turbulence phase screens as a function of height to the shadow band intensity scintillation index is simulated and excellent correspondence is found with the theory. Finally, the practical utility of the simulation is illustrated by creating intensity frames that show the temporal evolution of the patterns due to wind. The simulation approach is adaptable and can be applied to scintillation and imaging problems involving other incoherent objects or sources that subtend relatively large angles and are observed through atmospheric turbulence.

Single and double scattering event analysis for ultraviolet communication channels.

This paper presents a channel analysis method for single and double scattering events in non-line-of-sight (NLOS) ultraviolet (UV) communication systems. In general, the calculations of path loss and impulse response of such systems require Monte Carlo random number generations. However, the high computational costs of Monte Carlo methods impose severe limitations on quick reliable evaluations of system performance under complex atmospheric conditions. This paper proposes a sample-based UV channel characterization approach that improves computational performance by multiple orders of magnitude. The proposed novel approach uses fixed probability-based sampling. The method focuses only on single and double scattering events which dominate the received signal. The effects of various fog and dust aerosols are discussed under non-planar realistic conditions. The results demonstrate reliable channel characterization with significantly lower complexity using the proposed approach.

Investigating Habitability with an Integrated Rock-Climbing Robot and Astrobiology Instrument Suite.

A prototype rover carrying an astrobiology payload was developed and deployed at analog field sites to mature generalized system architectures capable of searching for biosignatures in extreme terrain across the Solar System. Specifically, the four-legged Limbed Excursion Mechanical Utility Robot (LEMUR) 3 climbing robot with microspine grippers carried three instruments: a micro-X-ray fluorescence instrument based on the Mars 2020 mission's Planetary Instrument for X-ray Lithochemistry provided elemental chemistry; a deep-ultraviolet fluorescence instrument based on Mars 2020's Scanning Habitable Environments with Raman and Luminescence for Organics and Chemicals mapped organics in bacterial communities on opaque substrates; and a near-infrared acousto-optic tunable filter-based point spectrometer identified minerals and organics in the 1.6-3.6 µm range. The rover also carried a light detection and ranging and a color camera for both science and navigation. Combined, this payload detects astrobiologically important classes of rock components (elements, minerals, and organics) in extreme terrain, which, as demonstrated in this work, can reveal a correlation between textural biosignatures and the organics or elements expected to preserve them in a habitable environment. Across >10 field tests, milestones were achieved in instrument operations, autonomous mobility in extreme terrain, and system integration that can inform future planetary science mission architectures. Contributions include (1) system-level demonstration of mock missions to the vertical exposures of Mars lava tube caves and Mars canyon walls, (2) demonstration of multi-instrument integration into a confocal arrangement with surface scanning capabilities, and (3) demonstration of automated focus stacking algorithms for improved signal-to-noise ratios and reduced operation time.

Parameter-based imaging from passive multispectral polarimetric measurements.

A modified pBRDF model with a diffuse scattering component is applied to estimate the complex refractive index, slope variance roughness, and diffuse scattering coefficients of object surfaces from time sequences of polarimetric images. The approach is used for the first time to produce parameter-based images from multispectral Stokes imagery of outdoor target scenes collected by the Ground Multiangle Spectro-Polarimetric Imager. The images of the estimated surface parameters show distinctions between different objects in the scenes and the parameter values are consistent with reasonable expectations for the object surfaces.

Generating electromagnetic nonuniformly correlated beams.

We develop a method to generate electromagnetic nonuniformly correlated (ENUC) sources from vector Gaussian Schell-model (GSM) beams. Having spatially varying correlation properties, ENUC sources are more difficult to synthesize than their Schell-model counterparts (which can be generated by filtering circular complex Gaussian random numbers) and, in past work, have only been realized using Cholesky decomposition-a computationally intensive procedure. Here we transform electromagnetic GSM field instances directly into ENUC instances, thereby avoiding computing Cholesky factors resulting in significant savings in time and computing resources. We validate our method by generating (via simulation) an ENUC beam with desired parameters. We find the simulated results to be in excellent agreement with the theoretical predictions. This new method for generating ENUC sources can be directly implemented on existing spatial-light-modulator-based vector beam generators and will be useful in applications where nonuniformly correlated beams have shown promise, e.g., free-space/underwater optical communications.

The Characterization of Biosignatures in Caves Using an Instrument Suite.

The search for life and habitable environments on other Solar System bodies is a major motivator for planetary exploration. Due to the difficulty and significance of detecting extant or extinct extraterrestrial life in situ, several independent measurements from multiple instrument techniques will bolster the community's confidence in making any such claim. We demonstrate the detection of subsurface biosignatures using a suite of instrument techniques including IR reflectance spectroscopy, laser-induced breakdown spectroscopy, and scanning electron microscopy/energy dispersive X-ray spectroscopy. We focus our measurements on subterranean calcium carbonate field samples, whose biosignatures are analogous to those that might be expected on some high-interest astrobiology targets. In this work, we discuss the feasibility and advantages of using each of the aforementioned instrument techniques for the in situ search for biosignatures and present results on the autonomous characterization of biosignatures using multivariate statistical analysis techniques. Key Words: Biosignature suites-Caves-Mars-Life detection. Astrobiology 17, 1203-1218.

Modeling random screens for predefined electromagnetic Gaussian-Schell model sources.

In a previous paper [Opt. Express22, 31691 (2014)] two different wave optics methodologies (phase screen and complex screen) were introduced to generate electromagnetic Gaussian Schell-model sources. A numerical optimization approach based on theoretical realizability conditions was used to determine the screen parameters. In this work we describe a practical modeling approach for the two methodologies that employs a common numerical recipe for generating correlated Gaussian random sequences and establish exact relationships between the screen simulation parameters and the source parameters. Both methodologies are demonstrated in a wave-optics simulation framework for an example source. The two methodologies are found to have some differing features, for example, the phase screen method is more flexible than the complex screen in terms of the range of combinations of beam parameter values that can be modeled. This work supports numerical wave optics simulations or laboratory experiments involving electromagnetic Gaussian Schell-model sources.

Experimental study of a compressive line sensing imaging system in a turbulent environment.

Turbulence poses challenges in many atmospheric and underwater surveillance applications. The compressive line sensing (CLS) active imaging scheme has been demonstrated in simulations and test tank experiments to be effective in scattering media such as turbid coastal water, fog, and mist. The CLS sensing model adopts the distributed compressive sensing theoretical framework that exploits both intrasignal sparsity and the highly correlated nature of adjacent areas in a natural scene. During sensing operation, the laser illuminates the spatial light modulator digital micromirror device to generate a series of one-dimensional binary sensing patterns from a codebook to encode the current target line segment. A single element detector photomultiplier tube acquires target reflections as the 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 turbulent environment. The development of a compact CLS prototype will be discussed, as will a series of experiments using various turbulence intensities at the Naval Research Lab's Simulated Turbulence and Turbidity Environment. The experimental results showed that the time-averaged measurements improved both the signal-to-noise radio and the resolution of the reconstructed image in the extreme turbulence environment. The contributing factors for this intriguing and promising result will be discussed.

Gaussian beam propagation in anisotropic turbulence along horizontal links: theory, simulation, and laboratory implementation.

Experimental and theoretical work has shown that atmospheric turbulence can exhibit "non-Kolmogorov" behavior including anisotropy and modifications of the classically accepted spatial power spectral slope, -11/3. In typical horizontal scenarios, atmospheric anisotropy implies that the variations in the refractive index are more spatially correlated in both horizontal directions than in the vertical. In this work, we extend Gaussian beam theory for propagation through Kolmogorov turbulence to the case of anisotropic turbulence along the horizontal direction. We also study the effects of different spatial power spectral slopes on the beam propagation. A description is developed for the average beam intensity profile, and the results for a range of scenarios are demonstrated for the first time with a wave optics simulation and a spatial light modulator-based laboratory benchtop counterpart. The theoretical, simulation, and benchtop intensity profiles show good agreement and illustrate that an elliptically shaped beam profile can develop upon propagation. For stronger turbulent fluctuation regimes and larger anisotropies, the theory predicts a slightly more elliptical form of the beam than is generated by the simulation or benchtop setup. The theory also predicts that without an outer scale limit, the beam width becomes unbounded as the power spectral slope index α approaches a maximum value of 4. This behavior is not seen in the simulation or benchtop results because the numerical phase screens used for these studies do not model the unbounded wavefront tilt component implied in the analytic theory.

SLM-based laboratory simulations of Kolmogorov and non-Kolmogorov anisotropic turbulence.

In this paper, we present a laboratory setup to simulate anisotropic, non-Kolmogorov turbulence. A sequence of numerical phase screens that incorporate the turbulence characteristics were applied to a spatial light modulator placed in the path of a laser beam with a Gaussian intensity profile and the resulting far-field intensity patterns were recorded by a CCD camera. The values of scintillation at the position of the maximum intensity were extracted from the images and compared with theoretical values. Our experimental results show a trend that is in agreement with known theoretical expressions; however, the turbulence rescaling due to anisotropy shows some discrepancy with theory and requires more investigation.

Numerical modeling of Schell-model beams with arbitrary far-field patterns.

An approach is described for creating random complex screens to be used in computer simulations of arbitrary Schell-model beams with a prescribed far-field intensity distribution. Simulation examples including beam profiles with reflection symmetry and rotational symmetry, flat-top, and pyramidal shapes are presented to verify the proposed approach. A more general scenario with a nonsymmetric far-field beam shape is illustrated to demonstrate the evolution in the free-space propagation from the source plane to the far zone.

Complex index of refraction estimation from degree of polarization with diffuse scattering consideration.

The estimation of the refractive index from optical scattering off a target's surface is an important task for remote sensing applications. Optical polarimetry is an approach that shows promise for refractive index estimation. However, this estimation often relies on polarimetric models that are limited to specular targets involving single surface scattering. Here, an analytic model is developed for the degree of polarization (DOP) associated with reflection from a rough surface that includes the effect of diffuse scattering. A multiplicative factor is derived to account for the diffuse component and evaluation of the model indicates that diffuse scattering can significantly affect the DOP values. The scattering model is used in a new approach for refractive index estimation from a series of DOP values that involves jointly estimating n, k, and ρ(d)with a nonlinear equation solver. The approach is shown to work well with simulation data and additive noise. When applied to laboratory-measured DOP values, the approach produces significantly improved index estimation results relative to reference values.

Propagation of rotational field correlation through atmospheric turbulence.

A general formulation is presented that describes the propagation of the rotational field correlation of an optical beam through atmospheric turbulence. The associated influence on the orbital angular momentum (OAM) of a single photon is described analytically. The analysis predicts the probability of change in the OAM state due to the process of propagating through turbulence. The probability of a change in an OAM state depends on the Fresnel number and on the ratio of the beam diameter to the Fried parameter.

Computational approaches for generating electromagnetic Gaussian Schell-model sources.

Two different methodologies for generating an electromagnetic Gaussian-Schell model source are discussed. One approach uses a sequence of random phase screens at the source plane and the other uses a sequence of random complex transmittance screens. The relationships between the screen parameters and the desired electromagnetic Gaussian-Schell model source parameters are derived. The approaches are verified by comparing numerical simulation results with published theory. This work enables one to design an electromagnetic Gaussian-Schell model source with pre-defined characteristics for wave optics simulations or laboratory experiments.

Analysis and simulation of a fiber bundle method for creating a partially spatially coherent beam.

A fiber bundle arrangement containing a distribution of fiber lengths has been proposed in the literature to produce a partially spatially coherent beam. Light input to the bundle with limited temporal coherence is translated into limited spatial coherence. Expressions are developed for the bundle pupil autocorrelation function and far-field irradiance pattern. A numerical simulation approach is implemented and results are compared with a speckle-free result. The fiber bundle approach tends to create an irradiance pattern whose average shape matches the pattern produced by a single fiber. A "smoothed" far-field pattern is obtained if the fiber length difference is much greater than the source temporal coherence length.

Scintillation analysis of truncated Bessel beams via numerical turbulence propagation simulation.

Scintillation aspects of truncated Bessel beams propagated through atmospheric turbulence are investigated using a numerical wave optics random phase screen simulation method. On-axis, aperture averaged scintillation and scintillation relative to a classical Gaussian beam of equal source power and scintillation per unit received power are evaluated. It is found that in almost all circumstances studied, the zeroth-order Bessel beam will deliver the lowest scintillation. Low aperture averaged scintillation levels are also observed for the fourth-order Bessel beam truncated by a narrower source window. When assessed relative to the scintillation of a Gaussian beam of equal source power, Bessel beams generally have less scintillation, particularly at small receiver aperture sizes and small beam orders. Upon including in this relative performance measure the criteria of per unit received power, this advantageous position of Bessel beams mostly disappears, but zeroth- and first-order Bessel beams continue to offer some advantage for relatively smaller aperture sizes, larger source powers, larger source plane dimensions, and intermediate propagation lengths.