This PDF file contains the front matter associated with SPIE Proceedings Volume 9982 including the Title Page, Copyright information, Table of Contents, Introduction, and Conference Committee listing.

For vortex beams, characterization and optimization of the optical system are important. However, wavefront measurements on focused vortex beams are difficult because they have complex phase and intensity distributions. As a measurement method, we proposed the use of ptychography, in which the intensity and phase of the beams are retrieved using several far-field diffraction patterns. We constructed an optical system with a He-Ne laser light source to clarify the usefulness of ptychography. Test vortex beams were produced by a spatial light modulator (SLM) and focused by a plano-convex lens. A pinhole was scanned on the focal plane for collection of the diffraction intensity profiles. The phase and intensity of the vortex beams on the focal plane were retrieved so that the calculated beams were consistent with the intensity data. The retrieved intensity and phase distributions were compared with distributions predicted using the inputs for the SLM. They agreed well, indicating that the ptychographic phase retrieval method can be used for precise characterization of vortex beams. This method is valuable for improving the performance of applications using vortex beams.

Phase retrieval is a simple and concise way of reconstructing wavefront, especially the method based on single far field formed by just a lens. However, for the symmetry of Zernike polynomial aberrations, light with different wavefront could form the same far-field intensity distribution. The distribution of reconstructed wavefront is likely to be quite different from the real one. In other words, it suffers in the multi-solution problem. A kind of wavefront reconstruction method based on quadrant binary phase plate is proposed. Incident light is modulated by a first-order Modified-Walshfunction pattern quadrant binary phase mask, which violates the special symmetries. Simulation experiments show that this method can retrieval random wavefront distributions accurately. It provides a practical technical solution for precise wavefront sensing with single far field image.

Standard adaptive optics systems measure the aberrations in the wavefronts of a beacon guide star caused by atmospheric turbulence, which limits the corrected field of view to the isoplanatic patch, the solid angle over which the optical aberration is roughly constant. For imaging systems that require a corrected field of view larger than the isoplanatic angle, a three-dimensional estimate of the aberration is required. We are developing a wide-field imaging Shack-Hartmann wavefront sensor (WFS) that will characterize turbulence over a large field of view tens of times the size of the isoplanatic angle. The technique will find application in horizontal and downward looking remote sensing scenarios where high resolution imaging through extended atmospheric turbulence is required. The laboratory prototype system consists of a scene generator, turbulence simulator, a Shack Hartman WFS arm, and an imaging arm. The system has a high intrinsic Strehl ratio, is telecentric, and diffraction limited. We present preliminary data and analysis from the system.

We report on digital holographic imaging through atmospheric turbulence. Data recorded with aberrations is corrected during post processing using an iterative sharpness-metric maximization algorithm. Assuming the correction cancels the actual wavefront error, this process is equivalent to wavefront sensing. Much of our past work focused on imaging through isotropic turbulence with phase corrections using a Zernike-polynomial expansion. Here, we describe algorithm modifications for imaging through anisotropic turbulence, similar to what is seen when looking through the aero-optic boundary layer surrounding a moving aircraft. Specifically, we explore tradeoffs associated with switching from a Zernike representation to Karhunen-Loève basis functions. In some cases, the dimensionality of the phase correction estimation algorithm can be reduced significantly by this change. This reduces the computational burden

A novel scintillation resistant wavefront sensor based on a densely packed array of classical Zernike filters, referred to as the multi-aperture Zernike wavefront sensor (MAZ-WFS), is introduced and analyzed through numerical simulations. Wavefront phase reconstruction in the MAZ-WFS is performed using iterative algorithms that are optimized for phase aberration sensing in severe atmospheric turbulence conditions. The results demonstrate the potential of the MAZ-WFS for high-resolution retrieval of turbulence-induced phase aberrations in strong scintillation conditions for atmospheric sensing and adaptive optics applications.

Adaptive optics or numerical restoration algorithms that restore high resolution imaging through atmospheric turbulence are subject to isoplanatic wave-front errors. Mitigating those errors requires that the wave-front aberrations be estimated within the 3D volume of the atmosphere. Present techniques rely on multiple beacons, either natural stars or laser guide stars, to probe the atmospheric aberration along different lines of sight, followed by tomographic projection of the measurements onto layers at defined ranges. In this paper we show that a three-dimensional estimate of the wave-front aberration can be recovered from measurements by a single guide star in the case where the aberration is stratified, provided that the telescope tracks across the sky with non-uniform angular velocity. This is generally the case for observations of artificial earth-orbiting satellites, and the new method is likely to find application in ground-based telescopes used for space situational awareness.

Digital holography in the pupil-plane recording geometry shows promise as a wavefront sensor for use in adaptive-optics systems. Because current wavefront sensors suffer from decreased performance in the presence of turbulence and thermal blooming, there is a need for a more robust wavefront sensor in such distributed-volume atmospheric conditions. Digital holography fulfills this roll by accurately estimating the wrapped phase of the complex optical field after propagation through the atmosphere to the pupil plane of an optical system. This paper examines wave-optics simulations of spherical-wave propagation through both turbulence and thermal blooming; it also quantifies the performance of digital holography as a wavefront sensor by generating field-estimated Strehl ratios as a function of the number of pixels in the detector array, the Rytov number, and the Fried coherence diameter. Altogether the results indicate that digital holography wavefront sensing in the pupil-plane recording geometry is a valid and accurate method for estimating the wrapped phase of the complex optical field in the presence of distributed-volume atmospheric aberrations.

Polychromatic laser light can reduce speckle contrast in wavefront-sensing and imaging applications that use direct detection schemes. To help quantify the associated reduction in speckle contrast, this study investigates the accuracy and numerical efficiency of three separate wave-optics models that simulate the active illumination of extended objects with polychromatic laser light. The three separate models use spectral slicing, Monte Carlo averaging, and depth slicing, respectively, to simulate the laser-target interaction. The sampling requirements of all three models are discussed. Comparisons to analytical solutions and experimental data are made when possible. In general, the experiments and theory compare favorably with the models.

Digital holography has received recent attention for many imaging and sensing applications, including imaging through turbulent and turbid media, adaptive optics, three dimensional projective display technology and optical tweezing. A significant obstacle for digital holography in real-time applications, such as wavefront sensing for high energy laser systems and high speed imaging for target tracking, is the fact that digital holography is computationally intensive; it requires iterative virtual wavefront propagation and hill-climbing to optimize some sharpness criteria. This paper demonstrates real-time methods for digital holography based on approaches developed recently at UCLA for optimal and adaptive identification, prediction, and control of optical wavefronts. The methods presented integrate minimum variance wavefront prediction into digital holography schemes to short-circuit the computationally intensive algorithms for iterative propagation of virtual wavefronts and hill climbing for sharpness optimization.

An extension to zonal wavefront reconstruction estimation algorithms is proposed for irregular and discontinuous apertures. Many applications in astronomy and directed energy feature wavefront reconstruction over apertures partially obscured by a secondary mirror and its supports. In the worst case, these obscurations can separate the aperture into multiple discontinuous regions. The method proposed uses integration equations derived from the Taylor theorem assuming missing slope data. These integration equations are included in the least-squares solution of the wavefront and provide constants of slope integration which minimize the error introduced by the discontinuities. The equations can be included in any zonal estimation scheme. Several algorithms with and without the additional integration equations are evaluated against wavefronts gathered in recent optical flight tests. Finally, an evaluation of the noise-induced error is given for the same set of algorithms.

Shadow imaging is a technique to obtain highly resolved silhouettes of resident space objects (RSOs) which would otherwise be unattainable using conventional terrestrial based imaging approaches. This is done by post processing the measured irradiance pattern (shadow) cast onto the Earth as the RSO occults a star. The research presented here focuses on shadow imaging of geosynchronous (GEO) satellites with near stationary orbits approximately 36,000 km from the Earth. Shadows pertaining to a set of diverse observing scenarios are simulated and used as inputs to a Fresnel based phase retrieval algorithm. Spatial resolution limits are evaluated and correlated to signal to noise (SNR) metrics. Resolvable feature sizes of less than 1 m are shown to be readily achievable using foreseeable observing scenarios. Initial output from a shadow prediction tool indicates that there are, on average, over 1000 shadows on the Earth on any given time from a single GEO satellite for stars brighter than m_v=10. Shadow ground track uncertainties are correlated to stellar astrometric errors. Global and localized shadow track maps are presented demonstrating a high feasibility for future shadow collections.

We present a physics-based model for analysis of atmospheric turbulence and aerosol scattering effects on imaging of remote extended objects under daylight and laser illumination. The technique is based on joint solution of the parabolic wave equation and equation for the brightness function. Turbulent distortions are simulated with the use of the conventional phase-screen approach. Scattering effects are accounted for by representing the aerosol medium by a set of aerosol screens. The coherent and incoherent components of the scattered field are obtained in the single scattering approximation at each aerosol screen. In addition, a simplified model considering the natural background radiation effect on the contrast of an image formed is discussed. Numerical simulation results are presented.

Active illumination is often used when passive illumination cannot produce enough signal intensity to be a reliable imaging method. However, an increase in signal intensity is often achieved by using highly coherent laser sources, which produce undesirable effects such as speckle and scintillation. The deleterious effects of speckle and scintillation are often so immense that the imaging camera cannot receive intelligible data, thereby rendering the active illumination technique useless. By reducing the spatial coherence of the laser beam that is actively illuminating the object, it is possible to reduce the corruption of the received data caused by speckle and scintillation. The waveguide method discussed in this paper reduces spatial coherence through multiple total internal reflections, which create multiple virtual sources of diverse path lengths. The differing path lengths between the virtual sources and the target allow for the temporal coherence properties of the laser to be translated into spatial coherence properties. The resulting partial spatial coherence helps to mitigate the self-interference of the beam as it travels through the atmosphere and reflects off of optically rough targets. This mitigation method results in a cleaner, intelligible image that may be further processed for the intended use, unlike its unmitigated counterpart. Previous research has been done to independently reduce speckle or scintillation by way of spatial incoherence, but there has been no focus on modeling the waveguide, specifically the image plane the waveguide creates. Utilizing a ray-tracing method we can determine the coherence length of the source necessary to create incoherent spots in the image plane, as well as accurately modeling the image plane.

Standard Synthetic Aperture LADAR (SAL) image processing techniques use fast Fourier transforms (FFTs) to render images. This leads to noise amplification and estimates of the complex-valued reflection coefficient, thus resulting in high variation known as speckle. In this paper we propose a model-based iterative reconstruction (MBIR) approach using a Bayesian framework to form SAL images. The resulting images are the maximum a posteriori (MAP) estimate of object's real-valued surface reflectance. To overcome the complexity of the MAP cost function, we use the expectation maximization (EM) algorithm to derive a surrogate function which is then optimized. The proposed algorithm is tested on simulated data and compared against the Fourier-based approach.

Laser illuminated imaging has a number of applications in the areas of night time air-to-ground target surveillance, ID, and pointing and tracking. Using a laser illuminator, the illumination intensity and thus the signal to noise ratio can be controlled. With the advent of high performance range gated cameras in the short-wave infra-red band, higher spatial resolution can be achieved over passive thermal night imaging cameras in the mid-wave infra-red due to the shorter wave-length. If a coherent illuminator is used the resulting imagery often suffers from speckle noise due to the scattering off of a rough target surface, which gives it a grainy “salt and pepper” appearance. The probability density function for the intensity of focal plane speckle is well understood to follow a negative exponential distribution. This can be exploited to develop a Bayesian speckle noise filter. The filter has the advantage over simple frame averaging approaches in that it preserves target features and motion while reducing speckle noise without smearing or blurring the images. The resulting filtered images have the appearance of passive imagery and so are more amenable to sensor fusion with simultaneous mid-wave infra-red thermal images for enhanced target ID. The noise filter improvement is demonstrated using examples from real world laser imaging tests on tactical targets.

Direct liquid-cooling is a promising way of power scaling and heat management for solid-state lasers. A side-pumped direct liquid-cooled solid-state pulsed zigzag MOPA system is established based on this advanced concept. However, its beam quality is degraded by the thermal distortions in the non-zigzag direction and the flowing coolant. We develop an adaptive optics system to improve its beam quality, which primarily includes a low-order aberration compensator and a 59-actuator deformable mirror. The beam is first corrected by the low-order aberration compensator to remove large defocus and astigmatism, and its size is reshaped simultaneously to fulfill the demands of applications. Then the beam is further corrected by the deformable mirror. With collaborative operation of the low-order aberration compensator and the deformable mirror, we have achieved average beam quality of β=2.8.

Imaging of distant objects in a terrestrial environment involves propagation of light through significant turbulence. Conventional methods for imaging for these applications are radar or focal plane imaging. Both of these methods have limitations, such as object rotation rate and post-processing. A different class of imaging approaches involving coherent illumination has several advantages (a) reduced sensitivity to illumination conditions, (b) reduced sensitivity to object rotation, (c) the use of arrayed receivers that are lighter and lower in cost, and (d) snapshot reconstruction of aberrated images with just one or a few frames. These advantages must be balanced by the challenges of speckle noise in the image reconstructions, and more difficult algorithms. Coherent pupil-plane and focal-plane techniques are investigated for image formation. The associated algorithms include root-reconstruction techniques, phase smoothing methods, polynomial fit approaches, blind iterative deconvolution, and multi-frame blind deconvolution (MFBD). These techniques and algorithms are surveyed for speed and quality of image formation.

In this paper, we present two analytic theories developed recently to predict the performance of an imaging system composed of a phased array illuminator and a set of receiver subapertures. The receiver need not coincide with the transmitter. The two theories have been documented separately (ref. 1, 2), and the reader can find more details there – the theories present the analytic phased array irradiance on target in the presence of piston errors, and the resulting speckle pattern-induced imaging noise. The principal results presented here are the Signal to Noise Ratios (SNR) for both the radiometric portion of the problem and the speckle imaging portion of the problem.

Since telescopes were first trained on the heavens, nearly every attempt to locate new objects in the sky has been accomplished using long-exposure images (images taken with exposures longer than one second). For many decades astronomers have utilized short-exposure images to achieve high spatial resolution and mitigate the effect of Earth’s atmosphere. This is due to the fact that short-exposure images contain higher spatial frequency content than their long exposure counterparts. New objects, such as dim companions of binary stars have been revealed using these techniques, thus achieving some discoveries via short-exposure images, but always in context of a detailed analysis of a specific area of the sky, not through a synoptic search of the heavens like the kind carried out by asteroid research programs like Space Watch, PAN-STARRS or the Catalina Sky Survey. In this paper simulated short-exposure images are processed to detect simulated stars in the presence of strong atmospheric turbulence. The strong turbulence condition produces long-exposures with wide star patterns, while the short-exposure images feature better concentration of the available photons, but large random position variance. A new processing strategy involving a matched-filter technique using a short-exposure atmospheric impulse response model is utilized. The results from this process are compared to efforts to detect stars in long exposure images taken over the same interval the short-exposure images are collected. The two techniques are compared and the short-exposure imaging technique is found to produce the higher probability of detection.

In this paper a new detection algorithm is proposed and developed for detecting space objects from images obtained using a ground-based telescope with the goal to improve space situational awareness. Most current space object detection algorithms rely on developing a likelihood ratio test (LRT) for the observed data based on a binary hypothesis test. These algorithms are based on the assumption that the observed data is Gaussian or Poisson distributed under both the hypothesis that a low signal-to-noise ratio (SNR) space object is present in the data and the hypothesis that an object is absent from the data. The LRT algorithm in this paper was developed based on the assumption that the distribution of the Fourier transform of the observed data will be different when a low SNR object is present in the data compared to when the data only contains background noise and known space objects. When an object is present the probability distribution of the real component of the Fourier transform of the intensity was found to follow a Gaussian distribution with a mean significantly different than in the data that doesn’t contain an object even at low SNR levels. As the separation of these two probability distribution functions increases, it becomes more likely that an object can be detected. In this paper, simulated data are used to demonstrate the effectiveness and to highlight the benefits gained from this algorithm.

At the Starfire Optical Range in 2011, the first measurements of photonic orbital angular momentum in starlight were made. Although that survey conclusively demonstrated that POAM exists in starlight, the survey was limited. We have subsequently obtained access to the SAM data archive with its seven years of data. Here the SAM data is analyzed to include the two metrics, branch point density, ρ , and the conversion efficiency η, that were used in the analysis of the 2011 observations.

An experiment, specifically undertaken in order to measure terrestrial turbulence-induced photonic orbital angular momentum, was conducted at the RACHL site at the Starfire Optical Range. We present an overview of the experiment, to include methodology and calibration.

We develop a metric that measures the isotropy of atmospheric turbulence. We then apply that metric to data from the RACHL experiment as a test of the Kolmogarity of the turbulence encountered in that experiment.

The detection of near Earth space objects and potentially threatening asteroids is a challenging problem. The goal of this paper is to present a new method useful for detecting objects in space and to prove that it is more efficient than other existing methods. Instead of simply looking at a single, specified point in an image, this new method would use vectors created by summing across the rows and columns of the CCD array. The data is processed by a likelihood ratio test designed to process vector data under Poisson noise assumptions. The summing is done on the chip before readout noise is added to the image, so this method might have a higher signal to noise ratio than other techniques. Using this method, it is possible to search the same amount of space as you would with other techniques, while using less data. In order to prove that this method is more efficient, a likelihood ratio test will be derived and compared to the same kind of test using simulated data. It will be shown that this new method has a higher detection probability and lower false alarm rate than other methods under certain conditions; and that it will be more useful for detecting potentially deadly asteroids or other space objects that would threaten national security.

In this work we calculate the effect caused by roughness on the light reflected by an optical surface like a mirror, the numerical calculation is carry out within the Rayleigh approximation. We focus our study in the comparison of the results obtained numerically using different roughness parameters and calculate its effect on the aberrations of the wavefront, which without the effect of the roughness is considered perfect surface.

Object detection algorithms typically implement a Likelihood Ratio Test (LRT) for determining if an image-pixel contains a star. Implementing a LRT requires prior knowledge about the statistics of the data, such as the mean and variance. Assuming the background noise follows a Gaussian distribution, the mean and the variance have to be calculated separately. If the background data follows a Poisson distribution, the mean is the only calculation needed, as mean and variance of the Poisson distribution equal each other. This paper will compare the possible detection improvements when using a Poisson assumption. Many star detection LRTs will use a windowing technique to limit the amount of background data that is being tested. Various window sizes will also be tested to determine possible detection improvements that can be realized.

Photo-detector arrays have imperfections that cause response differences between pixels, incurring a need for Non- Uniformity Correction (NUC) to be normalized. Static Scene Statistical Non-Uniformity Correction (S3NUC) was developed as method that takes advantage of higher order statistical moments to achieve NUC without the use of dedicated calibration hardware, and without sacrificing accuracy. Data in a photo-detector array is modeled as a Poisson random process that is changed by a system gain, bias, and readout noise. While successful, the first iteration of this method relied on higher order moments to reach an overdetermined system of equations that allows the noise to be recovered. Because the third moment is relied upon for a solution, a very large data set with high calculation time is required. By treating the statistics of one Poisson data set as proportional to the integration time, the number of variables can be reduced and allow for a perfectly determined system that relies only on the mean and variance of the data. This assumption is particularly well suited for space object detection, where the scene is stationary enough for two data sets to be collected which vary only by controlled integration time. This new algorithm is tested against the S3NUC algorithm in simulated data to find the errors in noise recovery with respect to the size of the data set. This new SANUC algorithm will be compared in speed in calculation and error in the recovered gain, bias, and readout noise.

To catalog space objects, the position and angular rate of the detected object must be determined; however, the quality of this data is restricted by the capability to determine the telescope’s pointing azimuth and elevation. The commonly used Binary Hypothesis Test (BHT) determines whether an object is present in an image or not by calculating the ratio of the probability of whether an object is present in each pixel to the probability of an object not being present. If this ratio exceeds a specified threshold, an object has been detected. The Multiple Hypothesis Test (MHT) operates similarly to the BHT but includes the additional step of correlating the image data against sampled Point Spread Functions (PSF). These PSFs appear differently based on the sub-pixel location of the object. The PSF with the strongest correlation to the image data indicates that the detected object is likely in the same sub-pixel location. Using the MHT can improve the ability to determine the telescope’s azimuth and elevation by observing objects at known locations. The data will be gathered through projecting a star map and using a telescope to locate the objects. This experimental data will provide verification and quantification of the improved accuracy of using the multi-hypothesis test.