Comparative analysis of C n2 estimation methods for sonic anemometer data.

Wind speed and sonic temperature measured with ultrasonic anemometers are often utilized to estimate the refractive index structure parameter C n2, a vital parameter for optical propagation. In this work, we compare four methods to estimate C n2 from C T2, using the same temporal sonic temperature data streams for two separated sonic anemometers on a homogenous path. Values of C n2 obtained with these four methods using field trial data are compared to those from a commercial scintillometer and from the differential image motion method using a grid of light sources positioned at the end of a common path. In addition to the comparison between the methods, we also consider appropriate error bars for C n2 based on sonic temperature considering only the errors from having a finite number of turbulent samples. The Bayesian and power spectral methods were found to give adequate estimates for strong turbulence levels but consistently overestimated the C n2 for weak turbulence. The nearest neighbors and structure function methods performed well under all turbulence strengths tested.

Equivalent refractive-index structure constant of non-Kolmogorov turbulence: comment.

The paper by Y. Li, W. Zhu, X. Wu, and R. Rao entitled "Equivalent refractive-index structure constant of non-Kolmogorov turbulence," Opt. Express23(18), 23004 (2015).10.1364/OE.23.023004 relates the non-Kolmogorov turbulence structure constant to the classical structure constant for Kolmogorov turbulence by imposing equality of their respective structure functions at large separation distances, higher than the outer scale. As opposed to previous attempts to relate the two structure constants, the approach of Li et al. is anchored on a measurable meteorological parameter, the outer scale. The error lies in the fact that the authors have used a default Kolmogorov structure function with an infinite outer scale. A subsequent assumption of a finite outer scale is not compatible with the initial assumption. In this paper we show the correct procedure to obtain the relationship between the non-Kolmogorov and Kolmogorov structure constants which is based on an explicitly finite outer scale used throughout all calculations.

Atmospheric optical turbulence mitigation using iterative image registration and least squares lucky look fusion.

This paper presents an atmospheric optical turbulence mitigation method that uses a sequence of short-exposure frames. An iterative block matching registration method is proposed for image dewarping. The dewarped frames are combined in a least squares lucky look (LL) fusion process. Here image patches are weighted so as to produce a fused image that is consistent with a theoretical LL optical transfer function (OTF) model. Finally, a Wiener filter is applied to provide deconvolution of the LL OTF. We also explore the LL selectivity tradespace. As the selectivity increases, the LL OTF becomes more favorable but the signal-to-noise ratio suffers, and vice versa. A restoration algorithm is applied to simulated data for quantitative analysis and two different real-world datasets for subjective evaluation. The proposed approach provides improved results compared with the benchmark methods.

Optimal, blind-search modal wavefront correction in atmospheric turbulence. Part I: simulations.

Modal control is an established tool in adaptive optics. It allows not only for the reduction in the controllable degrees of freedom, but also for filtering out unseen modes and optimizing gain on a mode-by-mode basis. When Zernike polynomials are employed as the modal basis for correcting atmospheric turbulence, their cross-correlations translate to correction errors. We propose optimal modal decomposition for gradient-descent-based wavefront sensorless adaptive optics, which is free of this problem. We adopt statistically independent Karhunen-Loève functions for iterative blind correction and analyze performance of the algorithm in static as well as in dynamic simulated turbulence conditions.

Influence of bandwidth error on the performance of adaptive optics systems for uncooperative beacons.

We discuss the capability of adaptive optics to increase the performance of laser systems operating in atmospheric turbulence. Our approach is based on the Zernike filter functions, Taylor's frozen-flow hypothesis, and bandwidth limitations of a realistic servo control system. System performance is analyzed in terms of the Strehl ratio on target. Our results for plane-wave geometry indicate that adaptive optics can be effective even when engaging fast moving targets and that moderate closed-loop bandwidths of ∼100Hz would suffice for most analyzed scenarios. Applications of interest are beam delivery systems and free-space optical communications.

Optimization of the holographic wavefront sensor for open-loop adaptive optics under realistic turbulence. Part I: simulations.

The modal holographic wavefront sensor enables fast measurement of individual aberration modes without the need for time-consuming calculations. However, the measurement accuracy suffers greatly from intermodal crosstalk, caused when the wavefront contains more aberrations than the one to be measured. In this paper, we present sensor optimization to minimize this effect and show the improvement when using Karhunen-Lòeve instead of Zernike modes as the basis. Finally, we show in simulation that an open-loop adaptive optics system based on the optimized sensor can be used to correct the effect of realistic, dynamic atmospheric turbulence on a wavefront and increase its Strehl ratio significantly.

Fraunhofer Institute of Optronics, System Technologies and Image Exploitation: introduction to the focus issue.

This focus issue offers a glimpse into the breadth and depth of research in optics and image processing at the Fraunhofer Institute of Optronics, System Technologies and Image Exploitation (abbreviated Fraunhofer IOSB). The institute belongs to the Fraunhofer Society, which is Europe's largest organization for applied research. The society comprises 72 institutes spread throughout Germany as well as subsidiaries in several European countries, and the USA, UK, Chile and Singapore, each focusing on different fields of applied science. It is named after the Bavarian physicist Joseph von Fraunhofer (1787-1826), the inventor of the spectrometer, optical lens manufacturer and an entrepreneur, who exemplified the goals of the society, i.e.: a focus on research excellence, innovation, and commitment to market and customer-oriented research.

Straightness metric for measurement of turbulence-induced distortion in long-range imaging.

Algorithms used for mitigation of the effects of atmospheric turbulence on video sequences often rely on a process for creating a reference image to register all of the frames. Because such a pristine image is generally not available, no-reference image quality metrics can be used to identify frames in a sequence that have minimum distortion. Here, we propose a metric that quantifies image warping by measuring image straightness based on line detection. The average length of straight lines in a frame is used to select best frames in a sequence and to generate a reference frame for a subsequent dewarping algorithm. We perform tests with this metric on simulated data that exhibits varying degrees of distortion and blur and spans normalized turbulence strengths between 0.75 and 4.5. We show, through these simulations, that the metric can differentiate between weak and moderate turbulence effects. We also show in simulations that the optical flow that uses a reference frame generated by this metric produces consistently improved image quality. This improvement is even higher when we employ the metric to guide optical flow that is applied to three real video sequences taken over a 7 km path.

Improving system performance by using adaptive optics and aperture averaging for laser communications in oceanic turbulence.

We theoretically investigate the effectiveness of adaptive optics correction for Gaussian beams affected by oceanic turbulence. Action of an idealized adaptive optics system is modeled as a perfect removal of a certain number of Zernike modes from the aberrated wavefront. We focused on direct detection systems and we used the aperture-averaged scintillation as the main metric to evaluate optical system performances. We found that, similar to laser beam propagation in atmospheric turbulence, adaptive optics is very effective in improving the performance of laser communication links if an optimum aperture size is used. For the specific cases we analyzed in this study, scintillation was reduced by a factor of ∼7 when 15 modes were removed and when the aperture size of the transceiver was large enough to capture 4-5 speckles of the oceanic turbulence-affected beam.

Adaptable Shack-Hartmann wavefront sensor with diffractive lenslet arrays to mitigate the effects of scintillation.

Adaptive optics systems are used to compensate for distortions of the wavefront of light induced by turbulence in the atmosphere. Shack-Hartmann wavefront sensors are used to measure this wavefront distortion before correction. However, in turbulence conditions where strong scintillation (intensity fluctuation) is present, these sensors show considerably worse performance. This is partly because the lenslet arrays of the sensor are designed without regard to scintillation and are not adaptable to changes in turbulence strength. Therefore, we have developed an adaptable Shack-Hartmann wavefront sensor that can flexibly exchange its lenslet array by relying on diffractive lenses displayed on a spatial light modulator instead of utilizing a physical microlens array. This paper presents the principle of the sensor, the design of a deterministic turbulence simulation test-bed, and an analysis how different lenslet arrays perform in scintillation conditions. Our experiments with different turbulence conditions showed that it is advantageous to increase the lenslet size when scintillation is present. The residual phase variance for an array with 24 lenslets was up to 71% lower than for a 112 lenslet array. This shows that the measurement error of focal spots has a strong influence on the performance of a Shack-Hartmann wavefront sensor and that in many cases it makes sense to increase the lenslet size. With our adaptable wavefront sensor such changes in lenslet configurations can be done very quickly and flexibly.

Comparison of probability density functions for aperture-averaged irradiance fluctuations of a Gaussian beam with beam wander.

Over the years, there has been much interest in the use of optical wavelengths for communication because of the potential for high data rates. However, the performance of these systems can become significantly degraded due to turbulence-induced signal fluctuations. These fluctuations can be minimized by enlarging the receiving aperture, thereby averaging the fluctuations. There is extensive interest in developing probability density functions (PDFs) describing these intensity fluctuations so as to accurately predict system performance. This work examines several PDF models that have been suggested to represent fluctuations by comparing them to simulations of realistic propagation scenarios of a collimated Gaussian beam with centroid wander. Unlike with an infinite plane or spherical wave, the empirical PDF shape in these simulations changed significantly with increased aperture, going from a positively skewed to a negatively skewed distribution; therefore, the PDF model that describes it also must change. This change in skew can have serious consequences on the metrics of an optical communication system, e.g., number of fades and bit-error rate. In this work, we examine the evolution of the empirical PDF with aperture size and the fit of potential PDF models under various strengths of turbulence. We show that the change in skew with increasing aperture size occurred for all strengths of turbulence and that the currently used PDF models do not adequately characterize this for realistically sized apertures where beam wander is present.

Statistics of intensity in adaptive-optics images and their usefulness for detection and photometry of exoplanets.

This paper is an introduction to the problem of modeling the probability density function of adaptive-optics speckle. We show that with the modified Rician distribution one cannot describe the statistics of light on axis. A dual solution is proposed: the modified Rician distribution for off-axis speckle and gamma-based distribution for the core of the point spread function. From these two distributions we derive optimal statistical discriminators between real sources and quasi-static speckles. In the second part of the paper the morphological difference between the two probability density functions is used to constrain a one-dimensional, "blind," iterative deconvolution at the position of an exoplanet. Separation of the probability density functions of signal and speckle yields accurate differential photometry in our simulations of the SPHERE planet finder instrument.

Fainter and closer: finding planets by symmetry breaking.

Imaging of planets is very difficult, due to the glare from their nearby, much brighter suns. Static and slowly-evolving aberrations are the limiting factors, even after application of adaptive optics. The residual speckle pattern is highly symmetrical due to diffraction from the telescope's aperture. We suggest to break this symmetry and thus to locate planets hidden beneath it. An eccentric pupil mask is rotated to modulate the residual light pattern not removed by other means. This modulation is then exploited to reveal the planet's constant signal. In well-corrected ground-based observations we can reach planets six stellar magnitudes fainter than their sun, and only 2-3 times the diffraction limit from it. At ten times the diffraction limit, we detect planets 16 magnitudes fainter. The stellar background drops by five magnitudes.

On Advanced Estimation Techniques for Exoplanet Detection and Characterization Using Ground-based Coronagraphs.

The direct imaging of planets around nearby stars is exceedingly difficult. Only about 14 exoplanets have been imaged to date that have masses less than 13 times that of Jupiter. The next generation of planet-finding coronagraphs, including VLT-SPHERE, the Gemini Planet Imager, Palomar P1640, and Subaru HiCIAO have predicted contrast performance of roughly a thousand times less than would be needed to detect Earth-like planets. In this paper we review the state of the art in exoplanet imaging, most notably the method of Locally Optimized Combination of Images (LOCI), and we investigate the potential of improving the detectability of faint exoplanets through the use of advanced statistical methods based on the concepts of the ideal observer and the Hotelling observer. We propose a formal comparison of techniques using a blind data challenge with an evaluation of performance using the Receiver Operating Characteristic (ROC) and Localization ROC (LROC) curves. We place particular emphasis on the understanding and modeling of realistic sources of measurement noise in ground-based AO-corrected coronagraphs. The work reported in this paper is the result of interactions between the co-authors during a week-long workshop on exoplanet imaging that was held in Squaw Valley, California, in March of 2012.