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Neurobiologists from Tübingen and Munich find clues as to how the brain separates the important from the unimportant
The precise interaction of brain waves and nerve cells may be decisive for the amazing ability of our brain to separate important from unimportant information, even when we are flooded with stimuli.
Researchers at the University of Tübingen and the Technical University of Munich have been able to show through experiments on Rhesus monkeys that the exact point in time at which certain nerve cells discharge seems to play a key role in separating "the wheat from the chaff" in working memory. The findings will be published on Wednesday in the scientific journal "Neuron".
At work, on the road or in the midst of a crowd – every day we are all exposed to situations in which we are confronted with a multitude of stimuli. Nevertheless, we act purposefully and safely in such situations. Our working memory seems to be able to effortlessly filter out relevant information and ignore the other, unimportant stimuli.
In order to find out what is happening in the brain, the Tübingen researchers trained rhesus monkeys to separate relevant numbers, which they had to remember in a short time, from interfering numbers. During the experiment, the electrical signals of nerve cells in the cerebral cortex of the animals were measured using microelectrodes. The scientists observed that the simultaneous discharge of thousands of nerve cells caused large-scale oscillating fluctuations ("brain waves") in electrical brain activity.
Low frequency waves (known as theta waves) of four to ten cycles per second, proved to be particularly decisive. "We observed that both the relevant and the interfering information was transmitted in this theta frequency range," said Professor Andreas Nieder from the Institute of Neu-robiology at the University of Tübingen.
"However, the nerve cells responsible for the relevant information always discharged when the theta wave was at its lowest point. Contrarily, the nerve cells responsible for the disturbing stimulus always fired at the time when the theta wave was at its peak. We believe that the brain uses certain frequency channels to transmit information synchronously, but at the same time this wealth of information is also sorted according to whether it is important and unimportant during the transmission between brain areas," explains Nieder.
The leading author of the study, Dr. Simon Jacob, a neurologist at the Klinikum rechts der Isar at the Technical University of Munich, emphasizes the medical significance of the study: "Our results show that cognitive brain functions require precise interaction of nerve cells. It makes sense to use the mechanisms investigated in the animal model for therapeutic purposes in patients with memory dis-orders, for example by stimulating coordinated communication between the brain regions studied."
Further studies will, however, be necessary to show whether the results of the study can be regarded as a general principle for how the brain processes cognitive information across separate areas of the brain.
Prof. Dr. Andreas Nieder
University of Tübingen
Institute of Neurobiology
Phone +49 7071 29-75347
Simon N. Jacob, Daniel Hähnke, and Andreas Nieder: Structuring of abstract working memory con-tent by fronto-parietal synchrony in primate cortex. Neuron. Online in the week from August 6 to 10, 2018. https://www.cell.com/neuron/newarticles
Antje Karbe | idw - Informationsdienst Wissenschaft
Further information:
Further reports about: > Nerve > Neuron > brain areas > brain processes > cerebral cortex > nerve cells > waves > working memory
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Commercial Property to rentHigh Road, Wembley, Middlesex, HA9
£5,000 pcm
Do you like this property?
Call: 020 8012 5640
Property Description
Letting information:
|Not Specified
|Letting type:
Full description
Lanmor house is a brand new development with Luxury Apartments sitting right over this commercial premises. All of these apartments are occupied by young professionals.
The premises boast a showroom area made up of approximately 1,740 sqft with an additional office area of approximately 441 sqft comprising toilets.
This impressive building is located on Wembley High Road and is within walking distance to Wembley Central, Wembley Stadium & Wembley Park Station.
Wembley Central - London Overground, West Midland Trains & Southern Services
Wembley Park - Jubilee & Metropolitan Services
Wembley Stadium - Chiltern Railways
By car - The A40, North Circular & M1 are within each reach
For years Wembley has been synonymous to Football. Wembley is now a prominent destination in London and has a vibrant and diverse community that appeals to several retail business.
The commercial space is in shell condition which offers a choice for a variety of retail uses such as
Mini Supermarket
Fashion Designer Showroom
Beauty Salon
Landlord would consider alternative use subject to change of use
Cross-fit, gym, fitness centre
Wine bar
Banks, money exchange outlet
Nursery / Tuition Centre
Dental Clinic
Car Park at the rear of the building
Large Frontage
Excellent natural light
New lease direct from the landlord for a term by arrangement.
£70k per annum exclusive
As this is a brand new unit, we recommend interested parties verify this with the local authority (Brent Council).
EPC - Contact us for the EPC
By arrangement with Empire Chase
Nearest stations
- Wembley Stadium (0.2 mi)
- Wembley Central (0.3 mi)
- Wembley Park (0.8 mi)
BroadbandShow average broadband speed at this postcode Average broadband speed within this postcode Finding the fastest speed... Compare broadband deals
To view this property or request more details, contact:
Empire Chase Estate Agent, Harrow14 Peterborough Road, Harrow, HA1 2BQ
How much will it cost me to call the number displayed on the site?
Standard geographic charges from landlines and mobiles apply and calls may be included in your telecom provider's call package.
Map & Street View
Street View is unavailable in this location
Nearest stations
- Wembley Stadium (0.2 mi)
- Wembley Central (0.3 mi)
- Wembley Park (0.8 mi)
To view this property or request more details, contact:
Empire Chase Estate Agent, Harrow14 Peterborough Road, Harrow, HA1 2BQ
How much will it cost me to call the number displayed on the site?
Standard geographic charges from landlines and mobiles apply and calls may be included in your telecom provider's call package.
Disclaimer - Administration fees may apply when renting a property in England, Wales or Northern Ireland. For more details, please contact the agent.
Property reference LANCOM. The information displayed about this property comprises a property advertisement. Rightmove.co.uk makes no warranty as to the accuracy or completeness of the advertisement or any linked or associated information, and Rightmove has no control over the content. This property advertisement does not constitute property particulars. The information is provided and maintained by Empire Chase Estate Agent, Harrow.
Please refer to our Renting Guides for further information on how to safely rent a property.
* Average speeds are based on the download speeds of at least 50% of customers at peak time (8pm to 10pm) from packages available on comparethemarket.com. Speed can be affected by a range of technical and environmental factors. The speed you receive where you live may be lower than that listed above. You can check the estimated speed to your property prior to purchasing. Fibre/cable services at your postcode are subject to availability. You can confirm availability on the provider's website. Providers may increase charges. You should have the right to exit your contract without penalty if this happens. The information is provided and maintained by Decision Technologies Limited.
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LONDON — Wayne Rooney believes he left Manchester United at the right time, even though he wanted to finish his career at Old Trafford. The 33-year-old, who is set to make his final England appearance against the United States in a friendly international at Wembley on Thursday, is now playing for North American club side DC United in Major League Soccer. But there is no denying his place in United's history books, with Rooney the club's leading goalscorer in a career that also saw him win five Premier League titles, the Champions League, Europa League, FA Cup and three League Cups with the Red Devils. In total, Rooney made 559 appearances for United from 2004-2017 after joining from boyhood club Everton. But he started a mere seven of the final 19 Premier League appearances of his United career, with Rooney no longer a first-choice player under manager Jose Mourinho. Rooney returned to Everton before leaving English club football completely when he joined DC … [Read more...] about Rooney reckons he picked 'right time' to leave Man Utd
Rooney man utd
Man City set win record, Lukaku lifts Man Utd
Football LONDON — David Silva scored twice as runaway Premier League leaders Manchester City won 4-0 at Swansea City on Wednesday to set a new English top-flight record of 15 consecutive victories. Pep Guardiola's side, 2-1 winners at second-place Manchester United on Sunday, won comfortably at the Liberty Stadium to eclipse the mark of 14 successive wins set by Arsenal in 2002. United bounced back from their derby defeat by beating Bournemouth 1-0, while slip-ups for Liverpool and Arsenal allowed Tottenham Hotspur to steal into fourth place by beating Brighton and Hove Albion 2-0. "Winning 15 games in a row gives us a lot of confidence. If people are happy watching us, that is the best gift," Guardiola said. "You suffer and enjoy, like a manager you see many things. When the team play good, we are happy." City remain 11 points clear of United and have now scored 52 goals in their 17 league games to date as they stride towards what seems like an inevitable title … [Read more...] about Man City set win record, Lukaku lifts Man Utd


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There either is or is not, that's the way things are. The colour of the day. The way it felt to be a child. The saltwater on your sunburnt legs. Sometimes the water is yellow, sometimes it's red. But what colour it may be in memory, depends on the day. I'm not going to tell you the story the way it happened. I'm going to tell it the way I remember it.
The Lizzie Bennet Diaries is an innovative, original episodic video and social media series produced for the web. Adapting Pride and Prejudice to the modern era, Lizzie Bennet tells the classic Jane Austen tale from the point of view of an Elizabeth "Lizzie" Bennet who grew up in a world of cell phones, video cameras, and social media. The series was created by popular YouTube personality Hank Green and Streamy Award winning web video writer Bernie Su.
The holiday season is bringing more than cheer for actress Jessica Capshaw. The Grey's Anatomy star announced on Monday that she and her husband, Honest Company co-founder Christopher Gavigan, are expecting their fourth child. "The holidays have certainly arrived … All of our lives are being added to by the lights, the music and cheer!!" she captioned a photo of her family at a Christmas tree farm on Instagram. "This year our family has reason to further broaden our smile … baby number four is on the way!! I am a lucky, lucky girl…"
The quickest way to tell whether an actor is serious about his or her career is to look at their "headshot".Is it a professional photo? Or is it a snapshot taken on prom night? If you're using a snapshot, it's like showing up to race the Indy 500 in a VW Beetle. Nobody is going to take you seriously. I'm sorry, people… you can send me as much angry e-mail as you want about this, but it's true! Don't tell me you're destined to be a major Hollywood star but you cannot scrape together the cash to get professional headshots.
The Grinch from Dr. Seuss' How the Grinch Stole Christmas! The Musical stole the spotlight at the Empire State Building's 86th Floor Observatory December 14, 2012, to promote the musical's limited holiday engagement. Discover the magic of Dr. Seuss' classic holiday tale as it comes to life on stage. Featuring the hit songs "You're A Mean One, Mr. Grinch" and "Welcome Christmas," The Grinch discovers there's more to Christmas then he bargained for in this heart-warming holiday classic.
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U.S. stock markets witnessed a strong rally on Wednesday after Fed chair Jerome Powell indicated that key rates were close to a "neutral" level. Moreover, investors' confidence on equities gathered steam following news that President Trump is looking for a way out to ongoing trade disputes with China. Additionally, third quarter GDP data confirmed robustness of the U.S. economy. All three indexes jumped up following these positive developments.
The Dow Jones Industrial Average (DJI) closed at 25,366.43, rallied 2.5% or 617.70 points. The S&P 500 Index (INX) increased 2.3% to close at 2,743.79. Meanwhile, the Nasdaq Composite Index (IXIC) closed at 7,291.59, gaining almost 3% or 208.89 points. A total of 8.04 billion shares were traded on Wednesday, higher than the last 20-session average of 7.82 billion shares. Advancers outnumbered decliners on the NYSE by 3.95-to-1 ratio. On the Nasdaq, advancers had an edge over decliners by 3.58-to-1 ratio. The CBOE VIX decreased 2.8% to close at 18.49.
How Did the Benchmarks Perform?
The Dow ended in positive territory for third successive day with twenty-seven components of the 30-stock index closing in the green while remaining three closed the red. Notably, the blue-chip index posted its biggest single-day gain since Mar 26 and is up nearly 1080 points in the first three trading sessions for the week started Nov 26.
The S&P 500 also closed in the green for third straight session. Moreover, the benchmark index recorded its biggest single-day gain since Mar 26. The Technology Select Sector SPDR (XLK) and Consumer Discretionary Select Sector SPDR (XLY) were major gainers with 3.5% and 3%, respectively. Notably, ten out of total 11 sectors of the broad-market index closed in the green while only one finished in the red.
Meanwhile, the tech-heavy Nasdaq Composite continued its bull-run for three consecutive days buoyed by strong performance of tech behemoths. The tech-laden index recorded its biggest single-day gain since Oct 25.
Fed Chairman Hints Soft Monetary Policy
On Nov 28, the Fed Chairman Jerome Powell indicated that the interest rate may be close to a neutral level while delivering a speech at the Economic Club of New York. He stated "Interest rates are still low by historical standards, and they remain just below the broad range of estimates of the level that would be neutral for the economy — that is, neither speeding up nor slowing down growth,"
Powell's latest comments regarding the benchmark interest rate was in sharp contrast to his earlier statement that there is a long way to go for the rate to hit a neutral level. Although Powell hasn't given any indication that the central bank will not opt for a fourth rate hike for 2018 in December, market participants, who were closely watching this event are of the opinion that the Fed is going to reduce the current pace of rate hikes reflecting a soft monetary stance.
Notably, possibility of a fourth rate hike in Decenter and continuation of tight monetary policy in 2019 were one of the major reasons for stock market routs in October and November. Recently, President Trump has severely criticized the Fed chairman for his hawkish stance which significantly undermined Trump's fiscal stimulus.
A Ray of Hope on Trade War Front
On Nov 28, citing U.S. government officials, The New York Times reported that President Trump is looking for a respectable compromise deal with China to resolve the eight month old tariff conflict between the two largest trading partners of the world. The newspaper reported that Trump is highly concerned about the negative impact of trade war on U.S. economy, particularly on the financial sector. Notably,President Donald Trump and Chinese President Xi Jinping are scheduled to meet on the sidelines of a G-20 summit in Argentina at the end of this week.
On Nov 27, U.S. National Economic Council Director Larry Kudlow said the U.S. government has reopened negotiations on trade-related issues with China at several high powered levels. Healso stated that President Trump is hopeful that an amicable solution to the eight-month old trade related conflict between two largest trading partners in the world can be reached during the upcoming G-20 summit.
Following these developments, shares of trade-sensitive stocks like Caterpillar Inc. (CAT - Free Report) and The Boeing Co. (BA - Free Report) increased 5% and 4.9%, respectively. The Boeing carries a Zacks Rank #2 (Buy). You can see the complete list of today's Zacks #1 Rank (Strong Buy) stocks here.
Economic Data
In its second estimate, the Department of Commerce confirmed that the U.S. GDP for the third quarter of 2018 expanded by 3.5%. The figure was in line with the consensus estimate. However, consumer spending, which constitutes around 70% of the U.S. economy, grew at 3.6% instead of 4% estimated earlier. On the other hand, business investment on equipment rose 3.5% in contrast to the earlier estimate that it had remained flat over the period.
The Department of Commerce also reported that the U.S. trade deficit for the month of October increased to $77.2 billion from a revised $76.3 billion deficit in September.
Stocks That Made Headline
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FULL REPORT: Auditor General probe uncovers various questionable practices at Petrojam
A report of an investigation conducted by the Office of the Auditor General into the state-owned oil refinery, Petrojam, has catalogued a series of lavish parties and unapproved sponsorships as well as glaring human resources breaches costing millions of dollars (One Jamaica dollar=US$0.008 cents).
The findings of the Auditor General was tabled in the House of Representatives on Tuesday and it warned that bad management practices, if left unresolved, would increase the risk of corruption and further erode Petrojam's profitability, which has declined over the last three years.
The probe found that although liquidity levels were inadequate to cover Petrojam's obligations, the state-owned company made questionable payments related to procurement activities, had…


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Understanding the physics of optical wave front distortions caused by turbulence in the atmospheric refractive-index field is essential for the design and operation of optical systems used in free-space optical communication, surveillance, navigation, remote sensing, astronomy, and directed-energy technologies.126.96.36.199.–6 If particle scattering, absorption, coupling, and depolarization effects are negligible then there are two phenomena that determine the optical field: refraction and diffraction. The combined effects of refraction and diffraction lead to phase-gradient fluctuations (angle-of-arrival fluctuations) and intensity fluctuations (scintillation), both of which limit the performance of a variety of optical systems.
The analysis of propagation scenarios through both deterministic and stochastic refractive-index fields may be substantially simplified if diffraction effects can be neglected, and considerable theoretical effort has been devoted to establishing criteria for the negligibility of diffraction effects.12.–3,7,8 These theoretical constraints, however, tend to be excessively conservative, as pointed out by Strohbehn 50 years ago.9 In other words, certain geometrical-optics predictions often agree well with field observations, but it remains unclear, from the theoretician's perspective, why that is so.
In addition to simplifying theoretical analyses, geometrical optics and ray tracing can also substantially reduce computation time for numerical simulations of propagation through turbulence. The utility of geometrical and ray optics is exemplified in a variety of publications from the last several decades. For example, Churnside and Lataitis10 presented a simple geometrical optics equation for the variance of beam displacements caused by propagation through weak turbulence, and geometrical optics simulation models have been developed by Yuksel et al.11 to investigate effects of aperture averaging on intensity fluctuations. More recently, Lachinova et al.12 have compared the performance of a brightness function-based numerical simulation method with a wave optics-based method for incoherent imaging through turbulence. The brightness function at the receiving pupil is estimated using ray-like trajectories that are perturbed by the turbulent refractive index gradients. These authors found that the brightness approach can reduce computation times by several orders of magnitude. Other recent examples include ray-tracing methods applied for simulating laser beam-steering effects in turbulent media,13 the derivation of turbulence strength profiles from radiometer temperature measurements with a geometrical ray-tracing analysis,14 and the application of ray tracing through phase screens for the simulation of images from optical survey telescopes.15
Since the 1980s, powerful phase-screen techniques have been developed1617.18.–19 that allow optical propagation through atmospheric turbulence to be accurately simulated well into the "strong-scattering" regime, that is, for scenarios where the negligibility of diffraction effects and the "weak-scattering" assumption become invalid, or at least questionable. Such simulations can be used to test and refine the traditional, often excessively conservative, criteria for the negligibility of diffraction effects.
Here, we present and discuss computer simulations of plane waves of visible light () propagating through fully turbulent, homogeneous, and isotropic refractive-index fields. We study the optical angle-of-arrival (AOA) fluctuations by means of both a wave-optics propagation simulation and a ray-tracing simulation through a turbulent path that is characterized by a sequence of phase screens with Kolmogorov statistics. The path length assumed is and the refractive-index structure parameter ranges from to , which corresponds to Rytov variances that span from 0.0267 (weak scattering) to 26.7 (strong scattering), where and is the optical wave number. For the two simulation methods, we examine the variance and histograms of the aperture-filtered (aperture-averaged) AOA fluctuations for aperture diameters ranging from 0.6 to 13 Fresnel lengths. We compare the simulation results with theoretical predictions20 based on the Rytov theory, which accounts for both refraction and diffraction effects but does not capture strong-scattering effects. Our specific interests are: (1) to better understand under what conditions the Rytov theory for AOA fluctuations becomes invalid, (2) to reveal the behavior of the AOA fluctuations in strong scattering conditions, and (3) to investigate the consequences of ignoring diffraction and the applicability of ray tracing for modeling AOA fluctuations.
A plane wave is propagated through a set of split-step phase screens that model atmospheric turbulence [Fig. 1(a)] and similarly, a bundle of parallel rays is traced through the same screens [Fig. 1(b)]. The wave optics simulation provides a coherent wave result that accounts for refraction, diffraction, and interference. On the other hand, the ray-tracing simulations provide the trajectories of a large number of individual rays, where the phases and amplitudes are left undefined.
The simulation parameters of interest are defined in Table 1 and the values used for the simulations are listed. The turbulence along the path is assumed to be statistically homogeneous and isotropic. The path is divided into equal length segments and a phase screen is positioned at the center of each segment. The screens are created with the Fourier filtering method and have Kolmogorov statistics. To model an infinite outer scale, a random tilt component is added to each screen that compensates for turbulent wave-front tilts with length scales greater than the grid width (see Ref. 18 and references therein). Zero inner scale is assumed for the turbulence spectrum; however, the period of the highest spatial frequency of a screen is twice the grid spacing, so the modeled inner scale is no smaller than 2 mm.
Table 1
Simulation parameter values.
|Grid physical size
|Grid samples
|Grid spacing
|1 mm
|Path length
|2 km
|Fresnel length
|3.2 cm
|Aperture diameter
|0.02 to 0.4 m
|Turbulence spectrum
|Structure parameter
|Rytov variance
|0.0267 to 26.7
|Number of phase screens
|6 (for ); 6 (for ); 10 (for ); 22 (for )
The number of turbulence screens required along the path is an integer and should be greater than , which ensures each screen corresponds to weak scattering, and therefore phase-only screens are adequate.19 The minimum value of for the strongest scattering case is 22 screens. Fewer screens can be used for the weaker scattering cases, which reduces computational time. However, we implemented more than the required minimum number of screens for the weak scattering cases to provide a better representation of the continuous volume turbulence that is assumed along the path.
The grid parameters are chosen to provide a grid spacing of , where is the grid side length. This sampling choice has been shown to make artifacts that arise from the discrete Fourier transform implementation of the Fresnel diffraction integral to be sufficiently small to be negligible.21 The resulting grid spacing of 1 mm allows about sampling of the minimum Fried parameter () value encountered in our study. The propagation length , wavelength , and four choices of turbulence structure parameter (, , , and ) correspond to Rytov variances of 0.0267, 0.267, 2.67, and 26.7, which range in scattering strength from weak () to strong (). Corresponding Fried diameter [] values for the four cases are calculated to be 21.3, 5.3, 1.33, and 0.33 cm.
Ultimately, our interest is to examine the variance and histogram of the fluctuations of the aperture-averaged AOA. This requires running the simulation many times for independent turbulence realizations, obtaining the aperture-averaged AOA for each realization, and then computing the variance.
Wave Optics Simulation
The initial plane wave at the entrance plane, , is a unit-amplitude, zero-phase field that is propagated in steps between the entrance plane and the observation plane using a discretized form of the Fresnel diffraction integral.21 At the 'th intermediate plane, the phase screen is applied in the usual way as , where is the incident field and is the field that exits the plane. The discrete Fourier transform-based simulation produces a periodicity of the electric field in the - plane across the grid boundaries. In addition, the compensating random tilt component in the turbulence phase screens creates some "ringing" artifacts in the receiving plane near the grid boundaries. To minimize unwanted periodicity and edge effects, the aperture is only applied to the center fraction of the receiving plane grid.
One approach to find the aperture-averaged AOA for a given turbulence realization is to numerically compute the field phase gradients at the observation plane grid points and average the results within the aperture region. However, direct calculation of the phase gradients at the grid points is problematic for strong scattering because of branch points (implying discontinuous phase changes from to 0, or 0 to ) that appear in the wave front and correspond to theoretically infinite phase gradients.
For the results presented here, we use an approach where the wave front within the aperture for a given turbulence realization is numerically focused with a focus transmittance function.21 The - and -direction centroid positions of the intensity spot at the focal plane are found and the aperture-averaged AOA is the angle defined by the ratio of the centroid displacement (from the optical axis) and the focal length. This AOA is computed for many independent turbulence realizations and the variance is calculated. This approach has the advantage that it is representative of a practical AOA measurement that can be made with a lens and camera system.22 It also effectively weighs the angle contributions by the spatial field amplitude in the pupil, where, for example, the amplitude is vanishing near a branch point so the sometimes extremely large gradients associated with these features are not significant for the AOA variance calculation.
Ray Tracing Simulation
For the ray simulation, as shown in Fig. 1(b), the source is comprised of a set of rays where each ray is positioned at a grid point corresponding to the wave simulation and is initially directed parallel to the optical axis. For a given turbulence realization, the rays are traced from one plane to the next where at the 'th plane, the phase screen changes the -direction ray angle as12 however, we do not compute the brightness function that is part of their incoherent image simulation.
The variance of the aperture-filtered AOA fluctuations for a circular aperture and for a plane wave propagated through homogeneous and locally isotropic inertial subrange turbulence is given by Cheon and Muschinski20 as
Observation Plane Illustration
Before presenting the AOA results, we first examine the character of the rays and waves arriving at the observation plane for a single turbulence realization. Figure 2 shows single realization examples within the central area for the scattering scenarios corresponding to , 0.267, 2.67, and 26.7. Shown for comparison are: (1) ray-density fields obtained from the ray simulation and (2) intensity and phase fields obtained from the wave optics simulation. The ray density fields were obtained by counting the rays within areas defined by the binning values. The binning is relative to the grid spacing , for example, binning indicates an area of . The bin size was selected to emphasize the most apparent characteristic feature sizes within the frame. A contour plot algorithm was also applied to the ray density plot to reduce the blockiness of the display.
Common spatial features are apparent in the intensity and ray-density fields as shown in Fig. 2. The corresponding features are related to the effects of refraction as ray tracing does not account for the interference and diffractive effects provided in the wave simulation. The phase cross-sections, displayed modulo-, illustrate the increasing wave front complexity as a function of the Rytov variance. As noted previously, after the ray and wave fields are generated at the observation plane as shown in Fig. 2, a circular aperture of diameter is imposed and the methods described in Sec. 2 are applied to find the aperture-averaged AOA field for the particular turbulence realization.
Variances of Aperture-Filtered Angle-of-Arrival Fluctuations
The variances of aperture-averaged AOA fluctuations are computed from many independent turbulence realizations. Figure 3 shows results for the theoretical [Eq. (2)] and simulated aperture-averaged AOA variances as a function of the normalized aperture diameter for the four values of listed in Table 1. Each data point was estimated from 1000 turbulence realizations. The general behavior is that the AOA variance decreases as a function of increasing aperture diameter. Both simulation results generally agree well with the AOA theory20 for weak scattering (e.g., ) but decrease significantly below the theory curve as the Rytov variance increases. The results also show the agreement between theory and simulation is better in stronger scattering for larger apertures (e.g., and ). The over-prediction of the AOA variances by the Rytov theory is likely a result of the well-known failure of the Rytov approximation in the strong-moderate- to strong-scattering regime. We note that the Rytov theory is also known to over-predict intensity scintillation as a function of the Rytov variance in the moderate- and strong-scattering regimes.
In general, the ray-based and wave-based simulation variances compare favorably in Fig. 3. The largest discrepancy is a 15% higher variance for the rays in strong scattering with a small aperture ( and ). For the weak-to-moderate scattering cases [Figs. 3(a)–3(c)], the ray and wave results match well for . That is, diffraction effects are negligible in the weak- and moderate-scattering regime if the aperture diameter is larger than about twice the Fresnel length. This result is consistent with the theoretical analysis by Cheon and Muschinski20 who found that for weak scattering, the AOA variance predicted by geometrical optics deviates from that predicted by the Rytov theory by if . For smaller , the wave simulations predict a lower AOA variance than the ray simulations. For the strongest scattering case [Fig. 3(d)], the wave and ray variance values converge for .
Figure 4 shows an alternative presentation of the results where aperture-averaged AOA variances for the small aperture (; ) and the large aperture (; ) are plotted as a function of the Rytov variance, . The Rytov theory curves demonstrate the linear dependence described by Eq. (2). For the small aperture [Fig. 4(a)], the simulations show a positive slope as a function of scattering strength that is significantly shallower than the theory line. For large aperture diameters, the Rytov-based theory is expected to collapse to the geometrical optics solution.20 This behavior is suggested in the large aperture case [Fig. 4(b)], where the simulation results follow the theory line much more closely.
Figure 4 also shows a small difference between the ray-based and wave-based results for the small aperture (), but essentially no difference for the large aperture (). As noted previously, geometrical optics is known to be questionable for , which is consistent with the fact that our wave-optics simulations produce smaller AOA variances than the AOA variances produced by our ray-tracing simulations. We attribute this to "Fresnel filtering." The Fresnel-filter kernel in the wave-number representation of the AOA variance for plane waves predicted by the Rytov theory has the form ,20 where is the wave number normalized by the Fresnel wave number . The case (Fresnel length is small compared with , the wave-front tilt length scale under consideration) is the geometrical-optics limit where the Fresnel length has no effect on the AOA variance. For comparable to and , the Fresnel length (and therefore diffraction) does play a role: becomes smaller than in the geometrical-optics limit. Therefore, diffraction causes the AOA variance predicted by wave optics to be smaller than the AOA variance predicted by geometrical optics.
That is, a finite Fresnel length acts as a characteristic filter scale similar to the filtering effects due to a finite inner turbulence length scale or a finite aperture diameter. Essentially, diffraction causes wave-front tilt components with length scales comparable to and smaller than the Fresnel length scales to be smoothed out. The Fresnel-filtering effect is significant when the aperture size and the inner scale of turbulence are both comparable to or smaller than the Fresnel length, and it is negligible otherwise. The Fresnel filtering is accounted for in the wave-optics simulations but not in the ray-tracing simulations.
To examine the AOA distribution results in detail, we generated histogram estimates of the probability density functions (pdfs). Figures 5(a)–5(c) show the histogram plots for the weakest scattering case and for three aperture diameters. To reduce noise in the histogram, we used 10,000 realizations for these results. We also generated corresponding quantile–quantile (q–q) plots23 shown in Figs. 5(d)–5(f). The q–q plots compare the simulation sample distribution to a standard normal (Gaussian) distribution. In all cases, the ray and wave samples create straight lines that indicate Gaussian distributions. The two different slopes in the q–q curves in Fig. 5(d) correspond to a difference in the AOA variance for the wave and ray results, which was discussed previously for small . Histogram and q–q plots for strong scattering are shown in Fig. 6. These distributions are also Gaussian and q–q plot slope differences in Figs. 6(d)–6(f) are consistent with the variance results in Fig. 3(d). We expect a Gaussian distribution for the aperture-averaged AOA if the propagation through turbulence and aperture averaging represents a large sum of independent tilt components such that the central limit theorem applies.
The simulations illustrate that after propagation through homogeneous turbulence, wave and ray results share obvious intensity/ray-density and AOA characteristics related to the effects of refraction. We find that both the wave and ray simulation results generally predict variances of the aperture-averaged AOA fluctuations that agree well with the Rytov theory for weak scattering (e.g., ), but as scattering strength (i.e., the Rytov variance) increases, the simulation results demonstrate a positive slope that can be significantly shallower than that predicted by the weak-scattering (Rytov) theory. This over-prediction by the Rytov theory is likely a result of the failure of the Rytov approximation in the strong-scattering regime.
Some insights related to the negligibility of diffraction effects are gained from a comparison of the wave and ray simulation results. For weak-to-moderate scattering regimes (), the ray and wave results match well for apertures where . This result is consistent with the theoretical analysis by Cheon and Muschinski20 who found that for weak scattering, the AOA variance predicted by geometrical optics deviates from that predicted by the Rytov theory by if . For the strongest scattering case studied here (), the wave and ray variance values agree well for . For smaller apertures, we find the wave simulation variances are smaller than those produced by the ray simulations, and we attribute this to a "Fresnel filtering" effect associated with diffraction. Both the wave and ray AOA distributions are found to be Gaussian.
Earlier results of this work appeared in the conference proceedings paper: D. Voelz, E. Wijerathna, X. Xiao, A. Muschinski, "Angle-of-arrival variance of waves and rays in strong atmospheric scattering: split-step simulation results," Proc. SPIE 10410, Unconventional and Indirect Imaging, Image Reconstruction, and Wavefront Sensing 2017, 104100Y (6 September 2017). This work was funded by Air Force Office of Science Research (AFOSR) (FA9550-17-C-0021 and FA9550-18-C-0011), Air Force Office of Science Research (AFOSR) Multidisciplinary University Research Initiatives (MURI) Program (FA9550-12-1-0449 and FA9550-18-1-0009), National Science Foundation (NSF) Physical and Dynamics Meteorology Program (AGS-1547476), and U.S. Department of Defense (DOD) High Performance Computing Modernization Program (Frontier Project FP-CFD-FY14-007).
David Voelz is a professor in the Klipsch School of Electrical and Computer Engineering at New Mexico State University. His research interests include spectral and polarization sensing, laser beam propagation through atmospheric turbulence, laser communications, imaging theory, and astronomical instrumentation development. He earned his PhD EE degree from the University of Illinois in 1987. He is a fellow of SPIE.
Erandi Wijerathna is a PhD student in the Klipsch School of Electrical and Computer Engineering at New Mexico State University. Her research interests include laser beam propagation through atmospheric turbulence, imaging theory, and polarimetric lidar. She earned her BS (honors) in physics from the University of Colombo, Sri Lanka, in 2011. She received her MS degree in physics and in electrical engineering from New Mexico State University in 2016.
Andreas Muschinski (MS in physics, TU Braunschweig, Germany, 1990; PhD in meteorology, U Hannover, Germany, 1992; habilitation in meteorology, U Hannover, Germany, 1998) is an atmospheric physicist. He was a CIRES research scientist at the University of Colorado at Boulder, Colorado (1998–2004) and a professor of electrical engineering at UMass Amherst (2004–2011). Since 2011, he has been a senior research scientist at NorthWest Research Associates, Boulder, Colorado. During the last 28 years, he has conducted research on atmospheric turbulence and atmospheric wave propagation.
Xifeng Xiao received her BS and MS degrees in physics from Xiamen University Fujian, China, in 1998 and 2001, respectively. She earned her MS and PhD degrees in electrical engineering from New Mexico State University in 2004 and 2008, respectively. Currently, she is a software engineer at Ball Aerospace, Albuquerque, NM. Her research interests include simulation and modeling of free-space laser communication, liquid-crystal polarization, and demonstration and implementation of AOTF technologies.


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California mandated as a whole the deinstitutionalization of the mentally ill in 1967 when Gov. Ronald Reagan signed the Lanterman-Petris-Short Act (LPS). Under this act, "Among other things, it prohibited forced medication or extended hospital stays without a...
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