Measuring turbulence and winds aloft using solar and lunar observable features

Presented is a system and method for detecting turbulence in the atmosphere comprising an image capturing device for capturing a plurality of images of a visual feature of a celestial object such as the sun, combined with a lens having focal length adapted to focus an image onto image capturing device such that the combination of the lens and the image capturing device are adapted to resolve a distortion caused by a turbule of turbulent air, and an image processor adapted to compare said plurality of images of said visual feature to detect the transit of a turbule of turbulent air in between said image capturing device and said celestial object, and compute a measurement of the angular velocity of the turbule. A second plurality of images is used to triangulate the distance to the turbule and the velocity of the turbule.

FIELD

Embodiments of the subject matter described herein relate generally to a system and method to estimating turbulence and wind in the atmosphere using solar and lunar observable features, and in particular to using a camera-based system on an airborne mobile platform to develop turbulence and wind profiles of the atmosphere using features of the sun and moon.

BACKGROUND

Measuring atmospheric conditions including turbulence and winds aloft allows aircraft and airborne vehicles to make flight adjustments to achieve a desired level of performance and avoid undesirable flying conditions. Winds aloft affect the fuel consumption and speed of aircraft. Airplane encounters with clear air turbulence at cruise altitude may produce serious injury. Clear air turbulence is difficult to forecast and even more difficult to detect with current methods. Clear air turbulence is turbulence that results where there are no clouds, precipitation, or visible particles such as dust in the air.

In addition, measuring the present state of atmospheric conditions is necessary to forecast future atmospheric events such as storms. Measuring atmospheric conditions can be performed to varying degrees using ground-based instrumentation, by sensors carried aloft in balloons or other airborne vehicles, by sensors in aircraft as they pass through a region of atmosphere, and by using predictive modeling based on past measurements.

However, over oceans and in underdeveloped regions of the world, ground-based instrumentation and dedicated sensor equipment like weather balloons either do not exist or it may be economically impractical to cover an area with sufficient sensors to provide the desired level of accuracy. Additionally, aircraft may pass through an area too infrequently to provide current conditions for other later aircraft. Dynamic atmospheric conditions generally make modeling grow less precise over time, and although good for approximating general conditions for regional conditions, modeling can be inaccurate at finer granularities. Sensors, and especially fixed instrumentation, are limited to surveying portions of the atmosphere proximate to the sensor apparatus at the time the sensor measurements were made. A moving aircraft or airborne vehicle may travel through multiple overlapping zones of coverage and areas without coverage during a flight.

SUMMARY

Presented is a system and method for measuring the turbulence and winds aloft in the atmosphere using solar and lunar observable features. In an embodiment, the measuring is performed from the Earth's surface. In other embodiments, the measuring is performed by moving aircraft or vehicles. The system and method detects distortions in a visual scene, for example the lunar surface or the edge of the sun, that are caused by changes in the refractivity of the atmosphere, and measures the characteristics of these distortions to estimate turbulence and winds aloft. The system and method can also be used to develop refractivity profiles of the atmosphere in accordance with the disclosure presented in U.S. patent application Ser. No. 12/533,807 filed on Jul. 31, 2009 and entitled “Visual Occultation to Measure Refractivity Profile”.

The system and method reports an indication of the estimate of the turbulence and winds aloft to pilots of aircraft. The pilots use the turbulence estimates to maneuver their aircraft to avoid the turbulence. The pilots use the winds aloft estimates to maneuver their aircraft to minimize the affect of headwinds and maximize tailwinds. Because winds aloft have a strong effect on airliner fuel consumption, measurements or predictions of winds aloft can be used to increase aircraft efficiency and maximize operating range.

The system and method offers remote measurements of meteorological variables with lower certification cost and faster certification schedule, lower unit cost, and lower weight compared to other methods such as aircraft-based GPS occultation. Further, the system and method provides coverage over ocean regions beyond sight of land.

The features, functions, and advantages discussed can be achieved independently in various embodiments of the present invention or may be combined in yet other embodiments further details of which can be seen with reference to the following description and drawings.

DETAILED DESCRIPTION

The following detailed description is merely illustrative in nature and is not intended to limit the embodiments of the invention or the application and uses of such embodiments. Furthermore, there is no intention to be bound by any expressed or implied theory presented in the preceding technical field, background, brief summary or the following detailed description.

Clear air turbulence is difficult to forecast and even more difficult to detect using current methods. Clear air turbulence is turbulence that results where there are no clouds, precipitation, or visible particles such as dust in the air. Pilots may learn of clear air turbulence from forecasts and other pilots that have recently flown through a pocket of turbulence. Generally, pilots turn on a “seat belt required” light and/or slow their aircraft's speed in anticipation of passing through suspected pockets of turbulence to reduce structural stresses on the aircraft and reduce discomfort to passengers. However, if the pilot is unaware of turbulence, the pilot may have little warning time to alert the passengers or otherwise change the configuration and velocity of the aircraft.

A turbulence and winds aloft measurement system100detects turbulence in the atmosphere and communicates it to pilots, which enables the pilots to maneuver their aircraft to avoid any turbulent pockets of air. In one embodiment, the turbulence and winds aloft measurement system100warns the pilot of turbulence in the path of the aircraft. In another embodiment, turbulence and winds aloft measurement system100provides a visual navigational aid to enable a pilot to navigate around pockets of turbulent air. The turbulence and winds aloft measurement system100may improve air safety, allowing airplanes to fly at cruise speeds with a reduced risk of running into unexpected turbulence that could damage the airplane or harm passengers. The turbulence and winds aloft measurement system100also may increase the comfort of passengers in the airplane by allowing the pilot to navigate around pockets of turbulence or, if the turbulence is widespread, by allowing the pilot to change the airplane's speed profile or configuration and navigate through the least turbulent areas of the sky. Further, reducing the amount of turbulence that an airplane flies through over the airplane's useful life may also reduce the stresses on airframe and engine components that accrue during a lifetime of continuous operation. The turbulence and winds aloft measurement system100therefore reduces component fatigue, permits safer long term operation of the aircraft, and reduces or shortens necessary maintenance cycles.

The turbulence and winds aloft measurement system100allows pilots use the winds aloft estimates to maneuver their aircraft to minimize the affect of headwinds and maximize tailwinds. Because winds aloft have a strong effect on airliner fuel consumption, measurements or predictions of winds aloft can be used to increase aircraft efficiency and maximize operating range.

System Components and Operation

Referring now toFIG. 1a, a turbulence and winds aloft measurement system100is shown. The turbulence and winds aloft measurement system100obtains optical turbulence information of the atmosphere using observable features of the sun124and moon122or other celestial objects128, for example a grouping of stars126, to predict atmospheric conditions in the parcel of atmosphere. The turbulence and winds aloft measurement system100uses distortions in visual measurements of observable features of the sun124, moon122, stars126, or other celestial objects128to measure and track refractivity fluctuations in intervening parcels of atmosphere. The refractivity fluctuations correspond to turbules112of turbulent air, and tracking the turbules112allows the turbulence and winds aloft measurement system100to determine the velocity of winds aloft114. In addition to tracking turbules112or turbulence in general, the visual measurements can be used to improve atmospheric models, for example models of winds aloft114, and thereby improve weather forecasts and/or aircraft routing.

In an embodiment, the turbulence and winds aloft measurement system100comprises a mobile platform or vehicle102, for example a ship, traversing a section of the earth110, a first camera104a, and a second camera104b, a position and orientation system106, and a computer108. In embodiments, the platform is a commercial vessel, a military vessel, a buoy, a train, a building or structure, an aircraft, or any other stationary or mobile platform positioned with a view of the surrounding atmosphere.

The cameras104a,104b(collectively104) are mounted on or to the vehicle102and separated by a modest distance. In an embodiment the cameras104are mounted on different sides of the vehicle102. A computer108analyzes images from the cameras104. The computer108can be any suitable computing platform capable of manipulating digital image data, including but not limited to a PC, workstation, a customized circuit board, or an image processor. The cameras104are communicatively linked to the computer108that receives the images from the cameras104. In an embodiment, the computer108is physically located on the vehicle102. In embodiments, the computer108is physically located on another platform or operations center, for example at a weather service provider130. In embodiments, data from cameras104are networked to one or more computers via a network or plurality of networks.

In an embodiment, the camera104uses a telephoto lens. In operation, the cameras104are pointed at an celestial object128or a particular feature of an celestial object128having sufficient known detail, and a series of images or video is delivered to the computer108. In embodiments, the celestial object128is the moon122, the sun124, or stars126and planets. For example, the stars126could be a well known constellation of stars126such as the Pleiades, or any other grouping of stars having close proximity to one another. The cameras104output digitized data of the image to the computer108. In another embodiment, the computer108digitizes analog inputs from the cameras104into digital images using a digital frame grabber.

The images from the cameras104can be analyzed to detect small local deviations in the refractive index of air. For example, light returning to the cameras104from the sun124passes through the atmosphere along light path132. Changes in refraction are due to the density and composition of air in the atmosphere, for example due to differences in humidity levels, temperatures, and pressures. As a result of the small local changes in refraction due to turbulence, features of the sun124can appear shifted spatially. The mean-square angular displacement of small features is given by a well-known formula shown in equation1. In this formula, φ is the angular displacement in radians, angle brackets < > indicate the mean expected value of the enclosed quantity, D is the camera aperture, L is the total distance from the light source to the camera, η is a measure of distance along the optical path from the light source to the camera, and Cn2is a measure of optical turbulence at each point along the path. Cn2is mathematically related to mechanical turbulence, which can pose a danger to aircraft.
<φ2>=2.91D−1/3∫0LCn2(η)dηEquation (1)

Referring now toFIG. 1b, a telephoto lens142focuses light from the sun124through a helium I filter200onto a CCD140. For purposes of illustration only, part of a granule202of the sun124is shown on the CDD140as an inverted image146. The inverted image146is where the granule202is resolved on the CCD140due the distortion caused by the turbule112carried in the winds aloft114. The dashed inverted image144illustrates where the solar granule202will be imaged once the turbule112passes. Turbulence-induced deviations in the refractive bending of light can be on the order of three microradians or less, which may be too small to be detected accurately by many cameras104using normal snapshot lenses. To increase accuracy and provide a finer level of granularity, the cameras104in the turbulence and winds aloft measurement system100use a telephoto focusing system such as a lens or mirror having a long focal length that magnifies the image and provides a suitable resolution for imaging by the cameras104.

In an embodiment, the telephoto lens142and the pixel resolution of the image capturing element, for example a CCD140or charge coupled device, are adapted to resolve at least 2.5 microradians of angle. For example, a telephoto lens having a 30-cm aperture and a 1-meter focal length can resolve approximately 2.5×10−6radians in visible wavelengths when coupled with a 1×1 cm CCD chip having 2.5 micron pixels arranged in a 4000×4000 pixel matrix. In one embodiment, the telephoto lens142is a zoom lens, capable of adjusting the magnification and therefore allowing the system operator to selectively trade off measurement accuracy for a wider field of view.

In an embodiment, the cameras104include a CCD140having a very fine pitch, or a similar image capturing means, which is used to gather an image, either alone or in combination with a telephoto lens. To maximize the resolution, the CCD140is a black and white CCD. Color CCDs generally use tiny filters arranged in a pattern over the CCD elements, which can cause unwanted image artifacts such as color changes near sharp edges of object depending upon how the light falls onto the CCD chip. Edge artifacts are unwanted image distortions that have the potential of being misinterpreted by the computer. In other embodiments, the system uses a 3-CCD camera104that divides the image into three different CCDs, for example using birefringent materials, and therefore does not induce unwanted edge artifacts.

In embodiments, the cameras104are digital frame cameras, video cameras, high-resolution CCD cameras, or HD camcorders. In embodiments, to enhance the image depth and dynamic range of the captured image, the cameras104selectively use filters, such as a solar filter, a hydrogen alpha filter, a helium I filter, a polarization filter, a neutral density filter, or a red filter to avoid backscattered blue light. In embodiments, the optical filters reduce the brightness and/or pass only selected wavelengths of light. In embodiments, the cameras104additionally are infrared cameras or selectively uses image intensifiers, such as a night vision tubes, allowing the turbulence and winds aloft measurement system100to perform better in low light situations such as when viewing unlit portions of the moon122or other celestial objects128at night time. In embodiments, the cameras104are image capturing devices using a CCD chip, an analog sensor, a linear sensor such as a linear sensor array, or any other photosensitive sensor capable of determining fine pitch in a visual scene.

In an embodiment, the cameras104are mounted on a rotatable swivel mounts that allow the cameras104to be rotated to view different portions of the sky. In an embodiment, the cameras104are mounted on multi-axis gimbals, allowing the cameras104to be angularly rotated in any direction. In these embodiments, the cameras104may be rotated or oriented in order to scan a larger area. The outputs from the cameras104are synchronized with an output from a rotational encoder or other similar orientation identifying means to correlate images from the cameras104with the orientation of the cameras104.

The motion of the cameras104are linked to the motion of the vehicle102, for example through a position and orientation system106such as a navigation and control system, a GPS receiver, an inertial measurement unit or IMU, or any similar system or combination of systems. The IMU measures changes in camera104orientation due to rotation or twisting of the vehicle102and can be used to maintain orientation of the cameras104towards a desired celestial object128. In an embodiment, one or both of the cameras104are substantially fixed and a rotatable mirror is used to change the direction of viewing of or more of the cameras104. In an embodiment, the mirrors are first surface mirrors for better clarity. In an embodiment, the cameras104are mounted in vibration reducing mounts. In an embodiment, the cameras104are gyroscopically stabilized.

Image Processing

Continuing to refer toFIG. 1a, the computer108processes one or more images from the cameras104. The processing identifies visual features whose physical location is well known, e.g., features on the sun124or moon122. The sun124and the moon122both have visible features that can be distorted by turbulence in ways that allows detection of the turbulence.

Referring now toFIG. 2c, the lunar features206of the moon122, including mountains and craters, are well known and are static. However, different portions of the moon122are illuminated by the sun124, depending upon the particular lunar phase. The angle of illumination of lunar features206by the sun124also varies with the particular lunar phase, creating shadows that vary with the particular lunar phase. Polarizing filters and neutral density filters can be used to enhance the resolving capability of the cameras104. The moon122is shown inFIG. 2cusing a polarizing filter220. The moon122also wobbles slightly, thus allowing slightly more than half of the surface of the moon122to be usable as visual features.

Referring toFIGS. 2aand2b, to detect features of the sun124, special filters such as solar filters, hydrogen alpha filters, helium I filters, etc. are utilized. Using solar filters, features such as the edge of the sun124and sunspots204, when present, can be resolved by the cameras104. Using filters such as helium I filters200and hydrogen alpha filters210, the sun124also presents full-time surface features during daylight hours called “granules”202.FIGS. 2aand2bshow granules202. Granules202are always present, are easily observable with a telephoto lens and a narrowband spectral filter and have a fine-grained texture. The sun124is shown inFIG. 2ausing a helium I filter200. The sun124is shown inFIG. 2busing a hydrogen alpha filter210. Granules202provide a good background against which to detect turbules112.

Referring again toFIG. 1a, using the spatial position (in pixel rows and columns) of each visual feature on the focal plane, the pitch of pixels in the camera focal plane, and the focal length of the lens, the computer108measures the angular position of those visual features in the scene. The computer108compares the visual features in a plurality of frames to detect changes in the angular position of those features. The changes in angular position are caused by differences in the refractivity of the atmosphere due to turbulence, or turbules112, and winds aloft114. For ease of exposition, the following examples use the sun124as the background object for detecting turbules112and winds aloft114, however any celestial object128including the moon122, the sun124, stars126can be utilized with appropriate lenses and filters.

The computer108processes a series of time-tagged frames from each camera104. When no clouds or turbulence are present in the field of view, each frame will look essentially the same as the next frame from the same camera104. For example, two consecutive frames of the sun124will look essentially the same, with a slight change in position of the sun124due to the ordinary movement of the sun124relative to the earth110. When turbulence is present, however, some parts of the sun124will appear distorted, and the distortion will vary from frame to frame. A feature in one frame captured at time t0cannot be easily registered with that feature in a later frame at time t0+Δt.

Registering features in one frame with the same features in another frame involves using linear image transformation methods. In a comparison between a two frames, for example a frame at time t0and a frame at time t0+Δt, features in one frame can be easily registered with similar features in another frame using simple geometric transformations. In one embodiment, the computer108performs a transformation of a first frame at time t0into a predicted subsequent frame, and compares the predicted subsequent frame with the actual subsequent frame at time t0+Δt. In another embodiment, the computer108performs a similar process but transforms the subsequent frame into a predicted first frame. However, transforming the subsequent frame has the disadvantage that the system must wait until the subsequent frame is received by the computer108before performing the transformation, creating a possible time lag.

In another embodiment, both a first and a subsequent frame are transformed to a internal standard frame format used by the computer before being compared. This embodiment has the advantage that each frame is transformed independently of any camera104related artifacts of the other frame and simplifying computations. For example, using an internal standard frame, each frame can be different in terms of angle, rotation, zooming, and aperture and then mapped to the angle, rotation, zoom level and aperture of the internal standard frame. Further, using the internal standard frame simplifies comparing frames from different cameras104, which may have different focal lengths or may look at the same scene from different angles, for example if two cameras104are mounted on opposite sides of a ship, or vehicle102.

To perform the transformation, the computer108performs an estimate of the motion of the vehicle102including changes in direction and orientation, for example by using information from an onboard inertial navigation system and GPS system. The computer108also performs an estimate of the motion of the feature, for example the small changes in position of the sun124or moon122relative to the earth110. The computer108uses the motion estimates along with the time between the frames, t0and t0+Δt to perform a transformation of features in one or both frames. The computer108registers the frames by adjusting the size, position, and orientation of the feature in one or both of the frames, for example by registering the features in frame at t0to the feature in the frame at t0+Δt. In this example, the frame at t0is digitally translated, scaled, and rotated so that features in frame at t0are aligned with matching features in the frame at t0+Δt.

After image registrations methods are applied, any mismatch between frames from a camera104indicates temporary distortion caused by turbulence or darkening due to clouds. Clouds can be distinguished from turbulence as clouds decrease the overall brightness in an image, whereas distortion cause by turbulence rearranges the brightness, but does not generally decrease the overall brightness in the frame. In one embodiment, the computer108eliminates frames containing clouds. In another embodiment, the computer108uses only those features in the frame where the moon122or sun124is not blocked by clouds.

Referring now toFIG. 3b, in one embodiment, a camera104observes a turbule302encroach on the edge of the sun124at time t0. Referring now toFIG. 3c, at a later time, t1=t0+Δt, the camera104images the turbule302begin to exit the other edge of the sun124. Referring now toFIG. 3a, the interval Δt depends on three variables: the angular width, α, of the sun124; the distance to the turbule302or height, ht; and the velocity, v, of the turbule302. The distance to the sun124, or hsis known, and α is also known. Given Δt, the ratio of htand v can be computed using trigonometry. In one embodiment, the values for htand v are estimated, for example based upon expected values such as the expected velocity or expected height of the jet stream.

In another embodiment, two cameras104are utilized to determine the distance htto the turbule302, which allows determining the value of the velocity, v, of the turbule302. Referring now toFIG. 4a, left camera104ais separated from right camera104bby distance d, for example by mounting the left camera104aand right camera104b, collectively cameras104, on opposite ends of the vehicle102. Note that although two cameras104are described as an exemplary embodiment, it is also possible to perform the operation using additional cameras104, or even a single camera104capable of imaging a feature from two or more vantage points, for example using lenses, mirrors, or fiber optics.

Continuing to refer toFIG. 4a, and now referring toFIG. 4b, for purposes of illustrating an aspect of the invention, a simplified embodiment of the system is shown as follows: left camera104aand right camera104bare shown in a line that is approximately horizontal and the sun124is in a vertical orientation perpendicular to that the line between the cameras104. Turbule302is shown moving parallel to the line between the cameras104, in a direction from left to right. As turbule302crosses in front of the sun124, the left camera104awill detect distortion caused by the turbule302at time t0before the right camera104bdetects the distortion at time t2=t0+Δt, where Δt is equal to distance between the cameras104, d, and the velocity of the turbule, v. Because t2, t0, and d can be measured, v is computed as follows:
v=d/(t2−t0).  Equation (2)
Once the turbule transits the feature at time t1=t0+αht/v for left camera104a, or time t3=t2+αht/v, then htcan be computed by either
ht=(t1−t0)v/αEquation (3)
or
ht=(t3−t2)v/αEquation (4)
and therefore both the height htor distance to the turbule302, and the velocity vector, v, of the turbule302can be computed. The computer108uses the distance to the turbule302and the angle to the turbule302to determine the altitude of the turbule302relative to the earth110. Although this example assumes the sun124is directly above the cameras104, it will be apparent to those skilled in the art that the sun124or other celestial objects128may be viewed at any angle from vertical to nearly horizontal, and at any azimuth relative to the vector d connecting the two cameras104, and that suitable trigonometry formulas may be used to compute the correct height, ht, and velocity vector, v, of the turbule302.

Referring now toFIG. 5aandFIG. 5b, an alternative mathematical approach is to determine the offset angle θ of the turbule302from the center of the sun124by both cameras104. Left camera104aimages an offset of θ1and right camera104bimages an offset of θr. The angular difference between turbule302measured positions by each camera104is Δθ=θ1−θr, andhtcan be computed as
ht≅d/Δθ  Equation (5)
where all angles are in radians and are assumed to be smaller than 0.1 radian. A turbules302measured angular speed ω relative to the cameras104is computed by measuring the time Δt for turbule302to transit the angular width α of the sun124. The turbule302velocity vector v is computed as
v=ω/ht.  Equation (6)

In practice, turbules302may be irregularly shaped, there may be multiple turbules302, and each turbule302may appear at a different altitude with a different wind speed and direction. The following embodiments correlate image features to resolve individual turbules302within a sequence of images taken by a single camera104and between images taken by two or more cameras104.

Correlation of Images from a Camera

Referring now toFIG. 6aandFIG. 6b, a first turbule602moves in a first direction at velocity va, shown inFIG. 6bas generally traveling in the direction of the x-axis, and a second turbule604moves in a second direction at velocity vb, shown inFIG. 6bas traveling more or less in the direction of the y-axis. To distinguish the data associated with the first turbule602from data associated with the second turbule602, a mathematical correlation operation is performed to the data.

The correlation coefficient for two data sets, xiand yi, each having N elements, is defined as
r=sxy/sxsy,  Equation (7)
where sxand syare the standard deviations of xiand yiand where sxyis the covariance of x and y, defined as
sxy=(Σxiyi−1/NΣxiΣyi)/(N−1)  Equation (8)
where all sums are over the range I=1 . . . N.

For a pair of images x and y, where each image in an mxn array of pixels indexed by
{(j,k):j=a . . . m,k=1. . . n},Equation (9)
let N=mxn and the summation index I=j+m(k−1). Then the correlation coefficient of two images is defined as
r=sx/sxsyEquation (10)
where
sxy=(ΣΣxj,kyj,k−1/NΣΣxj,kΣσyj,k)/(N−1)  Equation (11)
and all double sums are over the range j=1 . . . m, k=1 . . . n.

The sequences of difference images from a single camera are correlated to reveal the magnitude and angular velocity of turbulence at various altitudes. Continuing to refer toFIG. 6aandFIG. 6b, and now referring now toFIG. 7a,FIG. 7b, andFIG. 7c, first turbule602is at height htaand second turbule604is at height htb. Both the first turbule602and the second turbule604are moving across the visible disc of the sun124at the same time, but in two different directions x, y, and at two different speeds, va, vbrespectively. The images inFIGS. 7a,7b, and7cillustrate the turbules602,604at four different times, t1, t2, t3, t4.

Referring now toFIG. 8a,FIG. 8b, andFIG. 8c, in an embodiment, the turbulence and winds aloft measurement system100computes a sequence of difference images802,804, and806, at various temporal and angular offsets. The first difference image802is the difference between the image frame that captured first turbule602and second turbule604at time t1, and the image frame that captured first turbule602and second turbule604at time t2. Similarly, second difference image804is the difference between the images when turbules602,604are at times t2and t3, and third difference image806is the difference image between times t3and t4. As is understood in the art, an angular offset in the scene corresponds to a pixel offset in the digital image. The angle is proportional to the number of pixels by which the image is offset, multiplied by the spatial width of a pixel, divided by the focal length of the lens. The temporal offset is the difference between the times when the images were captured. An angular offset θ combined with a temporal offset Δt corresponds to an angular velocity of
ω=θ/Δt.Equation (12)
When the temporal and angular offsets match the angular velocity of turbules602,604at a particular altitude hta, htb, there is a peak in the correlation coefficient, r(ωθ, ωφ).

Referring now toFIG. 9aandFIG. 9b, the correlation contour plots illustrate the correlation r2(ωθ, ωφ)900of the difference images802,804, and806for angular velocity vectors ωθ906, and ωφ908. The correlation contour plots have two peaks,902,904. The peaks902,904represent the angular velocities of the turbules602,604with one peak corresponding to ωa902and one peak corresponding to ωb904. To measure the linear velocities va, vbof the turbules602,604requires knowledge of the altitudes htaand htb.

Correlation of Images from Cameras

To compute the altitudes htaand htband the linear velocities va, vbof the turbules602,604, the positions of the turbules602,604are triangulated using two or more cameras104. Referring now toFIGS. 10aand10b, a turbule1002moves at angular speed ω across the sun124.FIG. 10aillustrates the imaging of the turbule1002by a first camera104aat times t1, t2, t3, and t4as the turbule1002transits the sun124.FIG. 10billustrates the imaging of the same turbule1002by the second camera104bat times t3, t4, t5, and t6.

Referring now toFIG. 11, the turbule1002is visible to both cameras104during times t3and t4. To measure the angular offset Δθ, or spatial shift of the position of the turbule1002, the difference image from one of the cameras104is shifted along the direction of the other camera104, and the correlation coefficient r(Δθ) is computed at various angular distances Δθ. The distance Δθ at which a correlation peak occurs reveals the altitude htof the turbule1002relative to the camera104, as given by ht≅=d/Δθ (Equation (5).)

Referring now toFIGS. 12aand12b, the turbule1002is not visible to both cameras104at the same times, t1-t7. The turbule is visible to camera104aduring times t1, t2, t3, and t4; and the turbule is visible to camera104bduring times t5, t6, and t7. There is therefore no angular offset Δθ that allows a correlation peak in r(Δθ) to match the turbule1002images from both cameras104. Instead, the difference images from one camera104are correlated with the difference images taken by another camera104at a different time, either earlier or later, and using angular offsets with non-zero Δφ.

Referring now toFIG. 13, a correlation peak in r(Δt, Δθ, Δφ) occurs when Δt=4 frames, Δθ˜0.4α, and Δφ˜0.6α, where α is the angular width of the sun124. Correlating over a three-dimensional range of offsets Δt, Δθ, and Δφ is computationally more expensive than correlating over the one-dimensional range, Δθ. In one embodiment, the computer108first attempts to correlated over the one-dimensional range, Δθ, and then attempts to correlate over the three dimensional range of offsets Δt, Δθ, and Δφ if computational bandwidth is available. In another embodiment, the computer108is optimized to correlate over the three dimensional range of offsets Δt, Δθ, and Δφ.

Multiple Camera Configurations

In various embodiments, the turbulence and winds aloft measurement system100comprises one, two, or multiple cameras104. The ability for the turbulence and winds aloft measurement system100to accurately resolve the altitude of turbules112,302,602,604, and1002, depends in part upon the distance between the cameras104. For example, cameras104that are close together generally see the same turbules112,302,602,604, and1002, making computations easier, but cameras104that further apart can resolve angular distances to a finer granularity. Also turbules112,302,602,604, and1002at lower altitudes will have greater angular displacements frame-to-frame for a given linear velocity because they are closer to the cameras104, making computations possible even for relatively closely placed cameras104, that is, cameras104that have a relatively small d between them. Turbules112,302,602,604, and1002that are higher in the atmosphere will have relatively lower angular displacement frame-to-frame, and thus will require greater distances between cameras104in order to resolve accurately.

In an embodiment, a first pair of cameras104are separate by a distance of approximately 10 meters, while a third camera104is separated from the pair of cameras104by approximately 100 meters. The first pair of cameras104provide good characterization of turbules112,302,602,604, and1002at lower altitudes, while the third camera104facilitates characterizing turbules112,302,602,604, and1002at high altitudes.

In an embodiment, the cameras104are mounted on an ocean-going vehicle102, for example a ship or vessel. For example, the first pair of cameras104might be mounted near the bow of a vessel on either side of the deck, while the third camera might be mounted further back on the vessel closer to the stern.

In an embodiment, the cameras104are located roughly at the corners of an equilateral triangle on the surface of the earth110. This configuration ensures that turbules112,302,602,604, and1002traveling in any direction within a selected altitude range will be simultaneously visible to at least two of the cameras104during part of the turbules112,302,602,604, and1002transit across the sun124. This configuration also allows using one-dimensional angular offsets for correlation between each pair of cameras104, which is computationally less costly than the three-dimensional offsets needed to achieve similar coverage with, for example, two cameras104.

Communications

In an embodiment, the turbulence and winds aloft measurement system100further comprises a communications link116to transfer estimates of turbulence, turbules112, and winds114aloft. In embodiments, the communications link116both receives estimates and transmits estimates. In embodiments, the communications links116permits transfers of estimates with aircraft118, a weather service provider130, a national weather agency, an airline operations center, a military aircraft command center, and/or a solar or lunar information service for obtaining up-to-date images of the sun124and moon122.

In an embodiment, the turbulence and winds aloft measurement system100communicates information to the pilot of the vehicle102. In an embodiment, the turbulence and winds aloft measurement system100sends the estimates to a weather forecasting center or weather service provider130. In an embodiment, the turbulence and winds aloft measurement system100shares the information with nearby aircraft118or systems on the ground. In an embodiment, the turbulence and winds aloft measurement system100shares raw or interpreted data with nearby vehicle102to develop a better indication of local turbulence, turbules112, and winds aloft114. In an embodiment, the data is shared via military communications links, for example Link-16.

The embodiments of the invention shown in the drawings and described above are exemplary of numerous embodiments that may be made within the scope of the appended claims. It is contemplated that numerous other configurations of the turbulence and winds aloft measurement system100may be created taking advantage of the disclosed approach. It is the applicant's intention that the scope of the patent issuing herefrom will be limited only by the scope of the appended claims.