# Patent

## Title
Measuring turbulence and winds aloft using solar and lunar observable features

## Abstract

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.

## Background
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.



BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying figures depict various embodiments of the system and method for measuring the turbulence and winds aloft in the atmosphere using solar and lunar observable features. A brief description of each figure is provided below. Elements with the same reference number in each figure indicated identical or functionally similar elements. Additionally, the left-most digit(s) of a reference number indicate the drawing in which the reference number first appears.
FIG. 1a is a diagram of a turbulence detection system on a ship traversing the earth, an aircraft in flight above the earth, and the relationship of the ship and the aircraft in relation to  winds aloft and celestial objects;
FIG. 1b is a diagram of a granule of the sun being focused onto a charge coupled device through a lens and the effect of a turbule on the position of the granule in the image;
FIG. 2a is a picture of the sun seen through a helium I filter;
FIG. 2b is a picture of the sun seen through a hydrogen alpha filter;
FIG. 2c is a picture of the moon seen through a polarizing filter;
FIG. 3a is a diagram illustrating the geometry of camera system visualizing a turbule of turbulent air as it passes in front of the sun;
FIG. 3b is an exaggerated view of the effect that a turbule of turbulent air has on the edge of the sun's disc as visualized by the camera system;
FIG. 3c is an exaggerated view of the effect that a turbule of turbulent air has on the edge of the sun's disc as visualized by the camera system;
FIG. 4a is a diagram of a two camera system for visualizing turbules and determining the distance to the turbules;
FIG. 4b is a diagram illustrating the differences in turbule position as imaged by two cameras displaced by distance d;
FIG. 5a is a alternative diagram of the geometry of a two camera system for visualizing turbules and determining the distance to the turbules;
FIG. 5b is an alternative diagram illustrating a method of visually determining the angular offset between two cameras that are visualizing the same turbule from separated viewing positions;
FIG. 6a is a diagram illustrating two different altitudes and paths taken by two different turbules;
FIG. 6b is a graph showing the paths of the two turbules that are at different altitudes;
FIG. 7a are images captured by a camera of a first turbule at four different time intervals as it transits in front of the sun;
FIG. 7b are images captured by a camera of a second turbule at four different time intervals as it transits in front of the sun;
FIG. 7c are images captured by a camera showing the relative paths of a first turbule and a second turbule at four different times intervals as they transit in front of the sun;
FIGS. 8a, 8b, and 8c are images of the differences between two consecutive images of the two turbules of FIG. 7c; 
FIGS. 9a and 9b are contour plots showing the correlation of the angular velocities of the two turbules computed from the difference images of FIGS. 8a, 8b, and 8c; 
FIGS. 10a and 10b are images of left and right camera sequences respectively of a turbule transiting in front of the sun where the turbule is imaged by both the left and right cameras during a common interval of time;
FIG. 11 is an illustration of the use of angular offset to correlate the images of the turbule when the turbule is imaged by both cameras during a common interval of time;
FIGS. 12a and 12b are images of left and right camera sequences respectively of a turbule transiting in front of the sun where the turbule is not visible to both cameras during a common interval of time; and
FIG. 13 is an illustration of a multi-dimensional solution to correlate the images of the turbule when the turbule is imaged by different cameras at different times.



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 system 100 detects 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 system 100 warns the pilot of turbulence in the path of the aircraft. In another embodiment, turbulence and winds aloft measurement system 100 provides a visual navigational aid to enable a pilot to navigate around pockets of turbulent air. The turbulence and winds aloft measurement system 100 may 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 system 100 also 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 system 100 therefore reduces component fatigue, permits safer long term operation of the aircraft, and reduces or shortens necessary maintenance cycles.
The turbulence and winds aloft measurement system 100 allows 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 to FIG. 1a, a turbulence and winds aloft measurement system 100 is shown. The turbulence and winds aloft measurement system 100 obtains optical turbulence information of the atmosphere using observable features of the sun 124 and moon 122 or other celestial objects 128, for example a grouping of stars 126, to predict atmospheric conditions in the parcel of atmosphere. The turbulence and winds aloft measurement system 100 uses distortions in visual measurements of observable features of the sun 124, moon 122, stars 126, or other celestial objects 128 to measure and track refractivity fluctuations in intervening parcels of atmosphere. The refractivity fluctuations correspond to turbules 112 of turbulent air, and tracking the turbules 112 allows the turbulence and winds aloft measurement system 100 to determine the velocity of winds aloft 114. In addition to tracking turbules 112 or turbulence in general, the visual measurements can be used to improve atmospheric models, for example models of winds aloft 114, and thereby improve weather forecasts and/or aircraft routing.
In an embodiment, the turbulence and winds aloft measurement system 100 comprises a mobile platform or vehicle 102, for example a ship, traversing a section of the earth 110, a first camera 104a, and a second camera 104b, a position and orientation system 106, and a computer 108. 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 cameras 104a, 104b (collectively 104) are mounted on or to the vehicle 102 and separated by a modest distance. In an embodiment the cameras 104 are mounted on different sides of the vehicle 102. A computer 108 analyzes images from the cameras 104. The computer 108 can 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 cameras 104 are communicatively linked to the computer 108 that receives the images from the cameras 104. In an embodiment, the computer 108 is physically located on the vehicle 102. In embodiments, the computer 108 is physically located on another platform or operations center, for example at a weather service provider 130. In embodiments, data from cameras 104 are networked to one or more computers via a network or plurality of networks.
In an embodiment, the camera 104 uses a telephoto lens. In operation, the cameras 104 are pointed at an celestial object 128 or a particular feature of an celestial object 128 having sufficient known detail, and a series of images or video is delivered to the computer 108. In embodiments, the celestial object 128 is the moon 122, the sun 124, or stars 126 and planets. For example, the stars 126 could be a well known constellation of stars 126 such as the Pleiades, or any other grouping of stars having close proximity to one another. The cameras 104 output digitized data of the image to the computer 108. In another embodiment, the computer 108 digitizes analog inputs from the cameras 104 into digital images using a digital frame grabber.
The images from the cameras 104 can be analyzed to detect small local deviations in the refractive index of air. For example, light returning to the cameras 104 from the sun 124 passes through the atmosphere along light path 132. 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 sun 124 can appear shifted spatially. The mean-square angular displacement of small features is given by a well-known formula shown in equation 1. 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 Cn2 is a measure of optical turbulence at each point along the path. Cn2 is mathematically related to mechanical turbulence, which can pose a danger to aircraft.

<φ2>=2.91D−1/3∫0LCn2(η)dη  Equation (1)

Referring now to FIG. 1b, a telephoto lens 142 focuses light from the sun 124 through a helium I filter 200 onto a CCD 140. For purposes of illustration only, part of a granule 202 of the sun 124 is shown on the CDD 140 as an inverted image 146. The inverted image 146 is where the granule 202 is resolved on the CCD 140 due the distortion caused by the turbule 112 carried in the winds aloft 114. The dashed inverted image 144 illustrates where the solar granule 202 will be imaged once the turbule 112 passes. 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 cameras 104 using normal snapshot lenses. To increase accuracy and provide a finer level of granularity, the cameras 104 in the turbulence and winds aloft measurement system 100 use 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 cameras 104.
In an embodiment, the telephoto lens 142 and the pixel resolution of the image capturing element, for example a CCD 140 or 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 2.5×10−6 radians 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 lens 142 is 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 cameras 104 include a CCD 140 having 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 CCD 140 is 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 camera 104 that divides the image into three different CCDs, for example using birefringent materials, and therefore does not induce unwanted edge artifacts.
In embodiments, the cameras 104 are 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 cameras 104 selectively 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 cameras 104 additionally are infrared cameras or selectively uses image intensifiers, such as a night vision tubes, allowing the turbulence and winds aloft measurement system 100 to perform better in low light situations such as when viewing unlit portions of the moon 122 or other celestial objects 128 at night time. In embodiments, the cameras 104 are 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 cameras 104 are mounted on a rotatable swivel mounts that allow the cameras 104 to be rotated to view different portions of the sky. In an embodiment, the cameras 104 are mounted on multi-axis gimbals, allowing the cameras 104 to be angularly rotated in any direction. In these embodiments, the cameras 104 may be rotated or oriented in order to scan a larger area. The outputs from the cameras 104 are synchronized with an output from a rotational encoder or other similar orientation identifying means to correlate images from the cameras 104 with the orientation of the cameras 104.
The motion of the cameras 104 are linked to the motion of the vehicle 102, for example through a position and orientation system 106 such 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 camera 104 orientation due to rotation or twisting of the vehicle 102 and can be used to maintain orientation of the cameras 104 towards a desired celestial object 128. In an embodiment, one or both of the cameras 104 are substantially fixed and a rotatable mirror is used to change the direction of viewing of or more of the cameras 104. In an embodiment, the mirrors are first surface mirrors for better clarity. In an embodiment, the cameras 104 are mounted in vibration reducing mounts. In an embodiment, the cameras 104 are gyroscopically stabilized.
Image Processing
Continuing to refer to FIG. 1a, the computer 108 processes one or more images from the cameras 104. The processing identifies visual features whose physical location is well known, e.g., features on the sun 124 or moon 122. The sun 124 and the moon 122 both have visible features that can be distorted by turbulence in ways that allows detection of the turbulence.
Referring now to FIG. 2c, the lunar features 206 of the moon 122, including mountains and craters, are well known and are static. However, different portions of the moon 122 are illuminated by the sun 124, depending upon the particular lunar phase. The angle of illumination of lunar features 206 by the sun 124 also 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 cameras 104. The moon 122 is shown in FIG. 2c using a polarizing filter 220. The moon 122 also wobbles slightly, thus allowing slightly more than half of the surface of the moon 122 to be usable as visual features.
Referring to FIGS. 2a and 2b, to detect features of the sun 124, 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 sun 124 and sunspots 204, when present, can be resolved by the cameras 104. Using filters such as helium I filters 200 and hydrogen alpha filters 210, the sun 124 also presents full-time surface features during daylight hours called “granules” 202. FIGS. 2a and 2b show granules 202. Granules 202 are always present, are easily observable with a telephoto lens and a narrowband spectral filter and have a fine-grained texture. The sun 124 is shown in FIG. 2a using a helium I filter 200. The sun 124 is shown in FIG. 2b using a hydrogen alpha filter 210. Granules 202 provide a good background against which to detect turbules 112.
Referring again to FIG. 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 computer 108 measures the angular position of those visual features in the scene. The computer 108 compares 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 turbules 112, and winds aloft 114. For ease of exposition, the following examples use the sun 124 as the background object for detecting turbules 112 and winds aloft 114, however any celestial object 128 including the moon 122, the sun 124, stars 126 can be utilized with appropriate lenses and filters.
The computer 108 processes a series of time-tagged frames from each camera 104. 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 camera 104. For example, two consecutive frames of the sun 124 will look essentially the same, with a slight change in position of the sun 124 due to the ordinary movement of the sun 124 relative to the earth 110. When turbulence is present, however, some parts of the sun 124 will appear distorted, and the distortion will vary from frame to frame. A feature in one frame captured at time t0 cannot 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 t0 and 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 computer 108 performs a transformation of a first frame at time t0 into a predicted subsequent frame, and compares the predicted subsequent frame with the actual subsequent frame at time t0+Δt. In another embodiment, the computer 108 performs 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 computer 108 before 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 camera 104 related 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 cameras 104, which may have different focal lengths or may look at the same scene from different angles, for example if two cameras 104 are mounted on opposite sides of a ship, or vehicle 102.
To perform the transformation, the computer 108 performs an estimate of the motion of the vehicle 102 including changes in direction and orientation, for example by using information from an onboard inertial navigation system and GPS system. The computer 108 also performs an estimate of the motion of the feature, for example the small changes in position of the sun 124 or moon 122 relative to the earth 110. The computer 108 uses the motion estimates along with the time between the frames, t0 and t0+Δt to perform a transformation of features in one or both frames. The computer 108 registers 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 t0 to the feature in the frame at t0+Δt. In this example, the frame at t0 is digitally translated, scaled, and rotated so that features in frame at t0 are aligned with matching features in the frame at t0+Δt.
After image registrations methods are applied, any mismatch between frames from a camera 104 indicates 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 computer 108 eliminates frames containing clouds. In another embodiment, the computer 108 uses only those features in the frame where the moon 122 or sun 124 is not blocked by clouds.
Referring now to FIG. 3b, in one embodiment, a camera 104 observes a turbule 302 encroach on the edge of the sun 124 at time t0. Referring now to FIG. 3c, at a later time, t1=t0+Δt, the camera 104 images the turbule 302 begin to exit the other edge of the sun 124. Referring now to FIG. 3a, the interval Δt depends on three variables: the angular width, α, of the sun 124; the distance to the turbule 302 or height, ht; and the velocity, v, of the turbule 302. The distance to the sun 124, or hs is known, and α is also known. Given Δt, the ratio of ht and v can be computed using trigonometry. In one embodiment, the values for ht and 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 cameras 104 are utilized to determine the distance ht to the turbule 302, which allows determining the value of the velocity, v, of the turbule 302. Referring now to FIG. 4a, left camera 104a is separated from right camera 104b by distance d, for example by mounting the left camera 104a and right camera 104b, collectively cameras 104, on opposite ends of the vehicle 102. Note that although two cameras 104 are described as an exemplary embodiment, it is also possible to perform the operation using additional cameras 104, or even a single camera 104 capable of imaging a feature from two or more vantage points, for example using lenses, mirrors, or fiber optics.
Continuing to refer to FIG. 4a, and now referring to FIG. 4b, for purposes of illustrating an aspect of the invention, a simplified embodiment of the system is shown as follows: left camera 104a and right camera 104b are shown in a line that is approximately horizontal and the sun 124 is in a vertical orientation perpendicular to that the line between the cameras 104. Turbule 302 is shown moving parallel to the line between the cameras 104, in a direction from left to right. As turbule 302 crosses in front of the sun 124, the left camera 104a will detect distortion caused by the turbule 302 at time t0 before the right camera 104b detects the distortion at time t2=t0+Δt, where Δt is equal to distance between the cameras 104, 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 camera 104a, or time t3=t2+αht/v, then ht can be computed by either

ht=(t1−t0)v/α  Equation (3)

or

ht=(t3−t2)v/α  Equation (4)

and therefore both the height ht or distance to the turbule 302, and the velocity vector, v, of the turbule 302 can be computed. The computer 108 uses the distance to the turbule 302 and the angle to the turbule 302 to determine the altitude of the turbule 302 relative to the earth 110. Although this example assumes the sun 124 is directly above the cameras 104, it will be apparent to those skilled in the art that the sun 124 or other celestial objects 128 may be viewed at any angle from vertical to nearly horizontal, and at any azimuth relative to the vector d connecting the two cameras 104, and that suitable trigonometry formulas may be used to compute the correct height, ht, and velocity vector, v, of the turbule 302.

Referring now to FIG. 5a and FIG. 5b, an alternative mathematical approach is to determine the offset angle θ of the turbule 302 from the center of the sun 124 by both cameras 104. Left camera 104a images an offset of θ1 and right camera 104b images an offset of θr. The angular difference between turbule 302 measured positions by each camera 104 is Δθ=θ1−θr, and ht can 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 turbules 302 measured angular speed ω relative to the cameras 104 is computed by measuring the time Δt for turbule 302 to transit the angular width α of the sun 124. The turbule 302 velocity vector v is computed as

v=ω/ht.  Equation (6)

In practice, turbules 302 may be irregularly shaped, there may be multiple turbules 302, and each turbule 302 may appear at a different altitude with a different wind speed and direction. The following embodiments correlate image features to resolve individual turbules 302 within a sequence of images taken by a single camera 104 and between images taken by two or more cameras 104.
Correlation of Images from a Camera
Referring now to FIG. 6a and FIG. 6b, a first turbule 602 moves in a first direction at velocity va, shown in FIG. 6b as generally traveling in the direction of the x-axis, and a second turbule 604 moves in a second direction at velocity vb, shown in FIG. 6b as traveling more or less in the direction of the y-axis. To distinguish the data associated with the first turbule 602 from data associated with the second turbule 602, a mathematical correlation operation is performed to the data.
The correlation coefficient for two data sets, xi and yi, each having N elements, is defined as

r=sxy/sxsy,  Equation (7)

where sx and sy are the standard deviations of xi and yi and where sxy is 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 mx n 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/sxsy  Equation (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 to FIG. 6a and FIG. 6b, and now referring now to FIG. 7a, FIG. 7b, and FIG. 7c, first turbule 602 is at height hta and second turbule 604 is at height htb. Both the first turbule 602 and the second turbule 604 are moving across the visible disc of the sun 124 at the same time, but in two different directions x, y, and at two different speeds, va, vb respectively. The images in FIGS. 7a, 7b, and 7c illustrate the turbules 602, 604 at four different times, t1, t2, t3, t4.
Referring now to FIG. 8a, FIG. 8b, and FIG. 8c, in an embodiment, the turbulence and winds aloft measurement system 100 computes a sequence of difference images 802, 804, and 806, at various temporal and angular offsets. The first difference image 802 is the difference between the image frame that captured first turbule 602 and second turbule 604 at time t1, and the image frame that captured first turbule 602 and second turbule 604 at time t2. Similarly, second difference image 804 is the difference between the images when turbules 602, 604 are at times t2 and t3, and third difference image 806 is the difference image between times t3 and 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 turbules 602, 604 at a particular altitude hta, htb, there is a peak in the correlation coefficient, r(ωθ, ωφ).

Referring now to FIG. 9a and FIG. 9b, the correlation contour plots illustrate the correlation r2(ωθ, ωφ) 900 of the difference images 802, 804, and 806 for angular velocity vectors ωθ906, and ωφ908. The correlation contour plots have two peaks, 902, 904. The peaks 902, 904 represent the angular velocities of the turbules 602, 604 with one peak corresponding to ωa902 and one peak corresponding to ωb904. To measure the linear velocities va, vb of the turbules 602, 604 requires knowledge of the altitudes hta and htb.
Correlation of Images from Cameras
To compute the altitudes hta and htb and the linear velocities va, vb of the turbules 602, 604, the positions of the turbules 602, 604 are triangulated using two or more cameras 104. Referring now to FIGS. 10a and 10b, a turbule 1002 moves at angular speed ω across the sun 124. FIG. 10a illustrates the imaging of the turbule 1002 by a first camera 104a at times t1, t2, t3, and t4 as the turbule 1002 transits the sun 124. FIG. 10b illustrates the imaging of the same turbule 1002 by the second camera 104b at times t3, t4, t5, and t6.
Referring now to FIG. 11, the turbule 1002 is visible to both cameras 104 during times t3 and t4. To measure the angular offset Δθ, or spatial shift of the position of the turbule 1002, the difference image from one of the cameras 104 is shifted along the direction of the other camera 104, 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 ht of the turbule 1002 relative to the camera 104, as given by ht≅=d/Δθ (Equation (5).)
Referring now to FIGS. 12a and 12b, the turbule 1002 is not visible to both cameras 104 at the same times, t1-t7. The turbule is visible to camera 104a during times t1, t2, t3, and t4; and the turbule is visible to camera 104b during times t5, t6, and t7. There is therefore no angular offset Δθ that allows a correlation peak in r(Δθ) to match the turbule 1002 images from both cameras 104. Instead, the difference images from one camera 104 are correlated with the difference images taken by another camera 104 at a different time, either earlier or later, and using angular offsets with non-zero Δφ.
Referring now to FIG. 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 sun 124. 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 computer 108 first 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 computer 108 is 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 system 100 comprises one, two, or multiple cameras 104. The ability for the turbulence and winds aloft measurement system 100 to accurately resolve the altitude of turbules 112, 302, 602, 604, and 1002, depends in part upon the distance between the cameras 104. For example, cameras 104 that are close together generally see the same turbules 112, 302, 602, 604, and 1002, making computations easier, but cameras 104 that further apart can resolve angular distances to a finer granularity. Also turbules 112, 302, 602, 604, and 1002 at lower altitudes will have greater angular displacements frame-to-frame for a given linear velocity because they are closer to the cameras 104, making computations possible even for relatively closely placed cameras 104, that is, cameras 104 that have a relatively small d between them. Turbules 112, 302, 602, 604, and 1002 that are higher in the atmosphere will have relatively lower angular displacement frame-to-frame, and thus will require greater distances between cameras 104 in order to resolve accurately.
In an embodiment, a first pair of cameras 104 are separate by a distance of approximately 10 meters, while a third camera 104 is separated from the pair of cameras 104 by approximately 100 meters. The first pair of cameras 104 provide good characterization of turbules 112, 302, 602, 604, and 1002 at lower altitudes, while the third camera 104 facilitates characterizing turbules 112, 302, 602, 604, and 1002 at high altitudes.
In an embodiment, the cameras 104 are mounted on an ocean-going vehicle 102, for example a ship or vessel. For example, the first pair of cameras 104 might 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 cameras 104 are located roughly at the corners of an equilateral triangle on the surface of the earth 110. This configuration ensures that turbules 112, 302, 602, 604, and 1002 traveling in any direction within a selected altitude range will be simultaneously visible to at least two of the cameras 104 during part of the turbules 112, 302, 602, 604, and 1002 transit across the sun 124. This configuration also allows using one-dimensional angular offsets for correlation between each pair of cameras 104, which is computationally less costly than the three-dimensional offsets needed to achieve similar coverage with, for example, two cameras 104.
Communications
In an embodiment, the turbulence and winds aloft measurement system 100 further comprises a communications link 116 to transfer estimates of turbulence, turbules 112, and winds 114 aloft. In embodiments, the communications link 116 both receives estimates and transmits estimates. In embodiments, the communications links 116 permits transfers of estimates with aircraft 118, a weather service provider 130, 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 sun 124 and moon 122.
In an embodiment, the turbulence and winds aloft measurement system 100 communicates information to the pilot of the vehicle 102. In an embodiment, the turbulence and winds aloft measurement system 100 sends the estimates to a weather forecasting center or weather service provider 130. In an embodiment, the turbulence and winds aloft measurement system 100 shares the information with nearby aircraft 118 or systems on the ground. In an embodiment, the turbulence and winds aloft measurement system 100 shares raw or interpreted data with nearby vehicle 102 to develop a better indication of local turbulence, turbules 112, and winds aloft 114. 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 system 100 may 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.

## Claims

1. A turbulence and winds aloft detection system, comprising:
an image capturing device for capturing a plurality of images of a visual feature of a celestial object;
a lens having a focal length adapted to focus an image onto said image capturing device such that a combination of said lens and said image capturing device is adapted to resolve a distortion of said visual feature caused by 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 between said image capturing device and said celestial object; and
compute a measurement of angular velocity of said turbule with respect to said image capturing device.

2. The turbulence and winds aloft detection system of claim 1, wherein said combination of said lens and said image capturing device is adapted to resolve at least 2.5 microradians of angle.

3. The turbulence and winds aloft detection system of claim 1, wherein said image capturing device is a CCD camera.

4. The turbulence and winds aloft detection system of claim 1, wherein said celestial object is selected from the group consisting of the moon, the sun, a plurality of stars, and a planetary system, and wherein said visual feature is selected from the group consisting of an edge of a solar disc, a sunspot, a solar granule, an edge of a lunar disc, a lunar crater, a lunar shadow, a relative position of each of a plurality of stars, and a position of moons in a planetary system.

5. The turbulence and winds aloft detection system of claim 1, further comprising a filter disposed between said image capturing device and said celestial object, and wherein said filter is selected from the group consisting of a helium I filter, a hydrogen alpha filter, a solar filter, a neutral density filter, a polarizing filter, an narrowband filter, a wideband filter, and an optically colored filter.

6. The turbulence and winds aloft detection system of claim 1, further comprising:
a second image capturing device for capturing a second plurality of images of said visual feature of said celestial object; and
wherein said image processor is adapted to process said plurality of images and said second plurality of images to triangulate a distance to said turbule, and
wherein said image processor is adapted to determine a velocity of said turbule, and
wherein said distance to said turbule and said velocity of said turbule provide a winds aloft measurement.

7. The turbulence and winds aloft detection system of claim 1, wherein said image processor is adapted to process said plurality of images into a set of difference images, and wherein said image processor is adapted to correlate said set of difference images to produce an angular velocity measurement for each of a plurality of turbules transiting in between said image capturing device and said celestial object.

8. The turbulence and winds aloft detection system of claim 7, wherein said image processor is adapted to process said second plurality of images into a second set of difference images, and wherein said image processor is adapted to triangulate said distance to each of said plurality of turbules, and determine a distance and a velocity of each of said plurality of turbules.

9. The turbulence and winds aloft detection system of claim 8, wherein said image processor is adapted to triangulate said distance to each of said plurality of turbules by computing a correlation coefficient for a plurality of spatial shifts of a turbule from said set of difference images with said turbule from said second set of difference images to find a correlation peak, said correlation peak identifying an angular velocity vector of said turbule.

10. The turbulence and winds aloft detection system of claim 8, wherein said image processor is adapted to triangulate said distance to each of said plurality of turbules by computing a correlation coefficient for a plurality of spatial shifts, angular offsets, and temporal displacements of a turbule from said set of difference images with said turbule from said second set of difference images to find a correlation peak, said correlation peak identifying an angular velocity vector of said turbule.

11. A method of detecting turbulence and winds aloft, comprising:
capturing a plurality of images of a celestial object;
selecting a feature present in said plurality of images;
comparing said visual feature in said plurality of images to detect the transit of a turbule of turbulent air in front of said celestial object; and
computing a measurement of an angular velocity of said turbule.

12. The method of claim 11, wherein said capturing is performed by an image capturing means adapted to capture angular resolutions of at least 2.5 microradians in said plurality of images.

13. The method of claim 11, wherein said celestial object is selected from the group consisting of the moon, the sun, a plurality of stars, and a planetary system, and wherein said visual feature is selected from the group consisting of an edge of a solar disc, a sunspot, a solar granule, an edge of a lunar disc, a lunar crater, a lunar shadow, a relative position of each of a plurality of stars, and a position of moons in a planetary system.

14. The method of claim 11, wherein said capturing is performed through a filter selected from the group consisting of a helium I filter, a hydrogen alpha filter, a solar filter, a neutral density filter, a polarizing filter, an narrowband filter, a wideband filter, and an optically colored filter.

15. The method of claim 11, further comprising:
capturing a second plurality of images of said visual feature of said celestial object;
processing said plurality of images and said second plurality of images to triangulate a distance to said turbule; and
calculating a velocity of said turbule, and

wherein said distance to said turbule and said velocity of said turbule provide a winds aloft measurement.

16. The method of claim 11, further comprising:
processing said plurality of images into a set of difference images;
correlating said set of difference images to produce an angular velocity measurement for each of a plurality of turbules transiting in front of said celestial object.

17. The method of claim 16, further comprising:
processing said second plurality of images into a second set of difference images;
triangulating a distance to each of said plurality of turbules; and
calculating a velocity of each of said plurality of turbules.

18. The method of claim 17, wherein said triangulating operation further comprises:
computing a correlation coefficient for a plurality of spatial shifts of a turbule from said set of difference images with said turbule from said second set of difference images to find a correlation peak, said correlation peak identifying an angular velocity vector of a turbule.

19. The method of claim 17, wherein said triangulating operation further comprises:
computing a correlation coefficient for a plurality of spatial shifts, angular offsets, and temporal displacements of a turbule from said set of difference images with said turbule from said second set of difference images to find a correlation peak, said correlation peak identifying an angular velocity vector of a turbule.

20. A vehicle with a turbulence detection system, comprising:
one or more CCD cameras for capturing an plurality of images of a feature of a celestial object from a plurality of vantage points, said one or more CCD cameras adapted to resolve a change in position of said feature due to optical refraction cause by a turbule of turbulent atmosphere between said one or more CCD cameras and said feature of said celestial object;
a vehicle adapted to mount said one or more CCD cameras;
a processor adapted to compare said plurality of images of said visual feature to detect the transit of said turbule, and to compute a measurement of a distance to said turbule and a velocity of said turbule; and
a communication system configured to communicate said distance measurement and said velocity measurement of said turbule to an aircraft.