This invention relates generally to radiation emitting sources for sensing targets and, more particularly, to radiation emitting sources, for example radar systems, which emit radiation and sensing reflections for target detection.
In the past, there have been known methods employed for locating radar emitter sources, which required the knowledge of several parameters related to the operation of the emitter source measurements made from two or more known spatial locations, and/or the known rate of relative motion of the emitter source. Conventional radar sources can be vulnerable to countermeasures because the emitted radiation possesses rather simple phase fronts. The countermeasures that can be employed by an aircraft that is being imaged include sending a missile down a course perpendicular to the phase fronts to destroy the radar installation, or sending back “rogue” radiation with an altered phase front pattern to suggest a reflection from elsewhere. Each of these methods require an assessment of the phase front emitted by the source, which is easier to perform if the phase front lacks complexity.
The principles of phase-front analysis may be understood by considering a very simple phased array consisting of three dipole antennae at positions whose cylindrical polar coordinates (r, φ, z) have the values (0, 0, 0), (a,+π/2, 0) and (a,−π/2, 0)
If the dipole antennae are excited in phase at an angular frequency ω, it is simple to show that the signal received at time tP at a far-field observation point P with the spherical coordinates (RP>>a, θP=π/2, φP) will have the amplitude
where c is the speed of light in vacuo, and the origin of the time coordinate is chosen to remove any arbitrary phase. Note that the time-independent part of this expression has zero crossings at
where j is an integer (see
Now consider two closely-spaced detectors, labelled P and Q and placed at positions (RP, π/2, φP+δφP) and (RQ, π/2, φP−δφP). The signals VP and VQ detected by P and Q will be of the following form
VP=AP cos(ωtP−γP) and VQ=AQ cos(ωtP−γQ), (3)
where γP and γQ are phases that depend on the relative positions of P and Q. If the detectors are identical in all respects, and RP=RQ, then γP−γQ vanishes for all φP, apart from a very small region of angular width 2δφP around each of the zero-crossings defined by Eq. 2, where |γP−γQ|=π (see
The surface defined by RP=RQ therefore represents a surface of constant phase, or “phase front”.
The detection of such phase fronts, by appropriate positioning of P and Q, constitutes a method for locating the direction of the phased array. Although modifications can be made to the relative phases of the elements of a phased array to “steer” the beam or apply an apparent slant to the phase front, the very regular nature of the phase fronts that emanate from such systems makes them vulnerable to being located and subjected to countermeasures.
An essential part of warfare involving radiation sensing systems is the location of targets or reference marks by means of a detection system such as radar, and it is common that any potential enemy will take steps, such as the creation of interference utilizing countermeasure devices to prevent the effective use of detection equipment against targets. Such countermeasure devices can assume various forms such as for example an inverse gain repeater, a range gate pull-off repeater, chaff, radar decoys, image frequency jammers, and other forms. A usual target that utilizes such countermeasure technology is an aircraft.
In a known method, knowledge of the waveform modulation of the emitter source in the time or frequency domain can be utilized. An example of such a requirement included the scan rate, the pulse duration, the pulse interval and/or the frequency modulation patterns. In another known method, measurements can be provided in the form of the emitter signal angle of arrival or the emitter signal time of arrival. Measurements in the form of angle of arrival can be utilized in the process of triangulation. The emitter signal measurements of angle and time of arrival can then be employed in conjunction with the time and location of the measurements to ascertain emitter location. Yet another known method utilized for determining the range to a radar emitter involved the measurement of angular rates between the emitter source and the measurements site/platform.
In the field of microwave radar, a technique has long been used in which an interrogating radar signal is deceived by returning a distorted signal having a discontinuity or other alteration in the phase front, so that it appears to be coming from a different point in space. The art has long sought an equivalent for laser radar. The detection of the location of a radar source by way of analysis of a phase front and the ability to alter the phase front so that it appears that the target is at a different point, is made possible due to the non-complex nature of a conventional phase front. A more complex phase front is needed to avoid some of these countermeasure techniques.
The invention is a radiation source involving phase fronts emanating from an accelerated, oscillating, superluminal (that is, faster than light in vacuo) polarization current. The present invention using a superluminal source shows that the phase fronts from such a source can be made to be very complex. Consequently, it can be very difficult for an aircraft imaged by such radiation to detect where this radiation comes from. Moreover, the complexity of the phase fronts makes it almost impossible for electronics on an aircraft to synthesize a rogue reflection. A simple directional antenna and timing system should, on the other hand, be sufficient for the radar operators to locate the aircraft, given knowledge of their own source's speed and modulation pattern.
The superluminal source has another advantage; the radiation from the source may be steered electronically (that is, without moving the antenna) by changing the speed at which the distribution pattern of the polarization current propagates, which can be controlled by the voltage switching function of the elements. Indeed, the linearity of the emission process makes it possible for a superluminal source to emit tightly-beamed radiation of several different frequencies in several directions simultaneously.
Radar detection of aircraft (and indeed ships and other vehicles) is used by virtually all branches of the armed forces. The invention can limit the vulnerability of current radar systems.
The present invention involves a technique for generating phase fronts of considerable complexity using a polarization current with a superluminally moving distribution pattern that both oscillates and possesses centripetal acceleration. The test data indicates that the phase difference between signals detected by closely-spaced antennae assumes a wide range of values and is a rapidly varying function of both the absolute and relative positions of the detectors. The underlying reason for this complexity is that the reception time is a multi-valued function of the retarded time in the case of emission from superluminal sources. The distinctive traits of the phase fronts emanating from a superluminal source suggest that such a source could be employed in a radar system that would be much more robust against countermeasures.
These and other advantageous features of the present invention will be in part apparent and in part pointed out herein below.
For a better understanding of the present invention, reference may be made to the accompanying drawings in which:
a) is an illustration of positive and negative ions in a solid dielectric;
b) illustrates how applying a spatially varying electric field induces a polarization, where the distribution pattern of the electric field is moving causing the polarized region to move;
c) is a schematic side view of a practical superluminal emitter;
d) illustrates movement of the polarization region by varying the voltages of the electrodes;
e) is a schematic top view of a practical superluminal emitter showing the curvature of the dielectric;
f) is a view of the practical superliminal emitter illustrating the amplifiers that provide the voltage for the electrodes;
g) illustrates the means by which the practical superliminal emitter is rotated;
a) to 3(d) are graphical illustrations of the angular coordinates marking the spatial distribution of the radiation relative to the orientation of the array;
a) and 4(b) are graphical illustrations of a theoretical phase difference;
a), 5(b) and 5(c) are graphical illustrations of a theoretical phase difference;
a) and 6(b) are graphical illustrations of a theoretical phase difference;
a) and 7(b) are graphical illustrations of experimental and theoretical intensity and phase;
a) and 8(b) are graphical illustrations of experimental and theoretical intensity and phase;
a) to 9(b) are graphical illustrations of experimental and theoretical intensity and phase;
a) and 10(b) are graphical illustrations of experimental and theoretical intensity and phase for a full-circle array.
a) and 11(b) are illustrations of intensity and phase for a full-circle array.
While the invention is susceptible to various modifications and alterations and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that the drawings and detailed description presented herein are not intended to limit the invention to the particular embodiment disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the present invention as defined by the appended claims.
According to the embodiment(s) of the present invention, various views are illustrated in
One embodiment of the present invention comprising an oscillating superluminal polarization current radiation source teaches a novel apparatus and method for emitting a complex phase front. The apparatus can include a dipole antenna array
The method can include the steps of selectively switching on or switching off a voltage input 215 to each of a plurality of element antenna amplifiers 217 in an array (
The production and propagation of electromagnetic radiation is described by the following two Maxwell equations:
(SI units). Here H is the magnetic field strength, B is the magnetic induction, P is polarization, and E is the electric field; the (coupled) terms in B, E and H of Eqs. 4 and 5 describe the propagation of electromagnetic waves. The generation of electromagnetic radiation is encompassed by the source terms Jfree (the current density of free charges) and ∂P/∂t (the polarization current density); e.g., an oscillating Jfree is the basis of conventional radio transmitters. The charged particles that make up Jfree have finite rest mass, and therefore cannot move with a speed that exceeds the speed of light in vacuo; hence, practical superluminal sources employ a polarization current to generate electromagnetic radiation.
The principles of such sources are outlined in
The practical machine represents a discretized version of this process; it consists of a continuous strip of alumina (the material to be polarized by the applied electric field) on top of which is placed an array of metal electrodes; underneath is a continuous ground plate. This forms what is in effect a series of capacitors (a schematic is shown in
In practice, the dielectric in the experimental machine is a strip corresponding to approximately a 10° arc of a circle of approximate average radius a=10.025 m, made from alumina approximately 10 mm thick and 50 mm across. Above the alumina strip, there are 41 upper electrodes of mean width of approximately 42.6 mm, with centers approximately 44.6 mm apart (see photograph in
A polarization current j=∂P/∂t can be produced by a polarization (the electric dipole moment per unit volume) of the following form in the dielectric:
Pr,φ,z,t(r,φ,z,t)=sr,φ,z(r,z)cos(m{circumflex over (φ)})cos(Ωt); (6)
here Pr,φ,z are the components of the polarization (expressed in cylindrical polar coordinates), s(r, z) is a vector field describing the orientation of P (it vanishes outside the active volume of the source), {circumflex over (φ)} stands for the Lagrangian coordinate φ−ωt, and mω and Ω are the two angular frequencies used in the synthesis of the source.
One embodiment of the invention employs individual shielded amplifiers to drive each electrode of the array (see
Vj=V0 cos [η(jΔt−t)] cos Ωt. (7)
Comparison of Eqs. 7 and 6 shows that η≡mω and Δt≡Δφ/ω, where Δφ is the angle subtended by the effective center separation of adjacent electrodes. The speed υ with which the polarization current distribution propagates is set by adjusting Δt to give υ=aΔφ/Δt, where a=10.025 m and aΔφ=44.6 mm.
Given the dimensions of the experimental array, υ>c is achieved for Δt<148.8 ps. Most of the emission occurs at two frequencies, f±=|Ω±η|/2π. The current experiments use η/2π=552.654 MHz and Ω/2π=47.321 MHz, so that the higher-frequency, f+=(Ω+η)/2π=599.975 MHz was approximately 25 kHz below 600.000 MHz.
The angular distribution of the radiation is measured by fixing the detector a distance R from the array and rotating the array about two orthogonal axes. As shown in
A general way of determining the phase γ of an oscillating function f(t) at a given frequency is to expand f(t) once into a Fourier sine series and once into a Fourier cosine series and use
γ=arctan [{tilde over (f)}s(ω)/{tilde over (f)}c(ω)], (8)
where {tilde over (f)}s(ω) and {tilde over (f)}c(ω) are the Fourier sine and Fourier cosine components of f(t) at the frequency ω, respectively. An example is the basic monochromatic oscillation of Eq. 3;
V≡f=A cos(ωt−γ)=A[ cos γ cos(ωt)+sin γ sin(ωt)], (9)
whose Fourier sine and cosine series each consist of a single term with the components
{tilde over (f)}s(ω)=A sin γ and {tilde over (f)}c(ω)=A cos γ.
In the present case, we are interested in the phase of the electromagnetic waves that are generated by the polarization current j=∂P/∂t defined by Eq. 6.
The electromagnetic fields E and B of the generated radiation are described, in the absence of boundaries, by
and B={circumflex over (n)}×E, where (xP, tP)=(rP, φP, zP, tP) and (x, t)=(r, φ, z, t) are the space-time coordinates of the observation point and the source points, respectively, n≡xP/|xP|, δ is the Dirac delta function, and c is the speed of light in vacuo. (Here, we have set the origin of the coordinate system within the source so that |x|<<|xP| for an observation point in the radiation zone.)
The source term in the above expression has the following form for the polarization current j=∂P/∂t described in Eq. 6:
+[sφ cos θP sin(φ−φP)−sr cos θP cos(φ−φP)+sz sin θP]ê⊥}, (11)
where μ±≡Ω/ω±m. In this expression, ê∥, which is parallel to the plane of rotation pointing along the cylindrical base vector êφP, and ê195 ≡{circumflex over (n)}×ê∥ comprise a pair of unit vectors normal to the radiation direction {circumflex over (n)}. The detectors were set to measure the component of the radiation that is polarized parallel to the plane of the array. Hence the relevant component of the source term in Eq. 10 is
in the case of the present experimental array for which sφ is zero.
The fact that the array has the form of an arc (
to within a constant of proportionality depending on the source strength. Here,
in which {circumflex over (r)}≡rω/c≡υ/c is the source speed in units of c, {circumflex over (R)}P≡RPω/c=(rP2+zP2)1/2ω/C, and θP=arccos(zP/RP) [i.e., ({circumflex over (R)}P, θP, φP) comprise the spherical coordinates of the observation point P in units of the light-cylinder radius c/ω]. The integration with respect to φ extends over the interval (−π/36, π/36), and the integration with respect to {circumflex over (φ)} may be performed over any interval of length 2π in which the argument of the delta function has a zero (see below).
Measurements are made at the frequency μ+ω≡η+Ω. The coefficient corresponding to this frequency in the Fourier cosine series for E(xP, tP) has the value
where H stands for the Heaviside step function. The second line in this equation follows from inserting the expression for E(RP, θP, φP, tP) in its first line, interchanging the orders of integration with respect to tP and (φ, {circumflex over (φ)}), and evaluating the integral over tP first.
The above step functions (arising from the integration of the delta function over a finite interval) require that the values of {circumflex over (φ)} should be limited to the following interval:
{circumflex over (R)}+φ−π/μ+<{circumflex over (φ)}<{circumflex over (R)}+φ+π/μ+. (16)
Once the integration with respect to {circumflex over (φ)} is carried out over this interval, one obtains
an integral that has to be evaluated numerically.
The corresponding coefficient in the Fourier sine series for E(xP, tP) has the value
The same procedure that led to Eq. 17 now results in
Note that the expression in Eq. 19 differs from that in Eq. 17 not only in that cos(μ±{circumflex over (R)}±mφ) are replaced by sin(μ±{circumflex over (R)}±mφ), but also in that the sign of the second term in the square brackets is changed.
The phase of the waves that are detected at the observation point P are therefore given, according to Eq. 8, by
and Eqs. 17 and 19. Comparing this with the phase of the waves that are detected at a neighbouring point Q with the coordinates (RQ, θQ, φQ), we find that the phase difference is represented by
This phase difference can be expressed in terms of the experimentally measured coordinates (R(P), θV(P), ΦV(P)) and (R(Q), θV(Q), ΦV(Q)) of the points P and Q by means of the following transformations:
in which O can be either P or Q, and a=10.025 m is the average radius of the array.
The expressions in Eqs. 17 and 19 describe the electric-field vector of the wave that propagates from the source to the detector directly. In the presence of the ground, we need to take into account also the electric-field vector of the reflected wave that passes through the observation point P. This may be done by replacing {tilde over (E)}s(xP, μ+ω), {tilde over (E)}c(xP, μ+ω), {tilde over (E)}s(xQ, μ+ω) and {tilde over (E)}c(xQ, μ+ω) everywhere by
sin(φP+Φ0){tilde over (E)}s(xP,μ+ω)+q∥(P) sin(φP′+Φ0){tilde over (E)}s(xP′,μ+ω), (25)
sin(φP+Φ0){tilde over (E)}c(xP,μ+ω)+q∥(P) sin(φP′+Φ0){tilde over (E)}c(xP′,μ+ω), (26)
sin(φQ+Φ0){tilde over (E)}s(xQ,μ+ω)+q∥(Q) sin(φQ′+Φ0){tilde over (E)}s(xQ′,μ+ω), (27)
and
sin(φQ+Φ0){tilde over (E)}c(xQ,μ+ω)+q∥(Q) sin(φQ′+Φ0){tilde over (E)}c(xQ′,μ+ω), (28)
respectively, where P′ and Q′ are the images of the observation points P and Q across the surface of the ground, and Φ0 specifies the inclination of the array with respect to this surface. Here,
is the relevant Fresnel coefficient for reflections off a medium with the index of refraction N, where
α(O)=arctan {[R(O)
O stands for P or Q, and hA and hD(O) are the heights of the array and the detector at O, respectively. The coordinates of the image points P′ and Q′ are given, in terms of the experimentally measured coordinates of the detectors P and Q, by the following relationships:
in which O′ can be either P′ or Q′.
To obtain the intensity of the radiation from the expressions in Eqs. 17 and 19, it would be necessary to integrate {tilde over (E)}c2+{tilde over (E)}s2 with respect to the frequency μ+ω over the bandwidth of the receiver.
Measurements were performed at the upper frequency, f+=(Ω+mω)/2π≡(Ω+η)/2π. The detection system works at frequencies close to 600 MHz, and is based on two identical dipole aerials, each mounted at a height hD=2 m above the ground on adjustable tripod masts; the aerials P and Q. Each aerial is connected to a Group A and a Group B band-pass filter in series, to eliminate spurious signals away from 600 MHz; the filtered signals from P and Q are then amplified using two identical Maxview Triax MHF 3553 amplifiers. For the phase analysis, the output from each amplifier is individually mixed with a 600.000 MHz signal from a Minicircuits 2X05-C24MH resistive splitter driven by an Atlantec ANS2-0500-10-0 oscillator. The resulting 25 kHz signal from P was amplified using an EG and G 5113 amplifier to provide the reference phase for a Stanford Research SR830 DSP lock-in amplifier, the signal channel of which was connected to the 25 kHz signal from Q. As the mixing preserves the relative phases of P and Q, the phase difference between the signal and reference channels of the lock-in is, to within a constant offset dependent on the electronics, identical to the phase difference between the f+ signals at the two aerials. The amplitude and phase outputs of the lock-in amplifier were recorded; the intensity plotted in the following figures is proportional to the square of the amplitude. Note that for each measurement distance R, the phase measurement contains a systematic constant offset associated with the electronics and slight errors in the relative positioning of P and Q (i.e. R(P) and R(Q) are not quite equal—the error will typically be ˜0.5 m in distances R˜500 m).
The array was mounted in the configuration shown in
In particular, the coincidence of the strong phase excursions with the minima in intensity is a feature that can be directly inferred from Eq. 21. The vanishing of the denominator of the fraction in Eq. 21, which occurs close to a zero of intensity (for a small P-Q separation), would imply a shift from −π/2 to π/2 (or from π/2 to −π/2) in the value of Δγ if it occurs simultaneously with a change in the sign of the numerator of this fraction. In general, a change in the sign of the numerator of the fraction in Eq. 21 is not necessarily concurrent with the vanishing of the denomenator of this fraction. Correspondingly, the observed shift in the value of Δγ, though attaining its largest values in the vicinities of the zeros of intensity, is not as large as π in general.
a) shows experimental intensity and phase data for a source speed of υ/c=1.063, an array to detector distance of R=R(P)=R(Q)=180 m and a tangential P-Q antenna separation of R|θV(P)−θV(Q)|=3 m plotted as a function of θV for several values of ΦV. The data show that the characteristic phase variations observed at larger distances persist down to 180 m. Neither these nor the theoretical model indicate any characteristic trait of the phase fronts that evolves with distance.
b) displays experimental intensity and phase data for a source speed of υ/c=1.063 and an array to detector distance of R=R(P)=R(Q)=404 m as a function of θV for tangential P-Q antenna separations of 3 m, 5.9 m and 12 m. It shows that the observed differences in phase are essentially independent of the tangential separation of P and Q in regions where |γP−γQ| varies slowly with θV. This, and the fact that the phase differences are more sensitively dependent on the P-Q separation close to the minima of the amplitude, are both corroborated by the theoretical model.
In summary, the experimental data show extensive and continuous variations of the phase difference γP−γQ both as a function of the polar (θV) and azimuthal (ΦV) angles and of the source to detector distance (R). This indicates that the phase fronts from a superluminal source undergoing centripetal acceleration possess considerable complexity, in contrast to those from conventional phased-array systems. A relatively simple radar system based on a superluminal source would therefore be less vulnerable to countermeasures than conventional systems based on phased arrays.
Finally, note that the theoretical model is able to reproduce the experimental data quantitatively. This shows that the model is a good representation of the properties of superluminal sources, and that our understanding of this novel area of electromagnetism is valid.
The array of the current experimental superluminal source (see
Hence, the range of θV in which the phase variations occur would coincide with that in which the amplitude attains its extrema if the source is synthesized with a frequency Ω≡f+−η that is much lower than η.
Note that, in practice, the extent of the angular region (in θV) over which the phase and amplitude variations occur can be made as small, or as large, as desired by the choice of the two parameters υ/c and η/f+. In particular, it would be possible to generate a radiation beam propagating into the plane of rotation (θV=0) with an arbitrarily narrow width in θV by choosing the value of υ/c close to unity. This radiation would be distributed over all values of ΦV when the azimuthal variation of the source density is sinusoidal as in Eq. 6. To generate a corresponding radiation that is beamed in ΦV, as well as in θV, we would have to synthesize a superluminal source whose distribution pattern is localized (rather than sinusoidally varying) in {circumflex over (φ)}.
The present invention considers the phase fronts associated with the spherically-decaying component of the radiation that is generated by a superluminal source. The radiation that arises from the present source also entails a nonspherically-decaying component, a tightly beamed component that is composed of the collection of cusps of the wave fronts emanating from each source element. Given the crucial role played by the phases of the constructively interfering waves that form the cusps, a similar investigation of the characteristics of the phase difference Δγ for the nonspherically-decaying component of the radiation is essential to further development of the present invention.
A full-circle array would be more suited to such an investigation because, as illustrated by
The details of the invention and various embodiments can be better understood by further referring to the figures of the drawing. Referring to
a) and (b) are graphical illustrations of the phase difference γP−γQ (vertical axis) for a source speed υ/c=1.25 as a function of source to detector distance R and the polar angle θV [
a), (b), and (c) are graphical illustrations of the phase difference γP−γQ (vertical axis) for a source speed υ/c=1.25 as a function of (R, θV), including the effect of reflections from the ground. As before, P and Q are positioned such that R=R(P)=R(Q), with a tangential separation of 12 m between P and Q; the orientation of the array is described by the experimental coordinates θV and ΦV (see
a) and 6(b) are graphical illustrations of the phase difference γP−γQ (vertical axis) for a source speed υ/c=1.25 as a function of (R, ΦV), including the effect of reflections from the ground. As before, P and Q are positioned such that R=R(P)=R(Q), with a tangential separation of 12 m between P and Q; the orientation of the array is described by the experimental coordinates θV and ΦV (see
a) and 7(b) are illustrations of the theoretical intensity (a) and phase (b) for a source speed of υ/c=1.25, an array to detector distance of R=R(P)=R(Q)=980 m and a tangential P-Q antenna separation of R|θV(P)−θV(Q)|=12 m plotted as a function of θV for several values of ΦV (see inset key). The points are experimental data; the solid curves are the theoretical predictions of the model. Note that the model reproduces all aspects of the data quantitatively.
a) and 8(b) are illustrations of experimental and theoretical intensity [
a)-9(d) are illustrations of intensity and phase data for a source speed of υ/c=1.063, an array to detector distance of R=R(P)=R(Q)=180 m and a tangential P-Q antenna separation of 3 m plotted as a function of θV for several values of ΦV (see inset key).
a) and 10(b) are illustrations of intensity and phase for a full-circle array versus θV. A source speed of υ/c=1.25, an array to detector distance of R=R(P)=R(Q)=979.6 m and a tangential P-Q separation of R|θV(P)−θV(Q)|=12 m have been assumed; ΦV=0. The calculation ignores the effect of reflection from the ground; however, a comparison of
a) and 11(b) are illustrations of intensity [
The various polarization current base array examples shown above illustrate a novel array capable of producing a complex phase front effective against various countermeasure systems. A user of the present invention may choose any of the above, or an equivalent thereof, depending upon the desired application. In this regard, it is recognized that various forms of the subject invention could be utilized without departing from the spirit and scope of the present invention.
As is evident from the foregoing description, certain aspects of the present invention are not limited by the particular details of the examples illustrated herein, and it is therefore contemplated that other modifications and applications, or equivalents thereof, will occur to those skilled in the art. It is accordingly intended that the claims shall cover all such modifications and applications that do not depart from the spirit and scope of the present invention.
Other aspects, objects and advantages of the present invention can be obtained from a study of the drawings, the disclosure and the appended claims.
This invention was made with partial government support under Contract No. DE-AC52-06NA25396 awarded by the U.S. Department of Energy. The government has certain rights in the invention.
Number | Name | Date | Kind |
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4893071 | Miller | Jan 1990 | A |
Number | Date | Country | |
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20100039324 A1 | Feb 2010 | US |