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63-419: The FORESTER is a GMTI radar system with a resolution of 6 meters that is mounted inside a 21.5-foot (6.6 m) long pod and designed to be carried under an A160 Hummingbird helicopter unmanned aerial vehicle (UAV). The system is able to detect vehicles and walking soldiers underneath tree cover from a distance of 30 miles (48 km), giving battle planners the ability to detect potential ambushes. The pod

126-666: A wavefunction solution of the Schrödinger equation for a quantum mechanical object. Then the probability P ( x ) {\displaystyle P(x)} of observing the object at position x {\displaystyle x} is P ( x ) = | Ψ ( x , t ) | 2 = Ψ ∗ ( x , t ) Ψ ( x , t ) {\displaystyle P(x)=|\Psi (x,t)|^{2}=\Psi ^{*}(x,t)\Psi (x,t)} where * indicates complex conjugation . Quantum interference concerns

189-445: A 'spectrum' of fringe patterns each of slightly different spacing. If all the fringe patterns are in phase in the centre, then the fringes will increase in size as the wavelength decreases and the summed intensity will show three to four fringes of varying colour. Young describes this very elegantly in his discussion of two slit interference. Since white light fringes are obtained only when the two waves have travelled equal distances from

252-676: A frequency shift, thereby directly extracting the moving targets. This became common in the 1970s and especially the 1980s. Modern radars generally perform all of these MTI techniques as part of a wider suite of signal processing being carried out by digital signal processors . MTI may be specialized in terms of the type of clutter and environment: airborne MTI ( AMTI ), ground MTI ( GMTI ), etc., or may be combined mode: stationary and moving target indication ( SMTI ). The MTI radar uses low pulse repetition frequency (PRF) to avoid range ambiguities. Moving target indicator (MTI) begins with sampling two successive pulses. Sampling begins immediately after

315-603: A given range any time the radar beam scans across it, Pd is determined by factors that include the size of the antenna and the amount of power it radiates. A large antenna radiating at high power provides the best performance. For high quality information on moving targets the Pd must be very high. Location accuracy is a dependent on the certainty of the position of the radar, the radar-pointing accuracy, azimuth resolution, and range resolution. A long antenna or very short wavelength can provide fine azimuth resolution. Short antennas tend to have

378-407: A larger azimuth error, an error that increases with range to the target because signal-to-noise ratio varies inversely with range. Location accuracy is vital to tracking performance because it prevents track corruption when there are multiple targets and makes it possible to determine which road a vehicle is on if it is moving in an area with many roads. The target location accuracy is proportional to

441-454: A narrow spectrum of frequency waves of finite duration (but shorter than their coherence time), will give a series of fringe patterns of slightly differing spacings, and provided the spread of spacings is significantly less than the average fringe spacing, a fringe pattern will again be observed during the time when the two waves overlap. Conventional light sources emit waves of differing frequencies and at different times from different points in

504-454: A robust, wide-area, all-weather, standoff capability." Cost is anticipated to run US$ 2.5 million per unit, with a production goal of US$ 1 million per unit in quantities of 50 or more. The FORESTER program is being managed by DARPA's Information Innovation Office (I2O), and the hardware is manufactured for DARPA by SRC at their Syracuse, NY, headquarters. The initial prototype for the FORESTER

567-426: A single laser beam is used in interferometry, though interference has been observed using two independent lasers whose frequencies were sufficiently matched to satisfy the phase requirements. This has also been observed for widefield interference between two incoherent laser sources. It is also possible to observe interference fringes using white light. A white light fringe pattern can be considered to be made up of

630-400: A specific class (e.g., a T-80 tank). This would allow more reliable tracking of specific vehicles or groups of vehicles, even when they are moving in dense traffic or disappear for a period due to screening. The MDV comes from the frequency spread of the mainlobe clutter. MDV determines whether traffic will be detected. A GMTI radar must distinguish a moving target from ground clutter by using

693-414: A wave at the original frequency, traveling to the right like its components, whose amplitude is proportional to the cosine of φ / 2 {\displaystyle \varphi /2} . A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle. One wave is travelling horizontally, and the other is travelling downwards at an angle θ to

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756-480: A wave of a different polarization state . Quantum mechanically the theories of Paul Dirac and Richard Feynman offer a more modern approach. Dirac showed that every quanta or photon of light acts on its own which he famously stated as "every photon interferes with itself". Richard Feynman showed that by evaluating a path integral where all possible paths are considered, that a number of higher probability paths will emerge. In thin films for example, film thickness which

819-403: Is an odd multiple of π . If the difference between the phases is intermediate between these two extremes, then the magnitude of the displacement of the summed waves lies between the minimum and maximum values. Consider, for example, what happens when two identical stones are dropped into a still pool of water at different locations. Each stone generates a circular wave propagating outwards from

882-468: Is designed to swivel from its stowed in-line position 90 degrees to its deployed position. From a helicopter UAV hovering at 20,000 feet (6,100 m), FORESTER can cover a 155-square-mile (400 km) area. According to FORESTER program manager Lyndall Beamer, "Employing the sensor system on the DARPA/U.S. Army A160 Hummingbird unmanned aerial vehicle [UAV] helicopter or other suitable platform will provide

945-515: Is not a multiple of light wavelength will not allow the quanta to traverse, only reflection is possible. The discussion above assumes that the waves which interfere with one another are monochromatic, i.e. have a single frequency—this requires that they are infinite in time. This is not, however, either practical or necessary. Two identical waves of finite duration whose frequency is fixed over that period will give rise to an interference pattern while they overlap. Two identical waves which consist of

1008-436: Is slightly different so as to accommodate the additional samples. Phase jitter, Doppler effects, and environmental influences limit MTI sub-clutter visibility Measure of Performance to about 25 dB improvement. This allows moving objects about 300 times smaller to be detected in close proximity to larger stationary objects. Pulse-Doppler signal processing is required to achieve greater sub-clutter visibility. A target

1071-461: Is temporarily obscured, if only by trees along a road. Interference (wave propagation)#Constructive and destructive interference In physics , interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference . The resultant wave may have greater intensity ( constructive interference ) or lower amplitude ( destructive interference ) if

1134-553: Is the wavenumber and ω = 2 π f {\displaystyle \omega =2\pi f} is the angular frequency of the wave. Suppose a second wave of the same frequency and amplitude but with a different phase is also traveling to the right W 2 ( x , t ) = A cos ⁡ ( k x − ω t + φ ) {\displaystyle W_{2}(x,t)=A\cos(kx-\omega t+\varphi )} where φ {\displaystyle \varphi }

1197-460: Is the phase difference between the waves in radians . The two waves will superpose and add: the sum of the two waves is W 1 + W 2 = A [ cos ⁡ ( k x − ω t ) + cos ⁡ ( k x − ω t + φ ) ] . {\displaystyle W_{1}+W_{2}=A[\cos(kx-\omega t)+\cos(kx-\omega t+\varphi )].} Using

1260-402: Is traveling at velocity v p {\displaystyle v_{p}} at a maximum range R max {\displaystyle R_{\text{max}}} with elevation angle E L {\displaystyle EL} and azimuth A Z {\displaystyle AZ} in respect to a bistatic MTI radar. The probability of detecting a given target at

1323-563: Is used to divide the light into two beams travelling in different directions, which are then superimposed to produce the interference pattern. The Michelson interferometer and the Mach–Zehnder interferometer are examples of amplitude-division systems. In wavefront-division systems, the wave is divided in space—examples are Young's double slit interferometer and Lloyd's mirror . Interference can also be seen in everyday phenomena such as iridescence and structural coloration . For example,

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1386-786: The trigonometric identity for the sum of two cosines: cos ⁡ a + cos ⁡ b = 2 cos ⁡ ( a − b 2 ) cos ⁡ ( a + b 2 ) , {\textstyle \cos a+\cos b=2\cos \left({a-b \over 2}\right)\cos \left({a+b \over 2}\right),} this can be written W 1 + W 2 = 2 A cos ⁡ ( φ 2 ) cos ⁡ ( k x − ω t + φ 2 ) . {\displaystyle W_{1}+W_{2}=2A\cos \left({\varphi \over 2}\right)\cos \left(kx-\omega t+{\varphi \over 2}\right).} This represents

1449-446: The amount of power radiated from the antenna, and the effectiveness of its clutter cancellation mechanism. The earth's curvature and screening from terrain, foliage, and buildings cause system altitude to be another key factor determining depth of coverage. The ability to cover an area the size of an army corps commander's area of interest from a safe stand-off distance is the hallmark of an effective, advanced GMTI system. This equates to

1512-434: The colours seen in a soap bubble arise from interference of light reflecting off the front and back surfaces of the thin soap film. Depending on the thickness of the film, different colours interfere constructively and destructively. Quantum interference – the observed wave-behavior of matter – resembles optical interference . Let Ψ ( x , t ) {\displaystyle \Psi (x,t)} be

1575-402: The converse, then multiplies both sides by e i 2 π N . {\displaystyle e^{i{\frac {2\pi }{N}}}.} The Fabry–Pérot interferometer uses interference between multiple reflections. A diffraction grating can be considered to be a multiple-beam interferometer; since the peaks which it produces are generated by interference between

1638-455: The display along with the next received pulse. The result was that the signal from any objects that did not move mixed with the stored signal and became muted out. Only signals that changed, because they moved, remained on the display. These were subject to a wide variety of noise effects that made them useful only for strong signals, generally for aircraft or ship detection. The introduction of phase-coherent klystron transmitters, as opposed to

1701-421: The distance between the sources increases from left to right. When the plane of observation is far enough away, the fringe pattern will be a series of almost straight lines, since the waves will then be almost planar. Interference occurs when several waves are added together provided that the phase differences between them remain constant over the observation time. It is sometimes desirable for several waves of

1764-410: The energy is redistributed to other areas. For example, when two pebbles are dropped in a pond, a pattern is observable; but eventually waves continue, and only when they reach the shore is the energy absorbed away from the medium. Constructive interference occurs when the phase difference between the waves is an even multiple of π (180°), whereas destructive interference occurs when the difference

1827-404: The famous double-slit experiment , laser speckle , anti-reflective coatings and interferometers . In addition to classical wave model for understanding optical interference, quantum matter waves also demonstrate interference. The above can be demonstrated in one dimension by deriving the formula for the sum of two waves. The equation for the amplitude of a sinusoidal wave traveling to

1890-490: The figure above and to the right as stationary blue-green lines radiating from the centre. Interference of light is a unique phenomenon in that we can never observe superposition of the EM field directly as we can, for example, in water. Superposition in the EM field is an assumed phenomenon and necessary to explain how two light beams pass through each other and continue on their respective paths. Prime examples of light interference are

1953-493: The first wave. Assuming that the two waves are in phase at the point B , then the relative phase changes along the x -axis. The phase difference at the point A is given by Δ φ = 2 π d λ = 2 π x sin ⁡ θ λ . {\displaystyle \Delta \varphi ={\frac {2\pi d}{\lambda }}={\frac {2\pi x\sin \theta }{\lambda }}.} It can be seen that

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2016-409: The frequency of light waves (~10 Hz) is too high for currently available detectors to detect the variation of the electric field of the light, it is possible to observe only the intensity of an optical interference pattern. The intensity of the light at a given point is proportional to the square of the average amplitude of the wave. This can be expressed mathematically as follows. The displacement of

2079-420: The frequency with which the radar beam passes over a given area. Frequent revisits are very important to the radar's ability to achieve track continuity and contribute to an increased probability of target detection by lessening the chance of obscuration from screening by trees, buildings, or other objects. A fast revisit rate becomes critical to providing an uncorrupted track when a target moves in dense traffic or

2142-445: The incoherent cavity magnetron used on earlier radars, led to the introduction of a new MTI technique. In these systems, the signal was not fed directly to the display, but first fed into a phase detector . Stationary objects did not change the phase from pulse to pulse, but moving objects did. By storing the phase signal, instead of the original analog signal, or video , and comparing the stored and current signal for changes in phase,

2205-401: The initial phase of both transmit pulses must be sampled and the 180 degree phase rotation must be adjusted to achieve signal cancellation on stationary objects. A secondary influence is that phase rotation is induced by Doppler, and that creates blind velocities. For example, an object moving at 75 m/s (170 mile/hour) will produce 180 degree phase shift each 1 millisecond at L band . If

2268-595: The intensities of the individual waves as I ( r ) = I 1 ( r ) + I 2 ( r ) + 2 I 1 ( r ) I 2 ( r ) cos ⁡ [ φ 1 ( r ) − φ 2 ( r ) ] . {\displaystyle I(\mathbf {r} )=I_{1}(\mathbf {r} )+I_{2}(\mathbf {r} )+2{\sqrt {I_{1}(\mathbf {r} )I_{2}(\mathbf {r} )}}\cos[\varphi _{1}(\mathbf {r} )-\varphi _{2}(\mathbf {r} )].} Thus,

2331-577: The interference pattern maps out the difference in phase between the two waves, with maxima occurring when the phase difference is a multiple of 2 π . If the two beams are of equal intensity, the maxima are four times as bright as the individual beams, and the minima have zero intensity. Classically the two waves must have the same polarization to give rise to interference fringes since it is not possible for waves of different polarizations to cancel one another out or add together. Instead, when waves of different polarization are added together, they give rise to

2394-486: The invention of the laser was done using such sources and had a wide range of successful applications. A laser beam generally approximates much more closely to a monochromatic source, and thus it is much more straightforward to generate interference fringes using a laser. The ease with which interference fringes can be observed with a laser beam can sometimes cause problems in that stray reflections may give spurious interference fringes which can result in errors. Normally,

2457-801: The light at r is given by I ( r ) = ∫ U ( r , t ) U ∗ ( r , t ) d t ∝ A 1 2 ( r ) + A 2 2 ( r ) + 2 A 1 ( r ) A 2 ( r ) cos ⁡ [ φ 1 ( r ) − φ 2 ( r ) ] . {\displaystyle I(\mathbf {r} )=\int U(\mathbf {r} ,t)U^{*}(\mathbf {r} ,t)\,dt\propto A_{1}^{2}(\mathbf {r} )+A_{2}^{2}(\mathbf {r} )+2A_{1}(\mathbf {r} )A_{2}(\mathbf {r} )\cos[\varphi _{1}(\mathbf {r} )-\varphi _{2}(\mathbf {r} )].} This can be expressed in terms of

2520-415: The light source, they can be very useful in interferometry, as they allow the zero path difference fringe to be identified. To generate interference fringes, light from the source has to be divided into two waves which then have to be re-combined. Traditionally, interferometers have been classified as either amplitude-division or wavefront-division systems. In an amplitude-division system, a beam splitter

2583-418: The light transmitted by each of the elements in the grating; see interference vs. diffraction for further discussion. Mechanical and gravity waves can be directly observed: they are real-valued wave functions; optical and matter waves cannot be directly observed: they are complex valued wave functions . Some of the differences between real valued and complex valued wave interference include: Because

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2646-679: The magnitude of the displacement, φ represents the phase and ω represents the angular frequency . The displacement of the summed waves is U ( r , t ) = A 1 ( r ) e i [ φ 1 ( r ) − ω t ] + A 2 ( r ) e i [ φ 2 ( r ) − ω t ] . {\displaystyle U(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i[\varphi _{1}(\mathbf {r} )-\omega t]}+A_{2}(\mathbf {r} )e^{i[\varphi _{2}(\mathbf {r} )-\omega t]}.} The intensity of

2709-439: The modern stationary target indication (STI) technique, which uses details of the signal to directly determine the mechanical properties of the reflecting objects and thereby find targets whether they are moving or not. Early MTI systems generally used an acoustic delay line to store a single pulse of the received signal for exactly the time between broadcasts (the pulse repetition frequency ). This stored pulse will be sent to

2772-468: The moving targets are revealed. This technique is far more resistant to noise, and can easily be tuned to select different velocity thresholds to filter out different types of motion. Phase coherent signals also allowed for the direct measurement of velocity via the Doppler shift of a single received signal. This can be fed into a bandpass filter to filter out any part of the return signal that does not show

2835-416: The point where the stone was dropped. When the two waves overlap, the net displacement at a particular point is the sum of the displacements of the individual waves. At some points, these will be in phase, and will produce a maximum displacement. In other places, the waves will be in anti-phase, and there will be no net displacement at these points. Thus, parts of the surface will be stationary—these are seen in

2898-418: The power amplifier, module quantization, the number of beams processed and system losses. Stand-off distance is the distance separating a radar system from the area it is covering. Coverage area size is the area that the system can keep under continuous surveillance from a specific orbit. Well known design principles cause a radar's maximum detection range to depend on the size of its antenna (radar aperture),

2961-595: The pulse repetition interval is 0.002   s between transmit pulses, then the MTI process will produce 360 ∘ {\displaystyle 360^{\circ }} phase rotation. That is the same as a stationary object, which renders the system blind to objects traveling at this radial velocity. MTI requires 3 or 4 pulses to reduce the effect of blind velocities. Multi-pulse strategies use staggered pulses with irregular pulse repetition intervals to prevent signal cancellation on moving objects. The summation process

3024-405: The radar transmit pulse ends. The sampling continues until the next transmit pulse begins. Sampling is repeated in the same location for the next transmit pulse, and the sample taken (at the same distance) with the first pulse is rotated 180 degrees and added to the second sample. This is called destructive interference . If an object is moving in the location corresponding to both samples, then

3087-498: The radial component of a target's velocity approaches zero, the target will fall into the clutter or blind zone . This is calculated as: Any target with a velocity less than this minimum (MDV) cannot be detected because there is not sufficient Doppler shift in its echo to separate it from the mainlobe clutter return. The area coverage rate (measured in area per unit time) is proportional to system power and aperture size. Other factors which may be relevant include grid spacing, size of

3150-394: The right along the x-axis is W 1 ( x , t ) = A cos ⁡ ( k x − ω t ) {\displaystyle W_{1}(x,t)=A\cos(kx-\omega t)} where A {\displaystyle A} is the peak amplitude, k = 2 π / λ {\displaystyle k=2\pi /\lambda }

3213-1205: The same frequency and amplitude to sum to zero (that is, interfere destructively, cancel). This is the principle behind, for example, 3-phase power and the diffraction grating . In both of these cases, the result is achieved by uniform spacing of the phases. It is easy to see that a set of waves will cancel if they have the same amplitude and their phases are spaced equally in angle. Using phasors , each wave can be represented as A e i φ n {\displaystyle Ae^{i\varphi _{n}}} for N {\displaystyle N} waves from n = 0 {\displaystyle n=0} to n = N − 1 {\displaystyle n=N-1} , where φ n − φ n − 1 = 2 π N . {\displaystyle \varphi _{n}-\varphi _{n-1}={\frac {2\pi }{N}}.} To show that ∑ n = 0 N − 1 A e i φ n = 0 {\displaystyle \sum _{n=0}^{N-1}Ae^{i\varphi _{n}}=0} one merely assumes

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3276-443: The same point, then the amplitude is the sum of the individual amplitudes—this is constructive interference. If a crest of one wave meets a trough of another wave, then the amplitude is equal to the difference in the individual amplitudes—this is known as destructive interference. In ideal mediums (water, air are almost ideal) energy is always conserved, at points of destructive interference, the wave amplitudes cancel each other out, and

3339-447: The signal reflected from the object will survive this process because of constructive interference. If all objects are stationary, the two samples will cancel out and very little signal will remain. High-power microwave devices, like crossed-field amplifier , are not phase-stable. The phase of each transmit pulse is different from the previous and future transmit pulses. This phenomenon is called phase jitter . In order for MTI to work,

3402-401: The slant range, frequency and aperture length. Target range resolution determines whether two or more targets moving in close proximity will be detected as individual targets. With higher performance radars, target range resolution—known as high range resolution (HRR)—can be so precise that it may be possible to recognize a specific target (i.e., one that has been seen before) and to place it in

3465-606: The source. If the light is split into two waves and then re-combined, each individual light wave may generate an interference pattern with its other half, but the individual fringe patterns generated will have different phases and spacings, and normally no overall fringe pattern will be observable. However, single-element light sources, such as sodium- or mercury-vapor lamps have emission lines with quite narrow frequency spectra. When these are spatially and colour filtered, and then split into two waves, they can be superimposed to generate interference fringes. All interferometry prior to

3528-406: The target's Doppler signature to detect the radial component of the target's velocity vector (i.e., by measuring the component of the target's movement directly along the radar-target line). To capture most of this traffic, even when it is moving almost tangentially through the radar (i.e., perpendicular to the radar-target line), a system must have the ability to detect very slow radial velocities. As

3591-449: The two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light , radio , acoustic , surface water waves , gravity waves , or matter waves as well as in loudspeakers as electrical waves. The word interference is derived from the Latin words inter which means "between" and fere which means "hit or strike", and

3654-626: The two waves are in phase when x sin ⁡ θ λ = 0 , ± 1 , ± 2 , … , {\displaystyle {\frac {x\sin \theta }{\lambda }}=0,\pm 1,\pm 2,\ldots ,} and are half a cycle out of phase when x sin ⁡ θ λ = ± 1 2 , ± 3 2 , … {\displaystyle {\frac {x\sin \theta }{\lambda }}=\pm {\frac {1}{2}},\pm {\frac {3}{2}},\ldots } Constructive interference occurs when

3717-690: The two waves at a point r is: U 1 ( r , t ) = A 1 ( r ) e i [ φ 1 ( r ) − ω t ] {\displaystyle U_{1}(\mathbf {r} ,t)=A_{1}(\mathbf {r} )e^{i[\varphi _{1}(\mathbf {r} )-\omega t]}} U 2 ( r , t ) = A 2 ( r ) e i [ φ 2 ( r ) − ω t ] {\displaystyle U_{2}(\mathbf {r} ,t)=A_{2}(\mathbf {r} )e^{i[\varphi _{2}(\mathbf {r} )-\omega t]}} where A represents

3780-469: The two waves overlap and the fringe spacing is uniform throughout. A point source produces a spherical wave. If the light from two point sources overlaps, the interference pattern maps out the way in which the phase difference between the two waves varies in space. This depends on the wavelength and on the separation of the point sources. The figure to the right shows interference between two spherical waves. The wavelength increases from top to bottom, and

3843-520: The waves are in phase, and destructive interference when they are half a cycle out of phase. Thus, an interference fringe pattern is produced, where the separation of the maxima is d f = λ sin ⁡ θ {\displaystyle d_{f}={\frac {\lambda }{\sin \theta }}} and d f is known as the fringe spacing. The fringe spacing increases with increase in wavelength , and with decreasing angle θ . The fringes are observed wherever

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3906-585: Was flight tested using a UH-60 Blackhawk helicopter because the A160 had not yet completed its Phase 1 flight test program. Test flights with the A160 began in August 2008. Moving target indication Moving target indication ( MTI ) is a mode of operation of a radar to discriminate a target against the clutter . It describes a variety of techniques used for finding moving objects, like an aircraft, and filter out unmoving ones, like hills or trees. It contrasts with

3969-406: Was used in the context of wave superposition by Thomas Young in 1801. The principle of superposition of waves states that when two or more propagating waves of the same type are incident on the same point, the resultant amplitude at that point is equal to the vector sum of the amplitudes of the individual waves. If a crest of a wave meets a crest of another wave of the same frequency at

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