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`EXHIBIT 2007
`EXHIBIT 2007
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`3/14/2017
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`How an LDV/LDA works | Measurement Science Enterprise, INC
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`Introduction
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`A Laser Doppler Velocimeter (LDV), also known as a Laser Doppler Anemometer (LDA), is a type of
`interferometer that measures the velocity of objects using laser light. The objects can be microscopic particles
`in a fluid or solid surfaces—the concept is even used in some highend laser mice.
`
`A laser beam is split and the two “arms” are made to cross outside the sensor. This crossing region is called
`the probe volume. Because the two arms came from the same beam, when they cross, an interference pattern
`is generated, and light and dark stripes form inside the probe volume. These stripes are called “fringes”.
`
`Click image to view larger
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`Probe Volume Characteristics
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`The two beams must be focused at the probe volume to 1) create the smallest possible intersection zone
`(increasing the “brightness” of the light reflected by the particles), and 2) to ensure that the spacing between
`the fringes does not change much inside the probe volume. This critical alignment is easily maintained by the
`design of the miniLDV because both arms of the interferometer go through the same individual optics.
`
`There is always some “fringe divergence” as it is physically impossible to build a system in which the fringe
`spacing is absolutely constant within the probe volume. This is because the wavefront radius of the laser
`(according to beam propagation theory) is only zero at the waist, which is the exact focal point of the beam. All
`of MSE’s LDV products are built to achieve the minimum possible fringe divergence.
`
`Fundamentally an LDV or LDA uses the same Doppler effect that causes the siren from an ambulance driving
`by to change pitch—except that here the Doppler effect is with light, not sound. However, there are two ways
`to interpret how an LDV or LDA is able to measure the speed of an object. The more intuitive explanation (see
`figure) goes as follows.
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`
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`How Speed is Measured
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`The fringes formed by the interference of the beams is a pattern of light in space. When a particle passes
`through the probe volume, it goes through the light and dark regions, so if its reflected light is measured as it
`travels along, the intensity versus time curve looks like a sinusoid with a Gaussian envelope. The Gaussian
`envelope comes from the fact that the intensity of the beams is Gaussian in nature. The sinusoid is the
`physical travel of the particle through the fringes. The physical distance between the fringes is known from the
`calibration which is performed with every probe. So the frequency of the intensity signal is directly proportional
`to the velocity of the particle: velocity = fringe spacing x intensity frequency.
`
`Although perhaps less intuitive, the measurement still works if the object passing through the probe volume is
`a continuous surface. This is because the probe volumes are so small that any microscopic features in the
`surface will reflect different amount of light and behave almost as if the surface were a stream of individual
`particles.
`
`To measure the velocity of fluids like air or water, there must be something in the fluid to reflect light back. In
`air the particles can be as small as the smoke particles of an incense stick; for water, sometimes there’s
`enough signal straight out of the tap.
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`“D” is for Doppler
`
`The second explanation reveals how the “Doppler” in LDV/LDA comes about.
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`http://measurementsci.com/howanldvldaworks/
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`3/14/2017
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`How an LDV/LDA works | Measurement Science Enterprise, INC
`When a particle travels through the probe volume, it will have some velocity V. If the vectors corresponding to
`the directions of the two beams are decomposed into a coordinate system where V is the X axis, then there will
`always be one beam whose “Vvector” is positive when the other one’s is negative. Really this is a
`mathematical way of saying that the particle is always traveling “toward” one beam and “away” from the other.
`
`Much like the red and blue shift of galaxies moving away from or toward us, the particle will add a Doppler shift
`to the light it reflects from each beam: the frequency of the reflected light is higher for the beam toward which
`it’s traveling and lower for the other. This is exactly like the pitch of a siren being higher when the ambulance is
`coming toward you than when it’s going away from you.
`
`The frequency of light is extremely high. For a 658 nm (red) laser, it is 45.5 petahertz (45.5 quadrillion cycles
`per second), so to the detector it looks like a continuous beam. However the particle now is reflecting light at
`45.5 petahertz plus a little bit and 45.5 petahertz minus a little bit. When these waves arrive at the detector, it
`records a “beat” frequency not unlike what you hear when you press two adjacent keys on a piano. The beat
`frequency is significantly lower than the frequency of one beam by itself. Not only is this frequency easy to
`observe, but it is directly related to the wavelength of the light and the speed of the particle.
`
`For this beat frequency to be observable, the two light waves (one from each beam) being reflected from the
`particle must have been created nearly at the same time as each other. That is why a single laser beam is split
`into two arms. If two independent lasers are used, the beams are completely unrelated and no beat frequency
`is observable. Another way to put it is that two independent sources of light will not interfere with each other.
`Lasers have a given “coherence length” or “coherence time”, indicating how much one wave from the laser will
`interfere with another wave. If they are generated exactly at the same time, the interference is “perfect”; if they
`are generated within the coherence time, the beat frequency is still observable, though less intense, and if they
`are generated outside the coherence time, no beat frequency is observed. MSE’s LDV products are all
`designed to maintain the “optical path length” of each beam well within the coherence length to provide the
`highest possible signal.
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`
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`Frequency Shifting and the Determination of Direction
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`When two beams are crossed in space as in a classical LDV/LDA, the interference pattern is steady with
`space. This means that 1) it is impossible to know if the particle was traveling from left to right or right to left,
`and 2) it is impossible to measure very low velocities, because it will take too long for the particle to travel
`through a bright and dark region (alternatively, the beat frequency is too low).
`
`The trick is to add a Doppler shift to the beams themselves. When an LDV has “frequency shifting”, the beams
`already have a frequency difference when they are in space, so if a particle has velocity zero, the recorded
`signal will have the same frequency as the difference in frequency between the two beams.
`
`The effective frequency of the signal is the sum of the frequency due to the particle and the shift frequency. So
`when a particle is going one way, it will add to the shift frequency; going the other way it will subtract—and if it
`has velocity zero it does not change the shift frequency at all. Viewed another way, the fringes are moving in
`space, so the actual measurement is the velocity of the particle relative to the velocity of the fringes. MSE’s
`miniLDV can be ordered with or without frequency shifting. For ultrastable frequency shifting applications (to
`measure extremely low velocities), MSE offers the ultraLDV line.
`
`It should be noted that any LDV or LDA measures only the component of velocity along the direction of the
`interference pattern—so the instrument must be aligned to the flow (or some known direction so that
`adjustments to the results can be made). MSE also offers multicomponent systems: the 2D miniLDV and 3D
`miniLDV.
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`http://measurementsci.com/howanldvldaworks/
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