Patent Publication Number: US-7711441-B2

Title: Aiming feedback control for multiple energy beams

Description:
RELATED APPLICATIONS 
   This application is related to co-pending, commonly owned U.S. Pat. application Ser. No. 11/420,086, filed May 24, 2006, entitled “Network and System for Controlling a Network for Power Beam Transmission,” naming Brian J. Tillotson as the sole inventor. 
   FIELD OF THE INVENTION 
   The field of the present disclosure relates to energy beaming systems, and more specifically, to feedback control systems and methods for aiming multiple energy beams onto a moving target. 
   BACKGROUND OF THE INVENTION 
   It is possible to provide energy to a moving target or vehicle by way of an electromagnetic energy beam, such as a microwave or laser beam. Typically, the source of the energy beam is located separate and apart from the object being powered. For example, an energy beam source can be stationary relative to a vehicle or other apparatus that is being powered (to some extent) by the energy beam. In the case of a laser beam, photovoltaic cells can be used to convert the incident laser energy directly to usable electrical power at the receiving object. In the case of microwave energy, antenna grids, focusing dishes and/or other suitable means can be used to derive electrical power at the receiver. In any case, it is possible to construct a system wherein a receiving apparatus or vehicle need not carry voluminous and/or massive sources of energy (e.g., batteries, jet fuel, etc.) in order to be partially or fully provisioned with operating power. 
   When a system requires a relatively small amount of energy, a single-beam arrangement is usually adequate. Under such a system, sensing devices and controls maintain suitable aiming of the energy beam on the appropriate receiving area (i.e., antenna, photovoltaic array, etc.) of the object being powered. In other cases, there are vehicles or other apparatus that require considerably more energy than a single source (laser or microwave emitter, etc.) can economically and/or technologically provide. For example, a flying vehicle may require 100 kW of power in order to operate. Economically, it is desirable to use ten 10 kW lasers, rather than a single 100 kW laser, to provide the needed power in this example. Furthermore, it is often easier to package ten 10 kW lasers and their supporting hardware into a mobile platform (if desired) than to package a single 100 kW laser and it supporting hardware into the same sort of platform. Thus, economies of scale are an important—and sometime technologically imperative—matter of consideration in designing and operating systems powered by multiple energy beams. 
   However, a problem arises when attempting to use several energy sources in concert to power an apparatus. Specifically, it is necessary to independently control each energy beam source so as to keep all of the respective energy beams accurately aimed at the receiving area of the powered apparatus. Furthermore, it is economically desirable to provide an energy beam receiving area (or array) on the apparatus or vehicle that is not much larger than the meaningful width of an energy beam. 
   Use of various means and methods for aiming a single energy beam are known in the prior art. However, these prior art systems may be unsuitable when multiple energy beams must be accurately maintained on a single receiving apparatus. Therefore, novel systems and methods that resolve the foregoing problems and concerns would have great utility. 
   SUMMARY 
   Feedback control systems and methods in accordance with the teachings of the present disclosure can be used to maintain accurate aiming of several energy beams onto a single receiving target or area. Economies of scale are advantageously realized through the use of multiple sources relative to a single, relatively large energy beam source. Other advantages may stem from the use of energy beam source redundancy. 
   In one embodiment, a system includes a receiving assembly including a target area configured to receive an incident electromagnetic energy and to convert the incident electromagnetic energy into an electrical or thermal output. The incident electromagnetic energy includes a contribution from a plurality of energy sources. The system also includes a control assembly including a plurality of sensors disposed about the target area. Each sensor is configured to receive a portion of electromagnetic energy not incident on the target area and to provide a corresponding output signal. The control assembly further includes a processing device operatively coupled to the plurality of sensors and configured to analyze the output signals from the plurality of sensors. The control assembly is also configured to detect a misalignment of the contribution from at least one of the plurality of energy sources, and to provide at least one control signal to the at least one of the plurality of energy sources tending to correct the misalignment. 
   In another embodiment, a system includes an energy receiving device configured to convert incident electromagnetic energy into electrical or thermal energy. The system also includes a plurality of sources configured to emit respective energy beams, and a plurality of sensors configured to provide respective detection signals corresponding to one or more of the energy beams incident to the energy receiving device. The system further includes a controller configured to receive the detection signals and provide one or more control signals. The plurality of sources are further configured to controllably aim the respective energy beams at the energy receiving device in accordance with the one or more control signals. 
   In yet another embodiment, a method includes controllably aiming a plurality of modulated energy beams at an energy receiving device. The method also includes sensing a misalignment portion of at least one of the plurality of modulated energy beams proximate the energy receiving device. The method further includes providing at least one control signal to adjust an aiming of the at least one of the plurality of modulated energy beams corresponding to the misalignment. The method includes converting at least a portion of the plurality of modulated energy beams incident to the energy receiving device into electrical or thermal energy. 
   The features, functions, and advantages that are discussed herein can be achieved independently in various embodiments of the present invention or may be combined various other embodiments, the further details of which can be seen with reference to the following description and drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     Embodiments of systems and methods in accordance with the teachings of the present disclosure are described in detail below with reference to the following drawings. 
       FIG. 1  is a schematic plan view depicting an energy receiving device in accordance with an embodiment of the invention; 
       FIG. 2  is a schematic plan view depicting an energy beam incident to the energy receiving device of  FIG. 1 ; 
       FIG. 3  is a schematic plan view depicting another state of the energy beam and energy receiving device of  FIG. 2 ; 
       FIG. 4  is a graph showing an energy beam pattern in accordance with an embodiment; 
       FIG. 5  is a schematic plan view of an energy receiving system in accordance with another embodiment; 
       FIG. 6  is a schematic plan view of the energy receiving system of  FIG. 5  under exemplary operating conditions; 
       FIG. 7  is a schematic plan view of the energy receiving system of  FIG. 6  under other exemplary operating conditions; 
       FIG. 8  is a schematic block diagram of an energy beaming and receiving system in accordance with an embodiment; 
       FIG. 9  is a schematic plan view of an energy receiving device under exemplary operating conditions; 
       FIG. 10  is a schematic plan view of an energy receiving device under exemplary operating conditions; 
       FIG. 11  is a schematic plan view of the energy receiving system of  FIG. 10  under exemplary operating conditions; 
       FIG. 12  is an isometric schematic view of an energy receiving device under exemplary operating conditions; 
       FIG. 13  is a schematic plan view of an energy receiving device under exemplary operating conditions; 
       FIG. 14  is a schematic plan view of an energy beaming system in accordance with another embodiment; 
       FIG. 15  is a schematic plan view depicting an energy receiving device in accordance with an embodiment; 
       FIG. 16  is a data plot depicting simulated operating conditions in accordance with an embodiment; 
       FIG. 17  is a data plot corresponding to  FIG. 16 ; 
       FIG. 18  is a data plot corresponding to  FIGS. 16 and 17 ; 
       FIG. 19  is a data plot depicting simulated operating conditions in accordance with another embodiment; 
       FIG. 20  is a data plot corresponding to  FIG. 19 ; 
       FIG. 21  is a data plot corresponding to  FIGS. 19 and 20 ; 
   

   DETAILED DESCRIPTION 
   The present disclosure introduces energy beaming systems and feedback control of such systems. Many specific details of certain embodiments of the invention are set forth in the following description and in  FIGS. 1-21  to provide a thorough understanding of such embodiments. One skilled in the art, however, will understand that the invention may have additional embodiments, or that the invention may be practiced without several of the details described in the following description. 
   Principles of the Invention:  FIG. 1  is a schematic plan view of an energy receiving device  100  in accordance with an embodiment of the invention. The energy receiving device  100  is comprised of a plurality of photovoltaic (PV) panels  102 . Each of the PV panels  102  can be defined by a single PV cell, or a plurality of PV cells (not discretely shown) electrically coupled to function as an entity. In any case, the PV panels  102  are configured to directly convert incident photonic (i.e., light) energy into electrical power. In turn, the PV panels  102  of the energy receiving device  100  are electrically interconnected so as to provide an aggregate quantity of electrical power in response to being illuminated by a corresponding energy beam (e.g., a laser beam). Thus, the energy receiving device  100  is an array of plural PV panels  102  arranged so as to define an overall energy-converting surface area “A”. 
     FIG. 2  is a schematic plan view of the energy receiving device  100  of  FIG. 1  with an energy beam  104  incident thereon. For purposes of example, it is assumed that the energy beam  104  is defined by a laser beam of appropriate center frequency for use with the energy receiving device  100 . That is, the energy beam  104  is of appropriate photonic energy for optimal conversion to electrical power by the PV panels  102  of the receiving device  104 . In the interest of clarity, the energy beam  104  of  FIG. 2  is depicted as a generally circular or disk-shaped illumination area “B” having a sharply defined boundary or perimeter  106 . However, it is to be understood that a typical energy beam  104  is in fact defined by an energy gradient with highest intensity at the center of the beam and decreasing energy intensity moving radially outward from the beam center. The cross-sectional intensity of energy beams is discussed in further detail below in accordance with  FIG. 4 . 
   For purposes of  FIG. 2 , the illumination area “B” represents the meaningful or useful cross-sectional area of the energy beam  104 . It is noted that the area “A” of the energy receiving device  100  is slightly larger, but of different shape, than the illumination area “B” of the energy beam  104 . In this way, the energy receiving device  100  has sufficient area to capture and convert essentially all of the meaningful energy content of energy beam  104 , provided that the energy beam  104  remains centered on the energy receiving device  100 . In another embodiment (not shown), the PV panels (e.g.,  102 ) may be differently arranged and/or of different number so as to define an energy receiving device (e.g.,  100 ) of different shape and/or area than that of the energy receiving device  100 . 
     FIG. 3  is a schematic plan view of the energy receiving device  100  and energy beam  104  as introduced above. However, the energy beam  104  is no longer centered on the energy receiving device  100 , but is shifted to the upper right. In this case, an appreciable portion of the illumination area “B” of the energy beam  104  is no longer incident to the energy-converting surface area “A” of the energy receiving device  100 . As a result, there is lost beam energy that is not being converted to electrical power. 
     FIG. 4  is a graph  200  showing an energy beam pattern in accordance with an embodiment of the invention.  FIG. 4  includes a source  202  that emits an energy beam  204 . In one embodiment, the energy beam  204  is a laser beam. In another embodiment, the energy beam  204  is a highly collimated microwave emission. Electromagnetic energy beams at other suitable center frequencies can also be used. The graph  200  is defined by a Gaussian curve  206  representing the radial intensity of the energy beam  204 . Intensity is considered in terms of energy per unit of cross-sectional area incident to a surface normal to the energy beam  204  (e.g., Watts per square centimeter, etc.). As depicted, the intensity of the beam  204  is greatest at the beam center, and decreases radially away from the beam center in accordance with the Gaussian curve  206 . 
     FIG. 4  also includes a cross-sectional view of the beam pattern  208  of the energy beam  204 . As shown, the radius of the beam pattern  208  is considered in terms of a non-dimensional distance σ (sigma). The beam pattern  208  is depicted as having a central area 0.5σ in radius, and an outer area that is 1σ in radius. The energy intensity at 1σ (one sigma) is about 0.368 times the intensity at the center of the energy beam  204 —that is, about 0.368I 0 , wherein I 0  is the peak intensity of the energy beam  204 . While a real energy beam typically has usable energy content out beyond 1σ in radius (2σ in diameter), energy beams (e.g.,  104 ) are depicted herein as limited to 1σ in radius for purposes of clarity and simplicity. While the energy beam  204  is described in terms of a Gaussian distribution of energy intensity, it is to be understood the that present teachings contemplate use of other energy beams with correspondingly varying energy intensity patterns. 
     FIGS. 1 through 3  exemplify the sort of control concerns that the present teachings are directed to solving. Specifically, if the beam  104  is pointed at the center of the receiving device  100 , optimum energy conversion occurs. However, in a case where the energy receiving device  104  is used on a flight vehicle that moves, or when atmospheric turbulence distorts the path of the beam, the energy beam  104  may not be pointed at the center of the energy receiving element or device  100 . If the receiving device  100  is not much larger than the beam width, which is typically the case in the interest of economics, then part of the beam  104  will miss the receiving element. To minimize the loss of efficiency, the beam-receiving vehicle or apparatus typically includes means to provide feedback to the beam source. This feedback tells the beam source, through appropriate instrumentation and control, whether the beam is aimed too high or too low; too far right or too far left. Using this feedback, the beam source corrects the aiming of the beam, thereby keeping the energy beam  104  centered on the energy receiving device  100 . 
   Several suitable feedback methods have been described in the prior art. However, these prior art methods may be unsuitable when multiple beams are used. Therefore, the prior art systems may lack the means to consistently exploit the economic and technical benefits of using multiple smaller beam sources rather than a large single beam source. 
     FIG. 5  is a schematic plan view of an energy receiving system  300  in accordance with another embodiment of the invention. The system  300  includes a plurality of PV panels (or cells)  302  that collectively define an energy receiving device  310 . Each of the PV panels  302  is configured to convert incident photonic energy into electrical power. In turn, an aggregate quantity of electrical power is produced by the energy receiving device  310 . The energy receiving system  300  of  FIG. 5  also includes four sensors respectively labeled  312 ,  314 ,  316  and  318 . Each of the sensors  312 - 318  is configured to provide a detection signal corresponding to beam energy incident thereto. 
     FIG. 6  is a schematic plan view of the energy receiving system  300  as introduced above under typical exemplary operation. As depicted, an energy beam  308  is incident to and centered on the energy receiving device  310 . Each of the four sensors  312 - 318  is located at a distance of about 1σ away from the center of the energy receiving device  310 . Thus, the sensors  312 - 318  are exposed to equal quantities of illumination from the energy beam  308  of about 0.368I 0 . In turn, the four sensors  312 - 318  are understood to provide generally equal detection signals corresponding to the incident illumination. 
     FIG. 7  is a schematic plan view of the energy receiving system  300  under different exemplary operating conditions as compared to  FIG. 6 . As depicted, the energy beam  308  is no longer centered on the energy receiving device  310 , but is shifted about σ/3 to the right. Sensor  314  is about 2σ/3 from beam center and measures an intensity of about 0.64I 0 . Sensor  318  is located about 4σ/3 from beam center and measures an intensity of about 0.17I 0 . Each of sensors  312  and  316  are exposed to slightly less than 0.368I 0  of energy beam  308 . In any case, each of the sensors  312 - 318  provides a respective detection signal corresponding to the energy beam intensity incident thereon. Thus, sensor  314  provides a signal indicating the greatest intensity, sensor  318  provides a signal indicating the least intensity, and sensors  312  and  316  provide respective signals indicating intensity between the greatest and least intensity values. Typical use of the respective detection signals provided by the sensors  312 - 318  is described in greater detail hereinafter. 
   Reference is now made to  FIG. 8 , which is a schematic block diagram of an energy beaming and receiving system  400  in accordance with an embodiment of the invention. The system  400  includes a vehicle  402 . The vehicle  402  can be, for example, an aircraft, a marine vessel, a track-mounted locomotive, etc. The vehicle  402  can also be defined by other apparatus and/or systems. The vehicle  402  includes an energy receiving device  410 . The energy receiving device  410  can be defined by a number of photovoltaic panels, an antenna or dish, or any other suitable device for receiving energy from an energy beam. For purposes of example, it is assumed that the energy receiving device  410  includes an array of PV panels configured to convert incident laser energy directly to electrical power. 
   The vehicle  402  of the system  400  of  FIG. 8  also includes four sensors  412 ,  414 ,  416  and  418  located proximate to the energy receiving device  410 . Each of the sensors  412 - 418  is configured to provide a detection signal corresponding to an energy beam or beams incident to the energy receiving device  410 . Thus, each of the sensors  412 - 418  operates substantially as described above in regard to the sensors  312 - 318  of  FIGS. 5-7 . 
   The vehicle  402  also includes control electronics  420 . Control electronics (also referred to as a controller)  420  can include, for example, one or more processors, software- and/or firmware-based executable program code, a state machine, digital and/or fuzzy logic, a neural network, tuned analog filters, signal amplification stages, etc. In any case, the control electronics  420  is configured to receive the respective detection signals from the sensors  412 - 418  and to derive a plurality of control signals  422 . The vehicle  402  further includes power electronics and load (PEL)  424 . The PEL  424  is defined by one or more subsystems considered in the aggregate. The PEL  424  includes electronic and electrical circuitry configured to receive electrical power from the energy receiving device  410 , and provide conditioned and/or regulated electrical power to one or more loads of the vehicle  402 . Power conditioning and regulation are well known in the electrical arts and further elaboration is not required for purposes of the present teachings. 
   The system  400  of  FIG. 8  includes three energy beam sources  426 ,  428  and  430 . Each of the energy beam sources (hereinafter, sources)  426 - 430  is configured to emit a respective energy beam  426 A,  428 A and  430 A toward the energy receiving device  410  of the vehicle  402 . For purposes of example, it is assumed that each of the energy beams  426 A- 430 A is defined by a laser beam suitably tuned for optimal energy conversion by the energy receiving device  410 . Each of the sources  426 - 430  is further configured to controllably aim the corresponding energy beam  426 A- 430 A at the energy receiving device  410  in accordance with the control signals  422 . The control signals  422  can be provided to the sources  426 - 430  by wireless means, or by optical and/or wired connection. Each of the sources  426 - 430  can include, for example, gimbaled support hardware, a positionable mirror or mirrors, servo-motors and related drive electronics, etc. Other suitable known means can also be used to controllably aim the respective energy beams  426 A- 430 A by way of the control signals  422 . 
   As depicted, the system  400  of  FIG. 8  comprises a closed-loop, feedback control system for beaming energy to a receiving vehicle  402 . At the vehicle  402 , beam energy  426 A- 430 A incident to an energy receiving device (or array)  410  is converted to useful quantities of electrical power for energizing one or more loads  424  of the vehicle  402  itself. The controller  420  of  FIG. 8  is located aboard the vehicle  402 . In another embodiment, similar or other suitable control electronics can be located apart from the vehicle, such as at one or more of the sources  426 - 430 . All of the sources  426 - 430  can be ground-based (i.e., stationary with respect to the vehicle  402 ). In the alternative, one or more of the sources  426 - 430  can be located aboard another vehicle or moving platform (e.g. keeping pace with the vehicle  402 ). Other arrangements of the components of the system  400  can also be defined and used. While the system  400  includes a total of three energy beam sources  426 - 430 , it is to be understood that any number of sources can be used in accordance with the present teachings. 
   The foregoing descriptions are directed to embodiments wherein plural energy beams are converted to electrical power by an energy receiving device. However, the present teachings also contemplate other embodiments in which the energy beams are converted to thermal energy (i.e., heat). For example, plural laser beams can be directed onto a heat exchanger device carried by a vehicle. In turn, liquid propellant flows into the heat exchanger and exits as hot gas. The hot gas is then expelled through one or more nozzles to provide propulsion and/or control thrust for the vehicle. In the immediately foregoing example, a plurality of sensors and other controls, substantially as described above, maintain accurate aiming of the plural laser beams on the heat exchanger. Other embodiments that convert incident electromagnetic energy beams into thermal energy can also be used. 
   Known control techniques work adequately for controlling a single beam system. But, such known techniques may fail if more than one energy beam is targeted to the same receiving device (and corresponding sensors). Thus, known techniques may not be suitable for use with the system  400  of  FIG. 8 . Reference is now made to  FIG. 9 , which depicts an energy receiving device  510  with two energy beams  508 A and  508 B incident thereto. As shown, the energy beams  508 A and  508 B are centered on respectively different locations of the energy receiving device  510 . However, neither energy beam  508 A nor  508 B is centered on the center of the energy receiving device  510 . Furthermore, the four sensors  512 - 518  detect respectively different intensities of both energy beams  508 A and  508 B. This presents a problem, in that known techniques typically do not provide for distinguishing one energy beam from another at the sensors  512 - 518 . In turn, such known techniques typically do not provide for appropriate control signals so as to correct the aiming of the energy beams  508 A and  508 B. 
   In order to resolve the location of each energy beam incident to a receiving device, there must be some way to make each beam distinct from all other incident energy beams. One approach is to use a different wavelength (i.e., center frequency) for each energy beam, and use multiple sets of sensors with each set tuned to a specific wavelength. Each sensor set detects the location of only one energy beam, so the sensor element can clearly distinguish each beam&#39;s incident location and a feedback control signal can be provided to the appropriate source for each energy beam. 
   However, the foregoing approach is generally effective only for microwave energy sources, and is not generally effective for laser sources, for at least two reasons. First, the wavelength of a laser is determined by its lasing medium. For example, a CO 2  laser emits only a small bandwidth of wavelengths. It is not possible to arbitrarily choose more convenient wavelengths in order to easily distinguish between plural laser beams. This is especially so in the realm of high-power, continuous-operation lasers, where the choices of lasing medium are quite limited, and therefore the choice of wavelengths is limited as well. Second, the wavelength of the laser must be carefully matched to the band gap of the PV panel or cell receiving the light. When a PV cell receives a photon of light at the appropriate wavelength, it produces only enough energy to create one electron-hole pair in that cell&#39;s semiconductor junction. If the wavelength of the incident laser light is too long, there is insufficient photon energy to create the electron-hole pair. If the wavelength is too short, only a portion of the photonic energy is used to create the electron hole pair, with a relatively large residual energy portion wasted as heat. The result of the two constraints above is that distinguishing laser power beams by wavelength is unlikely to be technically or economically effective. Other techniques must be used. 
   The present teachings solves the problem with respect to laser beams (and is applicable to microwaves as well) by modulating each energy beam so that each is mathematically orthogonal to all other beams incident on an energy receiving device. Three types of orthogonal modulation are contemplated herein: amplitude, polarization, and angular “coning”. Each is described in turn below. 
   Amplitude Modulation: Consider two energy beams that, for purposes of the following discussion, are respectively referred to as beam α (alpha) and beam β (beta). Further assume that beam α is modulated at its source so that it amplitude A(t) varies with time as: 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   And let energy beam β be modulated so its amplitude varies as: 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   where: A 0  and B 0  are the mean amplitudes of the two energy beams α and β at the center of each beam (corresponding to I o  in  FIG. 4 ), a mod  and b mod  are the magnitude by which the amplitudes vary, and f α  and f β  are the frequencies by which the energy beams vary. 
   Given these amplitudes at the energy beam sources, each energy beam&#39;s amplitude A(t,r) at a particular location r is a scalar multiple of the beam&#39;s center amplitude at the source. Boldface indicates that r is a vector. Thus: 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   Where: c(α,r) is a coefficient determined by range from the energy beam source α and the distance x radially from the energy beam center. Specifically:
 
 c (α, r )= c (range) c ( x/σ   α )  (Eq. 4)
 
   Where: x/σ α  indicates that distance from the center of energy beam α is measured as a fraction of that energy beam&#39;s width at a given distance from the source. Equations substantially identical to Eqs. 3a-b and 4 above, and Eqs. 5a-5c, 6 and 7a-b below, can be derived for beam β. 
   Amplitude sensors (e.g., sensors  312 - 318  of  FIG. 7 ) distributed about the energy receiving device measure each energy beam&#39;s amplitude at the various sensor locations. For example, combining equations 3 and 4 above, it is seen that sensor  312  measure amplitude A 1  as given by: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
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   While sensor  514  measures amplitude A 2  given by:
 
 A   2 ( t,r   2 )= c (range α ) c ( x   2 /σ α ) A   0   +c (range α ) c ( x   2 /σ α ) a   mod  sin(2π f   α   t )]  (Eq. 6)
 
   It is assumed that the variation in c(range) between the two sensors  312 ,  314  is insignificant, given that the range from an energy beam source to a receiving vehicle (e.g.,  402  of  FIG. 8 ) can be, typically, on the order of at least a few kilometers. Furthermore, the size of the receiving device (e.g.,  510  of  FIG. 7 ) is typically no more than a few meters in span. 
   Given the assumption of the paragraph immediately above, and equations 5 and 6, it can been shown that the ratio of the amplitude modulation at the two sensors (e.g.,  312 ,  314  of  FIG. 7 ) is the same as the ratio of the average amplitudes at the two sensors. Namely: 
   
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 
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   Equation 7a shows the ratio of the amplitude modulation measurements at the two sensors. Equation 7b shows the ratio of the average amplitude at the two sensors, and that this ratio is equal to the ratio of amplitude modulation. Therefore, if it is possible to measure only the magnitude of amplitude modulation at each sensor, than it is possible to compute the ratios of those measurements and use the results as the ratios of the average amplitudes at each sensor. These ratios can be used as inputs to well-known algorithms to adjust energy beam aiming. 
   However, another question arises: how to distinguish the modulation amplitude of one beam (e.g.,  508 A) from that of another beam (e.g.,  508 B) illuminating the same sensors (e.g.,  512 - 518 )? The present invention solves this issue by way of orthogonal modulations. For example, let frequencies f α  and f β  be integral multiples of a lower frequency, f 0 . Given this constraint, the two energy beams exhibit orthogonal modulation over one period P 0  of the lower frequency, f 0 . For example, if f 0  is 10 KHz, then f α  could be 20 kHz and f β  could be 30 kHz. Then the period P 0  of f 0 , is given by:
 
 P   0 =1/ f   0 =1/10 4  sec −1 =100 microseconds  (Eq. 8)
 
   Therefore, if electronics (e.g.,  420  of  FIG. 8 ) connected to the sensors associated with an energy receiving device take multiple amplitude samples over a period of 100 microseconds (or an integral multiple thereof), the samples can be processed to isolate the magnitude of variation in beam α from the magnitude of variation in beam β. Processing of the samples can be described as a set of transfer functions, h i , where the index i covers the set of beams: in our example, i is an element of {α, β}. Transfer functions h α  and h β  transform the output of a sensor into c(x/σ α )a mod  or c(x/σ β )b mod , i.e. the measured magnitude of variation in beam α or beam β (e.g.,  508 A or  508 B of  FIG. 9 ). Appropriate forms of processing to implement the functions h i  are known. For example, if the samples are digital, they can be processed by a Fast Fourier Transform or Discrete Fourier Transform to isolate individual frequencies. If the samples are continuous analog inputs, tuned analog filters can be used to isolate individual frequencies. Other suitable signal processing methods can also be used. 
   The detection signal output of each sensor (e.g.,  512 - 518  of  FIG. 9 ) is input to a transfer function for each beam&#39;s modulation. Thus, the ongoing two-beam, four-sensor example would include eight measurements of variation in amplitude, as shown in Table 1 below: 
   
     
       
         
             
             
             
             
             
           
             
                 
               TABLE 1 
             
             
                 
                 
             
             
                 
               Sensor 1 
               Sensor 2 
               Sensor 3 
               Sensor 4 
             
             
                 
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
             
             
          
             
               Beam 
               α 
               c(x 1 /σ α )a mod   
               c(x 2 /σ α )a mod   
               c(x 3 /σ α )a mod   
               c(x 4 /σ α )a mod   
             
             
                 
               β 
               c(x 1 /σ β )b mod   
               c(x 2 /σ β )b mod   
               c(x 3 /σ β )b mod   
               c(x 4 /σ β )b mod   
             
             
                 
             
          
         
       
     
   
   Where: Each matrix cell (i, j) contains the measurement that results from applying transfer function h i  (for beam i) to the output of sensor j. 
   The detection signals corresponding to each energy beam&#39;s modulation magnitude are sent to the beam source for that beam. For example, measurements c(x 1 /σ β )b mod  through c(x 4 /σ β )b mod  can be sent directly to energy beam source β. New measurements may be transmitted periodically or only when user-specified conditions occur, such as a user-specified mismatch between measurement values, which indicates that a beam is off target by more than a selected distance. If periodic transmission is used, the interval between transmissions may be user-selected to meet the needs of the application. Likewise, the means of transmission can be any appropriate method for the particular application, e.g. digital messages sent via wireless means. The values transmitted may be scaled or normalized by the control electronics, or otherwise transformed for efficiency of transmission. 
   In addition, some embodiments of sensors may transmit data about sensor configuration (once) and about physical orientation (whenever it changes substantially). This can help the respective beam sources (e.g.,  426 - 430  of  FIG. 8 ) and/or the control electronics (e.g.,  420  of  FIG. 8 ) to properly interpret and respond to the detection signals.  FIGS. 10 and 11  illustrate why this is needed: a given set of sensor signals may correspond to different beam offsets if the sensors&#39; relative positions change.  FIG. 10  includes an energy receiving device  610  and four sensors  612 - 618 . As depicted, an energy beam  608  is incident to the energy receiving device  610 , and is focused off-center toward sensor  614 . Of particular note is that the energy beam  608  is shifted off center along a single Cartesian axis (i.e., X-axis), as indicated by arrow  620 A. In comparison,  FIG. 11  shows the same energy receiving device  610  rotated approximately 30 degrees clockwise with respect to the orientation depicted in  FIG. 10 . However, the energy beam  608  of  FIG. 11  is incident to the same relative location on the energy receiving device  610 . As a result, correcting the beam  608  location back to the center of the received requires either a diagonal move, or a two-step Cartesian pathway (i.e., distinct X-axis and Y-axis correction vectors) as indicated by the arrows  620 B and  620 C. 
   At the source and/or control electronics, one of several appropriate algorithms is applied to the energy beam modulation magnitude (and orientation of the receiving element, if included) as conveyed by the detection signals. These algorithms estimate the current offset of the energy beam relative to the center of the energy receiving device. The output of the algorithm drives a steering mechanism that moves the energy beam toward the center of the energy receiving device. Alternatively, the user may choose an embodiment wherein the energy beam offset (from center) is estimated at the energy receiving device, and only the offset is transmitted to the corresponding energy beam source. 
   Other embodiments may use intensity measurements (i.e., detection signals) rather than amplitude measurements, since intensity can be less costly to measure and to control. However, intensity of an electromagnetic beam is proportional to the square of the wave&#39;s amplitude. Thus, intensity modulation and intensity measurements are equivalent to amplitude modulation and amplitude measurements with appropriate scaling laws applied. Scaling also applies to the energy beam width: the width at which intensity drops to 1/e (approx. 0.368) of peak value is 1/√2 as large as the 1/e width for amplitude. 
   Polarization Modulation: With polarization modulation, the amplitude of each energy beam is constant at its source, but each energy beam is linearly polarized and its direction of polarization rotates. Consider two energy beams, α and β. Let beam α be modulated at its source so that its polarization vector A(t) varies with time as indicated below
 
 A ( t )=sin(2π f   α   t )+ j  cos(2π f   α   t )  (Eq. 9)
 
   And let energy beam β be modulated so its polarization vector B(t) varies as:
 
 B ( t )=sin(2π f   β   t )+ j  cos(2π f   β   t )  (Eq. 10)
 
   Where: boldface denotes vector quantities, f α  and f β  are the frequencies at which the polarization vectors rotate, and j is the square root of negative one (i.e., imaginary operator). The rotational frequencies of the energy beams (e.g.,  508 A and  508 B) are chosen to be orthogonal—that is, each is an integral multiple of a lower frequency, f 0 . 
   In a typical embodiment, each sensor (e.g.,  512 - 518  of  FIG. 9 ) is most sensitive to one polarization direction. This can be accomplished by covering each sensor with a polarizing filter. As each energy beam (e.g.,  508 A and  508 B) rotates, the intensity measured by each sensor oscillates between zero and the full local (i.e., incident) intensity of the energy beam: c(range α ) c(x j /σ α ) A 0 . The detected intensity is greatest when the energy beam polarization is aligned to the sensor polarization. A given energy beam is aligned with a particular sensor twice per rotation: once when the two are at a relative angle of zero and once when they are at a relative angle of 180 degrees. Therefore, the frequency of each sensor&#39;s single-beam oscillation is twice as great as a detected beam&#39;s rotational frequency, as expressed below:
 
f α     —     sensed =2f α   (Eq. 11)
 
   Just as for amplitude modulation, if control electronics (e.g.,  420  of  FIG. 8 ) connected to the sensors associated with an energy receiving device take multiple intensity samples over a period P 0 =1/f 0 , or an integral multiple thereof, the corresponding detection signals can be processed to isolate the magnitude of variation in beam α from the magnitude of variation in beam β. Processing of the detection signals can be described as a set of transfer functions, h i , where the index i covers the set of beams. This produces a set of measurements, each one indicating the value of c(range i ) c(x j /σ i ) A 0 , for beam i at sensor j. Corresponding control signals (e.g.,  422  of  FIG. 8 ) are then sent to the appropriate beam source or sources (e.g.,  426 - 430  of  FIG. 8 ). Ultimately, the ratios of the values at each sensor are used to compute an energy beam&#39;s offset from the center of the energy receiving device. The offset is then used to determine the proper adjustment to the energy beam aiming. 
   Angular “Coning”: Other embodiments of the present teachings use coning, wherein the aiming of each beam includes a small sinusoidal offset in azimuth and elevation. The result is that the nominal aim point of each beam cycles around the center of the receiving element. This cycling may be generally circular in pattern, or elliptical, or any other suitably shaped cycling pattern. 
   Reference is now made to  FIG. 12 , which includes an energy beam source (source)  702  emitting an energy beam  708  incident to an energy receiving device  710 . Four sensors  712 - 718  are distributed about the energy receiving device  710 . The energy beam  708  is defined by a centerline  720 . As depicted in  FIG. 12 , the source  702  is configured and controlled so as to impart a circular cyclic motion or “coning” modulation to the energy beam  708 . In other words, the energy beam  708  is modulated so as to whirl or revolve, as opposed to rotating about the centerline  720 . As a result, the center of the energy beam  708  repeatedly traces a circular pattern  722  incident to the energy receiving device  710  by virtue of the coning modulation. The center of the circular motion is referred to as the coning center. 
   In a typical embodiment that uses coning modulation, the intensity of each energy beam is constant (no amplitude or similar modulation). However, as the aim point revolves (e.g.,  722  of  FIG. 12 ), the beam center  720  moves closer to and farther from each sensor  712 - 718 , such that the intensity measured at each sensor  712 - 718  rises and falls. If a beam coning center matches the energy receiving device&#39;s center as in  FIG. 12 , the energy beam intensity measured at every sensor  712 - 718  rises and falls by the same amount, and at 90 degree phase intervals from the neighboring sensors. 
   Reference is now made to  FIG. 13 , which depicts the energy receiving device  710  and sensors  712 - 718  as respectively introduced above. A coning modulated energy beam (not shown in  FIG. 13 ) is incident to the energy receiving device  710 , wherein the coning center of the energy beam traces a circular pattern  724 . It is noted that the coning center  726  is shifted (i.e., offset) away from the center of the energy receiving device  710  toward the sensor  714 . With the coning center  726  offset from the center of the energy receiving device  710 , the intensity measured at every sensor  712 - 718  rises and falls by different amounts. More importantly, the maximum and minimum intensity at each sensor  712 - 718  does not occur at ninety-degree phase intervals from the preceding and following sensors. 
   The phase where each sensor  712 - 718  measures (i.e., detects) its greatest intensity reveals the direction from that sensor  712 - 718  to the coning center  726 . In most cases, two sensors are sufficient to locate the coning center using relative phase information alone. However, if the coning center  726  is collinear with two sensors—as it is with sensors  714  and  718  in FIG.  13 —the location is ambiguous unless intensity variation is used in addition to relative phase. Phase measurements from three or more non-collinear sensors  712 - 718  are sufficient to give a unique location for the coning center  726 . A numerical simulation of this approach is discussed hereinafter.  FIG. 13  depicts the respective phase angles  730 - 736  defined by consecutive pairs of the sensors  712 - 718  and the coning center  726 . It is these angles  730 - 736  that can be determined through appropriate signal processing of the detection signals provided by the sensors  712 - 718 , so as to derive corresponding control signals. 
   As with amplitude modulation and polarization modulation, it is necessary to be able to distinguish the offset or off-center position of each energy beam from the others. With coning modulation, each energy beam is modulated to cycle at a frequency fi that is orthogonal to the other energy beams&#39; coning frequencies. At each sensor, appropriate transfer functions isolate the oscillation caused by each energy beam and measure its phase and magnitude. These measurements, or corresponding control signals derived there from, are sent to each energy beam source (e.g.,  426 - 430  of  FIG. 8 , etc.), where they are used to estimate the offsets of the respective coning centers and thereby to drive the correction of the energy beam aiming. 
   One benefit, among others, of coning modulation is that it requires no additional hardware. This is an advantage relative to amplitude modulation, which requires hardware to modulate the amplitude of a high-power laser—not an easy problem with some lasers. It is also advantageous relative to polarization modulation, which requires polarizing filters on the sensors (e.g.,  712 - 718 ). Polarizing filters are not particularly costly, but add weight and potential failure modes. More important, polarization modulation requires hardware to modulate the polarization of a high-power laser—difficult or impossible with some lasers. By contrast, nearly any energy beam source that is capable of aiming the beam fast enough to track, for example, a moving vehicle through turbulent air has adequate hardware and dynamic characteristics to introduce a suitable coning modulation into the energy beam. 
   The cyclic speed and size of the coning circle (e.g.,  724  of  FIG. 13 ) may be determined by the user, based on tradeoffs of feedback communications bandwidth, vehicle or target maneuverability, range between source and energy receiving device, expected amount of turbulence, size of the receiving element, and efficiency. The speed and size of the coning circle may even be adjusted dynamically to optimize performance as each of these parameters changes. 
   Other Embodiments: Coning modulation can use retroreflectors at each sensor position, rather than sensors in the conventional sense. In such an embodiment, as an energy beam center gets closer to each retroreflector, that retroreflector reflects more light back toward the corresponding energy beam source. Each source observes the energy receiving device with a telescope or other suitable arrangement connected to one or more light sensors. Various optical designs allow a telescope to use the same primary optical element as the energy beam emitter, so a separate telescope is not required. Each light sensor&#39;s detection signal is input to a transfer function that selectively passes the coning frequency of the energy beam source. This selection of the coning frequency is needed when several beam sources are close together: due to diffraction, reflection from a small retroreflector will have a much wider beam pattern than an energy beam from a large aperture, so each energy beam&#39;s reflection may spread out enough to cover several energy beam sources. 
     FIG. 14  depicts an exemplary system  800  in which retroreflectors are used. The system  800  includes two energy beam sources  802  and  804 , which are emitting respective energy beams  806  and  808  toward an aircraft  810 . The aircraft  810  includes and supports an energy receiving device  812  that is suitably configured to receive and convert the incident energy beams  806 - 808  into electrical power. As depicted in  FIG. 14 , it is assumed that energy beams  806 - 808  are laser beams. The aircraft  810  also supports a plurality of retroreflectors  814  and  816 . While two retroreflectors are shown in  FIG. 14  for simplicity, it is to be understood that any suitable number (e.g., three, four, etc.) could be used. In any case, the retroreflectors  814 - 816  are configured to reflect a portion of the energy beam incident thereon back toward the corresponding sources  802  and  804 . 
     FIG. 14  also includes a reflected energy beam  818 . The reflected energy beam  818  results from respective portions of energy beams  802  and  804  incident to retroreflector  814 . Only a single reflected energy beam  818  is shown in  FIG. 14  for simplicity. The reflected energy beam  818  fans out as it moves away from the retroreflector  814  such that both sources  802  and  804  receive respective portions of the reflected energy beam  818 . Therefore, each beam source  802  and  804  must be able distinguish its own energy beam reflection. Such differentiation of signals is typically accomplished by way of control electronics (e.g.,  420  of  FIG. 8 , etc.) located at the sources  802 - 804  themselves, either individually or as a single control apparatus (not shown in  FIG. 14 ) serving both sources  802 - 804 . 
   Control electronics can utilize a suitable transfer function in order to distinguish the amplitude and phase of variation in reflected light from a selected energy beam. When the coning center is in the middle of (i.e., centered on) an energy receiving device, the reflected light&#39;s amplitude varies little. When the coning center is not centered on the receiving device, the reflected light is brightest when the beam is closest to a sensor—for example, sensor  714  of  FIG. 13 . The phase of the peak in reflected light tells the beam source the angle from the receiving element&#39;s center to the coning center. The magnitude of the variation tells it the distance from the energy receiving device&#39;s center to the coning center (e.g.,  726  of  FIG. 13 ). The corresponding energy beam source (or associated control electronics) measures the phase and magnitude of the variation. It uses these to estimate the offset of the coning center and thereby to drive a correction to the beam aiming. The advantage of an embodiment that uses retroreflectors is that no sensors and/or control electronics are required on or proximate to the energy receiving device, or the vehicle or apparatus being powered. Furthermore, retroreflectors are typically formed of solid chunks of material with no moving parts, so reliability is high and power consumption is zero. 
   Like coning modulation, polarizing modulation can use retroreflectors (e.g.,  814 - 816  of  FIG. 14 ) rather than actual sensors. However, the retroreflectors must each have polarizing optics so light with the proper polarization is most strongly reflected. The polarization of each retroreflector must be unique, and ideally the polarization directions should be distributed to give maximal isolation of each retroreflector from all other retroreflectors. For example,  FIG. 15  depicts an energy receiving device  910  including four retroreflectors  912 - 918  and the polarization corresponding to each. Light sensors at each energy beam source (e.g.,  802 - 804  of  FIG. 14 ), for example, sense the reflected light through a telescope. The sensors can use optics and/or control electronics to match the modulation frequency of each source, thereby excluding the reflected signal from other energy beam sources. 
   The BeamNet Architecture: The BeamNet architecture, as described in co-pending, commonly-owned U.S. patent application Ser. No. 11/420,086, filed May 24, 2006, enables many energy beam sources and many energy receiving devices to interoperate in a complex system of systems. In the long run, there will likely be many more energy beam sources in the world than the number of convenient, orthogonal modulation patterns. Therefore, means are typically included for each energy receiving device (or receiving element) to assign a modulation pattern to each source as each energy beam source initiates a link with the receiving element. This modulation pattern need only be unique within the set of beams that are currently incident to a particular energy receiving device. Thus, the energy receiving device needs only to keep track of what modulation patterns it can sense and which of those are already assigned to energy beam sources. When a source releases a link with a particular energy receiving device, that receiver notes that energy beam&#39;s modulation pattern as unassigned. It is then available to be assigned to another energy beam sources that links with the energy receiving device. 
   Likewise, each energy beam source is able to receive modulation pattern assignments from an energy receiving device (by way of control electronics, etc.) and implement the assigned pattern when it aims an energy beam at the energy receiving device. The present invention contemplates application and use within the context of the BeamNet Architecture, as well as other operational systems and embodiments. 
   Simulation Modeling: A software simulation has been used to verify the approach to coning modulation.  FIG. 16  shows an X-Y plot  1000  of simulated discrete energy beam center positions  1002  on a two meter by two meter energy receiving device. As depicted, the energy beam centers are plotted at 10 millisecond intervals. Thus,  FIG. 16  represents coning modulation with a cyclic period of 160 milliseconds and a coning radius of 0.2 meters. Cyclic motion is understood to be clockwise as seen by the viewer. While  FIG. 16  does not depict any sensors (or retroreflectors), it is assumed for purposes of ongoing example that a total of four sensors are used distributed about the simulated energy receiving device. Please refer to sensors  312 - 318  of  FIG. 5 . In the following discussion, these four sensors (not shown) will be referred to as Top, Right, Bottom and Left, respectively. It is further assumed that the simulated beam is Gaussian in energy distribution wherein σ=1.0 meter. 
   Reference is now directed to  FIG. 17 , which depicts an intensity-over-time plot  1100  of simulated energy intensity measurements corresponding to  FIG. 16 . The plot  1100  includes four data series respectively corresponding to the four sensors (not shown) of the data of  FIG. 16  as follows: series  1102 =Right sensor; series  1104 =Top sensor;  1106 =Bottom sensor; and  1108 =Left sensor. The data series  1104  (i.e., Top sensor) of the simulation was input to a Fast Fourier Transform (FFT), which derived the data plot  1200  of  FIG. 18 . 
     FIG. 18  depicts a plot  1200  of the FFT results for the simulated energy intensity measurements of  FIGS. 16 and 17 . The plot  1200  includes a spike  1202  in the data corresponding to a frequency of 16 cycles in 256 samples—exactly what is expected when considering a coning period of 160 milliseconds with a 10-millisecond sample interval. This is the frequency at which the transfer function for this energy beam measures the amplitude and phase of intensity variation for each sensor. Other energy beams—not included in this simulation—include coning modulation at different rates and therefore would yield FFT spikes at respectively different frequencies. 
   The amplitudes and phases for all four simulated sensors (data series  1102 - 1108  of  FIG. 17 ) at this same coning frequency are calculated by the simulation, and are presented in Table 2 below: 
   
     
       
         
             
             
             
             
             
           
             
                 
               TABLE 2 
             
             
                 
                 
             
             
                 
               Top Sensor 
               Right S. 
               Bottom S. 
               Left S. 
             
             
                 
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
             
             
          
             
                 
               Amplitude 
               30.996 
               12.287 
               30.996 
               21.580 
             
             
                 
               Phase 
               20.56 
               −90 
               159.44 
               90 
             
             
                 
               (deg.) 
             
             
                 
                 
             
          
         
       
     
   
   Table 2 above provides that the amplitude is largest for the Top sensor and Bottom sensor (data series  1104  and  1106  of  FIG. 17 ), which are at the steepest part of the curve for the simulated energy beam pattern. Therefore, each of sensors Top and Bottom measures the largest fluctuations for small motions of the simulated energy beam. More importantly, the phase of the amplitude peak for each sensor is exactly as we expect: the Top sensor leads the beginning of the cycle by:
 
tan −1 (0.375 meter/1 meter)=20.556 deg.  (Eq. 12)
 
   The Right sensor (data series  1102  of  FIG. 17 ) lags the beginning of the cycle by 90 degrees. The Bottom sensor (data series  1106  of  FIG. 17 ) leads the cycle by 159.44 degrees (or, equivalently, lags the cycle by 200.56 degrees). The Left sensor (data series  1108  of  FIG. 17 ) leads by 90 degrees (equivalent to lagging by 270 degrees). Using these simulated values to derive feedback to an energy beam source, the source would be able to correctly deduce the current location of the coning center by triangulation from the four sensors. 
   The simulated results discussed above in regard to  FIGS. 16-18  above are for an ideal case—one where the energy beam is centered exactly where the corresponding source&#39;s control system intends to point it. However, the present teachings also work in the presence of noise. The same data sets are now considered, but with the addition of 0.05 meter Gaussian random steering jitter in the X and Y position of the beam. 
     FIG. 19  depicts a plot  1300  of simulated energy beam&#39;s positions  1302  over 16 coning cycles including Gaussian random jitter. In turn,  FIG. 20  depicts an intensity-over-time plot  1400  of simulated energy intensity measurements corresponding to  FIG. 19  over one coning cycle. The plot  1400  includes four data series  1402 ,  1404 ,  1406  and  1408  respectively corresponding to the Right, Top, Bottom and Left sensors (not shown) as considered above. Subjecting the data series  1404  (i.e., Top sensor) of the 16-cycle simulation to a FFT resulted in the data plot  1500  of  FIG. 21 . Despite the distorted patterns for each sensor (data series  1402 - 1408 ), the overall frequency response shown in  FIG. 21  is still quite specific to the selected coning frequency. Thus, FFT techniques work well even with data (i.e., position detection signals) including notable jitter. 
   Table 3 below indicates that even with jitter noise present in the foregoing example, phase angles for three of the sensors are within 0.3 degrees of the correct value, and the phase angle for the other sensor is off by only 2.48 degrees. Even if the worst phase value were used, the error in locating the coning center is only 4.33 centimeters on an energy receiving device two meters-by-two meters in size. This error is easily tolerable and is a great improvement over the 0.375 meter (37.5 centimeters) offset of the coning center assumed in the simulation. 
   
     
       
         
             
             
             
             
             
           
             
                 
               TABLE 3 
             
             
                 
                 
             
             
                 
               Top Sensor 
               Right S. 
               Bottom S. 
               Left S. 
             
             
                 
                 
             
           
          
             
                 
             
          
         
         
             
             
             
             
             
             
          
             
                 
               Amplitude 
               31.193 
               12.442 
               30.856 
               21.380 
             
             
                 
               Phase 
               22.26 
               −89.93 
               161.92 
               89.99 
             
             
                 
               (deg.) 
             
             
                 
                 
             
          
         
       
     
   
   While specific embodiments of the invention have been illustrated and described herein, as noted above, many changes can be made without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should not be limited by the disclosure of the specific embodiments set forth above. Instead, the invention should be determined entirely by reference to the claims that follow.