Patent Publication Number: US-11398683-B2

Title: Perimeter-fed array

Description:
FIELD 
     The field of the disclosure relates generally to phased array antennas and, more specifically, to a perimeter-fed array and systems and methods for steering a beam radiated from a phased array antenna. 
     BACKGROUND 
     Conventional radar applications utilize “steerable,” or directed, beams. Such steering is often accomplished with an electronically steerable, or scanned, antenna as an alternative to traditional mechanically scanned arrays, which are often too large, too expensive, and consume too-much power for certain applications. Electronically steerable antennas generally include a phased array antenna having an array, or grid, of antenna elements spaced according to the operating wavelength for the system. Typically, each antenna element is individually fed a radio frequency (RF) signal that is offset in phase from each other. The phase shift from each antenna element to the next results in a beam radiated in a direction generally characterized by an azimuth angle and an elevation angle, and typically each defined with respect to boresight, which is the direction normal to the surface of the phased array. Accordingly, by enabling each antenna element to be dynamically phase shifted with respect to each other, the radiated beam is steerable. By steering the beam over a range of azimuth and a range of elevation over time, the phased array electronically “scans” that space. 
     This section is intended to introduce the reader to various aspects of art that may be related to various aspects of the present disclosure, which are described and/or claimed below. This discussion is believed to be helpful in providing the reader with background information to facilitate a better understanding of the various aspects of the present disclosure. Accordingly, it should be understood that these statements are to be read in this light, and not as admissions of prior art. 
     BRIEF DESCRIPTION 
     One aspect of the present disclosure includes a phased array antenna including a resonant cavity, a plurality of feed waveguides, an array of slot antenna elements, and a plurality of phase shifters. The resonant cavity includes a boresight surface having a normal vector oriented with boresight for the phased array antenna. The plurality of feed waveguides is distributed along a perimeter of the resonant cavity and is configured to supply respective electromagnetic waves to the resonant cavity. The array of slot antenna elements is distributed about the boresight surface and configured to radiate a beam based on standing waves within the resonant cavity. Each of the plurality of phase shifters is respectively coupled with the plurality of feed waveguides and independently controllable to modify the respective phases of the standing waves to steer the beam. 
     Another aspect of the present disclosure includes a method of steering a beam using a phased array antenna. The method includes shifting respective phases of a plurality of electromagnetic waves. The method includes feeding the plurality of Electromagnetic waves at a perimeter of a resonant cavity. The resonant cavity is configured to produce standing waves therein based on the Electromagnetic waves. The method includes radiating a steered beam from an array of slot antenna elements distributed about a boresight surface of the resonant cavity based on the standing waves. 
     Yet another aspect of the present disclosure includes a system including a phased array antenna, a scanner, and a computing system. The phased array antenna includes a resonant cavity, an array of slot antenna elements, and a plurality of phase shifters. The array of slot antenna elements is distributed about a boresight surface and configured to radiate a beam based on standing waves within the resonant cavity. Each of the plurality of phase shifters is coupled with a corresponding feed waveguide at a perimeter of the phased array antenna. The plurality of phase shifters are each independently controllable to sweep through a range of phases for electromagnetic waves fed to the phased array antenna to steer the beam. The scanner is configured to measure electromagnetic fields within the resonant cavity relative to the array of slot antenna elements for the range of phases. The computing system is in communication with the scanner and is configured to build a look up table relating the range of phases to beam directions corresponding to electromagnetic fields measured by the scanner. 
     Various refinements exist of the features noted in relation to the above-mentioned aspects. Further features may also be incorporated in the above-mentioned aspects as well. These refinements and additional features may exist individually or in any combination. For instance, various features discussed below in relation to any of the illustrated examples may be incorporated into any of the above-described aspects, alone or in any combination. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective diagram of an example phased array antenna; 
         FIG. 2  is a block diagram of the phased array antenna shown in  FIG. 1 ; 
         FIG. 3  is a block diagram of an example system for steering a beam radiated from the phased array antenna shown in  FIGS. 1 and 2 ; 
         FIG. 4  is an example current density map for a boresight beam; 
         FIG. 5  is a plot of example Smith charts corresponding to the current density map shown in  FIG. 4  and illustrating a steered beam in azimuth and elevation; 
         FIG. 6  is another example current density map for a steered beam; 
         FIG. 7  is a plot of example Smith charts corresponding to the current density map shown in  FIG. 6  and illustrating a steered beam in azimuth and elevation; 
         FIG. 8  is another example current density map for a steered beam; 
         FIG. 9  is a plot of example Smith charts corresponding to the current density map shown in  FIG. 8  and illustrating a steered beam in azimuth and elevation; and 
         FIG. 10  is a flow diagram for an example method of beam steering using the phased array antenna shown in  FIGS. 1-3 . 
     
    
    
     Corresponding reference characters indicate corresponding parts throughout the several views of the drawings. Although specific features of various examples may be shown in some drawings and not in others, this is for convenience only. Any feature of any drawing may be referenced and/or claimed in combination with any feature of any other drawing. 
     DETAILED DESCRIPTION 
     Embodiments of the systems described herein include a phased array antenna that is perimeter-fed. More specifically, the phased array antenna includes a plurality of slot antenna elements arranged in an array on the boresight surface of the phased array antenna. Behind the boresight surface is a resonant cavity fed at its perimeter by a plurality of feed waveguides, or “feeds.” Each row and each column of slot antenna elements in the array is fed by one feed waveguide, and each feed waveguide is coupled with a corresponding phase shifter that is independently controllable. By dynamically controlling the phase shifters, the standing waves within the resonant cavity are shifted, resulting in a steered beam radiated from the array of slot antenna elements. In contrast, a traditional phased array antenna would utilize one phase shifter and one feed per radiating element. For example, an N-by-M array (where N and M are integers greater than one) would utilize N×M phase shifters and feeds at great expense. Embodiments of the phased array antenna described herein would utilize N+M phase shifters and feeds arranged only at the perimeter to steer the beam radiated by the same number of radiating elements, dramatically reducing cost, complexity, and weight of the phased array antenna. The phased array antenna described herein is phase shifter type agnostic and can be easily scaled to higher frequencies, for example, up to K-band frequencies. 
       FIG. 1  is a perspective diagram of a phased array antenna  100 .  FIG. 2  is a block diagram of phased array antenna  100  shown in  FIG. 1 . Phased array antenna  100  radiates a beam (not shown) steered in a direction defined relative to boresight  102 , which is represented by a vector extending normal to a boresight surface  104  of phased array antenna  100 . Boresight surface  104  forms one boundary of a resonant cavity  106  and includes a plurality of slot antenna elements  108  arranged in an array. Each slot antenna element  108  is spaced from its neighboring slot antenna element  108  according to a wavelength corresponding to the operating frequency of phased array antenna  100 . For example, in at least some embodiments, a spacing  110  among slot antenna elements  108  is at most wavelength (lambda) divided by two, or λ/2. In other embodiments, where greater resolution in beam steering is desired, spacing  110  among slot antenna elements  108  is reduced, and a greater quantity of slot antenna elements  108  is utilized. 
     Resonant cavity  106  is generally rectangular and dimensioned according to the wavelength, or frequency, of standing waves it will produce in its volume. Resonant cavity  106  is perimeter-fed by a plurality of feed waveguides  112 . Accordingly, feed waveguides  112  are distributed along two perimeter sides  114  and  116  of resonant cavity  106 , sides  114  and  116  corresponding to the X-axis and the Y-axis, respectively (where boresight corresponds with a Z-axis). Feed waveguides  112  are also dimensioned according to the wavelength, or frequency, of electromagnetic waves that will most-efficiently propagate through their volume (e.g., cross-sectional dimensions decrease and increase with wavelength). Generally, electromagnetic waves are fed to resonant cavity  106  through each of feed waveguides  112 , and then reflect variously off the walls of resonant cavity  106 . Electromagnetic waves at a resonant frequency for resonant cavity  106  will produce standing waves within resonant cavity  106 . These standing waves result in radiation from the plurality of slot antenna elements  108  in boresight surface  104 . 
     Resonant cavity  106  and feed waveguides  112  are filled, or loaded, with a dielectric material, or dielectric, having some defined relative permittivity (ε r ), or dielectric constant. For example, resonant cavity  106  can be filled with air, which has a relative permittivity of 1.0058986, which is only slightly more than that of a vacuum. A dielectric  118  loaded into resonant cavity  106  affects the resonant frequency of resonant cavity  106 . For example, in certain embodiments, resonant cavity  106  can be loaded with dielectric  118  having a greater relative permittivity (e.g., silicon dioxide having ε r =3.9) to reduce the wavelength of the standing waves produced within resonant cavity. In alternative embodiments, dielectric  118  can be any other suitable dielectric material for the application, such as, for example, Rexolite, which has a relative permittivity of 2.53. Accordingly, dielectric  118  enables a reduction in spacing  110  among the plurality of slot antenna elements  108 . Likewise, the dielectric within feed waveguides  112  affects the frequency of electromagnetic waves it will propagate. 
     Phased array antenna  100  includes a plurality of phase shifters  120  (not shown in  FIG. 1 ) respectively coupled with each of feed waveguides  112  to modify the respective phases of the electromagnetic waves fed to resonant cavity  106 , and thereby modifying the phases of standing waves produced within resonant cavity  106 . Each of phase shifters  120  is independently controllable, for example, by a microcontroller, digital signal processor (DSP), or other processing device (not shown), to dynamically adjust, over time, the phase shift it applies. By adjusting the respective phases of the electromagnetic waves fed to resonant cavity  106  and, consequently, the phases of the standing waves produced therein, phased array antenna  100  enables steering, in azimuth and elevation relative to boresight  102 , of the beam radiated by the plurality of slot antenna elements  108 . 
     Phase shifters  120 , in certain embodiments, each include a monolithic microwave integrated circuit (MMIC) phase shifter coupled to a respective feed waveguide  112  at a feed-point for feed waveguide  112  itself. A phase-shifted electromagnetic wave then propagates through feed waveguide  112  and into resonant cavity  106 . In alternative embodiments, phase shifters  120  can include in-line waveguide phase shifters coupled in series with one or more waveguides that form a given feed waveguide  112 . In other alternative embodiments, phase shifters  120  can include any other form of microwave phase shifter that enables independent control of the phase shift applied to each feed to resonant cavity  106 . 
     Phased array antenna  100  includes, generally, an N-by-M array of slot antenna elements  108 , where N and M are integers greater than one. Accordingly, the array includes N×M slot antenna elements  108 . In  FIG. 1 , for example, phased array antenna  100  includes a four-by-four array of 16 slot antenna elements  108  (e.g., N and M=4). At least some known phased array antennas having an N-by-M array include an equal number of feeds and phase shifters to achieve effective beam steering. For example, a conventional 4×4 array would utilize 16 feeds and 16 phase shifters. Embodiments of the phased array antennas described herein, for example, phased array antenna  100 , utilizes no more than N+M feeds, e.g., feed waveguides  112 , and N+M phase shifters  120 . In the example of a 4×4 array, phased array antenna  100  utilizes eight feed waveguides  112  and eight phase shifters  120 . Similarly, in another example embodiment having a 100×100 array, a conventional implementation would need 10,000 feeds and 10,000 phase shifters. Conversely, embodiments of the phased array antenna described herein would utilize, for example, 200 feed waveguides  112  and 200 phase shifters  120  (i.e., 100+100). Accordingly, the quantity of components, cost, and complexity of phased array antenna  100  is reduced relative to conventional phased array antennas. 
     In certain embodiments, phased array antenna  100  includes a plurality of attenuators  122  (shown in  FIG. 2 ) respectively coupled with feed waveguides  112  to control respective amplitudes of the standing waves produced within resonant cavity  106 , which further enables control of antenna gain. In certain embodiments, phased array antenna  100  includes at least one variable impedance  124  disposed within resonant cavity  106 , e.g., on side walls of resonant cavity  106 , to modify cavity mode boundary conditions within resonant cavity  106 . In certain embodiments, phased array antenna  100  includes a plurality of variable impedances (not shown) respectively coupled with the plurality of feed waveguides  112  to modify cavity mode boundary conditions for resonant cavity  106 . In certain alternative embodiments, phased array antenna  100  further includes a polarizer (not shown) configured to apply, for example, a circular polarization to the radiated beam. 
       FIG. 3  is a block diagram of a system  300  for steering a beam radiated from phased array antenna  100  (shown in  FIGS. 1 and 2 ). Phased array antenna  100  is fed by an RF source  302  and controlled by a microcontroller  304 . Microcontroller  304  controls, for example, each of the plurality of phase shifters  120  (shown in  FIG. 2 ) of phased array antenna  100  independently to modify the respective phase shifts applied to the RF signal supplied by RF source  302 . Further, in certain embodiments, microcontroller  304  is configured to control RF source  302  to modify, for example, the amplitude, frequency, or phase of the original electromagnetic waves supplied to feed waveguides  112  (shown in  FIGS. 1 and 2 ). 
     RF source  302  can include one or more RF circuits or components, such as, for example, a modulator, amplifier, oscillator, or other wave generator. The electromagnetic waves generated by RF source  302  are inserted into feed waveguides  112  where they propagate to resonant cavity  106 . Along the path to resonant cavity  106 , the electromagnetic waves are phase shifted and, in certain embodiments, attenuated. 
     System  300  includes a scanner  306  configured to measure electromagnetic fields within resonant cavity  106  relative to the array of slot antenna elements  108 . Scanner  306  can include, for example, a planar scanner for testing near-field radiation performance from phased array antenna  100 , including, for example, gain and current density. 
     System  300  includes a computing system  308  communicatively coupled to scanner  306  and to microcontroller  304 . Computing system  308  includes a processor  310 , a memory  312 , and a communication interface  314 . Processor  310  is configured to execute instructions, or program code, stored in memory  312  or any other suitable local or remote memory device. Processor  310 , for example, is configured to gain access to program code for receiving, via communication interface  314 , and processing test data collected by scanner  306  for phased array antenna  100 . Such test data can be stored, for example in memory  312 . Processor  310  is further configured to gain access to program code for instructing microcontroller  304 , via communication interface  314 , to independently control phase shifters  120  (shown in  FIG. 2 ) to sweep through a range of phases for electromagnetic waves to be fed to phased array antenna  100  to steer the beam. Computing system  308  instructs both scanner  306  and microcontroller  304  to collect test data for each permutation of phases within the range among phase shifters  120 . The resolution of each step through the range of phases can be selected to correspond to the steering resolution of phased array antenna  100 . For example, in one embodiment, each phase shifter  120  sweeps through the range in 10 degree increments. In alternative embodiments, each phase shifter  120  sweeps through the range in 5 degree increments. 
     Processor  310  is further configured to gain access to program code for processing the test data collected by scanner  306  to determine a beam direction in azimuth and elevation relative to boresight  102  corresponding to electromagnetic fields measured by the scanner for each permutation of phase settings for phase shifters  120 . In certain embodiments, scanner  306  maps measured current densities to the array of slot antenna elements  108 . Then processor  310 , in certain embodiments, is further configured to correlate the measured current densities to the beam directions. 
     Processor  310  is further configured to build a look-up table that relates the range of phases to beam directions. The look-up table can then be loaded onto microcontroller  304  such that it can control phase shifters  120  to produce a pattern of electromagnetic waves within resonant cavity  106  that correspond to a desired beam direction. For example, microcontroller  304  can be programmed, or configured, to index into the look-up table based on the desired beam direction, in azimuth and elevation relative to boresight, and retrieve respective phase settings upon which control of the phase shifters by microcontroller  304  is based. 
       FIG. 4  is an example current density map  400  produced by scanner  306  when all phase shifters on each of feed waveguides  112  are set to zero degrees phase shift.  FIG. 5  is a plot of example Smith charts  500  and  502  corresponding to current density map  400  shown in  FIG. 4  and illustrating a steered beam  504  in the form of a directed gain.  FIGS. 4 and 5  together show the beam radiated by phased array antenna  100  with such phase shifter settings is steered to boresight  102 , or in the Z-axis direction. Current density map  400  shows current densities mapped over boresight surface  104  and the plurality of slot antenna elements  108 . Peak current densities (shown as the more intense and darker shading in  FIG. 4 ) represent amplitudes of the standing waves produced within resonant cavity  106 . Smith chart  500  illustrates steered beam  504 , or the highest gain, directed toward boresight elevation, or a Theta of zero. Likewise, Smith chart  502  illustrates an azimuth of zero degrees with respect to boresight  102 . Accordingly, system  300  (shown in  FIG. 3 ) would include in its look-up table phase shifter settings of zero degrees for a beam directed toward boresight  102 . 
       FIG. 6  is another example current density map  600  produced by scanner  306  when respective phase shifters  120  on each of feed waveguides  112  are set to the shown phase settings in degrees (clockwise from lower left: −90, 170, 70, −180, 0, 30, −60, 90) relative to boresight  102 .  FIG. 7  is a plot of example Smith charts  700  and  702  corresponding to current density map  600  shown in  FIG. 6  and illustrating a steered beam  704  in the form of a directed gain.  FIGS. 6 and 7  together show the beam radiated by phased array antenna  100  with such phase shifter settings is steered to −30 degrees azimuth and −30 degrees elevation relative to boresight  102 . Current density map  600  shows current densities mapped over boresight surface  104  and the plurality of slot antenna elements  108 . Peak current densities (shown as the more intense and darker shading in  FIG. 6 ) represent amplitudes of the standing waves produced within resonant cavity  106 . Smith chart  700  illustrates steered beam  704 , or the highest gain, having an elevation of −30 degrees, or Theta=−30 degrees. Likewise, Smith chart  702  illustrates an azimuth of −30 degrees with respect to boresight  102 . Accordingly, system  300  (shown in  FIG. 3 ) would include in its look-up table the shown phase shifter settings for a beam directed toward −30 degrees azimuth and −30 degrees elevation relative to boresight  102 . 
       FIG. 8  is another example current density map  800  produced by scanner  306  when respective phase shifters  120  on each of feed waveguides  112  are set to the shown phase settings in degrees (clockwise from lower left: 130, −15, −10, 180, 120, −10, −10, −20) relative to boresight  102 .  FIG. 9  is a plot of example Smith charts  900  and  902  corresponding to current density map  800  shown in  FIG. 8  and illustrating a steered beam  904  in the form of a directed gain.  FIGS. 8 and 9  together show the beam radiated by phased array antenna  100  with such phase shifter settings is steered to 60 degrees azimuth and 60 degrees elevation relative to boresight  102 . Current density map  800  shows current densities mapped over boresight surface  104  and the plurality of slot antenna elements  108 . Peak current densities (shown as the more intense and darker shading in  FIG. 8 ) represent amplitudes of the standing waves produced within resonant cavity  106 . Smith chart  900  illustrates steered beam  904 , or the highest gain, having an elevation of 60 degrees, or Theta=60 degrees. Likewise, Smith chart  902  illustrates an azimuth of 60 degrees with respect to boresight  102 . Accordingly, system  300  (shown in  FIG. 3 ) would include in its look-up table the shown phase shifter settings for a beam directed toward 60 degrees azimuth and 60 degrees elevation relative to boresight  102 . 
     In alternative embodiments, the locations of standing waves within resonant cavity  106  can be computed, by computing system  300  and/or by microcontroller  304 , based on respective phase settings for phase shifters  120 . The computed standing waves can then be correlated to a beam direction. The relationship between phase settings for phase shifters  120  and beam direction can be recorded in a look-up table as described above, or microcontroller  304  can compute the phase settings for a given beam direction during operation, or on the fly. Deterministically computing phase settings for phase shifters  120  in a large phased array antenna is generally computationally intense, making it more feasible to test phased array antenna  100  using scanner  306  and computing system  300  as described above to build a look-up table. 
       FIG. 10  is a flow diagram of an example method  1000  of beam steering using phased array antenna  100  (shown in  FIGS. 1, 2, and 3 ). Generally, electromagnetic waves are generated at an RF source such as RF source  302  (shown in  FIG. 3 ). Method  1000  includes shifting  1002  respective phases of a plurality of electromagnetic waves, and then feeding  1004  the plurality of electromagnetic waves through feed waveguides  112  at a perimeter of resonant cavity  106 , e.g., sides  114  and  116 . Resonant cavity  106  is configured to produce standing waves within resonant cavity  106  based on the electromagnetic waves fed into it. 
     Generally, shifting  1002  respective phases includes, for an N-by-M array of slot antenna elements  108 , shifting respective phases of N+M electromagnetic waves fed to the perimeter of resonant cavity  106  using no more than N+M phase shifters  120 . Phase shifting  1002  can be achieved, in certain embodiments, by independently controlling the plurality of phase shifters  120  coupled with corresponding feed waveguides  112  to modify respective phases of standing waves within resonant cavity  106 . 
     Method  1000  includes radiating  1006  a steered beam from the array of slot antenna elements  108  distributed about boresight surface  104  of resonant cavity  106 . The radiated beam is based on the standing waves in resonant cavity  106 . 
     In certain embodiments, method  1000  includes attenuating the plurality of electromagnetic waves fed to the perimeter of resonant cavity  106  to control amplitude of the standing waves. In certain embodiments, method  1000  includes varying at least one impedance disposed within resonant cavity  106 , such as impedance  124 , to modify cavity mode boundary conditions for resonant cavity  106 . In certain embodiments, method  1000  further includes varying a plurality of variable impedances respectively coupled with corresponding feed waveguides  112  to the perimeter of resonant cavity  106  to modify cavity mode boundary conditions for resonant cavity  106 . 
     The technical effects of embodiments of the systems and methods described herein include, for example: (a) forming a phased array antenna using a resonant cavity and an array of slot antenna elements; (b) feeding a phased array antenna at a perimeter rather than element-by-element; (c) reducing the quantity of feeds and phase shifters necessary to steer a beam radiated by a phased array antenna; (d) reducing complexity and cost of phased array antennas by using a perimeter fed resonant cavity; (e) enabling larger phased array antennas due to feeds being concentrated on two sides of the resonant cavity; and (f) independently controlling phase shifters for a perimeter-fed resonant cavity based on a mapping of phase settings to beam direction to modify phases of standing waves produced within the resonant cavity to steer the beam. 
     Generally, waveguides have a shape and dimensions that define the range of signals (e.g., frequency and mode) that will propagate through a given waveguide. Feed waveguides  112 , for example, can include a circular or rectangular waveguide, or any other shape of waveguide. Generally, waveguides are dimensioned for microwave signals, or signals having a frequency between about 300 Megahertz (MHz) and about 300 Gigahertz (GHz). Accordingly, an RF antenna can also be referred to as a microwave antenna. For example, a waveguide can be dimensioned for an operating frequency of 20 GHz. Likewise, microstrip transmission lines, slot antenna elements, resonant cavities, phase shifters, and attenuators are designed for efficient signal propagation (or suppression in the case of attenuators) at the desired operating frequency, and are further designed for impedance matching at, for example, transitions from a waveguide to a resonant cavity. As another example, slot antenna elements generally have a length and width corresponding to the desired operating frequency. Further, the orientation of apertures for slot antenna elements is selected for efficient signal propagation for the desired operating frequency. 
     Some embodiments involve the use of one or more electronic processing or computing devices. As used herein, the terms “processor” and “computer” and related terms, e.g., “processing device,” “computing device,” and “controller” are not limited to just those integrated circuits referred to in the art as a computer, but broadly refers to a processor, a processing device, a controller, a general purpose central processing unit (CPU), a graphics processing unit (GPU), a microcontroller, a microcomputer, a programmable logic controller (PLC), a reduced instruction set computer (RISC) processor, a field programmable gate array (FPGA), a digital signal processing (DSP) device, an application specific integrated circuit (ASIC), and other programmable circuits or processing devices capable of executing the functions described herein, and these terms are used interchangeably herein. The above embodiments are examples only, and thus are not intended to limit in any way the definition or meaning of the terms processor, processing device, and related terms. 
     In the embodiments described herein, memory can include, but is not limited to, a non-transitory computer-readable medium, such as flash memory, a random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), and non-volatile RAM (NVRAM). As used herein, the term “non-transitory computer-readable media” is intended to be representative of any tangible, computer-readable media, including, without limitation, non-transitory computer storage devices, including, without limitation, volatile and non-volatile media, and removable and non-removable media such as a firmware, physical and virtual storage, CD-ROMs, DVDs, and any other digital source such as a network or the Internet, as well as yet to be developed digital means, with the sole exception being a transitory, propagating signal. Alternatively, a floppy disk, a compact disc—read only memory (CD-ROM), a magneto-optical disk (MOD), a digital versatile disc (DVD), or any other computer-based device implemented in any method or technology for short-term and long-term storage of information, such as, computer-readable instructions, data structures, program modules and sub-modules, or other data may also be used. Therefore, the methods described herein may be encoded as executable instructions, e.g., “software” and “firmware,” embodied in a non-transitory computer-readable medium. Further, as used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory for execution by personal computers, workstations, clients and servers. Such instructions, when executed by a processor, cause the processor to perform at least a portion of the methods described herein. The systems and methods described herein are not limited to the specific embodiments described herein, but rather, components of the systems and/or steps of the methods may be utilized independently and separately from other components and/or steps described herein. 
     The systems and methods described herein are not limited to the specific embodiments described herein, but rather, components of the systems and/or steps of the methods may be utilized independently and separately from other components and/or steps described herein. 
     Although specific features of various embodiments of the disclosure may be shown in some drawings and not in others, this is for convenience only. In accordance with the principles of the disclosure, any feature of a drawing may be referenced and/or claimed in combination with any feature of any other drawing. 
     As used herein, an element or step recited in the singular and proceeded with the word “a” or “an” should be understood as not excluding plural elements or steps unless such exclusion is explicitly recited. Further, references to “one embodiment” of the present disclosure or “an example embodiment” are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Furthermore, to the extent the terms “includes,” “including,” “has,” “contains,” and variants thereof are used herein, such terms are intended to be inclusive in a manner similar to the term “comprises” as an open transition word without precluding any additional or other elements. 
     This written description uses examples to disclose various embodiments, which include the best mode, to enable any person skilled in the art to practice those embodiments, including making and using any devices or systems and performing any incorporated methods. The patentable scope is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.