Patent Publication Number: US-2023162611-A1

Title: Method and system for swath width normalization during airborne collection of terrain data

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Patent Application No. 63/281,556, filed Nov. 19, 2021, the contents of which are incorporated herein by reference in their entirety. 
    
    
     TECHNICAL FIELD 
     The present embodiments relate generally to terrain imaging and/or mapping, and more particularly to real-time management of imaging/mapping scanning parameters for swath width normalization during airborne collection of three-dimensional terrain data. 
     BACKGROUND 
     With a dramatic increase in the amount and type of autonomous control technologies becoming available and used by various platforms, maintaining accurate and up-to-date terrain imaging/mapping has become increasingly important. Many aerial imaging collection systems can be used to generate and maintain terrain maps, including LiDAR and other line-of-sight scanning/collection technologies. One of the most deleterious issues associated with aerial collection of base maps using such technologies relates to the adverse effects of topographically-variable terrain within the collection region. 
     It is against this technological backdrop that the present Applicant sought a technological solution to these and other problems rooted in this technology. 
     SUMMARY 
     Embodiments of the present disclosure relate generally to terrain mapping, and more particularly to a method and system for maintaining a normalized view of a terrain during an airborne data collection process. Embodiments include an intelligent sensing methodology that, on a near-real time basis, continually monitors the geometry and instantaneous height of the immediate 3D region (volume pixel, or “voxel”) under collection by an airborne sensor, thus maintaining complete, continual situational awareness of the topography under investigation. In this manner, swath asymmetries resulting from occlusion by local elevation maxima can be fully assessed, quantified, and mitigated at the terminus of and/or during each scan. In some embodiments, this is done by adjusting the platform&#39;s collection system scan parameters (e.g. by adjusting a scan angle for the affected direction) on a scan-by-scan basis to eliminate such asymmetries from each collection swath. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other aspects and features of the present embodiments will become apparent to those ordinarily skilled in the art upon review of the following description of specific embodiments in conjunction with the accompanying figures, wherein: 
         FIG.  1 A  illustrates an example of aerial data collection over relatively flat terrain 
         FIG.  1 B  illustrates an example of aerial data collection over topographically variable terrain. 
         FIG.  2 A  illustrates an example of collection system swath patterns collected over relatively level (left) and topographically variable (right) terrain. 
         FIG.  2 B  illustrates an example of a full set of aerial data collection (with approximately 10% swath overlap) over relatively flat/level terrain. (Northbound collection passes are notionally depicted in blue; southbound in green.) 
         FIG.  3 A  illustrates example results of an aggressive collection plan in a high-relief region, with gap areas indicated in red. 
         FIG.  3 B  illustrates example results of a conservative collection plan in a high-relief region. 
         FIG.  4    is an example system diagram according to embodiments. 
         FIG.  5    is a flowchart of an example methodology according to embodiments. 
         FIG.  6    illustrates example swath width normalization over high-relief topographic areas, via augmentation of nominal half-scan angle (x) by y. y=A(δx), where A is an integer greater than or equal to zero, according to embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     The present embodiments will now be described in detail with reference to the drawings, which are provided as illustrative examples of the embodiments so as to enable those skilled in the art to practice the embodiments and alternatives apparent to those skilled in the art. Notably, the figures and examples below are not meant to limit the scope of the present embodiments to a single embodiment, but other embodiments are possible by way of interchange of some or all of the described or illustrated elements. Moreover, where certain elements of the present embodiments can be partially or fully implemented using known components, only those portions of such known components that are necessary for an understanding of the present embodiments will be described, and detailed descriptions of other portions of such known components will be omitted so as not to obscure the present embodiments. Embodiments described as being implemented in software should not be limited thereto, but can include embodiments implemented in hardware, or combinations of software and hardware, and vice-versa, as will be apparent to those skilled in the art, unless otherwise specified herein. In the present specification, an embodiment showing a singular component should not be considered limiting; rather, the present disclosure is intended to encompass other embodiments including a plurality of the same component, and vice-versa, unless explicitly stated otherwise herein. Moreover, applicants do not intend for any term in the specification or claims to be ascribed an uncommon or special meaning unless explicitly set forth as such. Further, the present embodiments encompass present and future known equivalents to the known components referred to herein by way of illustration. 
     According to certain general aspects, the present embodiments relate to maintaining a normalized view of a terrain during an airborne data collection process. Embodiments include an intelligent sensing and control methodology that, on a near-real time basis, continually monitors the geometry and instantaneous height of the immediate region (voxel) under collection by an airborne sensor, and a method for maintaining complete, continual situational awareness of the topography under investigation. In this manner, swath asymmetries resulting from occlusion by local elevation maxima can be fully assessed, quantified, and mitigated at the terminus of and/or during each scan. 
     As set forth above, one of the most deleterious issues associated with aerial collection of terrain base maps relates to the adverse effects of topographically-variable terrain within the collection region. Presently, during airborne collection of geospatial and/or three-dimensional data using conventional collection systems such as those based on LiDAR and other line-of-sight imaging technologies, swath width can vary significantly over the course of a collection pass. Furthermore, the more topographically variable the overall region of collection, the more problematic the final data set—and the more difficult and wasteful the task of data fusion, registration and orthorectification. 
       FIGS.  1 A and  1 B  are perspective views that graphically depict how terrain elevation can significantly affect the nature and symmetry of a collection system swath, as recognized by the present Applicant. 
     As shown in  FIG.  1 A , an airborne vehicle  102  over a terrain carries a collection system  104  having an imaging swath  106 . For purposes of the present disclosure, vehicle  102  can include any type of piloted, autonomous, tethered, untethered, powered or unpowered airborne vehicle or platform including airplanes, helicopters, VTOL aircraft, drones, gliders, blimps, towers, etc. Also, the present disclosure is not limited to land terrain imaging, but can also include undersea terrain imaging, extraterrestrial terrain imaging, cityscape imaging, etc. Also for purposes of the present disclosure, collection system  104  refers to any type of topological/geospatial/three-dimensional data collection technology and/or system having an imaging or sensing directional line of sight, such as LiDAR, radar, sonar, infrared, etc., and capable of capturing, generating and/or collecting data useful for topological and/or terrain mapping. 
     In the example shown in  FIG.  1 A , in the case of a substantially even or level terrain, the widths  106 -L and  106 -R of swath  106  covering the terrain are substantially equal on both sides of vehicle  102 . Conversely, as shown in the example of  FIG.  1 B , in the case of an uneven terrain, the widths  116 -L and  116 -R of swath  116  covering the terrain are substantially unequal on both sides of vehicle  102 . This is because the scan angle of conventional system  104  is fixed at a given angle and equally established along a center line  118 . As such, the swath width cannot be adjusted in real time to account for topographical variations in the terrain such as those shown in the case of  FIG.  1 B . 
     Further to the above, the present Applicant recognizes that the more topographically variable the terrain is in the overall region of collection, the more analytically intractable the final data set will be—and the more difficult and wasteful the task of data fusion, registration and orthorectification will be. For example,  FIGS.  2 A and  2 B  are top plan views of a region  200  for which a terrain mapping is to be performed via aerial collection. As shown in  FIG.  2 A , during one collection flight path  220 -A, terrain data having an associated swath  206 -A is collected. As shown in this example, the profile of swath  206 -A is very close to a desired swath profile, having consistent coverage and being fairly uniform in width around flight path  220 -A due to a relatively uniform terrain below it. 
     Conversely, during a different collection flight path  220 -B, terrain data having an associated swath  206 -B is collected. As shown in this example, the profile of swath  206 -B has a very undesirable swath profile, with inconsistent coverage and being entirely non-uniform in width around flight path  220 -B. This can be caused by a highly variable terrain under flight path  220 -B (i.e. mountainous terrain or areas with high hills, deep valleys, etc.). 
     As can be appreciated from  FIGS.  1 A,  1 B,  2 A and  2 B , the term “swath” as used herein refers to the geographical or physical extent of terrain covered and/or captured by the collection system  104 , which is impacted by both the scan angle extent of the collection system and the topographical features of the terrain. Accordingly, given a constant maximum scan angle, the swath will be wider or narrower depending on the features of the terrain being analyzed by the collection system. Likewise, given a constant topographical terrain (e.g. a flat landscape), the swath will be wider or narrower depending on the maximum scan angle used by the collection system. It should be further appreciated that swath width can differ from scan to scan (assuming the maximum scan angle is constant) as an airborne collection system travels over a topographically varying terrain. 
     The present Applicant further recognizes that only under the most favorable of topographic scenarios (i.e., minimal elevation variability throughout a terrain) can a consistently uniform set of data swaths be generated and then successfully fused together in furtherance of a final geospatial 3D map.  FIG.  2 B  illustrates the nominal geospatial mapping scheme under such near-ideal circumstances: 
     After a data collection mission for a region  200 , comprising collection flight paths  220 -C,  220 D,  220 -E,  220 -F,  220 -G and  220 -H, terrain data is collected, the terrain data having respective associated swaths  206 -C,  206 -D,  206 -E,  206 -F,  206 -G and  206 -H. In this example, provided that swath  220 -C to  220 -H have fundamentally uniform profiles in which all adjacent swaths at least partially overlap, the processes of data fusion, registration and orthorectification are straightforward, and generation of the end mapping product is relatively efficient. Conversely, any scenario with nontrivial elevation variability does not lend itself to such straightforward methods. 
     It should be apparent that many conventional techniques for performing data fusion, registration and orthorectification can be used in conjunction with the data collection techniques of the present disclosure, and detailed descriptions of such conventional techniques are not necessary for an understanding of the present embodiments. As such, further details will be omitted here for sake of clarity of the present embodiments. 
     In view of the foregoing, the present Applicant further recognizes that there are generally two options available to the mission planner when planning and executing the collection of geospatial imagery over topographically complicated regions of terrain: 
     (1) Aggressive Collection Approach: The collection platform (e.g. as configured by a mission designer) ignores or is oblivious to these topographical variations, and executes a collection scheme or sortie over region  300  having a collection flight path  320 -A that essentially treats the collected terrain as flat (i.e. ignores the effects of mountains, valleys, etc.). As such, the spacings between different collection passes over region  300  are relatively wide and do not account for the widely varying terrain. Accordingly, in this example, as shown in  FIG.  3 A , the resulting swaths  306 -A to  306 -D yield significant gaps  322  in coverage, rendering the final data product (e.g. geospatial 3D map) virtually unusable for most purposes and applications. 
     (2) Conservative Collection Approach: The collection platform (e.g. as configured by a mission designer), typically through a series of complicated calculations by hand or via a computerized flight plan generator, executes a collection scheme or sortie over region  300  that ensures full overlap of all collection swaths using a collection flight path  320 -B that includes many more tightly-spaced passes over region  300  as compared to collection flight path  320 -A in  FIG.  3 A . In this example, as shown in  FIG.  3 B , the resulting swaths  306 -E to  306 -G overlap substantially and result in no gaps in coverage. On the contrary, there is considerable overlap  324  in adjacent swaths. This provides a very useful final data product (e.g. geospatial 3D map); however, this superior product as compared to the result in  FIG.  3 A  comes at the expense of tremendous and superfluous path overlap as shown in  FIG.  3 B . This redundant collection of topographical data can reduce the collection efficiency of the sortie by 50% or more (e.g. by comparison of flight paths  320 -A and  320 -B—and at a significant expense of time, money, and capital assets. 
     It is thus readily apparent how crippling the effects of variable topography can be with regard to the efficient, effective capture of high-quality 3D terrain data—especially given the fact that the geospatial data market has become largely commoditized (with corresponding thin profit margins) over the past 10+ years. There is thus a profound need for a more intelligent, agile method of collection that simultaneously eliminates gaps and minimizes collection waste. 
     In accordance with certain general aspects, the present embodiments provide an intelligent sensing methodology that, on a near-real time basis, continually monitors the geometry and instantaneous height of the immediate region (e.g. voxel) under collection by an airborne sensor (e.g. LiDAR sensor), thus maintaining complete, continual situational awareness of the topography under investigation. In this manner, swath asymmetries resulting from occlusion by local elevation maxima and/or minima can be fully assessed, quantified, and mitigated at the terminus of (and, in fact, during) each scan; more importantly, the platform&#39;s collection data scan parameters can be adjusted on a scan-by-scan basis to eliminate such asymmetries from each collection swath. The result is a geospatial collection product that much more closely resembles  FIG.  2 B  than either  FIG.  3 A  or  FIG.  3 B , even in areas of extreme topographical relief. 
     One example “iDAR” data collection system according to embodiments comprises an agile sensing LiDAR (i.e. ladar) system. Such an agile sensor system has, among other capabilities, the ability to adjust scan and laser shot parameters on a scan-by-scan and, indeed, even a shot-by-shot basis. As such, this preferred architecture is uniquely capable of providing a robust and elegant solution to the problem of inefficient, non-uniform swath generation. 
     An example LiDAR system  400  that can implement and/or replace system  104  in  FIG.  1    is shown in  FIG.  4   . As shown, system  400  includes a controller  402 , a transmitter  404  and a receiver  406 . It should be apparent that system  400  can include additional or fewer components than shown in  FIG.  4   . However, the details of any additional components that can be included, as well as details regarding functionalities of the illustrated components that are not necessary for an understanding of the present embodiments, are omitted here for sake of clarity of the present disclosure. Moreover, although shown together in  FIG.  4   , this illustration is also not limiting. In particular, some, all, or none of the components in  FIG.  4    may be separately located and/or may communicate with each other through various wired and wireless technologies. 
     In example LiDAR system  400 , transmitter  404  includes a light source comprising a laser and receiver  406  includes a sensor comprising charge-coupled devices (CCDs). Transmitter  404  and receiver  406  are preferably provided in a bistatic architecture, having independently controllable optical paths, one or both of which can include a set of scanning mirrors controlled by controller  402 , projection/focusing optics, filters, etc. An example system that can be adapted for use in the present embodiments is described in U.S. Pat. No. 9,885,778, the contents of which are incorporated herein by reference in their entirety. 
     Controller  402  receives plan information from collection plan  422 , such as information from topographical maps of the overflight area, flight collection parameters for the upcoming sortie such as airspeed, flight altitude, GPS coordinates of the boundaries of the region to be analyzed, beginning and ending GPS coordinates of collection passes through the region, number of collection passes, directions of collection passes, etc. 
     Controller  402  stores image data in terrain image data repository  424 . This can include raw voxel data from receiver  406  in addition to metadata (e.g. time, GPS geolocation position stamps, etc.) 
     According to certain “agile LiDAR” aspects, and as described in the incorporated patent, controller  402  includes a scan engine controller  410  that is capable of implementing a shot selection strategy in addition to, or in place of, a conventional raster scan strategy. In this regard, controller  410  is able to cause transmitter  404  to illuminate an environment using a raster scan strategy similar to conventional strategies, or using a group of individually programmed shots in a certain target area within an environment, or any combination thereof. Of particular relevance to the present disclosure, scan engine controller  410  is able to cause transmitter  404  to illuminate an environment (e.g. terrain) using a dynamically adjustable scan angle. 
     According to certain additional aspects of the present disclosure, controller  402  further includes a swath width controller  408 . As mentioned above, and as described in more detail herein, swath width controller  408  is configured to analyze data collected from receiver  406  in conjunction with an area illuminated by transmitter  404 , and to dynamically determine or adjust a swath width for a terrain being imaged. As shown in this example, swath width controller  408  does this by communicating with scan engine controller  410 , for example by providing dynamic scan parameters to scan engine controller  410 , so as to cause system  400  to maintain a substantially uniform swath width in accordance with the present embodiments. 
     One example airborne LiDAR collection methodology according to embodiments is shown in  FIG.  5   . 
     As shown in this example, processing begins in S 502  with a LiDAR mission definition. In advance of the collection sortie, and informed by a review of topographical maps of the overflight area, the flight collection parameters from  422  for the upcoming sortie (e.g. airspeed, flight altitude, etc.) are considered and then established/definitized as part of the mission. These can be considered along with other LiDAR system parameters such as scan rate, pulse/shot rate, maximum scan angle, etc. 
     In step S 502 , paired with these flight parameters, a nominal or “standard” (total) swath widthω for the sortie is selected—one that is laterally symmetric about the aircraft&#39;s body axis (measured in distance). This swath width “baseline” can be, for example, the swath width generated when operating the LiDAR sensor at the designated flight altitude over the lowest (and preferably level) region of the collection sortie. It should be apparent, however, that an elevation at other portions of the collection sortie can be selected as the baseline, and need not be the absolute lowest or other maximum or minimum elevation in the region being analyzed. Those skilled in the art will understand how to determine a swath width using flight collection parameters such as those described above after being taught by the present examples. 
     In the example shown in  FIG.  6   , the baseline elevation H occurs on the left side of vehicle  102  during a particular portion of the sortie. The scan half-angle x is the angle used by system  400  to collect data from this lowest elevation point in the terrain. This scan half-angle also corresponds to the baseline swath width ω. For example, a nominal collection baseline might be a flight altitude (e.g. above the lowest, predominantly flat region of the sortie) of 20,000 ft AGL, a (full) scan angle of 2x=10°, and a resulting nominal swath width ω of 1.06 km. 
     During flight, processing enters a loop S 504  of steps that are performed for each single combined scan from both a left side and a right side of the collection platform (e.g. a complete collection scan between a left most side of the collection platform and a right most side of the collection platform at each point in a flight path from one end of a collection region to the opposite end of the collection region). 
     In S 506 -L and S 506 -R, a shot is fired by transmitter  404  (e.g. a LiDAR pulse) based on the current scan parameter settings determined by scan engine controller  410  and swath width controller  408 . For ease of illustration,  FIG.  5    illustrates processing for half scans performed for both left and right sides of a collection platform. However, it should be apparent that processing steps S 508  and S 510  are performed for one shot at a time, starting from directly below the platform (e.g. a scan angle of zero) and at an increasing scan angle with respect to one side of the collection platform for each iteration of loop S 504 . Once it has been determined that a desired swath half-width has been achieved for one side of the platform (e.g. left or right) in a given scan (as indicated by S 512 ), processing is initiated for the other side of the platform, starting from directly below the platform (e.g. a scan angle of zero). Processing proceeds for this other side of the platform until the desired swath half-width has been achieved for this other side of the platform also, upon which processing for the given scan is complete, and processing for a new scan is performed, or a new collection path is initiated. 
     In S 508 , using the platform airspeed, instantaneous scan angle, and time-of-flight for photon returns from the most recent LiDAR detection event (i.e. ground return voxel), an algorithm in swath width controller  408  according to embodiments determines (on a half-scan-cycle basis) the instantaneous height and resulting swath half-width for the current shot. For example, as shown in  FIG.  6   , system  400  fires a shot at a scan angle x on the right side of the platform. Based on the voxel information returned by the receiver  406  at this point, the height h relative to a predetermined elevation baseline H of the most recent ground return is determined. From this height information h, the resulting half-width of the current collection swath, ω 1/2 ′ for this scan angle x can be calculated by simple geometrical transformation. 
     Using available measurements and calculated geometry of the instantaneous scenario, the algorithm establishes that some additional scan authority may be required to maintain the standard swath half width ω 1/2  for the current half scan on the right side of the platform. However, since it is not possible to know, a priori, the nature of topographic relief beyond the scan half-angle angle x, it is not possible to calculate at this stage what specific additional half-angle scan y is required to maintain the standard swath width ω 1/2  for the current half scan. All that is known is that the current half-scan angle x may be insufficient for purposes of maintaining swath width homogeneity. The need for a marginal increase to the baseline half-scan angle can be implemented as a set of instructions to the scan engine controller  410 . 
     As shown in  FIG.  5   , in steps S 510 -L and S 510 -R, the swath width controller  408 , as needed, instructs the scan engine controller  410  to increase the current scan angle (for example x as shown in  FIG.  6   ) by a marginal angle, 6x (for example, 0.5 deg), so as to increase ω 1/2 ′ by a resulting incremental width. With the goal for each half-scan being to incrementally increase ω 1/2 ′ until it is equivalent (at least approximately) to the baseline swath width ω 1/2 , steps S 506  and S 508  are repeated for the new angle [x+δx]. Accordingly, this process is repeated until ω 1/2 ′=ω 1/2 , (as shown in S 512 -L and S 512 -R) or at least (given algorithmic and timing limitations) ω 1/2 ′≈ω 1/2 . 
     It should be noted that, with respect to the example shown in  FIG.  6   , the final half-scan angle for the right side of the platform is ultimately defined by y=x+A δx, where A is an integer greater than or equal to zero, and is equal to the number of loop S 504  iterations that are necessary to secure ω 1/2 ′=ω 1/2 . It should be noted that for the situation in which no incremental increase in x is deemed necessary (e.g. no topographical complication is at play with respect to the baseline topographical situation), A=0 and y=x. 
     Upon the conclusion of one LiDAR collection pass, the aircraft executes a 180° turn and commences LiDAR collection in a direction that is antiparallel to, but laterally offset from, the previous pass, such that no more than 5-10% of the previous collection region is re-collected in the new pass. However, some nominal (i.e., 5%) amount of re-collection via swath overlap is preferred in order to ensure (a) the final map is not afflicted with gaps in coverage; (b) there is sufficient common geospatial data between each pair of successive passes to support precise splicing and registration of the disparate data sources, ensuring a properly fused and fully-orthorectified final 3D geospatial map product. 
     After flight, and/or at some point upon the conclusion of any LiDAR collection sortie, a 3D geospatial map is produced by processing and then splicing together the complete set of resulting LiDAR data swaths. Some amount of swath overlap is preferred for the success of this process; any gaps in coverage, such as those depicted in  FIG.  3 A , can render the full sortie collection product entirely unusable. On the other hand, as suggested by  FIG.  3 B , a lack of swath width uniformity can make this overlap and fusion process exceptionally inefficient. By taking a proactive technical approach to ensuring swath width homogeneity across each individual collection pass according to aspects of the embodiments, a significant improvement in geospatial mapping efficiency can be realized and capitalized upon. 
     As set forth above, many conventional techniques for performing data fusion, registration and orthorectification can be used in conjunction with the data collection techniques of the present disclosure, and detailed descriptions of such conventional techniques are not necessary for an understanding of the present embodiments. As such, further details will be omitted here for sake of clarity of the present embodiments. 
     The herein described subject matter sometimes illustrates different components contained within, or connected with, different other components. It is to be understood that such depicted architectures are illustrative, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively “associated” such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as “associated with” each other such that the desired functionality is achieved, irrespective of architectures or intermedial components. Likewise, any two components so associated can also be viewed as being “operably connected,” or “operably coupled,” to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being “operably coupleable,” to each other to achieve the desired functionality. Specific examples of operably coupleable include but are not limited to physically mateable and/or physically interacting components and/or wirelessly interactable and/or wirelessly interacting components and/or logically interacting and/or logically interactable components. 
     With respect to the use of plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity. 
     It will be understood by those within the art that, in general, terms used herein, and especially in the appended claims (e.g., bodies of the appended claims) are generally intended as “open” terms (e.g., the term “including” should be interpreted as “including but not limited to,” the term “having” should be interpreted as “having at least,” the term “includes” should be interpreted as “includes but is not limited to,” etc.). 
     Although the figures and description may illustrate a specific order of method steps, the order of such steps may differ from what is depicted and described, unless specified differently above. Also, two or more steps may be performed concurrently or with partial concurrence, unless specified differently above. Such variation may depend, for example, on the software and hardware systems chosen and on designer choice. All such variations are within the scope of the disclosure. Likewise, software implementations of the described methods could be accomplished with standard programming techniques with rule-based logic and other logic to accomplish the various connection steps, processing steps, comparison steps, and decision steps. 
     It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation, no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases “at least one” and “one or more” to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles “a” or “an” limits any particular claim containing such introduced claim recitation to inventions containing only one such recitation, even when the same claim includes the introductory phrases “one or more” or “at least one” and indefinite articles such as “a” or “an” (e.g., “a” and/or “an” should typically be interpreted to mean “at least one” or “one or more”); the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should typically be interpreted to mean at least the recited number (e.g., the bare recitation of “two recitations,” without other modifiers, typically means at least two recitations, or two or more recitations). 
     Furthermore, in those instances where a convention analogous to “at least one of A, B, and C, etc.” is used, in general such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, and C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). In those instances where a convention analogous to “at least one of A, B, or C, etc.” is used, in general, such a construction is intended in the sense one having skill in the art would understand the convention (e.g., “a system having at least one of A, B, or C” would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc.). It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase “A or B” will be understood to include the possibilities of “A” or “B” or “A and B.” 
     Further, unless otherwise noted, the use of the words “approximate,” “about,” “around,” “substantially,” etc., mean plus or minus ten percent. 
     Although the present embodiments have been particularly described with reference to preferred examples thereof, it should be readily apparent to those of ordinary skill in the art that changes and modifications in the form and details may be made without departing from the spirit and scope of the present disclosure. It is intended that the appended claims encompass such changes and modifications.