Patent Publication Number: US-10324200-B2

Title: Systems and methods for improved collimation sensitivity

Description:
RELATED APPLICATIONS 
     The present application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. No. 15/595,266, entitled “Systems and Methods for Improved Collimation Sensitivity,” filed May 15, 2017, the entire disclosure of which is incorporated by reference herein. 
    
    
     BACKGROUND OF THE INVENTION 
     The subject matter disclosed herein relates generally to apparatus and methods for diagnostic medical imaging, such as Nuclear Medicine (NM) imaging. 
     In NM imaging, systems with multiple detectors or detector heads may be used to image a subject, such as to scan a region of interest. For example, the detectors may be positioned adjacent the subject to acquire NM data, which is used to generate a three-dimensional (3D) image of the subject. 
     Single Photon Emission Computed Tomography (SPECT) systems may have moving detector heads, such as gamma detectors positioned to focus on a region of interest. For example, a number of gamma cameras may be moved (e.g., rotated) to different angular positions for acquiring image data. The acquired image data is then used to generate the 3D images. 
     The size of the detector heads may limit an available usable area for the placement of detectors, such as Cadmium Zinc Telluride (CZT) wafers. The sensitivity (e.g., the proportion of radiation received relative to the radiation emitted) may be limited by the size of the detector heads and/or the arrangement of CZT wafers. Conventional approaches to improving sensitivity may use thicker detectors, or detectors arranged in generally identical or similar layers stacked directly one on top of each other. Such conventional approaches may not provide a desired or required sensitivity. 
     BRIEF DESCRIPTION OF THE INVENTION 
     In one embodiment, a detector assembly is provided that includes a semiconductor detector, a pinhole collimator, and a processing unit. The semiconductor detector has a first surface and a second surface opposed to each other. The first surface includes pixels, and the second surface includes a cathode electrode. The pinhole collimator includes an array of pinhole openings corresponding to the pixels. Each pinhole opening is associated with a single pixel of the semiconductor detector, and the area of each pinhole opening is smaller than a corresponding area of the corresponding pixel, which is exposed to radiation. (It may be noted that the pixel area less the radiation blocking area of the collimator immediately above the pixel is exposed to radiation in some embodiments). The processing unit is operably coupled to the semiconductor detector and configured to identify detected events within virtual sub-pixels distributed along a length and width of the semiconductor detector. Each pixel includes (e.g., has associated therewith) a plurality of corresponding virtual sub-pixels (as interpreted by the processing unit), wherein absorbed photons are counted as events in a corresponding virtual sub-pixel. 
     In another embodiment, a detector assembly is provided that includes a semiconductor detector, a collimator, and a processing unit. The semiconductor detector has a first surface and a second surface opposed to each other. The first surface includes pixels (which in turn comprise corresponding pixelated anodes), and the second surface includes a cathode electrode. The collimator includes openings. Each opening is associated with a single corresponding pixelated anode of the semiconductor detector. The processing unit is configured to identify detected events within virtual sub-pixels distributed along a length and width of the semiconductor detector. Each pixel includes (e.g., has associated therewith) a plurality of corresponding virtual sub-pixels. Absorbed photons are counted as events in a corresponding virtual sub-pixel, with absorbed photons counted as events within a thickness of the semiconductor detector at a distance corresponding to one over an absorption coefficient of the detector. 
     In another embodiment, a detector assembly includes a semiconductor detector, a collimator and a processing unit. The semiconductor detector has a first surface and a second surface opposed to each other. The first surface includes pixels (which in turn comprise corresponding pixelated anodes), and the second surface includes a cathode electrode. The collimator includes openings, with each opening associated with a single corresponding pixel of the semiconductor detector. The processing unit is configured to identify detected events within virtual sub-pixels distributed along a length and width of the semiconductor detector. Each pixel includes (e.g., has associated therewith) a plurality of corresponding virtual sub-pixels, with absorbed photons are counted as events in a corresponding virtual sub-pixel. Absorbed photons are counted as events within a thickness of the semiconductor detector at a distance corresponding to an energy window width used to identify the events as photon impacts. 
     In another embodiment, a detector assembly includes a semiconductor detector, a pinhole collimator, and a processing unit. The semiconductor detector has a first surface and a second surface opposed to each other. The first surface includes pixelated anodes, and the second surface comprising a cathode electrode. The pinhole collimator includes an array of pinhole openings corresponding to the pixelated anodes. Each pinhole opening corresponds to a corresponding group of pixelated anodes, wherein an area of each pinhole opening is smaller than a corresponding radiation receiving area of the corresponding group of pixelated anodes. The processing unit is operably coupled to the semiconductor detector and configured to identify detected events from the pixelated anodes. The processing unit is configured to generate a trigger signal responsive to a given detected event in a given pixelated anode, provide the trigger signal to a readout, and, using the readout, read and sum signals arriving from the given pixelated anode and anodes surrounding the given pixelated anode. 
     In another embodiment, a method includes generating, with at least one processor, a trigger signal at a given pixelated anode of a semiconductor detector responsive to an event in the given pixelated anode. The semiconductor has a first surface and second surface opposed to each other. The first surface includes pixelated anodes including the given pixelated anode, and the second surface includes a cathode electrode. Radiation is passed to the semiconductor detector via a pinhole collimator including an array of pinhole openings corresponding to the pixelated anodes. Each pinhole opening corresponds to a corresponding group of pixelated anodes, and an area of each pinhole opening is smaller than a corresponding radiation receiving area of the corresponding group of pixelated anodes. The method also includes, responsive to receiving the trigger signal, reading and summing all signals arriving from the given pixelated anode and anodes surrounding the given pixelated anode to provide a given combined event signal. Further, the method includes, determining if the given combined event signal corresponds to reception of a photon; and, if the given combined event signal corresponds to reception of a photon, counting the event in the given pixelated anode as a true event. 
     In another embodiment, a tangible and non-transitory computer readable medium includes one or more computer software modules configured to direct one or more processors to: generate, with at least one processor, a trigger signal at a given pixelated anode of a semiconductor detector responsive to an event in the given pixelated anode; responsive to receiving the trigger signal, read and sum all signals arriving from the given pixelated anode and anodes surrounding the given pixelated anode to provide a given combined event signal; determine if the given combined event signal corresponds to reception of a photon; and, if the given combined event signal corresponds to reception of a photon, count the event in the given pixelated anode as a true event. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  provides a schematic block view of a detector assembly in accordance with various embodiments. 
         FIG. 2  provides an exploded view of aspects of the detector assembly of  FIG. 1 . 
         FIG. 3  provides a sectional view taken along line  3 - 3  of  FIG. 1 . 
         FIG. 4  illustrates a cross-section of a top plate formed in accordance with various embodiments. 
         FIG. 5  illustrates a cross-section of pinhole collimator septa in accordance with various embodiments. 
         FIG. 6  depicts examples of solid angles corresponding to use of a parallel hole collimator. 
         FIG. 7  is a schematic block diagram of a Nuclear Medicine (NM) imaging system in accordance with various embodiments. 
         FIG. 8  schematically shows parallel viewing angles of virtual sub-pixels in a configuration of detector assembly that is similar to  FIG. 3  but has one layer of virtual sub-pixels in a Z direction. 
         FIG. 9  illustrates a bottom view of a collimator formed in accordance with various embodiments. 
         FIG. 10  illustrates a top view of the collimator of  FIG. 9 . 
         FIG. 11  illustrates a side sectional view of the collimator of  FIG. 9 . 
         FIG. 12  illustrates a detection system formed in accordance with with various embodiments. 
         FIG. 13  illustrates a top view of a detector formed in accordance with accordance with various embodiments. 
         FIG. 14  illustrates a block diagram of processing components formed in accordance with various embodiments. 
         FIG. 15  schematically depicts a swiveling detector in accordance with various embodiments. 
         FIG. 16  schematically depicts a swiveling detector utilizing a conventional parallel-hole collimator. 
         FIG. 17  schematically depicts a system including swiveling detectors detectors in accordance with various embodiments. 
         FIG. 18  schematically depicts a system including swiveling detectors. 
         FIG. 19  provides a flowchart of a method in accordance with various embodiments. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The following detailed description of certain embodiments will be better understood when read in conjunction with the appended drawings. To the extent that the figures illustrate diagrams of the functional blocks of various embodiments, the functional blocks are not necessarily indicative of the division between hardware circuitry. For example, one or more of the functional blocks (e.g., processors or memories) may be implemented in a single piece of hardware (e.g., a general purpose signal processor or a block of random access memory, hard disk, or the like) or multiple pieces of hardware. Similarly, the programs may be stand alone programs, may be incorporated as subroutines in an operating system, may be functions in an installed software package, and the like. It should be understood that the various embodiments are not limited to the arrangements and instrumentality shown in the drawings. 
     As used herein, the terms “system,” “unit,” or “module” may include a hardware and/or software system that operates to perform one or more functions. For example, a module, unit, or system may include a computer processor, controller, or other logic-based device that performs operations based on instructions stored on a tangible and non-transitory computer readable storage medium, such as a computer memory. Alternatively, a module, unit, or system may include a hard-wired device that performs operations based on hard-wired logic of the device. Various modules or units shown in the attached figures may represent the hardware that operates based on software or hardwired instructions, the software that directs hardware to perform the operations, or a combination thereof. 
     “Systems,” “units,” or “modules” may include or represent hardware and associated instructions (e.g., software stored on a tangible and non-transitory computer readable storage medium, such as a computer hard drive, ROM, RAM, or the like) that perform one or more operations described herein. The hardware may include electronic circuits that include and/or are connected to one or more logic-based devices, such as microprocessors, processors, controllers, or the like. These devices may be off-the-shelf devices that are appropriately programmed or instructed to perform operations described herein from the instructions described above. Additionally or alternatively, one or more of these devices may be hard-wired with logic circuits to perform these operations. 
     As used herein, an element or step recited in the singular and preceded with the word “a” or “an” should be understood as not excluding plural of said elements or steps, unless such exclusion is explicitly stated. Furthermore, references to “one embodiment” of are not intended to be interpreted as excluding the existence of additional embodiments that also incorporate the recited features. Moreover, unless explicitly stated to the contrary, embodiments “comprising” or “having” an element or a plurality of elements having a particular property may include additional elements not having that property. 
     Various embodiments provide systems and methods for improving the sensitivity of image acquisition, for example in Nuclear Medicine (NM) imaging applications. Various embodiments provide one or more different approaches for improving sensitivity and/or other aspects of detector performance. For example, in one approach, an array of pinhole openings are used in a collimator for a detector system. As another example, additionally or alternatively, in a second approach, all events are identified as being absorbed at a location and/or within a range corresponding to an absorption coefficient of the detector (e.g., one over the absorption coefficient of the detector). As one more example, in a third approach, all events are identified as being absorbed at a location and/or within a range that ensures that the energy of the events is measured within the energy window used for imaging. It may be noted that each of the three approaches discussed above in this paragraph may be employed with the use of virtual sub-pixels (or virtual division of the detector) along X and Y directions (or along the width and length of the detector). 
     In various embodiments, a pinhole collimator includes an array of pinholes that defines multiples cells. Each cell includes or corresponds to only a single physical pixel of the detector and only a single pinhole of the array. In various embodiments, in contrast to certain conventional approaches, radiation from a given pinhole (also referred to herein as a pinhole opening) only arrives at one particular physical pixel corresponding to the given pinhole. It may be noted that the physical pixel may be viewed as including a number of virtual sub-pixels by a processing unit. Each event detected in the physical pixel is counted as related to one of the virtual sub-pixels into which the physical pixel is divided to. The virtual sub-pixel to which the event belongs to is determined by the location of the event within the physical pixel that includes the virtual sub-pixels. There are known methods to derive the location of the event within the physical pixel, such as the method described in U.S. patent application Ser. No. 15/280,640 entitled “SYSTEMS AND METHODS FOR SUB-PIXEL LOCATION DETERMINATION” filed Sep. 29, 2016. The pinhole collimator provides improved image quality and spatial resolution as is explained below in reference to  FIG. 8 . 
     Further, use of a pinhole array instead of a parallel hole array in various embodiments provides for a smaller area of opening that collects radiation. For example, the size of a pinhole opening may be ⅓ of the width (or 1/9 of the area) of a pixel, whereas an opening of a parallel hole array may be the pixel size less the septa thickness. Accordingly, the opening size in a parallel hole array may be dictated by the pixel size and wall (or septa) thickness; however, in various embodiments employing a pinhole array, the opening size may be selected as desired (e.g., to provide a desired sensitivity and/or collimator height). For example, for the same sensitivity as a parallel hole collimator, an opening size for a pinhole array may be selected to provide a desired height (e.g., ⅓ of the height of a comparable parallel hole array). Additionally, in various embodiments, thicker septa may be used for a pinhole array in comparison to a parallel hole array. In some embodiments, physical pixels may be divided in multiple virtual sub-pixels (e.g., an associated processing unit may assign virtual sub-pixels to each physical pixel) along X and Y directions (or length and width of a detector), while having a single layer in the Z direction (or thickness). Alternatively, in other embodiments, multiple virtual sub-pixels may be employed along the Z direction (or thickness). 
     Accordingly, various embodiments provide flexibility to selected collimator height while maintaining a desired sensitivity, by adjusting the size of the openings of a pinhole array, regardless of pixel size or pitch. Such flexibility is especially advantageous when using a collimator within a swiveling detector head. For example, the collimator height may dictate or influence the radius reserved for each head for swiveling motion. The shorter the collimator is, the smaller is the required radius. Accordingly, for a shorter collimator provided by a pinhole array, more heads may be placed around the object being imaged providing improved sensitivity and image quality in comparison with a taller parallel hole collimator. Additionally, the collimator openings produce solid angles through which the virtual pixels observe the object being imaged, with the smaller size of the pinhole openings providing larger and more separated solid angles for the virtual sub-pixels, with less overlap between the solid angles for the virtual sub-pixels of a physical pixel. Accordingly, the use of such pinhole openings improves spatial resolution, or may be used to maintain a desired resolution with a shorter collimator to increase sensitivity and improve image quality. Further, still, the use of thicker septa or walls helps prevent radiation penetration from a given collimator opening to non-associated pixels (or pixels other than a pixel immediately below the opening), thereby improving image quality. Further still, it may be noted that use of many sub-voxels over the thickness of a detector may reduce the number of events for each volume of interest, thereby increasing statistical noise and degrading image quality. In various embodiments, using only one location (or range) or layer along the Z direction (or thickness) reduces statistical noise and improves image quality. 
     It may be noted that in some embodiments, in connection with sub-pixelization along the X and Y directions, a single Z layer, location, or range may be used to identify events along a thickness of a detector. For example, a Z position-range for all events may be defined at or around an average absorption depth of 1/μ, where μ is the absorption coefficient for a specific photon energy for a particular detector material. For example, events may be distributed linearly, as one example, or exponentially, as another example, within a range centered about or otherwise corresponding to distance of 1/μ from the cathode. As another example, a Z position-range for all events may be defined within a range corresponding to energies of the energy window used for imaging. For example, in some embodiments, an absorption location for each absorbed photon within the thickness of the semiconductor detector is defined within a range such that ΔL/D=ΔE/E, where ΔL is a distance from the cathode, D is the detector thickness, ΔE is an energy window width, and E is a photopeak energy of an absorbed photon. Again, the events may be distributed linearly, as one example, or exponentially, as another example. In various embodiments, use of such Z position-ranges (in contrast, for example, to multiple virtual sub-pixels along a detector thickness) helps to reduce statistical noise and to improve image quality. Also, it may be noted that use of such Z position-ranges may be accomplished with simpler hardwired or software (in comparison to, for example, use of multiple virtual sub-pixels along a detector thickness), providing for easier implementation and/or lower cost. 
     A technical effect provided by various embodiments includes increased sensitivity of a detector system, such as a NM imaging detector system. The detector system may be provided in a rotating head detector module that may be used as part of a group of similar rotating head detector modules in an imaging system. A technical effect of various embodiments includes improved image quality and spatial resolution. A technical effect of various embodiments includes reduced collimator height allowing for less room needed to allow a detector head to pivot, allowing more detector heads to be placed closely to an object being imaged. A technical effect of various embodiments includes reduced penetration by radiation to pixels other than a pixel associated with (e.g., located directly below) a collimator opening. A technical effect of various embodiments included reduced statistical noise. 
       FIG. 1  provides a schematic block view of a detector assembly  100  in accordance with various embodiments,  FIG. 2  provides an exploded view of aspects of the detector assembly  100 , and  FIG. 3  provides a sectional view taken along line  3 - 3  of  FIG. 1 . As seen in  FIGS. 1-3 , the detector assembly  100  includes a semiconductor detector  110 , a pinhole collimator  130 , and a processing unit  150 , which for the clarity of the drawings is shown only in  FIG. 1 . Generally, the semiconductor detector  110  produces signals in response to absorption events (e.g., photons produced in response to a radiopharmaceutical that has been administered to an object being imaged that impact the semiconductor detector  110 ). The signals are provided to the processing unit  150 , which uses identified events to reconstruct an image of the object being imaged and to derive the location of the event inside the physical pixel as described, for example in U.S. patent application Ser. No. 15/280,640. The pinhole collimator  130  guides photons to the semiconductor detector  110 , and limits the angular range of approach of photons to a given pixel or portion of the semiconductor detector  110 , helping to allow for accurate determination of the portion of the object being imaged from which a given detected event originated. 
     As best seen in  FIG. 3 , the semiconductor detector  110  has a first surface  112  and a second surface  114 . The second surface  114  is opposed to the first surface  112  (and, likewise, the first surface  112  is opposed to the second surface  114 ). The semiconductor detector  110  is configured to generate electrical signal in response to photon impacts, and may be made of, for example, Cadmium Zinc Telluride (CZT). The second surface  114  includes pixelated anodes  116  disposed thereon, and the first surface  112  includes a cathode electrode  118  disposed thereon. In some embodiments, the cathode electrode  118  may be a monolithic, or single, cathode. The cathode electrode  118  collects an opposite electrical charge of the pixelated anodes  116 , and the pixelated anodes  116  are used to generate signals in response to charges generated by the semiconductor detector  110  responsive to photon impacts. The pixelated anodes  116  may be arranged in a grid, with the location of one or more pixelated anodes  116  at which a signal is generated responsive to a photon impact used to determine a corresponding location in the object corresponding to the photon impact. 
     As seen in  FIGS. 1-3 , the pinhole collimator  130  is interposed between the semiconductor detector  110  and an object being imaged (not shown), and is used to control passage of radiation from the object being imaged to the semiconductor detector  110  via the pinhole collimator  130 . For example, the pinhole collimator  130  guides photons to the semiconductor detector  110 , limiting an angular range of approach for photons that impact the semiconductor detector  110 . The pinhole collimator  130  includes an array  132  of pinhole openings  134  corresponding to the pixelated anodes  116  on the second surface  114 . In the illustrated embodiment, the array  132  of pinhole openings  134  has a 1:1 correspondence with an array or grid of pixelated anodes  116 , with both the pixelated anodes  116  and array  132  of pinhole openings  134  arranged in an 8×8 layout when the projections of openings  132  on the second surface  114  of the detector  110  are centered in the pixelated anodes  116 . Accordingly, in the illustrated embodiment, each pinhole opening  134  is associated with a single pixelated anode  116  of the semiconductor detector  110 . Accordingly, radiation that passes through a given pinhole opening  134  is confined within a single cell of collimator  130  and is absorbed at a location corresponding to one and only one pixelated anode  116  that is associated with the given pinhole opening  134  (e.g., located directly beneath the pinhole opening  134 ). Further, each pinhole opening  134  defines an area, with the area of each pinhole opening  134  smaller than a corresponding area of the corresponding pixelated anode  116 . For example, as seen in  FIG. 3 , the width of each pixelated anode  116  is greater than the width of a corresponding pinhole opening  134 . Accordingly, if the pixelated anode  116  and pinhole opening  134  are generally square-shaped, the area of the pixelated anode  116  is greater than the area of the pinhole opening  134 . It may be noted that the depicted examples have generally square-shaped cross-sections. Other shapes of opening (e.g., circular, rectangular, or triangular, among others), may be utilized in alternate embodiments. 
     As best seen in  FIGS. 1 and 3 , in various embodiments the pinhole collimator  130  includes a top plate  140  through which the pinhole openings  134  pass. The top plate  140  is mounted to a collimator base  131 . The pinhole collimator  130  also includes plural septa  142  (or walls) extending along a height of the collimator base  131  that define collimator cells  144  corresponding to the pinhole openings  134 . In the illustrated embodiment, each pinhole opening  134  is associated with a particular collimator cell  144  and a particular pixelated anode  116 , with photons that pass through the pinhole opening  134  passing through the corresponding collimator cell  144  toward the corresponding pixelated anode  116 . Each collimator cell  144  defines a cavity between the corresponding pinhole opening  134  and the corresponding pixelated anode  116 . The septa  142  act to reduce or eliminate passage of a photon through a pinhole opening  134  to non-corresponding pixelated anodes (e.g., pixelated anodes adjacent to the particular pixelated anode that corresponds to the particular pinhole opening). A cell width  148  defined by the septa  142  (e.g., a width between neighboring septa  142 ) is greater than an opening width  146  defined by the pinhole openings  134 . For example, in some embodiments, the cell width  148  is 3 times or more greater than the opening width  146 . In the example illustrated in  FIGS. 1 to 3 , the cell width  148  is d, and the opening width  146  is d/3, or the cell width  148  is 3 times greater than the opening width  146 . It may be noted that, in contrast, an opening width and width between neighboring walls may be identical for a parallel-hole collimator. 
     In the example illustrated in  FIGS. 1 to 3 , the septa  142  are parallel to each other and define square-shaped cross sections for each collimator cell  144 ; however, it may be noted that different configurations may be employed in alternate embodiments. As best seen in  FIGS. 2 and 3 , the top plate  140  has a thickness  141 , and the septa  142  have a thickness  143 . In the depicted example, the thickness  141  of the top plate  140  is greater than the thickness  143  of the septa  142 . In the example illustrated in  FIGS. 1 to 3 , the septa  142  are parallel to each other and define square-shaped cross sections for each collimator cell  144 ; however, it may be noted that different configurations may be employed in alternate embodiments. 
       FIG. 4  illustrates a cross-section of an example embodiment of a top plate  400  (e.g., which may be used as top plate  140 ) that may be used with pinhole collimator  130  in various embodiments. The top plate  400  includes a first surface  402  configured to be positioned proximate a semiconductor detector (e.g., semiconductor detector  110 ), or oriented toward an interior  410  of a collimator (e.g., pinhole collimator  130 ) including the top plate  400 . The top plate  400  also includes a second surface  404  that is opposed to the first surface  402 . The second surface  404  is farther away from the semiconductor detector than the first surface  402  is, or the second surface  404  is oriented toward an object  420  being imaged from which photons  422  are emitted. The top plate  400  includes pinhole openings  430  through which photons  422  pass toward the semiconductor detector. The depicted pinhole openings  430  each have a first width  432  at the first surface  402 , and a second width  434  at the second surface  404 . The first width  432  is greater than the second width  434 . Accordingly, the pinhole openings  430  are tapered, and are larger at the first surface  402  than at the second surface  404 . It may be noted that the taper orientation of the openings  430  in the plate  400  of  FIG. 4  is opposite to the taper orientation of the openings  134  in the plate  140  of  FIGS. 1-3 . The tapered shape in various embodiments is configured to facilitate passage of photons over a preferred or desired angular range. 
     Alternatively or additionally, it may be noted that pinhole collimators in various embodiments may include tapered walls.  FIG. 5  illustrates a cross-section of an example embodiment of pinhole collimator septa  500  that may be used with pinhole collimator  130  in various embodiments. Septa  500  include a first surface  502  proximate to a top plate (e.g., top plate  141 , top plate  400 ; top plate not shown in  FIG. 5 ), and a second surface  504  proximate to a semiconductor detector (e.g., semiconductor detector  110 ; semiconductor detector not shown in  FIG. 5 ). Cells  506 , through which photons pass, are defined between neighboring septa  500 . The cells  506  are a first width  512  at the first surface  502 , and a second width  514  at the second surface  504 , with the second width  514  greater than the first width  512 . Accordingly, a first width  503  of the septa  500  at the first surface  502  is greater than a second width  505  of the septa  500  at the second surface  504 . In the illustrated embodiment, a pitch  530  is defined by the septa  500 , with the first width  512  less than the pitch  530 . The tapered septa  500  in various embodiments may cooperate or be complementary with tapered openings (e.g., openings  434 ). In various embodiments, the tapered septa  500  may be formed by 3D printing a collimator block. The tapered septa  500  provide additional thickness (e.g., relative to septa thickness of a parallel hole collimator) for improved reduction of penetration by photons into adjacent collimator cells. The tapered shape in various embodiments is configured to facilitate passage of photons over a preferred or desired angular range. It may be noted that while the description above includes top plate  141  or  400 , the pinholes-array collimator of  FIG. 5  may not include a top plate at all when opening  512  is in the desired size of the pinholes openings such as the size of openings  134  and  434  of  FIGS. 4 and 1-3 , respectively. 
     It may be noted that use of pinhole collimation (e.g., using pinhole collimator  130 ) in various embodiments provides for reduced overlap of solid angles defined by virtual sub-pixels, thereby providing for greater independence of equations defined by the virtual sub-pixels and improved imaging by improving spatial-resolution. For example, in some embodiments, solid viewing angles defined by virtual sub-pixels  117  via corresponding pinhole openings  134  have less overlapping than solid viewing angles defined by identical virtual sub-pixels via a parallel hole collimator having a sensitivity equal to a sensitivity of the pinhole collimator  130 . 
     Examples of solid angles corresponding to the pinhole collimator  130  may be seen in  FIG. 3 . As seen in  FIG. 3 , the solid angles defined by virtual sub-pixels may vary based on a depth (or depths) within the semiconductor detector  110  assigned to events. For example, solid angles  320   a ,  320   b , and  320   c  result from using a common absorption depth (e.g., 1/μ, where μ is an abortion coefficient) for events from three adjacent virtual sub-pixels  117 . As another example, solid angles  330   a ,  330   b , and  330   c  result from using varying absorption depths for events from three adjacent virtual sub-pixels  117 . In  FIG. 3 , the cell width  148  between septa  142  of the pinhole collimator equals d, a height  149  of the pinhole collimator  130  is h/3, and the opening width  146  defined by the pinhole openings  134  is d/3. 
     By way of comparison, examples of solid angles corresponding to use of a parallel hole collimator may be seen in  FIG. 6 . In  FIG. 6 , a detector system  600  includes a parallel hole collimator  602  that includes walls  610  having a common opening width  612  therebetween. The opening width  612  defines the width of openings  620 . The detector system  600  also includes a detector unit  621  that includes pixelated anodes  616  having virtual sub-pixels  617  associated therewith (e.g., by a processing unit). As seen in  FIG. 6 , solid angles  660   a ,  660   b , and  660   c  result from using a common absorption depth (e.g., at the surface of the detector unit  621 ) for events from three adjacent virtual sub-pixels  617 . As seen in  FIGS. 3 and 6 , the solid angles (solid angles  320   a ,  320   b , and  320   c  and/or solid angles  330   a ,  330   b , and  330   c ) for the pinhole collimator  130  have noticeably less overlap than the solid angles for parallel hole collimator  602  (solid angles  660   a ,  660   b , and  660   c ). In  FIG. 6 , the width  612  between walls (as well as width of openings  620 ) is d, and the height  652  of the parallel hole collimator  602  is h. 
     It may be noted that the sensitivity of a detector system using a collimator corresponds to an aspect ratio defined by the ratio of the width of a collimator opening to the height of the collimator. Accordingly, for the example embodiment illustrated in  FIG. 3 , the aspect ratio is (d/3)/(h/3), or d/h. Similarly for the parallel hole example of  FIG. 6 , the aspect ratio is d/h. Accordingly, the collimators of  FIG. 6  and  FIG. 3  have identical aspect ratios and provide similar sensitivities; however, the collimator of  FIG. 3  has a much shorter height (⅓ of the height of the collimator of  FIG. 6 ). The pinhole collimator  130  in various embodiments accordingly provides various benefits when compared to conventional parallel hole collimator arrangements. For example, as discussed herein, the pinhole collimator  130  provides solid viewing angles that are more tilted and have less overlap than solid viewing angles of a parallel hole collimator, thereby providing better information for reconstruction of an image and resulting in improved spatial resolution. The improved spatial resolution capabilities in some embodiments may be used to improve sensitivity while maintaining a same or similar spatial resolution. Also, shorter collimator height allows for a more compact detector head, allowing for more detector heads to be used, to provide greater ranges of movement (e.g., rotation) of detector heads, and to reduce or eliminate collisions or interference between neighboring detector heads. 
     Returning to  FIGS. 1-3 , the processing unit  150  is operably coupled to the semiconductor detector  110 , and is configured to identify detected events, deriving the location of events within physical pixels  119  and based on their location, assigning them to virtual sub-pixels  117  distributed along a length  190  and width  191  of the semiconductor detector  110  to be counted there. In  FIG. 3 , the virtual sub-pixels  117  are represented by dashed lines passing through the semiconductor detector corresponding to the location of the virtual sub-pixels  117 . It may be noted that in the illustrated embodiment, the semiconductor detector  110  includes pixels  119 . In  FIG. 3 , there are 3 virtual sub-pixels across a width of each pixel  119 . Each pixel  119  may be understood as including a pixelated anode  116 , with each pixelated anode  116  smaller (having a smaller area) than the corresponding pixel  119 . In the illustrated embodiment, there are 9 virtual sub-pixels  117  per pixelated anode  116  or pixel  119  (e.g., a grid of 3×3 virtual sub-pixels  117  per pixelated anode  116  or pixel  119 ). Each pixel  119  includes a plurality of corresponding virtual sub-pixels, with absorbed photons in the semiconductor detector  110  counted as events in a corresponding virtual sub-pixel. Additional discussion regarding virtual sub-pixels and the use of virtual sub-pixels, and the use of collected and non-collected charge signals may be found in U.S. patent application Ser. No. 14/724,022, entitled “Systems and Method for Charge-Sharing Identification and Correction Using a Single Pixel,” filed 28 May 2015 (“the 022 Application); U.S. patent application Ser. No. 15/280,640, entitled “Systems and Methods for Sub-Pixel Location Determination,” filed 29Sep. 2016 (“the 640 Application”); and U.S. patent application Ser. No. 14/627,436, entitled “Systems and Methods for Improving Energy Resolution by Sub-Pixel Energy Calibration,” filed 20 Feb. 2015 (“the 436 Application). The subject matter of each of the 022 Application, the 640 Application, and the 436 Application are incorporated by reference in its entirety. 
     In various embodiments the processing unit  150  includes processing circuitry configured to perform one or more tasks, functions, or steps discussed herein. It may be noted that “processing unit” as used herein is not intended to necessarily be limited to a single processor or computer. For example, the processing unit  150  may include multiple processors, ASIC&#39;s, FPGA&#39;s, and/or computers, which may be integrated in a common housing or unit, or which may distributed among various units or housings. It may be noted that operations performed by the processing unit  150  (e.g., operations corresponding to process flows or methods discussed herein, or aspects thereof) may be sufficiently complex that the operations may not be performed by a human being within a reasonable time period. For example, the determination of values of collected, non-collected, and/or combined charge signals within the time constraints associated with such signals may rely on or utilize computations that may not be completed by a person within a reasonable time period. 
     As discussed, herein, signals are generated by one or more pixelated anodes  116  in response to a photon impact, with the location of the pixelated anode(s)  116  generating a signal used to determine a corresponding location in the object for which an event is counted. In various embodiments, as also discussed in the 022 Application, the 640 Application, and the 436 Application, signals from adjacent pixels may be used to assign a virtual sub-pixel location within a given pixelated anode  116 . In some embodiments, the processing unit  150  is configured to determine an absorption location for a given absorbed phone based on non-collected signals received from pixelated anodes adjacent to a pixelated anode absorbing the given absorbed photon. 
     Additionally or alternatively to the use of virtual pixels along a length and/or width of the semiconductor detector  110 , in various embodiments virtual pixels may be employed along a thickness of the semiconductor detector  110 . Virtual pixels employed along a thickness of the semiconductor detector  110  may be used to represent different depths of absorption of photons. For example, in various embodiments, as best seen in  FIG. 3 , the semiconductor detector  110  has a thickness  396 . Three rows of virtual pixels are distributed along the thickness  396 —a first row  390 , a second row  392 , and a third row  394 . The processing unit  150  in various embodiments is configured to identify detector events with the virtual sub-pixels in the first row  390 , second row  392 , and third row  394  distributed along the thickness  396 . Accordingly, in various embodiments, different virtual sub-pixels along a thickness may be used to provide different absorption depths for identifying event locations. For example, as seen in  FIG. 3 , event  331   a  is shown at a depth corresponding to the first row  390 , event  331   b  is shown at a depth corresponding to the third row  394 , and event  331   c  is shown at a depth corresponding to the second row  392 . 
     However, it may be noted that, in other embodiments that may or may not include a pinhole-array collimator, a single absorption depth may be employed. For example, in some embodiments, the processing unit  150  is configured to count absorbed photons as events within the thickness  396  of the semiconductor detector  110  at a location (e.g., a distance from the cathode  118 ) corresponding to one over an absorption coefficient of the semiconductor detector  110 . For example, with u as the absorption coefficient, photons (e.g., photons at a given energy corresponding with the absorption coefficient) may be counted as events at a location in the semiconductor detector a distance  395  from the second surface  112  (and/or cathode  118 ) along the thickness  396 , as shown for event locations  321   a ,  321   b , and  321   c  of  FIG. 3 . The distance  395  in various embodiments is 1/μ. It may be noted that μ may vary based on photon energy. It may further be noted that use of a single absorption depth as discussed herein and in the next paragraph may be used in connection with a pinhole collimator (e.g., pinhole collimator  130 ) in various embodiments, or may be used in connection with a parallel hole collimator (e.g., parallel hole collimator  602 ) in other embodiments. In some embodiments, the absorption location for each photon is defined within a range of 1/μ±1 millimeter. 
     As another example of use of a single absorption depth, in some embodiments, the processing unit  150  is configured to count absorbed photons as events within the thickness  396  of the semiconductor detector  110  at a distance corresponding to an energy window width used to identify the events as photon impacts. For example, in some embodiments, an absorption location for each absorbed photon within the thickness  396  of the semiconductor detector  110  is defined within a range such that ΔL/D=ΔE/E, where ΔL is the distance  395  from the first surface  112  (and/or the cathode  118 ), D is the detector thickness (e.g., thickness  396 ), ΔE is an energy window width, and E is a photopeak energy of an absorbed photon. The energy window width in various embodiments is a range of energies around the photopeak energy which are considered as true events. 
       FIG. 7  is a schematic illustration of a NM imaging system  1000  having a plurality of imaging detector head assemblies mounted on a gantry (which may be mounted, for example, in rows, in an iris shape, or other configurations, such as a configuration in which the movable detector carriers  1016  are aligned radially toward the patient-body  1010 ). In particular, a plurality of imaging detectors  1002  are mounted to a gantry  1004 . Each detector  1002  may include, for example, collimators and detectors arranged generally similarly to the arrangements discussed in connection with  FIGS. 1-6  and/or  FIGS. 9-19 . In the illustrated embodiment, the imaging detectors  1002  are configured as two separate detector arrays  1006  and  1008  coupled to the gantry  1004  above and below a subject  1010  (e.g., a patient), as viewed in  FIG. 7 . The detector arrays  1006  and  1008  may be coupled directly to the gantry  1004 , or may be coupled via support members  1012  to the gantry  1004  to allow movement of the entire arrays  1006  and/or  1008  relative to the gantry  1004  (e.g., transverse translating movement in the left or right direction as viewed by arrow T in  FIG. 7 ). Additionally, each of the imaging detectors  1002  includes a detector unit  1014  (which may include collimator and/or detector assemblies as discussed herein in connection with  FIGS. 1-6 ), at least some of which are mounted to a movable detector carrier  1016  (e.g., a support arm or actuator that may be driven by a motor to cause movement thereof) that extends from the gantry  1004 . In some embodiments, the detector carriers  1016  allow movement of the detector units  1014  towards and away from the subject  1010 , such as linearly. Thus, in the illustrated embodiment the detector arrays  1006  and  1008  are mounted in parallel above and below the subject  1010  and allow linear movement of the detector units  1014  in one direction (indicated by the arrow L), illustrated as perpendicular to the support member  1012  (that are coupled generally horizontally on the gantry  1004 ). However, other configurations and orientations are possible as described herein. It should be noted that the movable detector carrier  1016  may be any type of support that allows movement of the detector units  1014  relative to the support member  1012  and/or gantry  1004 , which in various embodiments allows the detector units  1014  to move linearly towards and away from the support member  1012 . 
     Each of the imaging detectors  1002  in various embodiments is smaller than a conventional whole body or general purpose imaging detector. A conventional imaging detector may be large enough to image most or all of a width of a patient&#39;s body at one time and may have a diameter or a larger dimension of approximately 50 cm or more. In contrast, each of the imaging detectors  1002  may include one or more detector units  1014  coupled to a respective detector carrier  1016  and having dimensions of, for example, 4 cm to 20 cm and may be formed of Cadmium Zinc Telluride (CZT) tiles or modules. For example, each of the detector units  1014  may be 8×8 cm in size and be composed of a plurality of CZT pixelated modules (not shown). For example, each module may be 4×4 cm in size and have 16×16=256 pixels. In some embodiments, each detector unit  1014  includes a plurality of modules, such as an array of 1×7 modules. However, different configurations and array sizes are contemplated including, for example, detector units  1014  having multiple rows of modules. 
     It should be understood that the imaging detectors  1002  may be different sizes and/or shapes with respect to each other, such as square, rectangular, circular or other shape. An actual field of view (FOV) of each of the imaging detectors  1002  may be directly proportional to the size and shape of the respective imaging detector. 
     The gantry  1004  may be formed with an aperture  1018  (e.g., opening or bore) therethrough as illustrated. A patient table  1020 , such as a patient bed, is configured with a support mechanism (not shown) to support and carry the subject  1010  in one or more of a plurality of viewing positions within the aperture  1018  and relative to the imaging detectors  1002 . Alternatively, the gantry  1004  may comprise a plurality of gantry segments (not shown), each of which may independently move a support member  1012  or one or more of the imaging detectors  1002 . 
     The gantry  1004  may also be configured in other shapes, such as a “C”, “H” and “L”, for example, and may be rotatable about the subject  1010 . For example, the gantry  1004  may be formed as a closed ring or circle, or as an open arc or arch which allows the subject  1010  to be easily accessed while imaging and facilitates loading and unloading of the subject  1010 , as well as reducing claustrophobia in some subjects  1010 . 
     Additional imaging detectors (not shown) may be positioned to form rows of detector arrays or an arc or ring around the subject  1010 . By positioning multiple imaging detectors  1002  at multiple positions with respect to the subject  1010 , such as along an imaging axis (e.g., head to toe direction of the subject  1010 ) image data specific for a larger FOV may be acquired more quickly. 
     Each of the imaging detectors  1002  has a radiation detection face, which is directed towards the subject  1010  or a region of interest within the subject. 
     In various embodiments, multi-bore collimators may be constructed to be registered with pixels of the detector units  1014 , which in one embodiment are CZT detectors. However, other materials may be used. Registered collimation may improve spatial resolution by forcing photons going through one bore to be collected primarily by one pixel. Additionally, registered collimation may improve sensitivity and energy response of pixelated detectors as detector area near the edges of a pixel or in-between two adjacent pixels may have reduced sensitivity or decreased energy resolution or other performance degradation. Having collimator septa directly above the edges of pixels reduces the chance of a photon impinging at these degraded-performance locations, without decreasing the overall probability of a photon passing through the collimator. As discussed herein, in various embodiments parallel-hole and/or pin-hole collimation may be employed. 
     A controller unit  1030  may control the movement and positioning of the patient table  1020 , imaging detectors  1002  (which may be configured as one or more arms), gantry  1004  and/or the collimators  1022  (that move with the imaging detectors  1002  in various embodiments, being coupled thereto). A range of motion before or during an acquisition, or between different image acquisitions, is set to maintain the actual FOV of each of the imaging detectors  1002  directed, for example, towards or “aimed at” a particular area or region of the subject  1010  or along the entire subject  1010 . The motion may be a combined or complex motion in multiple directions simultaneously, concurrently, or sequentially as described in more detail herein. 
     The controller unit  1030  may have a gantry motor controller  1032 , table controller  1034 , detector controller  1036 , pivot controller  1038 , and collimator controller  1040 . The controllers  1030 ,  1032 ,  1034 ,  1036 ,  1038 ,  1040  may be automatically commanded by a processing unit  1050 , manually controlled by an operator, or a combination thereof. The gantry motor controller  1032  may move the imaging detectors  1002  with respect to the subject  1010 , for example, individually, in segments or subsets, or simultaneously in a fixed relationship to one another. For example, in some embodiments, the gantry controller  1032  may cause the imaging detectors  1002  and/or support members  1012  to move relative to or rotate about the subject  1010 , which may include motion of less than or up to 180 degrees (or more). 
     The table controller  1034  may move the patient table  1020  to position the subject  1010  relative to the imaging detectors  1002 . The patient table  1020  may be moved in up-down directions, in-out directions, and right-left directions, for example. The detector controller  1036  may control movement of each of the imaging detectors  1002  to move together as a group or individually as described in more detail herein. The detector controller  1036  also may control movement of the imaging detectors  1002  in some embodiments to move closer to and farther from a surface of the subject  1010 , such as by controlling translating movement of the detector carriers  1016  linearly towards or away from the subject  1010  (e.g., sliding or telescoping movement). Optionally, the detector controller  1036  may control movement of the detector carriers  1016  to allow movement of the detector array  1006  or  1008 . For example, the detector controller  1036  may control lateral movement of the detector carriers  1016  illustrated by the T arrow (and shown as left and right as viewed in  FIG. 7 ). In various embodiments, the detector controller  1036  may control the detector carriers  1016  or the support members  1012  to move in different lateral directions. Detector controller  1036  may control the swiveling motion of detectors  1002  together with their collimators  1022 . 
     The pivot controller  1038  may control pivoting or rotating movement of the detector units  1014  at ends of the detector carriers  1016  and/or pivoting or rotating movement of the detector carrier  1016 . For example, one or more of the detector units  1014  or detector carriers  1016  may be rotated about at least one axis to view the subject  1010  from a plurality of angular orientations to acquire, for example, 3D image data in a 3D SPECT or 3D imaging mode of operation. The collimator controller  1040  may adjust a position of an adjustable collimator, such as a collimator with adjustable strips (or vanes) or adjustable pinhole(s). 
     It should be noted that motion of one or more imaging detectors  1002  may be in directions other than strictly axially or radially, and motions in several motion directions may be used in various embodiment. Therefore, the term “motion controller” may be used to indicate a collective name for all motion controllers. It should be noted that the various controllers may be combined, for example, the detector controller  1036  and pivot controller  1038  may be combined to provide the different movements described herein. 
     Prior to acquiring an image of the subject  1010  or a portion of the subject  1010 , the imaging detectors  1002 , gantry  1004 , patient table  1020  and/or collimators  1022  may be adjusted, such as to first or initial imaging positions, as well as subsequent imaging positions. The imaging detectors  1002  may each be positioned to image a portion of the subject  1010 . Alternatively, for example in a case of a small size subject  1010 , one or more of the imaging detectors  1002  may not be used to acquire data, such as the imaging detectors  1002  at ends of the detector arrays  1006  and  1008 , which as illustrated in  FIG. 7  are in a retracted position away from the subject  1010 . Positioning may be accomplished manually by the operator and/or automatically, which may include using, for example, image information such as other images acquired before the current acquisition, such as by another imaging modality such as X-ray Computed Tomography (CT), MRI, X-Ray, PET or ultrasound. In some embodiments, the additional information for positioning, such as the other images, may be acquired by the same system, such as in a hybrid system (e.g., a SPECT/CT system). Additionally, the detector units  1014  may be configured to acquire non-NM data, such as x-ray CT data. In some embodiments, a multi-modality imaging system may be provided, for example, to allow performing NM or SPECT imaging, as well as x-ray CT imaging, which may include a dual-modality or gantry design as described in more detail herein. 
     After the imaging detectors  1002 , gantry  1004 , patient table  1020 , and/or collimators  1022  are positioned, one or more images, such as three-dimensional (3D) SPECT images are acquired using one or more of the imaging detectors  1002 , which may include using a combined motion that reduces or minimizes spacing between detector units  1014 . The image data acquired by each imaging detector  1002  may be combined and reconstructed into a composite image or 3D images in various embodiments. 
     In one embodiment, at least one of detector arrays  1006  and/or  1008 , gantry  1004 , patient table  1020 , and/or collimators  1022  are moved after being initially positioned, which includes individual movement of one or more of the detector units  1014  (e.g., combined lateral and pivoting movement) together with the swiveling motion of detectors  1002 . For example, at least one of detector arrays  1006  and/or  1008  may be moved laterally while pivoted. Thus, in various embodiments, a plurality of small sized detectors, such as the detector units  1014  may be used for 3D imaging, such as when moving or sweeping the detector units  1014  in combination with other movements. 
     In various embodiments, a data acquisition system (DAS)  1060  receives electrical signal data produced by the imaging detectors  1002  and converts this data into digital signals for subsequent processing. However, in various embodiments, digital signals are generated by the imaging detectors  1002 . An image reconstruction device  1062  (which may be a processing device or computer) and a data storage device  1064  may be provided in addition to the processing unit  1050 . It should be noted that one or more functions related to one or more of data acquisition, motion control, data processing and image reconstruction may be accomplished through hardware, software and/or by shared processing resources, which may be located within or near the imaging system  1000 , or may be located remotely. Additionally, a user input device  1066  may be provided to receive user inputs (e.g., control commands), as well as a display  1068  for displaying images. DAS  1060  receives the acquired images from detectors  1002  together with the corresponding lateral, vertical, rotational and swiveling coordinates of gantry  1004 , support members  1012 , detector units  1014 , detector carriers  1016 , and detectors  1002  for accurate reconstruction of an image including 3D images and their slices. 
       FIG. 8  illustrates a detector assembly that is similar to the detector assembly illustrated by  FIG. 3  with the exception that the virtual sub-pixels of  FIG. 8  are arranged in one layer along a Z direction. In addition to  FIG. 3 ,  FIG. 8  specifically refers to collimator cells  2000 , with each collimator cell confining a single pixel  119  (and corresponding pixelated anode  116 ), and includes a single pinhole  134 . Each physical pixel  119  has size P that is equal to the pitch of the pixels  116 , pinholes  134  and cells  2000 . Each pixel  119  is divided into multiple virtual sub-pixels  2002 .  FIG. 8  shows viewing angles  2004  as observed from virtual sub-pixels  2002  via pinholes  134  to the object being imaged (not shown). Each viewing angle  2004  belong to a different cell  2000 . In each cell  2000 , the relative position between each virtual pixel  2002  corresponding to viewing angle  2004  and pinhole  134  is the same. Accordingly all the viewing angles  2004  form the same angle ϕ with the first surface  112  and thus, are parallel to each other and are displaced from each other by a distance that is equal to the pitch of pixels  119  and pinholes  134 . 
     The discussion about the system (detector assembly  100 ) spatial-resolution will be divided into two steps: The first step analyzes the system spatial-resolution for a single cell  2000  and the second step analyzes the system-spatial resolution for an array of multiple cells  2000  closely packed and butted together into a matrix of cells (collimator  130 ) that each of them includes a single pinhole  134  and confines a single pixels  116 . 
     System Spatial-Resolution for a Single Cell  2000 : 
     For a single cell  2000 , the system spatial-resolution is given by: 
                     R   s     =             (     R   c     )     2     +       (       r   i     ·   M     )     2         =           (       (     d   /   3     )     ·       (       h   /   s     +   b     )       h   /   3         )     2     +       (       r   i     ·     b     h   /   3         )     2                   Equation   ⁢           ⁢     (   1   )                 
When R s  is the system spatial-resolution, R c  is the collimator (cell  2000 ) spatial-resolution, d is distance  148  between the walls of cells  2000 , d/3 is the opening size of pinhole  134 , h/3 is the the height of collimator  130 , b is the distance from collimator  130  to the object being imaged (not shown), r i  is the intrinsic resolution of virtual sub-pixels  2002  and is equal to the size of virtual sub-pixels  2002 , and M is the magnification of cell  2000  in collimator  130  and M=b/(h/3)
 
     System Spatial-Resolution for an Array of Cells  2000 : 
     As explained above for collimator  130  including multiple cells  2000 , parallel viewing angles  2004  are displaced from each other by a distance P, which defines the intrinsic resolution in parallel collimation. 
     Accordingly, for an array of cells  2000 , the system spatial-resolution is given by: 
     
       
         
           
             
               
                 
                   
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                   ⁢ 
                   
                       
                   
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     Accordingly, the system spatial-resolution is the smaller value derived either from Equation (1) or Equation (2). 
     For conventional pinhole collimator, the mathematical term r i *M in Equation (1), which represent the contribution of the intrinsic resolution of the detector to the system spatial-resolution, is replaced by the mathematical term P×M, where P is the physical size of pixels  119  that is also equal to the pitch between the physical pixels  119 . According to  FIG. 8 , each cell  2000  having a single opening  134  above a single physical pixel  119 . The pitch P between the physical pixels  119  is equal to the pitch between pinholes  134  corresponding to adjacent cells  2000  in the array of cells  2000  in collimator  130 , with each cell  2000  above a single physical pixel  119 . Physical pixels  119  have size P and include multiple virtual sub-pixels  2002  having size r i . Accordingly, P»r i  and the system spatial resolution according to the invention is better than that of a conventional pinhole collimator. 
     The magnification M=b/(h/3) that appears in Equation (1) is the ratio between the distance b from the collimator to the imaged object and the collimator height (h/3). For large distances b of the object being imaged from the collimator, M is large. Accordingly, the value of the system spatial-resolution according to Equation (1) may be larger than the one according to Equation (2), and then the system spatial-resolution is determined by Equation (2). For short distances b of the object being imaged from the collimator, M is small, and, accordingly, the value of the system spatial-resolution according to Equation (1) may be smaller than the one according to Equation (2) and then the system spatial-resolution is determined by Equation (1). 
     This means that unlike conventional pinhole collimator having a pinhole above multiple physical pixels, the system spatial-resolution of pinhole collimator  130  in accordance with various embodiments herein is the smaller of the system spatial-resolution as derived either by Equations (1) or (2). 
     In general, for system spatial-resolution R S , collimator spatial-resolution R c , height h of collimator  130 , distance b of the object being imaged from collimator  130 , opening d of pinhole  134 , size r i  of virtual sub-pixel  2002 , and size and pitch P of physical pixel  119 , the condition in the paragraph above can be formulated as follows:
 
 R   S =√{square root over (( R   C ) 2 +( C ) 2 )}  Equation (3)
 
When C gets the smaller value of either:
 
             (     n   ·     b   h       )         
or P
 
     It can be seen that various embodiments have superior system spatial-resolution, relative to conventional pinhole collimator, for the following reasons: (1) The virtual sub-pixels  2002  have smaller size than the physical pixels  119 . (2) The system spatial resolution is the smaller of the one derived either from Equations (1) or (2). 
     When the object being imaged is close to collimator  130 , the term r i ×M is smaller than P. For this situation, the system spatial-resolution according to various embodiments is better than this of a parallel hole collimator. When the object being imaged is far from the collimator, P is smaller than the term r i ×M. For this situation, the system spatial-resolution according to the embodiments of the invention is better than this of a conventional pinhole collimator. Thereby the embodiments of the invention provide better image quality and spatial resolution than both, parallel-holes collimator and pinholes collimator. 
     Various embodiments discussed above have included the use of virtual sub-pixels. It may be noted that, in other embodiments, physical, real, or actual sub-pixellization may be employed. Physical sub-pixels, as used herein, may be understood as individual pixelated anodes of a radiation detector that are grouped together into multiple groups, and each group of pixelated anodes shares a common collimator opening in a configuration where each group of the groups of the pixelated anodes receives radiation via a corresponding single and only one collimator opening. It may be noted that, when physical sub-pixels are used, charge-sharing effects may be significant. Accordingly, various embodiments discussed herein provide charge-sharing recovery. 
       FIGS. 9-14  depict various aspects of a detector assembly  1390  (illustrated by  FIG. 12 ) in accordance with various embodiments. The detector assembly  1390  is generally similar in various respects to the detector assembly  100  discussed in connection with  FIGS. 1-5 , and may utilize various components or aspects discussed in connection with the detector assembly  100  (e.g., a similar collimator), but uses physical sub-pixels instead of virtual sub-pixels. Generally, the detector assembly  1390  includes a semiconductor detector  1312 , a pinhole collimator  1300 , and a processing unit  1410  (schematically shown as electrically connected to pixels  1308 ). Radiation emitted from an object being detected passes through the pinhole collimator  1300  and is received by the semiconductor detector  1312 , which generates signals responsive to the received radiation. The signals are provided to the processing unit  1410 , which uses the signals to determine counts corresponding to emitted radiation from the object being image. The counts may be used to reconstruct an image. 
       FIG. 9  provides a bottom view (showing the side of the collimator closest to the detector) of the pinhole collimator  1300 ,  FIG. 10  provides a top view of the collimator  1300  (showing the side of the collimator closes to the object being imaged), and  FIG. 11  provides a side sectional view of the pinhole collimator  1300 . As seen in  FIGS. 9-11 , the pinhole collimator  300  includes an array  1301  of pinhole openings  1302  that correspond to the pixelated anodes  1308 . Each pinhole opening  1302  corresponds to a corresponding group of pixelated anodes  1308  (see, e.g.,  FIGS. 12-13  and related discussion). An area of each pinhole opening  1302  (e.g., the area at the surface closest to the object being imaged) is smaller than a corresponding radiation receiving area of the corresponding group of pixelated anodes  1308 . For example, when four pixelated anodes form the group corresponding to a given collimator opening, the area of the collimator opening is smaller than the combined radiation receiving area defined by the four pixelated anodes. 
     The pinhole openings  1302  may be understood as being tapered. For example, as seen in  FIGS. 9-11 , the pinhole openings  1302  are tapered, with the pinhole openings  1302  being larger on a first surface  1327  that is proximate the semiconductor detector  1312  than on a second surface  1303  that is opposed to the first surface  1307  and farther away from the semiconductor detector  1312 . 
     It may further be noted that in various embodiments, the collimator  1300  may be a 3D printed collimator. Such a 3D printed collimator provides various advantages in various embodiments. For example, such a collimator may be produced with high accuracy to facilitate accurate registration of the collimator to groups of physical sub-pixels (e.g., a certain group of pixelated anodes sharing a single and only one common collimator opening). Additionally, such collimators may be produced at a relatively low cost. 
     However, it may be noted that materials used for 3D printed collimators may have a lower density than collimators produced using the same material (e.g., Tungsten) but fabricated using other methods, and, accordingly, may provide reduced penetration protection relative to other fabrication methods. To address the lower density of the material, the septa of the collimator may be made thicker to help prevent radiation penetration via septa  1304  from a volume under one opening of the collimator opening to another volume under another opening. Thicker septa using parallel holes may reduce sensitivity; however, various embodiments utilize tapered pinhole openings to provide improved sensitivity for thicker walled septa. 
     For example, as seen in  FIGS. 9-11 , the depicted pinhole collimator  1300  with thicker septa  1304  provides comparable sensitivity and spatial resolution achieved by a parallel-hole collimator having relatively thinner septa. The openings  1302  have narrow upper sides  1306  having a width d, and wider lower portions  1305 . 
     As best seen in  FIGS. 12-13 , the semiconductor detector  1312  has a first surface  1317  and a second surface  1319 . The first surface  1317  and the second surface  1309  are opposed to each other, with the first surface  1317  including pixelated anodes  1308 , and the second surface  1319  including a cathode electrode  1314 . As discussed herein, the detector assembly  1390  utilizes physical sub-pixelation. 
     It may be noted that virtual sub-pixelation may provide challenges with respect to signal-to-noise ratio due to the relatively small magnitude of non-collected induced signals. Physical sub-pixelation may be used by dividing a pixel defined by a collimator opening into a group of physically distinct pixelated anodes (e.g., pixelated anodes  1308 ). In various embodiments, each group of pixelated anodes  1308  (with each individual group corresponding to a particular collimator opening) may include N×M pixelated anodes  1308 , where N and M are integers greater than 1. In the illustrated embodiment, each group includes 2×2 pixelated anodes  1308 . It may be noted that the use of physical sub-pixels may increase the effect of charge-sharing, which may be addressed as discussed herein. (See, e.g.,  FIG. 14  and related discussion.) 
       FIG. 12  provides a side view of the detector assembly  1390 . As seen in  FIG. 12 , the collimator  1300  is disposed above (e.g., closer to the object being imaged) the cathode  1314  of a radiation detector  1312  made of a semiconductor (e.g., CdZnTe or CZT). The semiconductor detector  1312  includes the pixelated anodes  1308  which define corresponding sub-voxels  1310 . As also seen in  FIG. 12 , the pinhole collimator  1300  has a height h and an opening width d at its upper surface. 
       FIG. 13  provides a schematic top view of the semiconductor  1312 . Broken lines  1316  indicate the center of the septa  1304  of the pinhole collimator  1300  at the bottom surface of the pinhole collimator  1300 . Squares  1307  defined by broken lines depict projections from the smaller size of the openings  1302  from the upper surface  1303  of the pinhole collimator  1300 . For the example depicted in  FIG. 13 , one group  1318  of pixelated anodes  1308  corresponding to the opening in the upper left corner includes four pixelated anodes  1308  that correspond to a particular opening  1302   a . Accordingly, each opening  1302  may be understood as being registered to a particular group  1318 , with each pixelated anode  1308  of the group  1318  receiving radiation only from that corresponding opening  1302 , with the septa  1304  blocking radiation from other openings. 
     As seen in  FIG. 12 , charge  1309  is created by a photon absorbed in the semiconductor detector  1312 . The charge  1309  drifts along trajectory  1311  to be collected by a pixelated anode  1308 . Charge  1315  is created by another photon absorbed in the semiconductor  1312  and is located in a range containing the border between adjacent pixelated anodes. In such a case, the charge  1315  is split into charges  1317  drifting along trajectories  1313  and is collected by two different pixelated anodes  1308 , with neither pixelated anode collecting charge  1315  completely. 
     The smaller are the pixelated anodes  1308 , the more they will be adversely affected by charge-sharing events. Due to the large number of pixelated anodes  1308  in detector  1312 , which is in turn due to the small size of the pixelated anodes  1308 , the use of a sub-pixel map may be unwieldy or impractical. Accordingly, various embodiments address charge-sharing. 
     It may be noted that, for image reconstruction, the Z coordinate or depth of interaction (DOI) should be known. However, grouping events according to their DOI may create groups having small numbers of events that accordingly may be adversely affected by statistical noise. Accordingly, in various embodiments, the processing unit  1410  counts absorbed photons as events with a thickness of the semiconductor detector  1312  at a distance corresponding to 1/μ, where μ is the absorption coefficient of the semiconductor detector. For example, the events may be counted as being with a range of 1/μ plus or minus one millimeter. 
       FIG. 14  provides a block schematic view of a processing system  1401 . The processing system  1401  is configured to address charge-sharing as discussed herein. It may be noted that while processing unit  1410  is depicted as a separate block in the illustrated schematic view, the processing unit  1410  in various embodiments may include one or more physical blocks that incorporate various aspects of the processing system  1401 . 
     As seen in  FIG. 14 , the processing system  1401  includes electronic channels  1402 , terminals  1404 , readout unit  1406 , terminal  1408 , processing unit  1410 , terminals  1412 , terminal  1414 , and enable/disable unit  1418 . As seen in  FIG. 14 , pixelated anodes  1308  are electrically connected to electronic channels  1402 , which, for example, may be included on an ASIC. It may be noted that each electronic channel  1402  may includes a charge sensitive amplifier (CSA), shaper, comparator, amplifiers, and a peak &amp; hold (P&amp;H) (not shown). The comparator of the electronic channel  1402  may be controlled by input  1400  that controls the threshold level of the comparator to ensure that only signals above the threshold level will be transferred to the readout unit  1406  through terminals  1404 . 
     In the illustrated embodiment, each electronic channel  1402  produces a trigger upon its signal passing the threshold level. The trigger is transferred to the readout unit  1406  via terminals  1412  and enable/disable unit  1418 . When the readout unit  1406  receives such a trigger, it reads the signal from the electronic channels  1402  that are electrically connected to the particular pixelated anodes  1308  that are adjacent to the given pixelated anode  1308  that generated the trigger. The signals from those pixelated anodes are transferred, via terminal  1408  to the processing unit  1410 , which sums the signals together to produce a signal based on the complete charge collection achieved by summing those signals (e.g., the signals from the trigger-generating anode and its adjacent anodes). The summed signal exits terminal  1414  with the address of the pixelated anode that first generated the trigger in the illustrated example. 
     Accordingly, all charges split between adjacent pixelated anodes  1308  are summed to recover a complete charge collection without the use of a sub-pixel map. In the case of no charge-sharing, the signals from adjacent pixels do not cross the appropriately set threshold and accordingly are not summed. 
     It may be noted that in the depicted example, after receiving the first triggering signal at the readout unit  1406 , the enable/disable unit  1418  disables terminals  1412  for a predetermined amount of time to avoid additional triggering signals (e.g., triggering signals from adjacent pixelated anodes for the same shared event). After a time interval that allows the readout unit  1406  and the processing unit  1410  to read and sum all the signals arriving from the triggering pixelated anode  1308  and its adjacent anodes, the enable/disable unit  1418  returns to an enable state to allow a new trigger from another event to arrive to the readout unit  1406 . 
     Accordingly, in various embodiments, the processing system  1401  (e.g., one or more processors forming the processing unit  1410  and/or other aspects of the processing system  1401 ) is configured to identify detected events from the pixelated anodes  1308 . For example, the processing system  1401  (or aspects thereof) in various embodiments is configured to generate a trigger signal responsive to a given detected event (e.g., photon absorption) in a given pixelated anode  1308 , provide the trigger signal to a readout (which may be a part of the processing unit  1410 ), and, using the readout, read and sum signals arriving from the given pixelated anode and anodes surrounding the given pixelated anode. For example, the processing unit  1410  may be configured to read and sum the signals for the given pixelated anode and pixelated anodes immediately adjacent to the given pixelated anode. Further, the processing system  1401  in various embodiments is configured to block trigger signals from other pixelated anodes for a predetermined time interval after receiving the trigger signal. It may further be noted that in various embodiments, the processing unit  1410  is configured to assign the given detected event to the pixelated anode from which the trigger signal originated. Once a sufficient or desired number of counts have been acquired or imaging time has been performed, the processing system  1401  may use the identified counts to reconstruct an image. 
     It may be noted that in various embodiments swiveling detectors may be placed in close vicinity to a patient body/organ to be imaged, and closely packed with each other. Since the swiveling detectors rotate, the circle defined by the swiveling detector should not touch the patient body or a circle defined by the adjacent swiveling detector. (See  FIGS. 17 and 18 ). Accordingly, for a certain detector module, it is desirable to have the confining circle defined by the size of the detector module as small as possible to ensure that as many as possible swiveling detector modules can be placed around the patient body or organ to increase the detection sensitivity. 
     One of the main factors that dictates the size of the confining circle of the detector module is the length of the collimator.  FIGS. 15 and 16  illustrate the effect of the collimator size on overall size of detectors. The swiveling detectors of  FIGS. 15 and 16  both contain the same general detector module  1324  thus, the same referral numbers are used in drawings  15  and  16  to indicate the same detector-module  1324  and its components. Accordingly, size differences between the detectors of  FIGS. 15 and 16  are due to differences in collimator length. 
       FIG. 15  schematically shows a swiveling detector  1320  including a collimator  1300  according to various embodiments of the present disclosure (e.g., collimator  1300  discussed in connection with detector assembly  1390 ), and radiation detector module  1324 , which includes detector  1312  and electronic unit  1326 . The swiveling detector  1320  also contains radiation shielding material  1336  to which a cold finger  1330  of the detector module  1324  is attached by a screw  1328 . The cold finger  1330  is used for heat dissipation and mounting of the detector module  1324 . The swiveling detector  1320  rotates back and forth around its axis  1322  in the directions of arrows  1365 . The swiveling detector  1320  is confined in circle  1332  having radius R 1 . 
       FIG. 16  schematically shows a swiveling detector  1360  including a conventional parallel hole collimator  1370 , and radiation detector module  1324 , which includes detector  1312  and electronic unit  1326 . The swiveling detector  1360  contains radiation shielding material  1325  to which a cold finger  1330  of detector module  1324  is attached by screw  1368 . The swiveling detector  1360  rotates back and forth around its axis  1362  in the directions of arrows  1366 . Swiveling detector  1360  is confined in circle  1334  having radius R 2 . 
     It may be noted that swiveling detectors  1320  and  1360  both utilize the same detector module  1324 . Accordingly, for the swiveling detectors  1320  and  1360  to have similar spatial-resolution and sensitivity, their collimators  1300  and  1370  should satisfy: 
                   d   1       h   1       ≈       d   2       h   2         ,         
where d 1  and h 1  are the radiation receiving upper opening size and height of collimator  1300 , and d 2  and h 2  are the opening size and height of the conventional parallel hole collimator  1370 , respectively. Since d 1 &lt;d 2  then h 1 &lt;h 2  and thus R 1 &lt;R 2  and, as shown in  FIG. 15 , the confining circle  1332  of the swiveling detector  1320  is smaller than the confining circle  1334  of the swiveling detector  1360 .
 
     Accordingly, the collimator  1300  not only allows the production of a collimator without radiation penetration and without sensitivity loss using 3D printing, but also enables the use of swiveling detectors that are more compact than may be accomplished with a parallel hole collimator while having the same spatial-resolution and sensitivity for the swiveling detectors. 
     It may be noted that the fact that collimator  1300  allows a swiveling detector  1320  having the same spatial-resolution and sensitivity as can be produced with conventional parallel hole collimator  1370  but, with a smaller radius R 1  of the confining circle  1332 , provides the swiveling detector  1320  with collimator  1300  having various advantages as shown in  FIGS. 17 and 18 . 
       FIG. 17  schematically illustrates a system of swiveling detectors  1320  rotating back and forth around axis  1322  in the directions of arrows  1365 . Detectors  1320  are arranged around patient body  1380 .  FIG. 18  schematically illustrates a system of swiveling detectors  1360  rotating back and forth around axis  1362  in the directions of arrows  1366 . Detectors  1360  are arranged around the same patient body  1380  of  FIG. 17 . Since both swiveling detectors  1320  and  1360  have the same sensitivity and spatial-resolution, and, since the system of  FIG. 17  includes more swiveling detectors  1320  around patient  1380  than the system of  FIG. 18 , the system of  FIG. 17  according to various embodiments has a sensitivity that is significantly higher than the system of  FIG. 18  that is based on a conventional parallel hole collimator. 
       FIG. 19  provides a flowchart of a method  1900  in accordance with an embodiment. The method  1900  may be carried out or performed using imaging systems and/or detector assemblies as set forth herein. It may be noted that the steps of method  1900  may represent programs or instructions configured to direct operations of one or more processors (e.g., processing system  1401  or aspects thereof). In various embodiments, certain steps may be omitted or added, certain steps may be combined, certain steps may be performed simultaneously, certain steps may be performed concurrently, certain steps may be split into multiple steps, certain steps may be performed in a different order, or certain steps or series of steps may be re-performed in an iterative fashion. 
     At  1902 , an object to be imaged is positioned. Generally, the object (e.g., a human patient or portion thereof) will have been administered a radiopharmaceutical resulting in the emission of radiation from the object. The object may be placed in a bore of a gantry containing multiple detectors, for example detectors that individually pivot or sweep to image the object. 
     At  1904 , radiation from the object is received by one or more detectors of detectors of an imaging system (e.g., one or more detector assemblies  1390 ). Radiation received by each individual detector may be guided through a corresponding collimator (e.g., collimator  1300 ) for absorption by pixelated anodes  1308 , with the pixelated anodes  1308  being arranged in groups, with each group corresponding to a single and only one opening of the collimator, to provide physical sub-pixellation. 
     At  1906 , for a given detected event (e.g., a signal produced by a given pixelated anode of a detector), it is determined if the event satisfies a threshold. The threshold may be set to disregard signals that are too weak to form a significant part of a shared charge event. If the threshold is not satisfied, the event is disregarded and the system waits for the next detected event to be reported. If the event satisfies the threshold, the method  1900  proceeds to  1908 . 
     At  1908 , a trigger signal is generated responsive to the event detected at the given pixelated anode. At  1910 , all signals from the pixelated anode that resulted in the trigger signal along with the pixelated anodes surrounding that anode (e.g., all anodes immediately adjacent to the triggering anode) are read and summed to provide a given combined event signal. 
     At  1912 , trigger signals from other pixelated anodes than the one that resulted in the trigger signal at  1908  are blocked. For example, trigger signals from other anodes may be blocked for a predetermined time interval after receiving the triggering signal. Accordingly, for example, duplicate triggers from a shared event may be disregarded to avoid double-counting. 
     At  1914 , it is determined if the combined event signal corresponds to reception of a photon. For example, the magnitude of the combined event signal may be compared to a known magnitude/energy of photons emitted due to the radiopharmaceutical. If the combined event signal is within a predetermined range of the known magnitude/energy for the photons, the combined event signal may be determined to be a true event, or to correspond to absorption of a photon. 
     At  1916 , if the combined event signal corresponds to reception of a photon, the event is counted as a true event. The event may be assigned a location corresponding to the pixelated anode resulting in the original trigger, and may be assigned a Z location or DOI correspond to the absorption coefficient of the semiconductor used in the detector. At  1918 , after acquisition of all imaging information, the accumulated counts are used to reconstruct an image. 
     It should be noted that the various embodiments may be implemented in hardware, software or a combination thereof. The various embodiments and/or components, for example, the modules, or components and controllers therein, also may be implemented as part of one or more computers or processors. The computer or processor may include a computing device, an input device, a display unit and an interface, for example, for accessing the Internet. The computer or processor may include a microprocessor. The microprocessor may be connected to a communication bus. The computer or processor may also include a memory. The memory may include Random Access Memory (RAM) and Read Only Memory (ROM). The computer or processor further may include a storage device, which may be a hard disk drive or a removable storage drive such as a solid-state drive, optical disk drive, and the like. The storage device may also be other similar means for loading computer programs or other instructions into the computer or processor. 
     As used herein, the term “computer” or “module” may include any processor-based or microprocessor-based system including systems using microcontrollers, reduced instruction set computers (RISC), ASICs, logic circuits, and any other circuit or processor capable of executing the functions described herein. The above examples are exemplary only, and are thus not intended to limit in any way the definition and/or meaning of the term “computer”. 
     The computer or processor executes a set of instructions that are stored in one or more storage elements, in order to process input data. The storage elements may also store data or other information as desired or needed. The storage element may be in the form of an information source or a physical memory element within a processing machine. 
     The set of instructions may include various commands that instruct the computer or processor as a processing machine to perform specific operations such as the methods and processes of the various embodiments. The set of instructions may be in the form of a software program. The software may be in various forms such as system software or application software and which may be embodied as a tangible and non-transitory computer readable medium. Further, the software may be in the form of a collection of separate programs or modules, a program module within a larger program or a portion of a program module. The software also may include modular programming in the form of object-oriented programming. The processing of input data by the processing machine may be in response to operator commands, or in response to results of previous processing, or in response to a request made by another processing machine. 
     As used herein, a structure, limitation, or element that is “configured to” perform a task or operation is particularly structurally formed, constructed, or adapted in a manner corresponding to the task or operation. For purposes of clarity and the avoidance of doubt, an object that is merely capable of being modified to perform the task or operation is not “configured to” perform the task or operation as used herein. Instead, the use of “configured to” as used herein denotes structural adaptations or characteristics, and denotes structural requirements of any structure, limitation, or element that is described as being “configured to” perform the task or operation. For example, a processing unit, processor, or computer that is “configured to” perform a task or operation may be understood as being particularly structured to perform the task or operation (e.g., having one or more programs or instructions stored thereon or used in conjunction therewith tailored or intended to perform the task or operation, and/or having an arrangement of processing circuitry tailored or intended to perform the task or operation). For the purposes of clarity and the avoidance of doubt, a general purpose computer (which may become “configured to” perform the task or operation if appropriately programmed) is not “configured to” perform a task or operation unless or until specifically programmed or structurally modified to perform the task or operation. 
     As used herein, the terms “software” and “firmware” are interchangeable, and include any computer program stored in memory for execution by a computer, including RAM memory, ROM memory, EPROM memory, EEPROM memory, and non-volatile RAM (NVRAM) memory. The above memory types are exemplary only, and are thus not limiting as to the types of memory usable for storage of a computer program. 
     It is to be understood that the above description is intended to be illustrative, and not restrictive. For example, the above-described embodiments (and/or aspects thereof) may be used in combination with each other. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the various embodiments without departing from their scope. While the dimensions and types of materials described herein are intended to define the parameters of the various embodiments, they are by no means limiting and are merely exemplary. Many other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the various embodiments should, therefore, be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled. In the appended claims, the terms “including” and “in which” are used as the plain-English equivalents of the respective terms “comprising” and “wherein.” Moreover, in the following claims, the terms “first,” “second,” and “third,” etc. are used merely as labels, and are not intended to impose numerical requirements on their objects. Further, the limitations of the following claims are not written in means-plus-function format and are not intended to be interpreted based on 35 U.S.C. § 112(f) unless and until such claim limitations expressly use the phrase “means for” followed by a statement of function void of further structure. 
     This written description uses examples to disclose the various embodiments, including the best mode, and also to enable any person skilled in the art to practice the various embodiments, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the various embodiments 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 the examples have structural elements that do not differ from the literal language of the claims, or the examples include equivalent structural elements with insubstantial differences from the literal language of the claims.