Patent Publication Number: US-2021165117-A1

Title: Imaging system with one or more mask units and corresponding method of recording radiation

Description:
PRIORITY CLAIM 
     The present application is a continuation of and claims priority to and the benefit of U.S. patent application Ser. No. 16/177,769, filed on Nov. 1, 2018, the contents of which are herein incorporated by reference in their entirety. 
    
    
     INTRODUCTION 
     The present disclosure relates generally to an imaging system and corresponding method of recording radiation with one or more mask units in the imaging system. Coded aperture devices may be employed to block radiation by casting a coded shadow upon a detector and mathematically reconstructing the spatial distribution of the source of radiation from this shadow. However, when forming two-dimensional images, these devices tend to be bulky or compromise image quality to achieve compactness. 
     SUMMARY 
     Disclosed herein is an imaging system and a method of recording radiation data. The imaging system including a first mask unit having a hollow cavity surrounding a rotational axis. The first mask unit is characterized by a first pattern encoded on its surface. The first pattern defines a height along an axial direction parallel to the rotational axis. The first pattern includes a respective plurality of elements with at least one open element in each of the axial direction and a circumferential direction and at least one blocking element in each of the axial direction and the circumferential direction (minimum four elements, with at least two open and at least two closed). A detector is configured to receive radiation data from at least one source such that one of the detector and the source is located inside the hollow cavity and another of the detector and the source is located outside the hollow cavity. The first mask unit is configured to move relative to the rotational axis in at least one of the axial direction and the circumferential direction until the first pattern is at least partially recorded. 
     The first mask unit may be a cylindrical shell. A controller may be in communication with the detector, the controller including a processor and tangible, non-transitory memory on which is recorded instructions for executing a method. Execution of the instructions by the processor causes the controller to reconstruct an image or distribution of the source, the image including respective pixels in the circumferential direction and the axial direction. In one example, the open and blocking elements may each be configured with respective attenuation rates and the difference between the respective attenuation rates of the open element and the blocking element may be at or above 10%. 
     The detector is configured to be position sensitive. For example, the detector may include a cadmium zinc telluride (CdZnTe) compound with pixelated electrodes. The system may be characterized by an absence of a collimator. In one example, the first pattern is a cyclic-difference-set-based (CDS-based) pattern. 
     The first pattern may be divided into a first set and a second set, such that at least 50% of the first set and at least 50% of the second set are identical moving the mask only enough to record the basic pattern. The first set and the second set may be tiled on the surface in the axial direction. The imaging system may include an actuator configured to move the first mask unit. In one example, the first pattern extends in a single direction, the first pattern being wrapped around the first mask unit in a slant such that respective positions of the respective plurality of elements forms a helical route. The actuator may be configured to move the first mask unit along the helical route until the first pattern is traversed. 
     In another example, the first pattern may extend along at least two directions, including the axial direction and the circumferential direction. The actuator may be configured to sequentially rotate the first mask unit along the circumferential direction by 360 degrees. Additionally, the actuator may be configured to incrementally translate the first mask unit along the axial direction until the height of the first pattern is traversed. 
     In a second embodiment, the imaging system includes a second mask unit concentric with and positioned surrounding the first mask unit. The second mask unit defines a second surface, with the second mask unit being characterized by a second pattern encoded on the second surface. The second pattern includes the respective plurality of elements with another at least one open element in each of the axial direction and the circumferential direction and another at least one blocking element in each of the axial direction and the circumferential direction (total of at least two open and at least two closed elements). The first mask unit is configured to spin relative to the rotational axis at a first frequency and the second mask unit is configured to spin relative to the rotational axis at a second frequency. 
     The first mask unit and the second mask unit have respective positions indicated by an inner mask azimuth angle (φ i ) and an outer mask azimuth angle (φ o ), respectively. The first mask unit and the second mask unit are configured to spin through a combination of positions (φ i , φ o ), with the inner mask azimuth angle (φ i ) extending from 0 to 2π and the outer mask azimuth angle (φ o ) extending from 0 to 2π. In one example, the respective plurality of elements in the first and second patterns are arranged along the same slope angle but with the opposite sign in the first pattern compared to the second pattern. In other words, the first pattern defines a slope angle of alpha (α) and the second pattern defines a slope angle of beta (β), where β=α−(π/2). In one example, the slope angle of alpha (α) is between 10 and 80 degrees. 
     The above features and advantages and other features and advantages of the present disclosure are readily apparent from the following detailed description of the best modes for carrying out the disclosure when taken in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration of an imaging system having a first mask unit and a detector, in accordance with a first embodiment; 
         FIG. 2A  is a schematic illustration of an example first mask unit employable in the imaging system of  FIG. 1 ; 
         FIG. 2B  is the laid-out or flattened first pattern of the first mask unit shown in  FIG. 2A ; 
         FIG. 3A  is a schematic illustration of another example first mask unit employable in the imaging system of  FIG. 1 ; 
         FIG. 3B  is the laid-out or flattened first pattern of the first mask unit of  FIG. 3A ; 
         FIG. 4  is a schematic illustration of the imaging system of  FIG. 1 , showing displacement of the detector; 
         FIG. 5  is a schematic illustration of an imaging system in accordance with a second embodiment, the imaging system having a first mask unit, a second mask unit and a detector; 
         FIG. 6  is a schematic illustration of an example first pattern and an example second pattern employable in the first mask unit and second mask unit of  FIG. 5 , respectively; 
         FIG. 7A  is a schematic illustration of a time varying shadow from a point source at (φ=0, θ=θ s ), the shadow being formed with the patterns of  FIG. 6 ; 
         FIG. 7B  is a schematic illustration of a time varying shadow from a point source at (φ=0, θ=θ s +Δθ), the shadow being formed with the patterns of  FIG. 6 ; 
         FIG. 8  is a schematic illustration of a reconstructed image formed with the patterns of  FIG. 6 ; and 
         FIG. 9  is a flowchart of a method of recording radiation with one or more mask units. 
     
    
    
     DETAILED DESCRIPTION 
     Referring to the drawings, wherein like reference numbers refer to like components,  FIG. 1  schematically illustrates an imaging system  10 . The imaging system  10  includes a first mask unit  12  having a hollow cavity  14  defining a rotational axis A. For reference purposes, an XYZ axis is shown in  FIG. 1 . In the example shown, the rotational axis A is parallel to the Z axis. The first mask unit  12  defines a surface  16  between a first end  18  and a second end  20 . In the example illustrated in  FIG. 1 , the first mask unit  12  has a cylindrical shape. However, it is to be understood that other suitable shapes may be employed. In one example, the rotational axis A is coincident with the center of the hollow cavity  14 . In another example, the rotational axis A is off-center, i.e., not coincident with the center of the hollow cavity  14 . 
       FIG. 2A  illustrates an example first mask unit  12  employable in the imaging system  10 , in accordance with a first embodiment. The first mask unit  12  is characterized by a first pattern  22  encoded on the surface  16 .  FIG. 2B  is the laid-out or flattened version of first pattern  22  of the first mask unit  12  of  FIG. 2A . For clarity, the first pattern  22  is omitted in  FIG. 1 . Referring to  FIGS. 2A and 2B , the first pattern  22  includes a plurality of elements  24  of varying attenuation, with at least one open element  26  and at least one blocking element  28  (shown shaded in  FIGS. 2A and 2B ) in each of an axial direction  44  and a circumferential direction  42  (relative to the rotational axis A) and an axial direction  44  (parallel to the rotational axis A). In other words, plurality of elements  24  includes a minimum of four elements, at least two open and at least two closed. The open element  26  may be a through hole in the surface  16  of the mask  12 . Alternatively, the open element  26  may be composed of a layer of a dissimilar material. For example, the first mask unit  12  and the blocking element  28  may be composed of tungsten and the open element  26  may be composed of a layer of polymer or glass. The shape and sizes of the plurality of elements  24  may be varied based in the application at hand, including but not limited to, circles, squares and rectangles. 
     The respective attenuation rates of the open element  26  and the blocking element  28  may be varied based on the application at hand. In one example, the open element may be configured to have a respective attenuation rate at or below 10%, and the blocking element may be configured to have a respective attenuation rate at or above 80%. In another example, the open element  26  may be configured to have an attenuation rate at or below 1% such that the open element  26  allows 99% or more of incoming radiation to pass through it and the blocking element  28  may be configured with an attenuation rate at or above 95%. A second example of a first mask unit  112  employable in the imaging system  10  is shown in  FIG. 3A  and described below. 
     Referring to  FIG. 1 , the imaging system  10  includes a detector  30  configured to receive radiation data from at least one source, such as first source  32 . One of the detector  30  and the first source  32  is located inside the hollow cavity  14  and another of the detector  30  and the first source  32  is located outside the hollow cavity, such that the radiation data travels through the first mask unit  12  from the first source  32  to the detector  30 . If there is more than one source (for example, a second source  34  and a third source  36 ) and the detector  30  is positioned inside the hollow cavity  14 , then all the sources are to be positioned outside the hollow cavity  14 . If the detector  30  is positioned outside the hollow cavity  14 , then all the sources are to be positioned inside the hollow cavity  14 . The first source  32 , second source  34  and third source  36  may emit any type of radiation phenomenon known to those skilled in the art, including but not limited to, alpha, beta, electromagnetic radiation and neutrons. The detector  30  and the first mask unit  12  may be independently movable. It is to be understood that the imaging system  10  may take many different forms and include multiple and/or alternate components and facilities. Recording the shadow of a moving mask as opposed to a fixed mask offers additional resolvable image pixels, thereby enhancing image quality. 
     Referring to  FIG. 1 , an actuator  40  is operatively connected to or in electronic communication with and configured to move the first mask unit  12 . In one example, the actuator  40  is an electric motor. The actuator  40  may be a linear actuator, a rotary actuator, a stepper motor, a shape memory alloy or other type of actuator available to those skilled in the art. Referring to  FIG. 1 , the actuator  40  is configured to shift the first pattern  22  (see  FIGS. 2A, 2B ) relative to the rotational axis A in at least one of the circumferential direction  42  and the axial direction  44  until the first pattern  22  is recorded in 360 degrees in a field of view  41  (see  FIG. 1 ) and the height Z 1  (see  FIG. 2B ) of the first pattern  22  is traversed. This traversal may be accomplished in a number of ways. Firstly, referring to  FIG. 2A , the first mask unit  12  may be moved along a helical route  46 . Secondly, referring to  FIG. 1 , this traversal may be accomplished by sequentially rotating or spinning the first mask unit  12  by 360 degrees, and incrementally translating the first mask unit  12  along the axial direction  44 , from a first mask position  48  to a final mask position  49 . The sequence of rotation by 360 degrees and incremental translation is repeated until the whole first pattern  22  is sampled. 
     Alternatively, the detector  30  may be translated instead of the first mask unit  12 . Thirdly, referring to  FIG. 4 , this traversal may be accomplished by sequentially rotating the first mask unit  12  by 360 degrees in a circumferential direction  42 , and incrementally translating the detector  30  by a displacement (Δz) along an axial direction  44  (parallel to the rotational axis A). Referring to  FIG. 4 , the sequence continues until the entire first pattern  22  is sampled, with the detector  30  moving from a first detector position  50  to a final detector position  52 . 
     In the example shown in  FIG. 2A , the first pattern  22  extends along a single direction and is one-dimensional. The first pattern  22  is wrapped or encoded around the first mask unit  12  in a slant  54  such that respective positions of the plurality of elements  24  form a helical route  46 . Referring to  FIG. 2A , the slant  54  is characterized by a slant angle θ between a reference plane  56  perpendicular to the rotational axis A, and a reference line  58 . The reference line  58  is tangential to the slant  54  and intersects the reference plane  56 . The one directional first pattern of  FIG. 2A  is arranged in two dimensions in  FIG. 2B  such that each row includes the plurality of elements  24  for one revolution (ten elements per revolutions in this example). 
     Referring to  FIG. 2B , the first pattern  22  defines a height Z 1  and a width Y 1 . The actuator  40  of  FIG. 1  may be configured to move the first mask unit  12  along the helical route  46  (see  FIG. 2A ) that traces the one-dimensional first pattern  22  wrapped around the mask  12  until the height Z 1  and width Y 1  (see  FIG. 2B ) of the first pattern  22  is traversed. Referring to  FIG. 2A , to ensure adequate sampling, the incremental distance between revolutions along the helical route  46  is selected to be less than or equal to the element pitch (shown as separation S 1  in  FIG. 2A ) of the plurality of elements  24  along the Z direction. The length H 1  of the first mask unit  12  is chosen to be greater than the height Z 1  of the first pattern  22 . The diameter D 1  of the first mask unit  12  may be chosen such that: 
         Y   1 =Square root( S   1   2 +π 2   D   1   2 ).
 
     Referring to  FIG. 2A , the first pattern  22  includes a first set  60  and a second set  62 , with the first set  60  and the second set  62  being tiled on the surface  16  in a direction parallel to the rotational axis A. The first set  60  and the second set  62  each may include a portion of the base set  64  characterized by a plurality of members (such as I 1 , I 2 , I 3  . . . I 31  in  FIG. 2A ) between a first member  66  (block numbered I 1  in  FIGS. 2A and 2B ) and a last member  68  (block numbered I 31  in  FIGS. 2A and 2B ). In one example, the first set  60  (elements 1, 2, 3 . . . n−1, n) and the second set  62  (elements 1, 2, 3 . . . n−1, n) are identical. Here the first pattern  22  includes the base set  64  repeated once for a total of 2n elements (1, 2, 3 . . . n−1, n, 1, 2, 3 . . . n−1, n). In another example, the first set  60  may include the base set  64  without the first member  66  and the second set  62  may include the base set  64  without the last member  68 , with the first pattern  22  thus encoding the following plurality of elements  24 : (2, 3, . . . n−1, n, 1, 2, 3, . . . n−1). It is to be understood that the first pattern  22  is not limited to the number and sequence shown in  FIGS. 2A, 2B , which is intended to be a non-limiting example. The base set  64  is shifted cyclically because the end of the first set  60  meets with the start of the identical second set  62  (I 1 , . . . I 31 , I 1 , . . . I 31 ). 
     As noted above, in the example shown in  FIGS. 1 and 2A , the actuator  40  may be configured to move the first mask unit  12  helically until the first pattern  22  is fully sampled. Referring to  FIG. 1 , the first source  32  emits radiation along a first source direction  33 , inducing a time-varying signal according to the first pattern  22  that traverses the first source direction  33 . Other sources modulated by the first mask unit  12  will generate that same one-dimensional first pattern  22  over time, but shifted according to source direction. The second source  34  and the third source  36  emit radiation along a second source direction  35  and a third source direction  37 , respectively, inducing a respective time-varying signal according to the first pattern  22  that traverses those respective directions. The signal from the second source direction  35  is delayed by one element from the third source direction  37 , while the signal from the first source direction  33  is advanced by one revolution from the second source direction  35 . The shift is cyclic because the base set  64  in the first pattern  22  is serially repeated at least once along its helical route  46 . 
     The radius, height, thickness and material of the first mask unit  12  and the respective diameters, number of elements and relative sizes of the plurality of elements  24  may be selected based on the application at hand. For gamma rays, high-density, high-Z materials may be used for the first mask unit  12 . For fast neutrons, high-density, low-Z material may be used for the first mask unit  12 . For thermal neutrons, a material with high cross section (such as B-10 or Cd-113) may be employed. Optimal choice of parameters for the first mask unit  12  may depend on particle type, detector, desired field of view, desired resolution and other factors. 
     Referring to  FIG. 1 , the imaging system  10  includes a controller  70  in electronic communication with the detector  30  and the actuator  40 . Referring to  FIG. 1 , the controller  70  includes at least one processor  72  and at least one memory  74  (or any non-transitory, tangible computer readable storage medium) on which are recorded instructions for executing method  200 , shown in  FIG. 5  and described below. The memory M can store controller-executable instruction sets, and the processor P can execute the controller-executable instruction sets stored in the memory M. The controller  70  of  FIG. 1  is specifically programmed to execute the steps of the method  200 . 
     As described below, the controller  70  is configured to reconstruct an image or distribution of the at least one source based at least partially on the radiation data. The controller  70  may be configured to record a respective sequence of counts (e.g., 1=counts and 0=no counts) as a function of time or spatial location. The controller  70  may be configured to control the operation of the detector and as well as acquisition, processing and storage of the radiation data. The controller  70  may be an integral portion of the detector  30 , or a separate module in communication with components of the detector  30 . 
     The detector  30  of  FIGS. 1 and 4  may be configured to be time-sensitive and record the radiation data as a function of time. The detector  30  may include a spectrometer that detects distribution of intensity (counts) of radiation versus the energy of the respective radiation. It is to be appreciated that the detector  30  may include associated circuitry or electronics (not shown) appropriate to the application at hand. For instance, the circuitry may include a photomultiplier tube, a silicon photodiode, other photon-electron conversion devices, high voltage supply, preamplifier, amplifier and analog to digital converter (ADC). 
     In one example, the detector  30  is position sensitive. The detector  30  may include a semiconductor, such as for example, a cadmium zinc telluride (CdZnTe) compound. Any sensor technology available to those skilled in the art may be employed for the detector  30 . The detector  30  may include a Compton camera which utilizes Compton scattering to determine the spatial origin of the observed radiation. The respective positions of the first source  32 , second source  34  and third source  36  may be described or specified based on their respective polar angle measured from the Z axis, and respective azimuth angle of their orthogonal projection (on the XY plane that passes through the origin and orthogonal to the Z-axis), measured from the X-axis. The respective positions of the first source  32 , second source  34  and third source  36  may be specified as a 2D direction vector, a 3-D position or with any other system of reference known to those skilled in the art. 
       FIG. 3A  illustrates another example first mask unit  112  employable in the imaging system  10 . The first mask unit  112  includes a hollow cavity  114  surrounding a rotational axis A. The first mask unit  112  is characterized by a first pattern  122  encoded on the surface  116 .  FIG. 3B  is the laid-out or flattened version of first pattern  122  of the first mask unit  112  of  FIG. 2A . While the first mask unit  112  has a cylindrical shape in the example illustrated in  FIG. 3A , it is to be understood that other suitable shapes may be employed. Similar to the first embodiment, the first pattern  122  includes a plurality of elements of varying attenuation, with at least one open element  126  and at least one blocking element  128  (shown shaded in  FIGS. 3A and 3B ) in each of the circumferential direction  42  (see  FIG. 1 ) and the axial direction  44 . The open element  126  may be a through hole in the surface  116  or may include a dissimilar layer. 
     Referring now to  FIG. 3A , the first pattern  122  extends along at least two directions, including a first direction (Z axis) parallel to the rotational axis A and a second direction circumferential (on the surface  16 ) relative to the rotational axis A. The first pattern  122  includes a first set  160  and a second set  162 , with the first set  160  and the second set  162  being tiled on the surface along a direction (Z axis) parallel to the rotational axis. It is to be understood that the first pattern  122  is not limited to the number and sequence shown in  FIGS. 3A, 3B , which is intended to be a non-limiting example. 
     Referring to  FIGS. 3A and 3B , the first set  160  and the second set  162  each may include a portion of the base set  164  characterized by a plurality of rows  124  and a plurality of columns  125 . In one example, the first set  160  (5 rows by 7 columns, blocks J 1 , J 2 , J 3  . . . J 35 ) and the second set  62  (5 rows by 7 columns, blocks J 1 , J 2 , J 3  . . . J 35 ) are identical, with the first pattern  122  encoding the base set  164  repeated once (10 rows by 7 columns, encoding elements J 1 , J 2 , J 3  . . . J 35 , J 1 , J 2 , J 3  . . . J 35 ). 
     Alternatively, the first set  160  and the second set  162  each may include a portion of a base set  164 . In one example, the first set may include the base set  164  without the first row  166  and the second set  162  may include the base set  164  without the last row  168 , with the first pattern  122  encoded as follows: (J 8 , J 9 , J 10  . . . J 35 , J 1 , J 2 , J 3  . . . J 28 ). In another example, the first set may include the base set  164  without the first row  166  and the second set  162  may include the entire base set  164 , with the first pattern  122  encoded as follows: (J 8 , J 9 , J 10  . . . J 35 , J 1 , J 2 , J 3  . . . J 35 ). 
     Referring to  FIG. 3B , the first pattern  122  defines a height Z 2  and a width Y 2 . The actuator  40  of  FIGS. 1 and 4  may be configured to shift the first pattern  122  until the height Z 2  and width Y 2  of the first pattern  122  is traversed. In one example, the first mask unit  112  is sequentially rotated 360 degrees and the first mask unit  112  is incrementally translated (as shown in  FIG. 1 ) along the rotational axis A to sample the first pattern  112 . In another example, the first mask unit  112  is sequentially rotated 360 degrees and the detector  30  is incrementally translated (as shown in  FIG. 4 ) along the rotational axis A to scan a complete cycle of the first pattern  112 . To ensure adequate sampling, the incremental translation between revolutions along the rotational axis A is selected to be less than or equal to the element pitch or separation S 2  (see  FIG. 3A ) between rows  124  along the Z direction. The length H 2  of the first mask unit  112  is chosen to be greater than the height Z 2  of the first pattern  122 . The diameter D 2  (not labeled in  FIG. 3A ) of the first mask unit  112  may be chosen based on the width Y 2  of the first pattern  122  such that: 
     
       
      
       Y 
       2 
       =π*D 
       2  
      
     
     Referring now to  FIG. 5 , an imaging system  210  in accordance with a second embodiment is described. The imaging system  210  includes a first mask unit  212  with a hollow cavity  214  surrounding a rotational axis A. A second mask unit  213  is concentric with and surrounds the first mask unit  212 . In the example illustrated in  FIG. 5 , the first and second mask units  212 ,  213  are cylindrical shells, however, it is to be understood that other suitable shapes may be employed. As in the previous embodiments, the first and second mask units  212 ,  213  are characterized by patterns encoded on their respective surfaces  216 ,  217 . 
     Referring to  FIG. 5 , a detector  230  may be positioned in the hollow cavity  214  and configured to receive radiation data from at least one source, such as first source  232 , and second source  234 , outside of the first and second mask units  212 ,  213  with the respective signals travelling through both the first and second mask units  212 ,  213 . The first source  232  and second source  234  may emit any type of radiation phenomenon known to those skilled in the art. Alternatively, the positions may be reversed such that the sources are positioned inside the hollow cavity  214  and the detector  230  is positioned outside the exterior-most mask unit (if there are more than one mask units). For example, a third source  233  may be positioned in the hollow cavity  214  and configured to transmit the radiation data to a detector  231  positioned outside of both the first and second mask units  212 ,  213 . 
       FIG. 6  shows an example first pattern  222  and an example second pattern  223  employable in the first mask unit  212  and second mask unit  213 , of  FIG. 5 , respectively. Similar to the embodiment described relative to  FIGS. 2A and 3A , the first pattern  222  and second pattern  223  include a plurality of elements  224  of varying attenuation, each having at least two open elements  226  and at least two blocking elements  228  (shown stippled in  FIG. 6 ). The plurality of elements  224  may include through holes of different sizes and different shapes. 
     Referring to  FIG. 5 , the positions of the first source  232  defines a source azimuth angle (φ s ) and a source polar angle (θ s ). The second source  234  is shifted relative to the first source  232 , at a shifted source polar angle (θ s +Δθ). Alternatively, the second source  234  may represent the first source  232  at a different time (a moving source). Referring to  FIG. 5 , the positions of the first mask unit  212  and second mask unit  213  may be represented by an inner mask azimuth angle (φ i ) and an outer mask azimuth angle (φ o ), respectively, measured relative to an origin O. The first mask unit  212  is configured to spin relative to the rotational axis A at a first frequency and the second mask unit  213  is configured to spin relative to the rotational axis A at a second frequency. The first frequency may be different from the second frequency. The first mask unit  212  and the second mask unit  213  are rotated such that various combinations of positions (φ i , φ o ) are sampled, with the inner mask azimuth angle (φ i ) extending from 0 to 2π and the outer mask azimuth angle (φ o ) extending from 0 to 2π. 
     Referring to  FIG. 6 , the respective plurality of elements  224  may be arranged along a slope angle of alpha (α) in the first pattern  212  and along a slope angle of beta (β) in the second pattern  223 , where β=α−(π/2). In one example, the slope angle positive alpha (α) is between 10 and 80 degrees. Here, d is the width of the pattern in a direction perpendicular to the slope angle.  FIG. 6  illustrates a first signal set  256  showing the respective signals passing through the first pattern  222 , and the second signal set  258  showing the respective signals passing through the second pattern  223 . Line  252  denotes a travel path for a signal emanating from the source polar angle (θ s ). Line  254  denotes a travel path for a signal emanating from the shifted source polar angle (θ s +Δθ). In both of the first signal set  256  and the second signal set  258 , the respective signals emanating from the shifted source azimuth angle (θ s +Δθ) are shifted relative to the source polar angle (θ s ) (see first signal shift Qi and second signal shift Q o  in  FIG. 6 . However, the signals traveling through the first mask unit  212  and the second mask unit  213  are shifted in opposite directions. In other words, the first signal shift Qi is opposite to the second signal shift Q o . 
     Radiation data reaching the detector  230  (see  FIG. 5 ) travels through  3  possible states of transmission, including a first state of about zero thickness (encountering open elements  226  in both the first mask  212  and the second mask  213 ), a second state of a single mask thickness (encountering a blocking element  228  in one of the first mask  212  and the second mask  213  and an open element  226  in the other of the first mask  212  and the second mask  213 ), and a third state of double mask thicknesses (encountering blocking elements  228  in both the first mask  212  and the second mask  213 ).  FIG. 7A  is a schematic illustration of a time varying shadow from a point source at (φ=0, θ=θ s ), the shadow being formed with the patterns of  FIG. 6 .  FIG. 7B  is a schematic illustration of a time varying shadow from a point source at (φ=0, θ=θ s +Δθ), the shadow being formed with the patterns of  FIG. 6 . The blank portions of  FIGS. 7A and 7B  represent the first state of transmission described above (fraction of transparency of 1.0, see legend).  FIGS. 7A and 7B  also show the second state of a single mask thickness (fraction of transparency of 0.5, see legend) and the third state of double mask thickness (fraction of transparency of 0.25, see legend). In  FIGS. 7A and 7B , the left vertical border represents the inner mask azimuth angle (φ i ) extending from 0 to 2π and bottom horizontal border represents the outer mask azimuth angle (φ o ) extending from 0 to 2π. 
       FIG. 8  is a schematic illustration of a reconstructed image formed by the first pattern  222  and second pattern  223  of  FIG. 6 . The image is reconstructed from periodic correlation with a decoding pattern matched to the fraction of transparency. A peak intensity is detected at point  245 . The respective pixels P along the first axis  246  may represent decoded radiation data spanning the 2D space at least partially represented by the circumferential direction  242 . The respective pixels P along the second axis  248  may represent decoded radiation data spanning the 2D space at least partially represented by the axial direction  244 . 
     Referring now to  FIG. 9 , a flowchart of the method  300  stored on and executable by the controller C of  FIG. 1  is shown. Method  300  need not be applied in the specific order recited herein. Furthermore, it is to be understood that some steps may be eliminated. The method  300  may begin with block  302 , where one or more mask units are formed with a hollow cavity and encoding a pattern on their respective surfaces, as described in the embodiments shown in  FIGS. 1-8 . For example, referring to  FIGS. 2A and 3A , the first mask unit  12 ,  112  is formed with a hollow cavity  14 ,  114 , respectively defining a rotational axis A, and a first pattern  22 ,  122  is encoded on the surface  16 ,  116 , as described in detail above. The first pattern  22 ,  122  defines a respective height Z 1 , Z 2  shown in  FIGS. 2B and 3B  respectively. 
     Per block  304  of  FIG. 9 , a detector is configured to receive radiation data from at least one source such that one of the detector and the at least one source is located inside the hollow cavity and another of the detector and the at least one source is located outside the hollow cavity of the exterior-most mask. Per block  306  of  FIG. 9 , the first mask unit  12 ,  112 ,  212  (and the second mask unit  213 ) is configured to shift relative to the rotational axis A. For example, referring to  FIG. 1 , the first pattern  22 ,  122  is shifted relative to the rotational axis A, via the actuator  40 , in at least one of a circumferential direction  42  and an axial direction  44  until the first pattern  22 ,  122  is recorded in 360 degrees and the respective height Z 1 , Z 2 , shown in  FIGS. 2B and 3B  respectively, are traversed. The radiation data emanating from the at least one source is recorded, via the detector  30 . 
     Per block  308  of  FIG. 9 , the controller C is configured to reconstruct an image or distribution of the at least one source based at least partially on the radiation data. The image includes respective pixels P in both the circumferential direction  42  and the axial direction  44 . The first mask unit  12 ,  112 ,  212  and second mask unit  213  described above encode the distribution of detected particles with a uniquely identifying code that depends on incident particle direction. The measurement data includes the linear sum of codes from each direction with weights proportional to their corresponding source intensities. In one example, a 3-D array A may be defined as: (Aϵ[0, 1] P×R×Q ), 
     The elements of the 3-D array A are proportional to the probability a particle emitted from the qth source direction is counted by the pth detector element during the rth time interval. The 3-D array A may be calculated at least partially based on the first pattern  22 ,  122 ,  222 , second pattern  223  and the detector geometry at each time step. The expected value of a time-varying signal measured by the pth detector element may be described as: 
         A   p**   χ+E [ B   p*   T ], 
     where χ is a column vector with Q elements describing emission rates, B is a P by R matrix of counts due to an un-modulated background, and E [B p*   T ] is the expected value of the pth slice of the B matrix. Here the R by Q sub-matrix A p**  is the pth slice of the 3-D array A, which may be obtained via a calibration process with a known source, design-of-experiment (DOE), statistical and optimization methods, and other methods available to those skilled in the art. An estimate of χ may then be calculated from each respective time-varying signal then summed over all P detector elements to form an overall radiation image. The final step involves forming the image, which may be done with periodic correlation or other type of autocorrelation. For example, a decoding pattern may be employed. 
     In one example, the first pattern  22 ,  122  may be a cyclic-difference-set-based (CDS-based) pattern. Referring to  FIGS. 2A and 3A , the first pattern  22 ,  122  may be characterized by a base set  64 ,  164  that is repeated at least once, as described above. The base set  64 ,  164  may be chosen such that number of occurrences of each hole-to-hole distance within the respective base set  64 ,  164  and across two neighboring base sets  64 ,  164  is approximately constant for all distances greater than zero. The hole-to-hole distance is defined as the center-to-center distance between holes and expressed as an integer number of pattern elements. This distance is measured in the direction of the pattern, e.g., along the helical route for the 1D base set shown in  FIGS. 2A and 2B . For the 2D patterns (shown in  FIGS. 3A, 3B ) in the first embodiment, distance is measured along both vertical and horizontal pattern directions separately, i.e., the hole-to-hole distance (3,4) is unique from (4,3). For the 1D patterns of the second embodiment shown in  FIG. 6 , distances are considered separately for each mask unit  212 ,  213  along the two directions defined by alpha or beta. 
     Collimators are generally employed to restrict a field of view of the detector. More specifically, collimators are used to prevent cross talk between pattern rows. Avoiding cross talk is an important issue for uniformly redundant patterns. The systems  10 ,  210  may be characterized by an absence of a collimator that restrict an axial field of view of the detector. In other words, the systems  10 ,  210  do not require any collimators to prevent cross talk. The features provided in systems  10 ,  210  are a way to avoid this type of cross talk without having to use collimators. This may be achieved with the following embodiments. In a first example, a single mask with both axial motion  44  and circumferential motion  42  is employed, with any detector type. In a second example, a single mask with only circumferential motion  42  is employed, along with a detector  30  that is position sensitive. This example does not require axial motion due to the position-sensitive detector, as long as the axial extent of that detector is tall enough to record the entire “height” of the mask shadow, then a detector can record the circumferential part of the mask pattern as a function of time and the axial part of the mask pattern as a function of position. In a third example, multiple masks are employed with only circumferential motion, and with any type of detector. 
     While a non-limiting example is briefly described above, it is to be understood that other methods available to those skilled in the art may be employed. The controller C (and execution of the method  300 ) improves the functioning of the imaging systems  10 ,  210  by effectively pinpointing the location of one or more sources with a compact and portable system. The imaging systems  10 ,  210  are particularly effective for radiation imaging of particles that are more easily attenuated than focused. 
     The controller C includes a computer-readable medium (also referred to as a processor-readable medium), including any non-transitory (e.g., tangible) medium that participates in providing data (e.g., instructions) that may be read by a computer (e.g., by a processor of a computer). Such a medium may take many forms, including, but not limited to, non-volatile media and volatile media. Non-volatile media may include, for example, optical or magnetic disks and other persistent memory. Volatile media may include, for example, dynamic random access memory (DRAM), which may constitute a main memory. Such instructions may be transmitted by one or more transmission media, including coaxial cables, copper wire and fiber optics, including the wires that comprise a system bus coupled to a processor of a computer. Some forms of computer-readable media include, for example, a floppy disk, a flexible disk, hard disk, magnetic tape, any other magnetic medium, a CD-ROM, DVD, any other optical medium, punch cards, paper tape, any other physical medium with first patterns of holes, a RAM, a PROM, an EPROM, a FLASH-EEPROM, any other memory chip or cartridge, or any other medium from which a computer can read. 
     Look-up tables, databases, data repositories or other data stores described herein may include various kinds of mechanisms for storing, accessing, and retrieving various kinds of data, including a hierarchical database, a set of files in a file system, an application database in a proprietary format, a relational database management system (RDBMS), etc. Each such data store may be included within a computing device employing a computer operating system such as one of those mentioned above, and may be accessed via a network in any one or more of a variety of manners. A file system may be accessible from a computer operating system and may include files stored in various formats. An RDBMS may employ the Structured Query Language (SQL) in addition to a language for creating, storing, editing, and executing stored procedures, such as the PL/SQL language mentioned above. 
     The detailed description and the drawings or FIGS. are supportive and descriptive of the disclosure, but the scope of the disclosure is defined solely by the claims. While some of the best modes and other embodiments for carrying out the claimed disclosure have been described in detail, various alternative designs and embodiments exist for practicing the disclosure defined in the appended claims. Furthermore, the embodiments shown in the drawings or the characteristics of various embodiments mentioned in the present description are not necessarily to be understood as embodiments independent of each other. Rather, it is possible that each of the characteristics described in one of the examples of an embodiment can be combined with one or a plurality of other desired characteristics from other embodiments, resulting in other embodiments not described in words or by reference to the drawings. In other words, elements of various embodiments may be combined. Accordingly, such other embodiments fall within the framework of the scope of the appended claims.