Abstract:
Methods, systems, and apparatuses, including computer programs encoded on a computer storage medium, for generating location and size measurements for small scattered objects in a large medium are disclosed.

Description:
TECHNICAL FIELD 
       [0001]    This specification generally relates to imaging systems, and specifically to generating location and size measurements for small scattered objects in a large medium. 
       BACKGROUND 
       [0002]    When analyzing the distribution pattern of an explosion, the explosive under investigation may be surrounded by mediums (e.g., fiber bundles) that are adapted to capture fissile fragments within a test arena. The explosion causes fissile fragments (e.g., metal objects) to be embedded inside the fiber bundles. These fiber bundles are then dismantled by hand to map the locations of fissile fragments from the explosion. However, dismantling the fiber bundles by hand is a costly and labor intensive process. 
       SUMMARY 
       [0003]    According to an innovative aspect of the subject matter described in this specification, a radiation system is used to map the location of embedded objects inside a medium without destroying the absorbing media. To determine the location of the objects, the medium may be scanned with radiation (e.g., X-rays or neutrons). However, using one radiation source and one line of detectors may not provide the data necessary to locate the coordinates of each object. Accordingly, two orthogonal radiation sources and corresponding detectors may be used to determine the location of objects embedded in the mediums. The data collected by the detectors can then be used to determine the angular location of the objects for each source. The two angular locations can be used to determine the Cartesian coordinates that describe the absolute location of each of the objects in the medium. 
         [0004]    In general, one innovative aspect of the subject matter described in this specification may be embodied in systems that include a first radiation source; a first detector; a second radiation source oriented substantially orthogonally to the first radiation source; a second detector located substantially orthogonally to the first detector; and one or more computers and one or more storage devices. The first detector is configured to detect first radiation from the first radiation source during irradiation of a medium. The medium includes one or more embedded objects. The second detector is configured to detect second radiation from the second radiation source during irradiation of the medium. The one or more computers and the one or more storage devices store instructions that are operable and when executed by the one or more computers cause the one or more computers to perform the operations that include receiving first data from the first detector, the first data associated with the detected first radiation; receiving second data from the second detector, the second data associated with the detected second radiation; and determining a location of at least one of the one or more embedded objects based on the detected first data and the detected second data, the location being relative to the medium. 
         [0005]    These and other embodiments can each optionally include one or more of the following features. The location includes a first coordinate and a second coordinate, the first coordinate being associated with a first dimension and the second coordinate being associated with a second dimension, the first dimension and the second dimension being substantially orthogonal. The location includes a first coordinate and a second coordinate, the first coordinate and the second coordinate being Cartesian coordinates. The first radiation source and the second radiation source produce X-rays. The first radiation source and the second radiation source are neutron sources. The operation of receiving first data from the first detector, the first data associated with the detected first radiation includes determining, based on the first data, a first angle associated with at least one of the one or more embedded objects. 
         [0006]    The operation of receiving second data from the second detector, the second data associated with the second radiation includes determining, based on the second data, a second angle associated with at least one of the one or more embedded objects. The operation of determining a location of at least one of the one or more embedded objects based on the received first data and the received second data, the location being relative to the medium includes determining a distance between the first radiation source and the second radiation source; determining a first coordinate based on a first ratio of (i) the distance between the first radiation source and the second radiation source and (ii) a first function of the first angle and the second angle; and determining a second coordinate based on a second ratio of (i) the distance between the first radiation source and the second radiation source and a second function of the first angle and (ii) the first function of the first angle and the second angle. 
         [0007]    The operations further include determining a first magnification error based upon (i) a distance between the first detector and the first radiation source, (ii) a distance between the first detector and the at least one of the one or more embedded objects, and (iii) a size of the at least one of the one or more embedded objects; and determining a second magnification error based upon (i) a distance between the second detector and the second radiation source, (ii) a distance between the second detector and the at least one of the one or more embedded objects, and (iii) a size of the at least one of the one or more embedded objects. A direction of emission of the radiation from the first radiation source is substantially orthogonal to a direction of emission of the radiation from the second radiation source. 
         [0008]    In general, another innovative aspect of the subject matter described in this specification may be embodied in methods that include the actions of receiving first data from a first detector, wherein the first detector detects radiation from a first radiation source during irradiation of a medium, wherein the medium includes one or more embedded objects; receiving second data from a second detector oriented substantially orthogonally to the first detector, wherein the second detector receives radiation from a second radiation source located substantially orthogonally to the first radiation source during irradiation of the medium; and determining a location of at least one of the one or more embedded objects based on the received first data and the received second data, the location being relative to the medium. 
         [0009]    These and other embodiments can each optionally include one or more of the following features. The location comprises a first coordinate and a second coordinate, the first coordinate being associated with a first dimension and the second coordinate being associated with a second dimension, the first dimension and the second dimension being substantially orthogonal. The location comprises a first coordinate and a second coordinate, the first coordinate and the second coordinate being Cartesian coordinates. The first radiation source and the second radiation source produce X-rays. The first radiation source and the second radiation source are neutron sources. The action of receiving first data from the first detector, the first data associated with the received first radiation includes determining, based on the first data, a first angle associated with the at least one of the one or more embedded objects. 
         [0010]    The action of receiving second data from the second detector, the second data associated with the second radiation includes determining, based on the second data, a second angle associated with the at least one of the one or more embedded objects. The action of determining a location of at least one of the one or more embedded objects based on the received first data and the received second data, the location being relative to the medium includes determining a distance between the first radiation source and the second radiation source; determining a first coordinate based on a first ratio of (i) the distance between the first radiation source and the second radiation source and (ii) a first function of the first angle and the second angle; and determining a second coordinate based on a second ratio of (i) the distance between the first radiation source and the second radiation source and a second function of the first angle and (ii) the first function of the first angle and the second angle. 
         [0011]    The actions further include determining a first magnification error based upon (i) a distance between the first detector and the first radiation source, (ii) a distance between the first detector and the at least one of the one or more embedded objects, and (iii) a size of the at least one of the one or more embedded objects; and determining a second magnification error based upon (i) a distance between the second detector and the second radiation source, (ii) a distance between the second detector and the at least one of the one or more embedded objects, and (iii) a size of the at least one of the one or more embedded objects. A direction of emission of the radiation from the first radiation source is substantially orthogonal to a direction of emission of the radiation from the second radiation source. 
         [0012]    Particular embodiments of the subject matter described in this specification can be implemented so as to realize one or more of the following advantages. The absolute location of objects embedded in a medium can be determined. The location of imperfections in a medium can be determined. Voids within a medium can be detected. 
         [0013]    The details of one or more embodiments of the subject matter described in this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, the drawings, and the claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0014]      FIG. 1  is an example system for mapping the location of an object within a medium in three dimensions. 
           [0015]      FIG. 2A  shows a typical cross section of a medium being irradiated by a first radiation source. 
           [0016]      FIG. 2B  shows a typical cross section of a medium being irradiated by a second radiation source that is about orthogonal to the first radiation source. 
           [0017]      FIG. 3  shows a three-dimensional view of a medium with embedded objects. 
           [0018]      FIG. 4  shows the coordinate transformation geometry for an embedded object. 
           [0019]      FIG. 5  shows locations of an object detected by a first radiation detector and a second radiation detector. 
           [0020]      FIG. 6  is an example method for mapping an object in three dimensions. 
       
    
    
       [0021]    Like reference numbers and designations in the various drawings indicate like elements. 
       DETAILED DESCRIPTION 
       [0022]      FIG. 1  shows an example imaging system  100 . The imaging system  100  irradiates a medium to determine locations of objected embedded in the medium. As described herein, a medium may be a fiber bundle having metal objects embedded within it as a result of an explosion. A fiber bundle may be, for example, made from cellulose (C 6 H 10 O 5 ) or any other suitable material, and may be, for example, a 4′×4′×8′ block or have any other suitable dimensions. The metal objects may be, for example, steel, brass, aluminum, titanium, copper, and/or tungsten fragments ranging from approximately 0.2 g to approximately 1 kg. 
         [0023]    The system  100  includes a transport mechanism  110  that transports the medium through an enclosure  105 . The radiation sources  115  and  120  are located substantially orthogonally to each other and are positioned to scan (e.g., irradiate) a medium that is passing through the enclosure  105  along the transport mechanism  110 . As described herein, substantially orthogonal means about 90° with respect to each other. 
         [0024]    During operation of the imaging system  100 , a medium is placed on the transport mechanism  110 . An operator activates the transport mechanism  110  to move the medium through the enclosure  105 . As the medium passes through the enclosure  105 , the radiation sources  115  and  120  produce radiation in the direction of the medium passing along the transport mechanism  110 . The radiation from the first radiation source  115  is detected by the line of detectors  125 . Some of the radiation generated by the first radiation source  115  is absorbed by the medium and some of the radiation is absorbed by the first detector  125 . Similarly, some of the radiation generated from the second radiation source  120  is absorbed by the medium and some of the radiation is absorbed by the second detector  130 . As the transport mechanism  110  continues to advance the medium, a different cross section of the medium is exposed to the radiation. Once the object has completely passed through the path of the radiation sources  115  and  120 , the detectors  125  and  130  have two sets of data that are related to the radiation absorbed by the object, but from two orthogonal viewpoints. 
         [0025]    In some implementations, the medium being irradiated is a fiber bundle. Prior to irradiating the fiber bundle, the fiber absorbs small objects that are typically metal objects generated by an explosion. In some implementations, the medium may be composed of any other suitable material as long as the objects to be detected absorb radiation at a different level than the medium. For example, the medium may be a finished manufactured product with unknown defects. In this instance, the system  100  would identify the location of the defects. As another example, the medium may be a metal shell with explosive material inside the metal shell. The explosive material may not fill the entire area inside the metal shell. The system  100  would identify the location of air pockets within the explosive material. 
         [0026]    In some implementations, the first radiation source  115  and the second radiation source  120  generate X-rays and the first detector  125  and the second detector  130  detect X-rays. In other implementations, the radiation sources  115  and  120  are neutron sources and the detectors  125  and  130  are neutron detectors. In some implementations, the detectors  125  and  130  are composed of a line of detectors. For example, two lines of detectors may be placed adjacently to produce an L-shaped folded line of detectors. In other implementations, multiple detectors may be placed in an arc such that the distance between a radiation source and any detector is constant. 
         [0027]    In some implementations, the transport mechanism  110  is a conveyor belt. For example, the medium is placed on a belt and advances through the irradiation path of the radiation sources  115  and  120 . In other implementations, the transport mechanism  110  is an apparatus where the medium is kept stationary while the radiation source  115  and  120  and the detectors  125  and  130  move along a path defined by rails and irradiate a different cross section of the medium. In other implementations, the transport mechanism  110  is an apparatus where the medium is kept stationary while the radiation source  115  and  120  and the detectors  125  and  130  move along the detectors&#39; own wheels and irradiate a different cross section of the medium. In other implementations, the transport mechanism  110  is an apparatus where the medium is kept stationary while the radiation source  115  and  120  and the detectors  125  and  130  move on their own transport system, such as tractors with trails, and irradiate a different cross section of the medium. In other implementations, the transport mechanism  110  is an apparatus where the medium is pulled along a platen that is tugged by a pulling system while the radiation source  115  and  120  and the detectors  125  and  130  are kept stationary. 
         [0028]    As the medium advances, or is advanced, along the transport mechanism  110 , a cross section of the medium receives direct radiation from the radiation sources  115  and  120 . Radiation generated from the first radiation source  115  is projected in one direction, and radiation generated from the second radiation source  120  is projected in a direction that is about orthogonal to the direction of projection of the first radiation source  115 . The radiation from both radiation sources  115  and  120  are directed radially at a particular angle that is dictated by the radiation source. As the radiation encounters the cross section of the medium, some of the radiation is absorbed by the embedded objects within the medium if those objects are in the particular cross section under direct radiation. The radiation not absorbed by the object or the embedded particles will travel to the detectors. The detectors record the location and intensity of the received radiation. 
         [0029]    The location data recorded by one line of detectors, for example the first detector  125 , contains two coordinates (Θ1, z). The coordinates may be based upon a cylindrical coordinate system with an angle (Θ1) and a longitudinal direction (z) that is perpendicular to the measured angle. The longitudinal direction is parallel with the direction of motion. The location data recorded by the other line of detectors, for example, the second detector  130 , also may be based on a cylindrical coordinate system that contains two coordinates (Θ2, z). 
         [0030]    As noted above, in some implementations, the detectors  125  and  130  are arranged in an arch. In this instance the distance between a radiation source and different point along a detector is constant. In other implementations, the detectors  125  and  130  may be arranged in a straight line or in an L-shape. Whether the detectors  125  and  130  are arranged in a straight line, an arch, or an L-shape, the imaging system  100  can produce the angle measurement information. Where the detectors  125  and  130  are arranged in an L-shape, the imaging system  100  can use a table that shows the angular position of each detector. The table can include the distance between each detector and the radiation source. 
         [0031]    As illustrated in  FIG. 4 , the measured angles  425  and  430  are polar angles formed between the fixed lines  427  and  432  and the lines formed by the radiation beam  429  and  434 , respectively. The fixed line  427  defines the direction of the second Cartesian coordinate. The fixed line  427  for the first radiation source  115  is perpendicular to the transport mechanism  110 . The fixed line  432  defines the direction of the first Cartesian coordinate. The fixed line  432  for the second radiation source  120  is located perpendicular to the transport mechanism  110 . 
         [0032]      FIG. 2A  shows a typical cross section of the irradiated medium and the location of one of the radiation sources. Cross section  200   a  shows a typical cross section of irradiated medium  205  and the location of the first radiation source  210   a . The first radiation source  210   a  generates radiation that is absorbed by the medium  205 . The radiation that is not absorbed by the medium  205  is virtually all absorbed by the detector  215   a.    
         [0033]    In cross section  200   a , the medium  205  is square. In some implementations, the medium  205  is rectangular. Although the medium  205  is not required to be square or rectangular, a medium with a section that contains four sides and four right angles is selected for practical implementation. The objects embedded in the medium to be scanned can have any shape. Furthermore, a reference marker in the medium  205  is typically used. A reference marker is an intentionally embedded object within the medium. The reference marker absorbs radiation at a different rate than the medium. The reference marker provides a user defined origin for determining relative locations of the objects within the medium with respect to the marker. In some implementations, the enclosure may not be square or rectangular. For example, the enclosure may be triangular or circular. These types of enclosures may be used to accommodate different types and shapes of mediums. The transport mechanism (not shown) advances the medium  205  or the first radiation source  210   a  and the detector  215   a . As illustrated in  FIG. 2A , the medium  205  can either be traveling into the page or out of the page. 
         [0034]    The first radiation source  210   a  projects radiation in the direction of the medium  205 . The radiation source projects radiation throughout an angular range  220   a . The angular range  220   a  provides a wide enough range to irradiate the entire cross section of the medium  205  either at substantially the same time or as individual radiation beams that are projected individually over a period of time. The angular range  220   a  can be adjusted depending on the size and location of the medium  205 . For example, if the medium  205  has a square cross section, then the angular range  220   a  of the side radiation source  210   a  can be decreased so that only the object  205  is irradiated over the square cross section and not extra portions of the enclosure. 
         [0035]    The radiation from the first radiation source  210   a  is partly absorbed by the medium  205  and partly by the detector  215   a . In cross section  200   a , the detector  215   a  is an arc shaped detector and therefore the distance between the detector  215   a  and the first radiation source  210   a  remains constant for each location on the detector  215   a  for each cross section of medium  205 . In some implementations, the detector  215   a  requires minimum clearances between the medium  205  and the first detector  215   a.    
         [0036]      FIG. 2B  shows a typical cross section of the irradiated medium and the location of another of the radiation sources. Cross section  200   b  shows a similar cross section to  200   a , but in cross section  200   b , the second radiation source  210   b  is positioned above the medium  205 . Cross sections  200   a  and  200   b  may not represent two cross sections of different enclosures, but rather, the same cross section of an enclosure. Cross section  200   a  shows the medium  205  with the first radiation source  210   a  and the first detector  215   a . Cross section  200   b  shows the medium  205  with the second radiation source  210   b  and the second detector  215   b . A complete cross section of the enclosure would show both radiation sources  210   a  and  210   b  and both detectors  215   a  and  215   b  since they are all used for accurate imaging of the medium  205 . 
         [0037]    Similar to cross section  200   a , cross section  200   b  contains a radiation source  210   b  that can direct radiation for a particular angle range  220   b . The detector  215   b  is an arc shaped line of detector. In some implementations, the second detector  215   b  requires minimum clearances between the medium  205  and the second detector  215   b.    
         [0038]    The reference lines used to measure the angle of radiation on the detectors  215   a  and  215   b  is shown, for example, by reference lines  225   a  and  225   b . Reference line  225   a  denotes the base line used to measure the angle of the radiation detected by the first detector  215   a  and generated by the first radiation source  210   a . Reference line  225   b  denotes the base line used to measure the angle of the radiation detected by the second detector  215   b  and generated by the second radiation source  210   b.    
         [0039]      FIG. 3  shows a three dimensional view of a medium  300 . Medium  300  shows objects  350  distributed throughout the medium  300 . Each of the objects  350  embedded in the medium  300  is located at a particular Cartesian coordinate with respect to an origin. The direction of each Cartesian coordinate is indicated by directions  305 . The system can determine a Cartesian coordinate of each embedded object. 
         [0040]    The directions  305  indicate an x, y, and z direction and all three are orthogonal to each other. Medium face  310  is in the negative (x, y) plane. Medium face  315  is in the negative (x, z) plane. Medium face  320  is in the positive (x, y) plane. Medium face  325  is in the positive (x, z) plane. Medium face  330  is in the positive (y, z) plane. Medium face  335  is in the negative (y, z) plane. 
         [0041]      FIG. 4  shows a cross section of the medium and the measurements associated with an object embedded in the medium. The cross section  400  includes a cross section of the irradiated medium  405  and an embedded object  410 . The object  410  absorbs radiation differently than the medium  405 . The first radiation source  415  and the second source  420  generate radiation that is absorbed by the detectors. The detectors record data that indicates angle Θ1  425  for the first radiation source  415  and angle Θ2  430  for the second radiation source  420 . The distance between the first radiation source  415  and the second radiation source  420  is indicated by measurement C  435 . Using the angles Θ1  425  and Θ2  430 , the system can determine Cartesian distances x  440  and y  445 . Cartesian distance x  440  indicates the perpendicular distance from the line connecting the radiation sources  415  and  420 . Cartesian distance y  445  indicates the distance perpendicular to Cartesian distance x  440  and originating from a line intersecting the first radiation source  415 . In some implementations, Cartesian distance y  445  originates from a line intersecting the first radiation source  420 . 
         [0042]    Cartesian distances x  440  and y  445  identify the location of the embedded object  410  within the medium  405 . As discussed above, when a single radiation source is used, the angle identifies a range along the edge of the angle where an embedded object may be located. By using two radiation sources, the absolute location of the embedded particle can be determined. 
         [0043]    Right triangle  450  includes sides that equal Cartesian distances x  440  and y  445  and an angle that equals angle Θ1  425 . Therefore, equation (1) describes the relationship between the Cartesian distances x  440  and y  445  and angle Θ1  425 . 
         [0000]    
       
         
           
             
               
                 
                   
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         [0044]    Right triangle  455  includes a side that equals Cartesian distance  440  and an angle that equals angle Θ2  430 . Additionally, right triangle  455  includes a side  457  that is a function of distance C  435  and Cartesian distance y  445 . Therefore, equation (2) describes the relationship between Cartesian distances x  440  and y  445 , distance C  435 , and angle Θ1  430 . 
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         [0045]    In some implementations where Cartesian distance y  445  is measured from a line intersecting the second radiation source  420 . Equations (1) and (2) remain the same except in equation (1), Cartesian distance y  445  is replaced with (distance C  435 )−(Cartesian distance y  445 ). Similarly, in equation (2), (distance C  435 )−(Cartesian distance y  445 ) is replaced with distance y  445 . 
         [0046]    Algebraic manipulation of equations (1) and (2) yields equations for Cartesian distances x  440  and y  445  given by equations (3) and (4). 
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         [0047]    Equations (3) and (4) can be applied to each embedded object to determine the location within the medium  405 . When combined with the data describing the longitudinal location, each embedded object can be uniquely identified by its location using the derived Cartesian distances. 
         [0048]      FIG. 5  shows locations of an object detected by a first detector and a second detector. Graph  500   a  shows the location of an object within a medium as detected by a first detector. Graph  500   b  shows the location of the object within a medium as detected by a second detector. 
         [0049]    Graph  500   a  is composed of an angle axis  505   a  and a longitudinal axis  510   a . In Graph  500   a , angle axis  505   a  is marked with three angular measurements. First, the angular measurement  515   a  is the angle at which the first detector detected radiation that had been altered by the medium. Between zero degrees and angular measurement  515   a , the first detector did not detect radiation that had been altered by the medium. In some implementations, the first detector cannot detect radiation between zero degrees and a particular angle. For example, the first detector may not be able to detect radiation between zero degrees and fifteen degrees. Thus, zero degrees to fifteen degrees would not be in the field of view of the first detector. Second, the angular measurement  520   a  is the angle at which the first detector detected radiation that had been altered by an objected embedded in the medium. Third, the angular measurement  525   a  is the angle at which the first detector again did not detect radiation that had been altered by the medium. 
         [0050]    The longitudinal axis  510   a  is marked by three measurements. First, the measurement  530   a  is the location at which the medium first begins to pass through the radiation generated by the first radiation source. Second, the measurement  535   a  is the location at which the first detector detected radiation that had been altered by an objected embedded in the medium. Third, the measurement  540   a  is the location at which the medium last passed through the radiation generated by the first radiation source. Coordinate  545   a  indicates the location of the embedded object as measured by the first detector. 
         [0051]    Graph  500   a  summarizes the output of the first detector. The graph  500   a  displays the ranges of angular measurements and longitudinal measurements where the medium passes through the radiation produced by the first radiation source. If there were multiple objects embedded in the medium, then there would be multiple coordinates on the graph  500   a  indicating the location of the embedded objects. 
         [0052]    Similarly, graph  500   b  summarizes the output of the second detector. The graph displays the ranges of angular measurements and longitudinal measurements where the medium passes through the radiation produced by the second radiation source. For example, graph  500   b  shows angular measurements  515   b  and  525   b  on angular axis  505   b  as the range of angles where the medium altered radiation produced by the second radiation source. Angular measurement  520   b  on the angular axis  505   b  represents the location where the second detector detected radiation that had been altered by the object embedded in the medium. Longitudinal measurements  530   b  and  540   b  on the longitudinal axis  510   b  as the range of longitudinal measurements where the medium altered radiation produced by the second radiation source. Longitudinal measurement  535   b  on the longitudinal axis  510   b  represents the location where the radiation had been altered by the object embedded in the medium. Coordinate  545   b  indicates the location of the embedded object measured by the second detector. 
         [0053]      FIG. 6  shows an example of a process  600  for computing coordinates of an embedded object, for example, object  410  in  FIG. 4 , using radiation. The process  600  collects data received by a first detector and a second detector during irradiation of a medium. In some implementations, the medium is a fiber bundle that has many embedded objects that were embedded from an explosion that detonated near the medium. The process  600  processes the received data and computes coordinates that identify the location of each embedded object in three dimensions. The process  600  will be described as being performed by an imaging system, for example, the system  100  as shown in  FIG. 1 . 
         [0054]    The system receives first data from a first detector ( 605 ). The first detector absorbs radiation that is generated by a first radiation source, for example, radiation source  415  as shown in  FIG. 4 . The first radiation source is located in a position where it can expose a cross section of the medium, for example, medium  405  as shown in  FIG. 4 , to radiation. Some of the radiation is absorbed by the medium. Various levels of absorption occur depending on whether the radiation is absorbed by the medium or an object, for example, object  410  as shown in  FIG. 4 , embedded in the medium. The first detector absorbs the radiation that has passed through or been attenuated by the medium and the embedded objects. The system uses the data gathered by the first detector to determine two measurements associated with each object. The first measurement is a polar angle, for example, angle  425  as shown in  FIG. 4 , that measures the angle created between a reference line, for example, fixed line  427  as shown in  FIG. 4 , and a line passing through the object and the first radiation source, for example, radiation line  429  as shown in  FIG. 4 . The second measurement is a measurement along a longitudinal axis. The second measurement represents the location of the cross section of the medium where the object is located. 
         [0055]    When combined, the first and the second measurements are similar to cylindrical coordinates. Cylindrical coordinates typically contain a radius, an angle, and a longitudinal distance. The system determines the angle and the longitudinal distance. The radius is constant for each location on the first detector. For example, if a radiation photon is directed at a particular angle towards an embedded object that is a particular distance away and the photon is absorbed by the object, the first detector will detect attenuated radiation at the location of the particular angle on the detector. If a radiation photon is directed at the particular angle towards an embedded object that is double the particular distance away and the photon is absorbed by the object, the first detector will detect attenuated radiation at the location of the particular angle on the detector. In other words, the first detector detects the angle of the radiation produced by the first radiation source, but lacks enough information to determine the radial distance of the particle from the source. 
         [0056]    The system receives second data from a second detector that is located about orthogonally to the first detector ( 610 ). The second detector detects radiation from a second radiation source, for example, radiation source  420  as shown in  FIG. 4 . The second radiation source is located about orthogonally to the first radiation source. For example, if the first radiation source is located to the side of the medium and projects radiation generally horizontally, the second radiation source would be located above the medium and project radiation generally downward. Similar to the first detector, the second detector can detect the angle, for example, angle  430  as shown in  FIG. 4 , of the detected radiation, but lacks enough information to determine the radial distance, for example, radiation line  434  as shown in  FIG. 4 , from the second source to a particular object embedded in the medium. In some implementations, the longitudinal measurement is not determined with data collected by the first and second detectors. For example, the longitudinal measurement can be determined based upon the location of the transport mechanism used to move the medium through the path of the radiation. The location of the transport mechanism can be set to zero when the first cross section of the medium is irradiated. 
         [0057]    The system determines the first coordinate  440  and the second coordinate  445  of an embedded object based on the first angular data  425  and the second angular data  430  ( 615 ). The first data may correspond to the radiation angle  425  associated with the left vertical reference line  427  and the line  429  between the first source and the embedded object. The second data may correspond to the radiation angle  430  associated with the top horizontal reference line  432  and the line  434  between the second source and the embedded object. The first coordinate  440  corresponds to the first Cartesian distance identifying a location of the embedded object with respect to the reference point  415 . For example, the first coordinate may correspond to the first Cartesian distance  440  as shown in  FIG. 4 . The second coordinate  445  corresponds to the second Cartesian distance identifying a location of the embedded object. For example, the second coordinate may correspond to the second Cartesian distance  445  as shown in  FIG. 4 . 
         [0058]    As described above, (i) the radiation angle  425  associated with left vertical reference line  427  and the line  429  between the first source and the embedded object, (ii) the radiation angle associated with top horizontal reference line  432  and the line  434  between the second source and the embedded object, and (iii) the distance  435  between the first source and the second source, may be combined to determine the first Cartesian distance  440  and the second Cartesian distance  445 . The system determines the first Cartesian distance  440  and the second Cartesian distance  445  with respect to an origin  415 . In some implementations, the origin is the radiation point of the first source, for example, the first source  415  as shown in  FIG. 4 . If the origin is the first source, then the system determines the first Cartesian distance  440  and second Cartesian distance  445  using Equations (5) and (6). 
         [0000]    
       
         
           
             
               
                 
                   
                     first 
                      
                     
                         
                     
                      
                     cartesian 
                      
                     
                         
                     
                      
                     distance 
                      
                     
                         
                     
                      
                     
                       ( 
                       440 
                       ) 
                     
                   
                   = 
                   
                     
                       distance 
                        
                       
                           
                       
                        
                       between 
                        
                       
                           
                       
                        
                       sources 
                        
                       
                           
                       
                        
                       
                         ( 
                         435 
                         ) 
                       
                     
                     
                       
                         tan 
                          
                         
                           ( 
                           
                             second 
                              
                             
                                 
                             
                              
                             detector 
                              
                             
                                 
                             
                              
                             angle 
                              
                             
                                 
                             
                              
                             
                               ( 
                               430 
                               ) 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         cot 
                          
                         
                           ( 
                           
                             first 
                              
                             
                                 
                             
                              
                             detector 
                              
                             
                                 
                             
                              
                             angle 
                              
                             
                                 
                             
                              
                             
                               ( 
                               425 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   
                     second 
                      
                     
                         
                     
                      
                     cartesian 
                      
                     
                         
                     
                      
                     distance 
                      
                     
                         
                     
                      
                     
                       ( 
                       445 
                       ) 
                     
                   
                   = 
                   
                     
                       
                         ( 
                         
                           distance 
                            
                           
                               
                           
                            
                           between 
                            
                           
                               
                           
                            
                           sources 
                            
                           
                               
                           
                            
                           
                             ( 
                             435 
                             ) 
                           
                         
                         ) 
                       
                       * 
                       
                         ( 
                         
                           cot 
                            
                           
                             ( 
                             
                               first 
                                
                               
                                   
                               
                                
                               detector 
                                
                               
                                   
                               
                                
                               angle 
                                
                               
                                   
                               
                                
                               
                                 ( 
                                 425 
                                 ) 
                               
                             
                             ) 
                           
                         
                         ) 
                       
                     
                     
                       
                         tan 
                          
                         
                           ( 
                           
                             second 
                              
                             
                                 
                             
                              
                             detector 
                              
                             
                                 
                             
                              
                             angle 
                              
                             
                                 
                             
                              
                             
                               ( 
                               430 
                               ) 
                             
                           
                           ) 
                         
                       
                       + 
                       
                         cot 
                          
                         
                           ( 
                           
                             first 
                              
                             
                                 
                             
                              
                             detector 
                              
                             
                                 
                             
                              
                             angle 
                              
                             
                                 
                             
                              
                             
                               ( 
                               425 
                               ) 
                             
                           
                           ) 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0059]    Equations (5) and (6), along with the location of the transport mechanism, can be applied to each embedded object in the medium to uniquely identify the absolute location of each object in Cartesian coordinates. In other implementations, the user defined origin may not be one of the radiation sources, but rather a reference marker. For example, a metal cross may be placed at a corner of the medium, and the metal cross provides the user defined origin. In this case, the system calculates the first and second Cartesian distances as given in Equations (5) and (6) and adjusts the first and second Cartesian distances by additional offsets. As shown in  FIG. 4 , the reference marker may be placed at location  460 . The system would subtract offset  465  from the first Cartesian distance  440  and subtract offset  470  from the second Cartesian distance  445 . Additionally, the system would correct the longitudinal measurements based on the reference marker. 
         [0060]    The detectors typically cannot see the actual size of the particle, just the pattern of the detected radiation. Because the radiation is coming from a point source, the “shadow” cast by an object that absorbs a portion of the radiation will be greater at the detector than the size of the object. The “shadow” will be larger as the object is located farther from the detector. The “shadow” will be closer to the object size as the object is located closer to the detector. The error in estimation of the object size can be corrected once the system determines the location of the object. The magnification error can be calculated with equation (7). 
         [0000]    
       
         
           
             
               
                 
                   
                     measurement 
                      
                     
                         
                     
                      
                     error 
                      
                     
                         
                     
                      
                     due 
                      
                     
                         
                     
                      
                     to 
                      
                     
                         
                     
                      
                     magnification 
                   
                   = 
                   
                     
                       ( 
                       
                         
                           
                             ( 
                             
                               source 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               detector 
                                
                               
                                   
                               
                                
                               distance 
                             
                             ) 
                           
                           
                             ( 
                             
                               source 
                                
                               
                                   
                               
                                
                               to 
                                
                               
                                   
                               
                                
                               object 
                                
                               
                                   
                               
                                
                               distance 
                             
                             ) 
                           
                         
                         - 
                         1 
                       
                       ) 
                     
                     * 
                     
                       ( 
                       
                         object 
                          
                         
                             
                         
                          
                         size 
                       
                       ) 
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0061]    A number of implementations have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the disclosure. Accordingly, other implementations are within the scope of the following claims.