before explaining the disclosed embodiment of the present invention in detail it is understood that the invention is not limited in its application to the details of the particular arrangement shown since the invention is capable of other embodiments . also , the terminology used herein is for the purpose of description and not of limitation . the details are explained on the arccheck detector array , but the same approach is applicable to any 3d detector . all the equations are in the arccheck coordination system ( fig2 ) and linac coordination system ( fig1 ). for an initial example , it is assumed that arccheck coordinates are perfectly aligned with the linac coordinates , i . e . [ ax ; ay ; az ]=[ x ; y ; z ]=[ 0 ; 0 ; 0 ] and axis alignment : ax = x , ay = y ( no rotation is applied ). the gantry rotates in the xz plane at a distance from the center ( sad ). it can be expressed as the equation 2 , but it is more beneficial to express it in the cylindrical coordinate system : sad is a fixed value and the only variable is then angle w that defines position of the radiation beam . defining the projection plane as a plane that is parallel to the ay axis ( as well as y axis in this case ), goes through the point [ ax ; ay ; az ]=[ x ; y ; z ]=[ 0 ; 0 ; 0 ] and is always normal to the angle ω . the construction of the plane under these conditions assures that the arccheck detector array is cut in half . the next step is to calculate images of the halves of arccheck . the method described here is based on creation of projection plane transformation matrixes and using this transformation matrix for generating the images . this method has the advantage of being efficient from a computing perspective , although other methods are possible . the arccheck detector array is a cylinder and can be described very efficiently using cylindrical coordinate system . we can define a function mv ( measured value ) that returns measured value at given cylindrical coordinates : if the density of detectors is not infinite , one can select the closest detector , or use several types of interpolations . the projection plane transformation matrix is a 3d matrix with dimensions ( k , l , 3 ), where k and l represent size of the images on the projection plane the plane being measured in pixels . the third dimension contains three parameters : shift of the point on the y axis , angle α and an attenuation parameter ( at ). the plane transformation matrix has to be calculated only once and it has to be calculated for both halves of arccheck . the transformation matrix can be calculated for one , fixed position ignoring the other angles , because the system of gantry and arccheck array is invariant to rotation around y axis ( or ay axis ). fig7 demonstrates one , fixed position of the system linac and arccheck . the fig7 also demonstrates why it is necessary to calculate the transformation matrix only once and why it can be calculated at one , fixed angle . the top beamlet crosses arccheck at α − 1 + ω and β − 1 + ω , where these angles are angles in the arccheck coordinate system . the top beamlet crosses the projection plane in the point t . the point t has always the same location on the projection plane at all gantry angles ω , because the projection plane is always normal to the beam . at all gantry angles ω , the beamlet crosses the arccheck array at angle α − 1 with respect to the projection plane . target coordinates are : tartget = t [ x 2 ; y 2 ; z 2 ]= t [ sad ; 0 ; 0 ]] x =( x 2 − x 1 )· t + x 1 , y = ( y 2 − y 1 )· t + y 1 , z = ( z 2 − z 1 )· t + z 1 . equation 5 solving for intersections between the beamlet and arccheck detector array ( equation 2 and equation 3 ) and taking into account that coordination systems of arccheck and linac are identical , we can put ax = x , ay = y , az = z . (( x 2 − x 1 )· t + x 1 ) 2 +(( z 2 − z 1 )· t + z 1 ) 2 = radius 2 equation 6 t 2 └( x 2 − x 1 ) 2 +( z 2 − z 1 ) 2 ┘+ t · 2 ·[ x 1 ·( x 2 − x 1 )+ z 1 ·( z 2 − z 1 )]+ x 1 2 + z 1 2 − radius 2 = 0 equation 7 equation 7 is simplified by using the coordinates of the target ( beam source ). it is further simplified by taking into account that the projection plane x coordinate is 0 . t 2 ·[ sad 2 + z 1 2 ]+ t · 2 ·[− z 1 2 ]+ z 1 2 − radius 2 = 0 equation 8 note : equation 8 has only one variable , which is z 1 . this variable is used for filling the image with values . the variable z 1 corresponds to the image size k —( the image has k × l number of pixels , as was defined earlier ). the k variable corresponds to y axis and l variable corresponds to z axis in the linac coordination system . equation 8 gives two solutions for each beamlet going through point z 1 . using results of the equation 8 and equation 2 , one can calculate cross sections of the beamlet and arccheck detector array . the result is in cartesian coordinates , and should be converted into cylindrical coordinates . for each pixel location , with coordinates y 1 and z 1 , one can calculate angles α and β and also coordinate y on the arccheck detector array using equation 9 . these values are stored in the two projection plane transformation matrixes . one matrix contains y 1 and α 1 , the second contains y 2 and α 2 . graphical representation of the tm matrix is shown on the fig8 . the red spot represents one pixel of one of the images . the third value ( attenuation parameter — at ) can be calculated in theory using some beam transport calculation or other techniques , but it is easier to measure it . the measurement is preferably done for all energies and in case of arccheck , for scenarios with and without a plug . the projection plane transformation matrix contains angle and y axis coordinate for each pixel location . it also contains attenuation factor for that angle and y axis coordinate . the measurement can be done by open field measurement . fig3 shows beam attenuation at y = 0 coordinate . the attenuation profile is in cylindrical coordinates . each point represents one detector . attenuation at certain angles between detectors can be interpolated from two neighboring detectors , only if such an interpolation follows the true attenuation profile . the similar profiles ( similar to fig3 ) have to be measured for all y coordinates and stored in appropriate places in the projection plane transformation matrix . note : the fig3 is presented in the cylindrical coordinates , which are α and β coordinates . the a coordinates correspond to angles 270 - 0 - 90 and to β coordinates correspond angles 90 - 270 . the goal is to calculate diff function for all angles and locate the global minimum , which corresponds to the real source position . the diff function ( equation 1 ) requires two images for each angle ω . the images are calculated using the plane transformation matrixes as : there are moments when the 3d detector is shifted or even rotated in some clinical cases . the arccheck coordination system and linac coordination system are no longer identical anymore and the above approach is modified . once the 3d detector is shifted , rotated or both , the system ( linac and 3d detector ) is not invariant to rotation around y axis anymore , unless the shift is done in the y axis only . the shift in y direction is not described here , because it is almost identical to the equations above . because the system is not invariant to rotation , the projection plane transformation matrix has 4 dimensions , instead of 3 . the transformation matrix with shift and rotation can be presented as ( tm_sr ( k , l , 3 , ω )), where k and l represent size of the projection plane . the third dimension contains three parameters : shift of the point in y axis , angle a and attenuation parameter ( at ). the fourth dimension is angle of the gantry . the transformation matrix with shift and rotation ( tm_sr ) is like a tm matrix for each angle . the tm_sr has to be calculated only once . it is advantageous to use the arccheck coordination system for the tm_sr calculation . the method is the same as above , but with some modifications : taking the example of a 3d detector rotated around 3 different axis by angles τ , θ , φ and also shifted by a vector [ sx ; sy and sz ], the beam source coordinates in the linac coordination system are : the projection plane is still located in the middle of arccheck . because the system is not invariant to rotation around y axis , the projection plane has to rotate as well . the rotation should follow the gantry rotation , but it is not a requirement . the following equation describes coordinates of the projection plane that is normal to the angle ω . projection plane coordinates : pp = pp [ x 1 ; y 1 ; z 1 ]= pp [ k · cos ( ω ); l ; k · sin ( ω )], equation 12 arccheck is described by equation 2 . using beamlet equations ( equation 3 ) and transformed coordinates of the source , we can calculate : (( x ′ 2 ( ω )− x 1 ( ω ))· t + x 1 ( ω )) 2 +(( z ′ 2 ( ω )− z 1 ( ω ))· t + z 1 ( ω )) 2 = radius 2 equation 13 t 2 ·└( x ′ 2 ( ω )− x 1 ( ω )) 2 +( z ′ 2 ( ω )− z 1 ( ω )) 2 ┘+ t · 2 ·[ x 1 ( ω )·( x ′ 2 ( ω )− x 1 ( ω ))+ z 1 ( ω )·( z ′ 2 ( ω )− z 1 ( ω ))]+ x 1 2 ( ω )+ z 1 2 ( ω )− radius 2 = 0 equation 14 equation 14 results in two solutions for each beamlet at given angle . using results of the equation 14 and equation 3 , one can calculate cross sections of the beamlet and arccheck detector array . the result is in cartesian coordinates and should be converted into cylindrical coordinates : unless the shift or rotation is significant , the attenuation factors are very close to the default values . if greater accuracy is required , or if the shift and rotation are not negligible , the attenuation factors have to be measured or calculated for each specific system setup . the goal is to calculate diff function for all angles and locate the global minimum , which corresponds to the real source position . the diff function ( equation 1 ) requires two images for each angle ω . the images are calculated using the projection plane transformation matrixes with shift and rotation as : image1 i , j ( ω )= tm1 — sr ( i , j , 3 , ω )· mv ( tm1 — sr ( i , j , 1 , ω ), tm1 — sr ( i , j , 2 , ω )) image2 i , j ( ω )= tm2 — sr ( i , j , 3 , ω )· mv ( tm2 — sr ( i , j , 1 , ω ), tm2 — sr ( i , j , 2 , ω )) equation 16 the foregoing description is provided for exemplary and illustrative purposes ; the present invention is not necessarily limited thereto . rather , those skilled in the art will appreciate that various modifications , as well as adaptations for particular circumstances , fall with the scope of the invention herein shown and described and of the claims appended hereto .
a method has been developed to reconstruct angle of the radiation field using a 3d measurement device . the 3d measurement device is positioned in the radiation beam . the novel method uses measured values and information about attenuation in the 3d detector and calculates direction of the primary beam .