FFF.1.2.4 Positioner Movement

FFF.1.2.4.1 Positioner Movement in the Isocenter Coordinate System

The positioner coordinate system is defined in section C.8.19.6.13.1.2 of PS 3.3 where the positioner angles are represented as (Ap 1 , Ap 2 , Ap 3 ).

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system can be expressed as a point (P X , P Y , P Z ) in the Isocenter coordinate system by applying the following transformation:

(P X , P Y , P Z ) T = (R 2 . R 1 ) T . ( R 3 T . (P Xp , P Yp , P Zp ) T )

And inversely, a point (P X , P Y , P Z ) in the Isocenter coordinate system can be expressed as a point (P Xp , P Yp , P Zp ) in the positioner coordinate system by applying the following transformation:

(P Xp , P Yp , P Zp ) T = R 3 . ( (R 2 . R 1 ) . (P X , P Y , P Z ) T )

Where R 1 , R 2 and R 3 are defined as follows:

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FFF.1.2.4.2 X-Ray Incidence and Image Coordinate System

The following concepts illustrate the model of X-Ray cone-beam projection:

The X-Ray incidence represents the vector going from the X-Ray source to the Isocenter.

The receptor plane represents the plane perpendicular to the X-Ray Incidence, at distance SID from the X-Ray source. Applies for both image intensifier and digital detector. In case of digital detector it is equivalent to the detector plane.

The image coordinate system is represented by (o, u, v), where “o” is the projection of the Isocenter on the receptor plane.

The source to isocenter distance is called ISO. The source image receptor distance is called SID.

The projection of a point (P Xp , P Yp , P Zp ) in the positioner coordinate system is represented as a point (P u , P v ) in the image coordinate system.

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Figure FFF.1.2-8Projection of a Point of the Positioner Coordinate System

A point (P Xp , P Yp , P Zp ) in the positioner coordinate system (O p , X p , Y p , Z p ) can be expressed as a point (P u , P v ) in the image coordinate system by applying the following transformation:

P u = (SID / (ISO – P Yp ) ) . P Xp

P v = (SID / (ISO – P Yp ) ) . P Zp

The ratio SID / (ISO - P Yp ) is also called magnification ratio of this particular point.