The Volume to Transducer Mapping Matrix (0020,9309) is used to describe the relationship between the Transducer Frame of Reference coordinate system and the Volume Frame of Reference coordinate system.

The Volume to Transducer Mapping Matrix
^{
}
([M
_{
TV
}
]=[P]*[Q]) describes how to transform a point (X
_{
V
}
, Y
_{
V
}
, Z
_{
V
}
) in the Volume coordinate system into (X
_{
X
}
,Y
_{
X
}
, Z
_{
X
}
) in the Transducer coordinate system according to the equation below.

[pic]

Where:

X
_{
V
}
Y
_{
V
}
Z
_{
V
}
The voxel location (in mm) in the Volume Frame of Reference

X
_{
X
}
Y
_{
X
}
Z
_{
X
}
The voxel location (in mm) in the Transducer Frame of Reference

Pij,Pij,Pij A 3x3 matrix of direction cosine values as measured to the Transducer origin from the volume origin.

Qx,Qy,QzThe translation values (in mm) describe the location in mm of the Transducer Frame of Reference (X
_{
X
}
,Y
_{
X
}
, Z
_{
X
}
) origin from the Volume Reference Origin (X
_{
V
}
,Y
_{
V
}
, Z
_{
V
}
)measured in millimeters along the Volume axes i.e. to the transducer origin from the volume origin.

The Volume to Table Mapping Matrix (0020,930A) is used to describe the relationship between the Volume Frame of Reference coordinate system and a modality specific equipment coordinate system. This mapping can be used only with systems that have a well-defined equipment coordinate system.

The Volume to Table Mapping Matrix
^{
}
([M
_{
VG
}
]=[R]*[S]) describes how to transform a point (X
_{
V
}
Y
_{
V
}
Z
_{
V
}
) in the Volume coordinate system into (X
_{
T
}
, Y
_{
T
}
, Z
_{
T
}
) in the Table coordinate system according to the equation below.

[pic]

Where:

X
_{
V
}
Y
_{
V
}
Z
_{
V
}
The voxel location (in mm) in the Volume Frame of Reference

X
_{
T
}
Y
_{
T
}
Z
_{
T
}
The voxel location (in mm) in the Table Frame of Reference

Rij,Rij,Rij A 3x3 matrix of direction cosine values as measured to the gantry origin from the volume origin.

Sx,Sy,SzThe translation values (in mm) describe the location in mm of the Table Frame of Reference (X
_{
T
}
, Y
_{
T
}
, Z
_{
T
}
) origin from the Volume Reference Origin (X
_{
V
}
,Y
_{
V
}
, Z
_{
V
}
)measured in millimeters along the table axes I.e. to the table origin from the volume origin.

Note: The Mapping Matrices are rigid transformations that involve only translations and rotations. Mathematically, the matrix is orthonormal and describes six degrees of freedom: three translations, and three rotations.