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.