Transformation matix

Doppler systems derive the velocity from the Doppler shift along the acoustic transmit and receive axis. The acoustic transmit/receive paths are rarely orthogonal, which means that the "beam-data" have to be converted to an XYZ reference coordinate system.  This is done as follows:

Imagine that the three beams in your Doppler system form the unity vectors r1,r2,r3.  We can then formulate the matrix G:

G = [r1 r2 r3]

The transformation matrix from beam velocities V1, V2, V3 to the orthogonal components Vx, Vy Vz is the inverse of G:

[Vx, Vy Vz] = inv(G) * [V1 V2 V3];

In the case of the Aquadopp Profiler and most other Nortek equipment, the slant angle with respect to the vertical is 25 degrees.  The transfrom matix is then written:

G=
       |sin25                  0                      cos25     |
       |cos240sin25    sin240sin25             cos25   |
       |cos120sin25    sin120sin25             cos25   |

The inverse of G is:

inv(G)=
       |1.578  -0.789  -0.789  |
       |0      -1.366  1.366     |
       |0.368  0.368   0.368    |

In the Aquadopps, these values are then multiplied wth 4096 before they are entered into the head configuration file.  

You can find the specific values for your system in the *.hdr file.

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