# Ultrasonix linear probe calibration matrix

**URL:** <https://discourse.slicer.org/t/ultrasonix-linear-probe-calibration-matrix/11140>\
**Category:** Support\
**Tags:** surgical-navigation, ultrasound, slicerigt\
**Created:** [April 16, 2020, 2:54am UTC](https://discourse.slicer.org/t/ultrasonix-linear-probe-calibration-matrix/11140 "2020-04-16T02:54:51Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![mta152](https://avatars.discourse-cdn.com/v4/letter/m/8dc957/32.png) [@mta152](https://discourse.slicer.org/u/mta152)\
**Post date:** [April 16, 2020, 2:54am UTC](https://discourse.slicer.org/t/ultrasonix-linear-probe-calibration-matrix/11140/1 "2020-04-16T02:54:51Z")

</div>

Hi,

I have a little confusion about the calibration matrix (referred to as C matrix) for the linear probe. As written in this website: [GPS Data Collection - WikiSonix](http://www.ultrasonix.com/wikisonix/index.php/GPS_Data_Collection), C is a 3x3 matrix and based on this website [Plus applications user manual: Ultrasonix ultrasound systems](http://perk-software.cs.queensu.ca/plus/doc/nightly/user/DeviceSonixVideo.html), C is reformed to be a 4x4 transformation matrix (referred to as T). I can do simple math to verify both are fine, but here is what I am confused:

1. As written on both websites “% Ultrasonix uses [1yx] coordinates (first column is origin, second column is Y axis, third column is X axis)”, we can compute the missing Z axis by:  
Z axis vector = cross(X,Y). Now if [X, Y, Z] represents a rotation matrix, why norm(Y) != 1. Appreciate that norm(Y) is close to being 1, but why it is not 1.
2. Given the rotation matrix R = [X, Y, Z] and in order to avoid the confusion left-hand and right-hand rules may bring up, I used the combined transformation matrix (R\_ref = Rz_Ry_Rx) as written in the bottom of this website as a reference: [Yaw, pitch, and roll rotations](http://planning.cs.uiuc.edu/node102.html)  
My question is  
R = R\_ref or R = transpose(R\_ref) ?

Any suggestion is appreciated. Thank you.

Best regards,  
Mike