Coordinate Systems

Gridscan Coordinate System

The diagram below shows how the coordinate system used in the 3D gridscan relates to the beam and sample loop. The blue arrows indicate the direction of the beam. The red grids represent the grids used during the scan.

Motors Coordinate System

The diagram below shows the x,y,z directions of the smargon motor coordinate system. The smargon y, z axes change with the $\omega$. x,y,z are measured in millimetres.

• The pin runs from -ve x to +ve x
• y is +ve towards the ceiling when $\omega = 0$.
• z is +ve towards the detector/oav and parallel to the beam when $\omega = 0$.
• The x and y coordinates of the image are also shown, the image feed has x from left to right, y from top to bottom, with the pin to the right of the image.
• $\omega$ rotates from the y axis at $omega = 0$ (the floor to ceiling).

$\omega = 0$

$\omega = \alpha$

OAV Image Coordinate System

In the OAV image the below coordinate system is used (with units in pixels).

Conversion Between OAV Image and Smargon

At $\omega = 0$, $x$ and $y$ in the camera are antiparallel to $x$ and $y$ in the smargon. $y$ in the camera are is parallel to $z$ of the smargon at $x$ = $\frac{\pi}{2}$. Then to convert from the camera to smargon coordinate systems we map

$$x_\text{smargon} = -x, \quad y_\text{smargon} = -y\cos(\omega),\quad z_\text{smargon} = y sin(\omega).$$