Coordinate Systems

[insert link to Hovercal Coordinates pdf]

The Hovercal project uses four main coordinate systems, all of which are Cartesian and pictured below. Briefly, 

• World System: defined with an origin point on the surface of the Earth

• Telescope System: a translation of the world system, with its origin at the location of the telescope

• Camera System: defined by the orientation of the drone camera, with its origin at the location of the camera

• Line of Sight System: a rotation of the camera system, with its z-axis along the line connecting the telescope and camera system origins and x-axis completely horizontal

One of the goals of the project is to calculate the polarization angle of the electric field vector associated with the drone. This is also referred to as the roll, the angle of the electric field vector in the (x, y) plane of the line of sight coordinate system. Other relevant angles are the yaw (angle of the camera system z axis in the (x, z) plane of the line of sight coordinate system) and pitch (angle of the camera system z axis in the (y, z) plane of the line of sight coordinate system). Yaw and pitch can also be thought of as a measure of how rotated the drone camera is around the line of sight y axis (yaw) and x axis (pitch). 

We define the notation S_{bc} to denote the rotation matrix from the camera coordinate system to the line of sight (boresight) coordinate system and theta_c to denote the angle of the electric field vector in the (x, y) plane of the camera coordinate system. The angles for roll, yaw, and pitch are listed below. Full derivations for these equations can be found in the document linked at the top of this page.