Coordinate System

Figure 2.7: ZY mounted on monument, side view.

The ZY points the laser beam by moving the servo motors of the Beam Steering Mirror until they are at some predetermined position, as determined by the encoders (after they are homed). In the early days of the ZY, the position of the cubes in terms of encoder counts was determined manually for each ZY by trial and error. Should the ZP unit be swapped for another, the positions of the cubes would have to be determined anew. If the position of the cube changed with time, a trajectory of the cube would have to be calculated, in encoder counts, for each ZY. As the number of cubes and ZYs increased, this method of pointing the lasers to the cubes quickly became impractical, and was soon replaced by the current system[8]. In this system, the positions of the cubes and lasers were all given as cartesian coordinates in a common coordinate system whose origin is at the GBT pintle center, sea level, with X = East, Y = North and Z = Up[13]. It then is up to the ZY to convert these to the polar encoder coordinate system, whose origin is at the center of the ZP's beam steering mirror (as many as 6 of the ZP assemblies will be mounted on the telescope itself, so it is important that the ZY be able to make this conversion on the fly). This is done by the ZY's Coordinate System (see figure 2.3). To better understand how the Coordinate System works it helps to understand how the ZP ranger unit is mounted. Each ZP is to be mounted on a Kelvin mount, located atop a concrete monument or attached to some other structure, as seen in figure 2.7. The Kelvin mount consists of a socket mount, a ``V'' mount and a flat mount, all of which locate tooling balls mounted to the bottom of the ZP unit. The socket locates a tooling ball mounted directly under the center of the Beam Steering Mirrors. This tooling ball is constrained by the socket in all three dimensions. The V-mount locates a tooling ball mounted directly beneath the ZP's collecting optics, and constrains the ZP in two dimensions, allowing it freedom to move along its long axis. Finally, the ZP's third tooling ball rides on a flat mount, which fixes the ZP's mounting angle but allows the ball to slide along the ZP's length and width dimensions. For the Coordinate System to work properly, the ZY requires the following information:

1. The location, in the global coordinate system, of the monument mounting point where the ZP is mounted. This is the center of the tooling ball as it sits in the Kelvin mount's socket mount (see BP).
2. The orientation, in angles relative to the global coordinate system's unit basis vectors, of the monument's Kelvin mount (see ALPHA).
3. The location of the exact center of the Beam Steering Mirror, in the ZP's coordinate system, relative to the ZP's socket mounted tooling ball (see MO).
4. The correction angles for the beam steering mirror. These correct for any rotations in the mirror system (see BETA).
5. The zero-points of the encoders, used to compensate for differences in the physical location of the encoders (see EZ).
6. The location of the retroreflector target, in the global coordinate system (see COO).

Using all of this information, the ZY can calculate the Az/El encoder readings necessary to point the laser to the desired cube target. Because the coordinate transformations required are fairly lengthy and time consuming calculations, the ZY will cache the resulting Az/El coordinates calculated for a cube, and re-use them if none of the above items changes. Further, the ZY uses ``lazy evaluation'' in calculating the Az/El encoder values for a cube: The coordinate transformation is only made when the Az/El values are actually needed. The ZY will re-calculate the Az/El coordinates if the ZY is supplied with new cube coordinates. It will also recalculate the Az/El coordinates if any of the remaining items in the list above changed. In this case, all calculated Az/El coordinates cached by the ZY are declared invalid and are re-calculated as needed. This system provides the following advantages:

• All locations, of retroreflectors and ZY and others, can be determined by the use of established surveying techniques.
• The coordinates of a cube are the same for any ZY, no matter what the position of the ZY. This reduces the maintenance burden of keeping cube coordinates, and also allows trajectories of moving targets to be calculated in the global coordinate system.
• The ZP is now easily interchangeable. All that is required to install a new ZP is to update the information in items 3, 4, and 5 of the required information list presented above. The ZY will automatically know to recalculate the Az/El values for cubes as needed.