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## Definitions

Define the following variables:

F
The focal length (mm).
$ψ$
The sky position angle in radians.
$ψ$0
The offset between the coordinate system of the guide probe and that of the instrument rotator, in radians.
$ε$
The handedness of the guide-probe coordinate system ($±$1).
x y
Guide probe coordinates, in encoder units.
xmin xmax ymin ymax
xy limits on the area within which guide stars may be selected, in encoder units.
r $θ$
Polar coordinates of the guide probe (encoder units; r is positive by definition).
$θ$min θmax rmin rmax
Limits on the area within which guide stars may be selected, in polar coordinates; encoder units).
er eθ
The linear and angular encoder scales in mm/encoder unit and rad/encoder unit, respectively.
x0 y0
The position of the centre of rotation in encoder units in the guide probe coordinate system (used for xy systems only).
r0
The radial offset for guide probe coordinates, in encoder units (used for r$θ$ systems only).

All of the existing A&G boxes on the La Palma telescopes use xy stages for their guide probes, with the exception of the WHT Cassegrain system, which has an r$θ$ arrangement. A general description of the search areas may be given as follows (note that not all configurations use every constraint):

1. $x$min < x < xmax and $y$min < y < ymax (within a rectangle).
2. $[(x-x$0)2 + (y-y0)2]1/2 ≤rmax or $r ≤r$max (within a circle: this may be either a result of vignetting or a restriction on the mechanical travel of the probe).
3. $(x-x$0)2/l2 + (y-y0)2/m2 > 1 (inner ellipse excluded). A minimum radial travel for an r$θ$ system is a special case. A similar condition, $[(x-x$0)2 + (y-y0)2]1/2 > rmin or $r > r$min is used for the ROTATOR ANY option, where the available area is always a circular annulus.
4. $x < x$- or $x > x$+ or $y < y$- or $y > y$+ (i.e. the area $x$- < x < x+ and $y$- < y < y+ is excluded).
5. The probe azimuth is in the range $θ$min < θ< θmax.

Next: Conversion between equatorial coordinate Up: Search Procedures: General Previous: Search Procedures: General

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Mon Mar 1 17:52:09 GMT 1999