Choice of an initial search area

The object here is to choose an area of sky, bounded by curves of constant Right ascension and Declination, which just includes the guide field. The outer boundaries of the guide fields are either circular or rectangular in the tangent plane. In the former case (except for targets near the Poles), the ranges of RA and Dec are given by:

$\Delta \alpha =arctan(R/fcos\delta$₀)

$\Delta \delta =\; R/f$

where R is the radius of the guide field and f is the focal length. This formula fails for the case where $\delta$₀ + R/f > π/2 or $\delta$₀ - R/f > -π/2 (i.e. the guide field includes one of the Poles), in which case all stars with $\delta >\; \delta$₀ - R/f (in the North) or ₀ + R/f (in the South) are selected.

For rectangular guide fields, the RA and Dec of each corner are derived from its tangent-plane position using the formulae:

$tan(\alpha -\; \alpha$₀) = ξsecδ₀ / (f - ηtanδ₀)

$tan\delta =\; \{\eta +\; ftan\delta$₀[(f + ηtanδ₀)² + ξ²sec²δ₀]^1/2}

and the widest range in each coordinate is used in the initial search. A similar caveat applies to guide fields around the Poles, for which the selection is made on Declination alone, as for circular guide fields.