Mosaics of CCD fields are useful in various kinds of observing programs, such as sky surveys and recoveries of Near-Earth Objects (NEOs) and comets. Sky surveys would normally employ mosaics consisting of rows of fields-of-view aligned with the east-west direction. NEO and comet recoveries normally involve searching along a narrow line in the sky, whose orientation may be arbitrary. To minimize the telescope time required to perform the search, TAO allows one to specify mosaics whose rows are aligned at an arbitrary position angle. It is often the case that a single row of partially overlapping fields-of-view is enough to cover the recovery search line. If necessary, a mosaic consisting of various parallel rows of fields-of-view oriented at an arbitrary position angle may also be specified. The TAO scheduler automatically takes care of minimizing the overlap between the fields in the various rows of the mosaic, so as to maximize the sky coverage per unit time. Mosaics of CCD fields are also very useful when trying to confirm objects listed in the NEO Confirmation Page (NEOCP). In this case the observation requests specifying the search mosaics will be automatically written by script NEOCPMon to file TAO\targets\NEOCP.stg.

Minor planet recoveries usually start by determining the length and orientation of the ephemeris uncertainty line (which in reality is often a very elongated uncertainty ellipse). For a subset of the known minor planets, this information may be obtained from the following sources:

• Near-Earth Object Dynamics Site (NEODyS) (uncertainties for known NEOs)

• Minor Planet Ephemeris Service (uncertainties for unusual minor planets which are not NEOs)

• Asteroid Dynamics Site (AstDyS) (uncertainties for certain asteroids which are not NEOs)

• Asteroid Ephemeris (AstEph) service

As an example, let us consider a hypothetical attempt to recover the Amor object 2002 XH4 at Valinhos (MPC code 860) on 2004 August 21 UT:

2002 XH4; &
  PA=36.5 width=3.50 overlap=1.50 dRA=-.00137 ddec=-.02052 &
     0    0 &
    -1    0 &
     1    0 &
    -2    0 &
     2    0

The parameters specifying the search mosaic appear on continuation lines below the initial line

2002 XH4; &

The & character at the end of all lines but the last one indicates that the observation request continues on the next line.

The first continuation line specifies the mosaic geometry parameters through the following five keywords:

• PA. This is the position angle (expressed in degrees) of the mosaic rows, which for a recovery attempt should coincide with the position angle of the uncertainty line or the major axis of the uncertainty ellipse (blue line in the figure).

• width. This is the minimum width (expressed in arcminutes) of a strip oriented parallel to the mosaic rows and whose central line passes through the center of the mosaic (blue dot in the above figure; see discussion of dRA and dDec below) which is guaranteed to be covered by the central row (see next paragraph for a definition) of the search mosaic. Depending on the orientation of the mosaic rows, the search fields on the central row can cover a strip which is wider than the minimum width specified in this keyword. The value of width should be a fraction of the smallest dimension of the CCD field-of-view.

• overlap. This is the minimum overlap (in acrminutes) between adjacent fields in a search mosaic. This should be of the order of your telescope's worst-case pointing errors to avoid the possibility of leaving unsearched "holes" in the mosaic when the search is carried out. The mosaics built by the scheduler may actually have an overlap between fields which is greater than the minimum overlap specified in this option. This is sometimes necessary to ensure that the mosaic covers a strip of the specified width along the central row. Larger values of the width parameter tend to increase the amount of this "extra overlap", increasing the number of fields (and hence the amount of telescope time) required to cover a given area.

• dRA. This is the coordinate displacement in right ascension (expressed in hours) between the center of the mosaic (blue dot in the figure) and the target's nominal position (green dot in the figure; for minor planets and comets, this position is computed by interpolating on the ephemeris available in the moving object database). In the example we are considering, this parameter might have been safely set to zero, in which case the center of the mosaic would coincide with the target's nominal position. However, there are situations (most commonly in the confirmation of objects listed on the NEOCP) where the nominal position may be quite distant from the uncertainty region, so the whole search mosaic should be offset from the nominal position.

• dDec. This parameter represents the coordinate displacement in declination (expressed in degrees) between the center of the mosaic and the target's nominal position.

Each of the remaining continuation lines specifies one field-of-view to be imaged. Each field is identified by a pair of integers (i, j). The central field of the mosaic (0,0) is centered at the center of the mosaic (blue dot in the above figure). Field (1,0) is obtained by shifting the central field by a certain distance D toward the position angle specified in the PA keyword. This distance D depends on the values of PA, width, overlap, and the dimensions of the field-of-view. Fields (2,0), (3,0),... are obtained by shifting field (0,0) by distances 2D, 3D,... toward the same position angle. Fields (-1,0), (-2,0),... are directly opposite to (1,0), (2,0),..., respectively, with respect to the central field. The fields labeled (i,0), where i is an integer, form the central row of the mosaic. In the above example, the narrow uncertainty ellipse can be covered with the five fields (0,0), (1,0), (-1,0), (2,0), (-2,0) belonging to the central row. These are the five fields requested in the last five continuation lines of the observation request.

If one needs to cover a wider strip around the central row, one can request observations of fields located along rows which are parallel to the central row but displaced from it by multiples of a certain distance L. The two rows adjacent to the central row (one on each side) have fields labeled (i,1) and (i,-1), where i is an integer. Field (0,1) is obtained by displacing the central field by a certain distance towards a certain position angle which differs from the position angle specified by the keyword PA. In the above figure, the center of field (0,1) would be located at the end of the horizontal line segment emanating from the blue dot. Fields (1,1), (2,1),... are obtained by displacing (0,1) by distances D, 2D,... toward the position angle specified with the keyword PA. Fields (-1,1), (-2,1),... are directly opposite to (1,1), (2,1),..., respectively, with respect to (0,1). A field (i,-1) on the opposite row may be obtained by reflecting field (-i,1) with respect to the central field.

In general, the offset of the center of field (i,j) with respect to the center of field (0,0) is given by a vector

where u is a vector of length D pointing toward the position angle specified by keyword PA and v is another suitable vector which is not parallel to u. The centers of the mosaic fields form a regular lattice near the center of the mosaic, with basis vectors u and v.