Algorithm Descriptions

# Resolving Multiple Detections and Defining Samples

In addition to reading this section, we recommend that users familiarize themselves with the , which indicate what happened to each object during the Resolve procedure.

SDSS scans overlap, leading to duplicate detections of objects in the overlap regions. A variety of unique (i.e., containing no duplicate detections of any objects) well-defined (i.e., areas with explicit boundaries) samples may be derived from the SDSS database. This section describes how to define those samples. The resolve figure is a useful visual aid for the discussion presented below.

Consider a single drift scan along a stripe, called a run. The camera has six columns of CCDs, which scan six swaths across the sky. A given camera column is referred to throughout with the abbreviation camCol. The unit for data processing is the data from a single camCol for a single run. The same data may be processed more than once; repeat processing of the same run/camCol is assigned a unique rerun number. Thus, the fundamental unit of data process is identified by run/rerun/camCol.

While the data from a single run/rerun/camCol is a scan line of data 2048 columns wide by a variable number of rows (approximately 133000 rows per hour of scanning), for purposes of data processing the data is split up into frames 2048 columns wide by 1361 rows long, resulting in approximately 100 frames per scan line per hour of scanning. Additionally, the first 128 rows from the next frame is added to the previous frame, leading to frames 2048 columns wide by 1489 rows long, where the first and last 128 rows overlap the previous and next frame, respectively. Each frame is processed separately. This leads to duplicate detections for objects in the overlap regions between frames. For each frame, we split the overlap regions in half, and consider only those objects whose centroids lie between rows 64 and 1361+64 as the unique detection of that object for that run/rerun/camCol. These objects have the OK_RUN bit set in the "status" bit mask. Thus, if you want a unique sample of all objects detected in a given run/rerun/camCol, restrict yourself to all objects in that run/rerun/camCol with the OK_RUN bit set. The boundaries of this sample are poorly defined, as the area of sky covered depends on the telescope tracking. Objects must satisfy other criteria as well to be labeled OK_RUN; an object must not be flagged BRIGHT (as there is a duplicate "regular" detection of the same object); and must not be a deblended parent (as the children are already included); thus it must not be flagged BLENDED unless the NODEBLEND flag is set. Such objects have their GOOD bit set.

For each stripe, 12 non-overlapping but contiguous scan lines are defined parallel to the stripe great circle (that is, they are bounded by two lines of constant great circle latitude). Each scan line is 0.20977 arcdegrees wide (in great circle latitude). Each run/camCol scans along one of these scan lines, completely covering the extent of the scan line in latitude, and overlapping the adjacent scan lines by approximately 1 arcmin. Six of these scan lines are covered when the "north" strip of the stripe is scanned, and the remaining six are covered by the "south" strip. The fundamental unit for defining an area of the sky considered as observed at sufficient quality is the segment. A segment consists of all OK_RUN objects for a given run/rerun/camCol contained within a rectangle defined by two lines of constant great circle longitude (the east and west boundaries) and two lines of constant great circle latitude (the north and south boundaries, being the same two lines of constant great circle latitude which define the scan line). Such objects have their OK_SCANLINE bit set in the status bit mask. A segment consists of a contiguous set of fields, but only portions of the first and/or last field may be contained within the segment, and indeed a given field could be divided between two adjacent segments. If an object is in the first field in a segment, then its FIRST_FIELD bit is set, along with the OK_SCANLINE bit; if its not in the first field in the segment, then the OK_SCANLINE bit is set but the FIRST_FIELD bit is not set. This extra complication is necessary for fields which are split between two segments; those OK_SCANLINE objects without the FIRST_FIELD bit set would belong to the first segment (the segment for which this field is the last field in the segment), and those OK_SCANLINE objects with the FIRST_FIELD bit set would belong the the second segment (the segment for which this field is the first field in the segment).

A chunk consists of a non-overlapping contiguous set of segments which span a range in great circle longitude over all 12 scan lines for a single stripe. Thus, the set of OK_SCANLINE (with appropriate attention to the FIRST_FIELD bit) objects in all segments for a given chunk comprises a unique sample of objects in an area bounded by two lines of constant great circle longitude (the east and west boundaries of the chunk) and two lines of constant great circle latitude (+- 1.25865 degrees, the north and south boundaries of the chunk).

Segments and chunks are defined in great circle coordinates along their given stripe, and contain unique detections only when limited to other segments and chunks along the same stripe. Each stripe is defined by a great circle, which is a line of constant latitude in survey coordinates (in survey coordinates, lines of constant latitude are great circles while lines of constant longitude are small circles, switched from the usual meaning of latitude and longitude). Since chunks are 2.51729 arcdegrees wide, but stripes are separated by 2.5 degrees (in survey latitude), chunks on adjacent stripes can overlap (and towards the poles of the survey coordinate system chunks from more than two stripes can overlap in the same area of sky). A unique sample of objects spanning multiple stripes may then be defined by applying additional cuts in survey coordinates. For a given chunk, all objects that lie within +- 1.25 degrees in survey latitude of its stripe's great circle have the OK_STRIPE bit set in the "status" bit mask. All OK_STRIPE objects comprise a unique sample of objects across all chunks, and thus across the entire survey area. The southern stripes (stripes 76, 82, and 86) do not have adjacent stripes, and thus no cut in survey latitude is required; for the southern stripes only, all OK_SCANLINE objects are also marked as OK_STRIPE, with no additional survey latitude cuts.

Finally, the official survey area is defined by two lines of constant survey longitude for each stripe, with the lines being different for each stripe. All OK_STRIPE objects falling within the specified survey longitude boundaries for their stripe have the PRIMARY bit set in the "status" bit mask. Those objects comprise the unique SDSS sample of objects in that portion of the survey which has been finished to date. Those OK_RUN objects in a segment which fail either the great circle latitude cut for their segment, or the survey latitude or longitude cut for their stripe, have their SECONDARY bit set. They do not belong to the primary sample, and represent either duplicate detections of PRIMARY objects in the survey area, or detections outside the area of the survey which has been finished to date.

Objects that lie close to the bisector between frames, scan lines, or chunks present some difficulty. Errors in the centroids or astrometric calibrations can place such objects on either side of the bisector. A resolution is performed at all bisectors, and if two objects lie within 2 arcsec of each other, then one object is declared OK_RUN/OK_SCANLINE/OK_STRIPE (depending on the test), and the other is not.