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# Tiling: determining survey completeness

Up: Data Products Sections: Images - Object lists - Spectra - Tiling

When you are given a set of spectra from any survey, and you want to ask statistical questions about them, the first thing you should ask is "How were these objects selected?" The SDSS is designed such that you can answer this question easily for the tilable targets (for the most part QSOs, Main Sample galaxies, and Luminous Red Galaxies). The answer has several steps:

1. Photometric detection (requires understanding the photometric imaging mask)
2. Target selection (requires understanding the target selection algorithms)
3. Tiling (the algorithm is described in a separate document)
4. Spectroscopic completeness (whether or not a spectrum successfully yields a classification)
This section addresses the second and third aspects: how tilable targets are selected and assigned to each tile.

The way to understand the tiling window is as follows. In each direction of the sky we can ask two questions:

1. what version of the target algorithm was used in this direction (for example, to determine the flux limit in the targeted data)?
2. what set of tiles had the opportunity to put a fiber on a target in this direction?
Once you can answer these two questions, one can define a complete spectroscopic sample from the SDSS. The second question, in detail, is not the same as asking whether the direction in question is within 1.49 deg of the tile center in question. This is because tiles near edges of tiling regions (that is, virtually all tiles) extend beyond the tiling region area. In some cases, the survey then later observed and targeted the adjacent area. This fact, and the generally complex geometry which results from the survey configuration, make the expression of the window function nontrivial. In practice, we have solved these geometric problems and with the data release are giving you tools to answer these two questions.

To demonstrate the SDSS procedure, consider the following few figures, which represent how targets were selected and tiles defined along a section of the SDSS near the Northern Celestial Equator. The region shown was successively targeted in Tile Region 4, Tile Region 5 and Tile Region 14. The images show:

1. The area targeted (in dark grey) by Tile Region 4 and the boundaries of the defined tiles.
2. The area targeted (in dark grey) by Tile Region 5 and the boundaries of the defined tiles, plus (in lighter tones) the geometry of Tile Region 4. Note that there exist areas in Tile Region 5 which are within the boundaries of tiles from Tile Region 4; however, those old tiles could not have been assigned targets in Tile Region 5.
3. The area targeted (in dark grey) by Tile Region 14 and the boundaries of the defined tiles, plus (in lighter tones) the geometry of Tile Regions 4 and 5. The same issue of overlapping tiles exists in this case.
4. The full area covered by the targeting and all of the relevant Tile Region and tile boundaries. One can divide this region into all the disjoint polygons defined by these boundaries (for example using Andrew Hamilton's Mangle software).
5. One can ask for each disjoint polygon what tiles cover it. A unique set of tiles covering any area of sky is known as a "sector" or sometimes "overlap region." The last figure colors shows the same set of disjoint polygons but colors each one according to its sector. Note that sectors can consist of more than one polygon.
Since the SDSS is so complete, the details of exactly which set of tiles covered any given region would not be important, except that in certain cases there are resulting gaps, which are important to track.

The Catalog Archive Server provides all tiling information needed to interpret the details of the above geometry.

The tiling window describes only how tiling treated the geometry for the relevant set of data released here. It does not account for decisions about the photometric window released here or for fields identified as bad since the era of targeting. So in addition to the tiling window, one needs to also account for:

1. the fact that targets 100 arcsec from the tile center are excluded
2. the photometric window (including bad fields) of the data release
3. which tiles had corresponding plates released

This information can be acquired elsewhere in this data release documentation, as referenced at the beginning of this page.