7.6.1 Dither Strategies
There is no single observing strategy that is entirely satisfactory in all circumstances for WFPC2. One must consider cosmic rays, hot pixels (i.e. pixels with high, time variable dark count), spatial undersampling of the image, and large-scale irregularities such as the few arcsecond wide region where the CCDs adjoin. One strategy that can be used to minimize the effects of undersampling and to reduce the effects of hot pixels and imperfect flat fields is to dither, that is, to offset the telescope by either integer-pixel or sub-pixel steps. The best choice for the number and size of the dithers depends on the amount of time available and the goals of the project. In the following we will address a few issues related to dithering:
- Undersampling: Individual images taken with sub-pixel offsets can be combined to form an image with higher spatial resolution than that of the original images. A single dither from the original pixel position -- call it (0,0) -- to one offset by half a pixel in both x and y, (0.5,0.5) will produce a substantial gain in spatial information. On the other hand very little extra information is gained from obtaining more than four positions, if the standard four point dither is used, and if the telescope has successfully executed the dither. Therefore the recommended number of sub-pixel dither positions is between 2 and 4.
- Hot Pixels: There are three ways to deal with hot pixels: correct them by using "dark frames" that bracket the observation, dither by an integer amount of pixels, or use a task such as "WARMPIX" within STSDAS to filter out the known hot pixels. Note that the integer dither strategy would ideally use six images, i.e. two CR-SPLIT images at each of three different dither positions. This is because in addition to hot pixels, low or "cold" pixels1 can be present and simple strategies selecting the minimum of two pixel values can fail. However, even four images (two each at two dither positions) will greatly aid in eliminating hot pixel artifacts.
- Cosmic Rays: Although dithering naturally provides many images of the same field, it is better to take several images at each single pointing in order to remove cosmic rays. The dither package (see further below) has been developed to allow cosmic ray removal from dithered data. This, for example, might allow single images at each pointing, which will be important if observing time is quite limited (e.g. less than one orbit). This capability has now been tested and appears to work fairly well. For effective cosmic ray removal we generally recommend obtaining a minimum of three to four images, and preferably more if practical. For very long integrations it is convenient to split the exposure into more than two separate images. As an example, for two 1500s exposures, about 1500 pixels per chip will be hit in both images and will therefore be unrecoverable. However, dividing the same observation into 3x1000s results in only about 20 pixels on each chip that would be hit by cosmic rays in all three exposures. Moreover, since CR events typically affect 7 pixels per event, these pixels will not be independently placed, but rather will frequently be adjacent to other unrecoverable pixels.
- Accuracy of dithering: The telescope pointing accuracy is typically better than 10 mas, but on occasion can deviate by much more, depending on the quality of the guide stars. For example, during the Hubble Deep Field, nearly all dithers were placed to within 10 mas (during ±1.3" offsets and returns separated by multiple days), although in a few cases the dither was off by more than 25 mas, and on one occasion (out of 107 reacquisitions) the telescope locked on a secondary FGS peak causing the pointing to be off by approximately 1" as well as a field rotation of about 8 arcminutes. The STSDAS "drizzle" software (initially developed by Fruchter and Hook for the Hubble Deep Field, and now used generally for many other programs) is able to reconstruct images even for these non-optimal dithers, still gaining in resolution over non-dithered data.
The recommended way to schedule dithers is to specify dither patterns WFPC2-LINE (e.g. for two-point diagonal dithers) or WFPC2-BOX (for four-point dithers). An alternative approach is to use POS TARGs. Note that when the WF3 is specified as an aperture, the POS TARG axes run exactly along the WF3 rows and columns. For the other chips, they only run approximately along the rows and columns due to the small amount of rotation between CCDs. For small dithers (less than a few pixels) these rotations are unimportant.
Some specific offsets allow one to shift by convenient amounts both the PC and the WFC chips. For instance an offset of 0.5" is equivalent to 5 WFC pixels and 11 PC pixels. Likewise, the default WFPC2-LINE spacing of 0.3535" along the diagonal is equivalent to shifts of (2.5,2.5) pixels for the WFC and (5.5,5.5) pixels for the PC.
Dithers larger than a few pixels will incur errors due to the camera geometric distortion which increases toward the CCD corners and alters the image scale by about 2% at the corners. Hence a 1.993" offset will be 20.3 WF pixels at the field center, but suffer a 0.4 pixel error at the CCD corners. Large dithers may also occasionally require a different set of guide stars for each pointing, thus greatly reducing the expected pointing accuracy (accuracy only ~1" due to guide star catalogue).
The most up-to-date information about dither strategies and related issues can be found on the general WFPC2 dither web page:
http://www.stsci.edu/instruments/wfpc2/dither.html
1Cold pixels usually result from hot pixels in the dark calibration file which do not actually appear in the science data.
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