The MultiDrizzle Handbook

2.5 More Detailed Considerations

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2.5.1 Data Quality Issues involved in Dithering

The primary considerations in designing a dithered observational program are cosmic rays, hot pixels, spatial sampling and signal-to-noise. Finding the optimal strategy to deal with these issues is not always straightforward. Careful consideration must be given to the impact of breaking a long observation into multiple exposures, particularly in terms of increasing the overall read-out noise and reducing the amount of science exposure time due to observational overheads. The optimal strategy chosen will ultimately depend upon carefully weighing all these issues against one another, and also against the scientific questions involved such as: is the underlying structure totally unknown, is spatial resolution of paramount importance or is photometric accuracy the most crucial aspect?

• Cosmic rays: The best way to deal with cosmic rays is to obtain a minimum of two exposures, preferably 3 or more, thereby reducing the number of common cosmic ray hits according to the binomial theorem. Even two exposures can have a substantial number of pixels with overlapping cosmic ray hits. For example, 2x1500s WFPC2 exposures will have ~1500 pixels on each chip that are affected by cosmic rays on both images, but 3x1000s exposures have only ~20 pixels on each chip that would be hit by cosmic rays in all three exposures. Exact cosmic ray losses for any given observing scenario can be determined by running the appropriate Exposure Time Calculator which is available on the STScI Web site for each instrument.
• Hot Pixels: There are three ways to deal with hot pixels: (a) recalibrate using "dark frames" that bracket the date of the observation; (b) obtain a second image (or pair of images which will best reject cosmic rays) shifted by a small amount spatially (e.g. about 5 pixels); (c) use an IRAF/STSDAS task such as "warmpix" to filter out the obvious hot pixels. Since some hot pixels are variable on very short time scales, the most robust strategy is to obtain multiple images.
• Undersampling: to improve sampling of the PSF, together with increased spatial resolution, the images need to be shifted by sub-pixel amounts. Generally, subsampling by 1/2-pixel offsets provides the most dramatic improvement over non-dithered images. In some cases, observers wish to further explore the limits of the instrument and spacecraft pointing accuracy by considering sub-pixel shifts of 1/3 of a pixel or less. The extent to which such refinements can be explored depends primarily upon the number of orbits available and the instrument being used.
• Photometric Accuracy: HST instruments can have variations in the sensitivity across each individual pixel, this is referred to as intra-pixel sensitivity. If the PSF is undersampled, this can complicate the photometric analysis of dithered images. Thus, programs requiring maximal accuracy in photometry may not always benefit from dithering.

2.5.2 How Many Dither Positions - 2, 3, 4 or more?

If integer-pixel dithers are all that is required, specifically to ameliorate the effect of hot pixels, then 2 or 3 different locations should be sufficient to guarantee that sources falling on hot pixels are not completely unrecoverable. The remainder of this discussion focuses on sub-pixel dithering, including the strategies and issues involved. The best choice for the number of sub-pixel dithers depends on the amount of time available and the goals of the project. Dithering requires a noticeable amount of spacecraft overhead, with each dither offset typically adding ~2-3 minutes of overhead to the total observing plan.

• The very simplest type of sub-pixel dither is a two-point dither offset along only one axis, i.e. one image obtained at the original pixel position of and a second obtained at pixels where n is an arbitrary integer. This scenario is only really relevant to STIS long-slit spectroscopy, if it is desirable to improve the subsampling along the (spatial) slit direction.
• A two-point sub-pixel dither in imaging data takes one image at the original pixel position of , and a second image offset by half a pixel in both the and , i.e. at , where and are arbitrary integers. This produces a substantial increase in information over non-dithered data. In the case of a square pixel, this dither pattern forms the sampling that would be produced by an array with pixels smaller than the original array, rotated by a 45 degree angle from the original orientation. Setting and to be a few pixels (e.g. around 5-10) will also allow hot pixels to be moved by sufficient amounts to reduce their impact on objects of interest. Figure 2.1 shows the sampling of the WFC3 IR detector on the sky (note the slightly rectangular pixels), and Figure 2.2 shows the sampling produced by introducing a two-point dither. The original placement is shown in black, the additional dither is in red.

Figure 2.1: Sampling of the WFC3 IR Detector on the Sky


 
The sampling of the WFC3 IR detector on the sky.
 
Figure 2.2: Sampling for a 2-point Dither


 
The sampling produced by introducing a two-point dither using the WFC3 IR detector.
 

• The four-point dither is a very natural option given rectangular pixels. This dither yields a total of 4 images that are offset from one another by half pixels in and i.e. , , , . Again integer shifts can and should be used to reduce the effect of hot pixels. This yields uniform tiling along both axes of the (X,Y) plane using half-pixel offsets, thereby providing more robust half-pixel subsampling of the PSF than a simple two-point dither which is only along one direction (see Figure 2.3). In fact, given the native sampling of HST instruments, an accurate four-point dither recovers nearly all of the information available in an image.

Figure 2.3: Sampling for a 4-point Dither


 
A four-point dither.
 

• There may be cases, particularly for programs with only a few orbits, where the available time breaks down more naturally into blocks of 3 exposures instead of 2 or 4. However, the best placement of a three point dither is not obvious. This is because there is no natural way to tile the plane using three placements of a rectangular CCD grid. Therefore, if a user can afford a four-point dither they may prefer to do so. However, both the natural two and four-point dither placements minimize the maximum distance from any point on the image plane to the nearest dither location. One can ask what three point dither pattern also minimizes this maximum distance. Through a (computer) calculation one can show that this is done by offsets along the diagonal at pixel offsets of , and (the symmetric diagonal works just as well, of course). Again, additional integer offsets of a few pixels can (and should) be added to help remove detector defects. Figure 2.4 shows a three-point dither applied to the WFC3 IR detector.

Figure 2.4: Sampling for a 3-point Dither


 
A three-point dither applied to the WFC3 IR detector.
 

• Users with multiple-orbit visits attempting to obtain extremely accurate PSFs may consider even finer subsampling of the pixel. An eight-point dither can be performed by crossing a four point dither with a two-point dither. The two point dither should be of the form . This places a point in the center of each of the "squares" created by the four-point dither. Users should be advised that differential distortion across the field can mean that unless the integer offsets are small, a well-planned dither strategy for the center of the chip will perform worse near the edges. Again, the four-point dither, if performed accurately with the loss of few pixels to cosmic rays or other defects, recovers nearly all the information in an HST image. Therefore, users of instruments like ACS may prefer to cross a small four point dither with a larger two or three point dither that will cover the gap between the chips. The four point dithers will insure good subsampling in the final combined image.
• A number of WFC3 users have inquired about dithers in multiples of three, as many users find three exposures fit well into a single orbit. One can easily create a nine-point dither by dividing the original pixel with a grid. What is less clear is how to form a six-point dither. Again, a calculation suggests that crossing the linear three point dither described above with a two-point dither is the optimal strategy. For square pixels, the half-pixel dither could be taken in either direction, but the WFC3 IR pixels are slightly longer in the -direction, and so we take the dither along the -axis. In Figure 2.5, the black points show a single WFC3 image; the red points show the two additional dithers to form a single three-point dither; the blue points show the additional three-point dither to form the six-point dither.

Figure 2.5: A 6-point Dither


 
A six-point dither.
 

2.5.3 Data with Inaccurate Offsets in Position or Roll Angle

After the observations have executed, the pointing and orientation of the telescope can be determined directly by using cross-correlation techniques, as well as through examination of the jitter files that can be requested from the HST archive as part of the data products. The HST Data Handbook contains further details on the jitter file and other data products, and how to extract their information. The most recent version can be found at the following Web page:

http://www.stsci.edu/hst/HST_overview/documents/datahandbook/

For most programs, it is sufficient to determine the translational shift between images - the chance of a spurious roll angle offset is relatively small, and many long programs have now been performed without experiencing the roll offsets originally seen in the HDF. However, the drizzle software is capable of combining the shifts in rotation as well as position.

2.5.4 How many Images to Obtain at each Dither Location

It is generally possible to successfully remove cosmic rays using only a single image at each dither location, i.e, "singly-dithered" images, using the drizzle software that is incorporated with the dither package in STSDAS. If sub-pixel dithering is desired for small programs (less than about one orbit per target), or programs where reduction of read-noise is critical (e.g., narrow-band imaging of extremely faint sources), then the best approach is likely to involve obtaining only one image at each dither location. For larger programs, however, or when read-noise is not a serious issue, the user can choose between the slightly improved sampling of a larger number of independent dither pointings, or the relative simplicity and lower overhead of multiple exposures at a given dither pointing.

2.5.5 Specific Instrument Related Issues

2.5.5.1 WFPC2

In addition to increasing information on the smallest spatial scales, dithering can be used to reduce the effect of flat-field errors in very deep images. Large dithers (tens of pixels) were used in the HDF for this purpose. Furthermore, dithers greater than one or two pixels can be used effectively to eliminate chip defects such as hot-pixels and bad columns.

   

The Effect of WFPC2 Geometric Distortion on Dither Offsets

The pixels near the edge of the CCD differ in size on the sky from those near the center. Thus a shift of (10,10) pixels at (400, 400) corresponds to a shift of about (10.2, 10.2) pixels at (700, 700). The default dither-line spacing produces a shift of (2.5, 2.5) WF pixels and (5.5, 5.5) PC pixels. Therefore, over nearly the entire field of view the difference in offset - even on the PC - is less than 0.1 pixels, and the shift will be essentially optimal across the whole field. However, the standard dither-box spacing offsets the telescope by as much as 0.75 arcseconds or 15.5 PC pixels. This means that at (700, 700) the shift differs from that at the center by ~0.3 pixels in and . While the drizzle software removes this geometric offset, it cannot change the fact that the sampling will not be optimal across the entire field of view.

The dither-box defaults were chosen to avoid repeating the placement of objects on the same columns (to reduce the effects of bad columns). However, if one is willing to live with the possibility that a given position of interest may fall twice on one of the several bad columns per chip, then one can use smaller offsets to produce a box that is more nearly perfect across the entire chip, for instance a square box with side of 2.5 WF pixels (equivalently 5.5 PC pixels).

   

The Exact Relationship Between POS TARGs and WFPC2 CCD Rows and Columns

For WFPC2 an additional complication is introduced by the fact that the four chips are not precisely aligned with one another, but possess small rotational offsets (<0.5 degree) from their nominal alignments. Thus, the POSTARG axes run exactly along the CCD rows and columns on whichever aperture is specified for the observations. For example, if aperture WF3 is specified, the POSTARG axes will run exactly along the rows and columns on WF3, and will run only approximately along the rows and columns of the other CCDs. Note that if WFALL is specified, then the rotation for WF3 is used since WF3 is the reference chip for the WFALL aperture.

The CCD rotation misalignments lead to errors when attempting to dither by certain pixel amounts. For small dithers (<0.3 arcseconds) the rotational offsets between the CCDs are unimportant, as they imply pixel registration errors less than 3 milliarcseconds, which is roughly the nominal pointing and guiding stability for HST. But such small dithers do not allow integral pixel stepping simultaneously on the PC as well as the WF chips. A dither of 0.5 arcseconds (5 WFC pixels or 11 PC pixels) gives near-integral stepping on the PC and the WF chips, though the CCD rotations will then introduce registration errors up to 5 mas. An offset of (1.993, 0.000) arcseconds in on WF3 would cause spurious motion in of 0.17 pixel on WF4, due to the rotation.

Two basic types of dither patterns are defined for WFPC2, and are implemented in the APT software that is used to process Phase II observing programs. These patterns can also be used with non-default spacings when necessitated by very specific types of observations, although in general we recommend that observers use the default spacings which are optimized for a wide variety of scientific programs.

• WFPC2-LINE: a two-point dither with a single default offset of (0.25arcseconds, 0.25arcseconds), which produces an offset with half-pixel increments along both the and axes on all the chips: the offset corresponds to (2.5, 2.5) pixels on the WF chips and (5.5, 5.5) pixels on the PC. This pattern produces half-pixel subsampling of the PSF on all the chips, while at the same time including integer-pixel offsets to ameliorate the effects of hot pixels and other chip artifacts.
• WFPC2-BOX: a 4-point parallelogram dither, with default positions in arcseconds of (0.0, 0.0), (0.5, 0.25), (0.75, 0.75), (0.25, 0.5). This combination of integer-pixel and half-pixel shifts produces complete half-pixel subsampling of the PSF by all 4 quadrants of each pixel. Therefore this strategy is an improvement over the simple 2-point dither which only provides subsampling in two quadrants of each pixel. The disadvantage of the 4-point dither is that it involves more overhead, which has to be weighed against the relative improvement in subsampling.

2.5.5.2 ACS

For ACS, an important issue to consider in designing a dither strategy is its relatively large distortion: up to 8% across the WFC camera. Moreover, the projections of the detector pixels on the sky correspond to parallelograms with interior angles that differ from 90^o by up to 5 degrees, depending upon the location of the pixel on the detector. The differential distortion across the chip means that shifts of more than a few pixels produce noticeably different sub-pixel offsets across the entire chip. However, the two chips that compose the WFC are separated by a gap of order 2.5 arcseconds (~50 WFC pixels). As a result, many ACS dither strategies involve the use of offsets sufficiently large to allow the detectors to cover this gap. These will have differing sub-pixel effects across the detector. When taking several exposures of a field in a single filter, observers are generally encouraged to use dithers instead of CR-SPLIT exposures for a number of reasons: to change the placement of hot pixels on the field, to resample the point spread function and to reduce the impact of errors in the pixel-to-pixel flats.

Since dither offsets are achieved by specifying POSTARG shifts along the x and y axes of the detectors, this means that each POSTARG shift on the sky follows the edges of a parallelogram. The shifts have been defined so that displacements in rectilinear sky coordinates are aligned along the y-axes of the detectors (Mutchler and Cox 2001). Thus, for example, a displacement of one WFC pixel along the x- and y-axes of the detector is broken down as follows: the displacement of 1 pixel along the detector y-axis corresponds to 0.0497 arcseconds along the Y-POS direction; however, the displacement of 1 pixel along the detector x-axis corresponds to 0.0496 arcseconds along the X-POS direction, plus an additional 0.0038 arcseconds along the Y-POS direction, due to the non-orthogonality of the pixels on the sky.

For the WFC, HRC, and SBC, a number of pre-defined offset patterns have been created (Mutchler and Cox 2001). These are available in the APT Phase II software, and are aimed at covering a wide range of observing requirements:

• DITHER-LINE pattern has 2-point integer pixel spacing by default to ameliorate the effect of chip artifacts. For the WFC, HRC, and SBC, the offsets are (5, 60), (5, 5), (10, 10) pixels respectively. The large y-shift for the WFC is to enable the inter-chip gap to be covered. This pattern can also be modified to subsample the PSF using half-pixel spacing, for example (2.5, 1.5) pixels, or even 1/3-pixel spacing, e.g. dither positions of (0, 0), (2.3, 1.3), (4.6, 2.6) pixels.
• MOSAIC-LINE pattern with large offsets, comparable to the size of the detectors, to increase the field of view.
• DITHER-BOX pattern, by default a set of 4 offsets consisting of integer-pixel and half-pixel offsets (0, 0), (5.0, 1.5), (2.5, 4.5), (-2.5, 3.0), aimed at providing more complete 1/2-pixel subsampling of the PSF.
• MOSAIC-BOX pattern, a 4-point pattern with large offsets, comparable to the size of the SBC and HRC detectors. It should be noted that HST ground-system limitations currently prevent this pattern from being implemented for the WFC.

The above pre-defined patterns should prove sufficient for the vast majority of scientific programs, however, other patterns can also be created simply by using a combination of POSTARG offsets.

2.5.5.3 NICMOS

A wide variety of pre-defined patterns has been created for NICMOS, to allow an easy implementation of both integer-pixel and sub-pixel dithering. These are generalized extensions to the simple line and box dithers by including spiral and chopping dithers, which are necessary to allow successful removal of a number of NICMOS artifacts. The advantages offered by dithering with NICMOS are the following:

• Post-SAA Cosmic Ray Persistence: The NICMOS detectors suffer from persistent after-images when exposed to a strong signal. This can arise from astronomical objects, but it also occurs due to cosmic ray bombardment during every passage of HST through the South Atlantic Anomaly (SAA). After SAA passages, a very large fraction of NICMOS pixels glow with a persistent signal that can take up to a few orbit to decay completely. Dithering can help average over the additional noise (really non-Gaussian, spatially correlated signal) that results from SAA-induced persistence. The worst effects of CR persistence can sometimes be removed by the drizzle and blot techniques. The NICMOS team has also implemented Post-SAA cosmic ray persistence removal software and dark observations which ameliorate a substantial amount of the noise induced by traversing the contours. More information on the details of CR persistence removal can be found in the NICMOS Data Handbook (McLaughlin & Wiklind 2007).
• Photometric accuracy: the effects of large-scale flat-field variations and of bad-pixels can be controlled via integer-pixel dithering. In addition, for relatively bright objects, dithering can eliminate potential problems of image persistence. Geometric distortion in NICMOS is relatively small, except for the NIC3 camera in its out-of-focus position. We recommend dither steps of ~10 pixels for compact sources. The SPIRAL-DITH pattern can be used to generate dither patterns with 2 positions or more.
• Improved sampling: NIC3, NIC2 (shortward of 1.75 microns) and NIC1 (shortward of 1.0 microns) undersample the image. As in the case of WFPC2, the quality of the image can be improved by sub-pixel dithering. Most of the information can be recovered via a two-point dither, and virtually all the information can be recovered with four-point dithers. Since NICMOS geometric distortion is relatively small (except for NIC3 when out-of-focus), large dither steps of order ~10 pixels can be used. Telescope pointing errors, which can be of the order of 0".02, may prevent one from obtaining an optimal dither pattern in NIC1 and NIC2, since the uncertainty corresponds to 0.43 NIC1 pixels and 0.27 NIC2 pixels; in this case more than four dither positions are advisable. For NIC3, the telescope pointing uncertainty corresponds to 0.1 pixels shift only, and four dither positions should still be viable for recovering the information. The pre-defined SPIRAL-DITH pattern can be effectively used for this purpose.
• Background removal in uncrowded fields of compact objects: Observations with the NICMOS long wavelength filters (central wavelength longward of 1.7 microns) are affected by variable thermal emission from the telescope (NICMOS ISR 2003-007). To remove this contribution from the images, suitable background observations must be obtained. For compact targets and uncrowded fields, observations of the background can be obtained by dithering the targets across the detector's FOV. The use of the SPIRAL-DITH pattern with two or four positions, and a dither step of 10 pixels or more (depending on the size of the targets), may be appropriate for many cases, although the parameters may change according to the nature of the observations. The advantage of dithering in such a case (rather than chopping, for example) is that the target will remain on the chip for all observations, increasing the efficiency of the observation.

Dithering NICMOS observations may also have disadvantages that an observer should consider:

• Cosmic ray removal is not straightforward in pairs of sub-pixel dithered images. If you plan to use sub-pixel dithering to improve the image sampling, then MULTIACCUM mode or two ACCUM mode exposures per position should be obtained to help cosmic ray removal BEFORE image reconstruction. Some cosmic ray detection and removal is also performed during the calibration of Multiaccum datasets as multiple reads during the exposure allows for statistical elimination of abnormal flux values. In general, the use of ACCUM mode is discouraged because there is little on-orbit calibration done for this mode (e.g., dark frames, etc.).
• NICMOS Attached parallels: the three NICMOS cameras, NIC1, NIC2, and NIC3, have different plate scales; care should be taken in ensuring that if integer-pixel steps are desired in attached parallel (NIC1+NIC2) observations, the steps are carefully chosen to satisfy this requirement.
• Overheads: The implementation of patterns requires at least 10 - 12 seconds overhead per dither step. Large numbers of dithers can easily add up to minutes taken out of a visibility period for an entire pattern. The trade-off between the advantages offered by dithering, and the diminished amount of observing time should be considered in deciding whether or not to dither.
• Rapid dithering can impose an additional load on the full system in terms of command volume needed to execute the observations, overheads for science data buffer management, and in the volume of data that must be processed through the pipeline. In extreme cases, such as when the overheads required to execute the observations far surpass the actual exposure times, these extra loads can result in lowered overall efficiency of HST observations.

In general, the benefits of dithering greatly outweigh the disadvantages for NICMOS observations. Whenever possible without incurring excessive overhead, we recommend dithering as much as possible when taking NICMOS data. Note, however, that many NICMOS observations are significantly affected by read-out noise, especially for Cameras 1 and 2 and observations shorter than 1.8 micron. Therefore, the effects of read-out noise on multiply-dithered short exposures should always be carefully balanced against the benefits provided by extensive dithering.

2.5.5.4 STIS

The concept of dithering as applied to STIS observations is multifaceted, since STIS can be used to obtain either images or spectra, and the best method for dithering depends upon the science goals for the observing program. The goal may either be to increase the spatial resolution or to ameliorate the effect of hot pixels or uncertainties in pixel-to-pixel sensitivity with respect to the reference flat-fields.

   

Imaging-Mode Dithering

Observers can reduce the effect of flat-field uncertainties (particularly for the MAMA detectors) by using a small step pattern with integral pixel shifts. This stepping, or dithering, effectively smooths the detector response over the number of steps, achieving a reduction of pixel-to-pixel non-uniformity by the square root of the number of steps, assuming the pixel-to-pixel deviations are uncorrelated on the scale of the steps. This approach requires sufficient signal-to-noise to allow image registration.

Alternatively, one may improve the spatial resolution somewhat with a dither pattern that includes sub-pixel shifts. Images obtained with the STIS/CCD (0.05 arcsec/pixel), have nearly the same spatial scale as those obtained with the WFPC2/PC camera (0.045 arcseconds/pixel), so that the improvement in spatial resolution would be similar. The spatial scale of MAMA images is half that of the CCD, so the gain in spatial resolution from dithering MAMA images will be more modest, and probably insignificant in the majority of programs. Although the PSF on the MAMA detectors should be narrower than on the CCD because of the shorter wavelengths at which the MAMAs operate, in practice this advantage is offset by additional complications introduced through the instrument optics. It is important to realize that the focus varies across the field of view for STIS imaging modes, with the optical performance degrading by ~30% at the edges of the field of view. Thus, the achievable spatial resolution is significantly compromised in those regions.

Whether or not the dither pattern includes sub-pixel shifts, the effects on CCDs of bad columns, hot pixels, etc., can be reduced or eliminated if the dither pattern is greater than a few pixels. Predefined dither patterns that are available for observers to use, these include:

• STIS-CCD-BOX: This will produce a four-point parallelogram scan designed for dithering across the CCD pixels.
• STIS-SPIRAL-DITH: This produces a spiral dither pattern, starting at the center and moving outward counterclockwise. Note that a STIS-SPIRAL-DITH with four points yields a square pattern, but the optimum pattern for detector dithering to enhance resolution is either STIS-CCD-BOX or STIS-MAMA-BOX.

   

Spectroscopic-Mode Dithering

Dither patterns can be used with STIS spectroscopic modes for the following purposes:

• to average over pixel-to-pixel flat-field uncertainties;
• to facilitate removal of hot and cold pixels (e.g., by using integer pixel steps);
• to subsample the spatial PSF along the slit (by sub-pixel steps along the slit);
• Stepping along the dispersion direction, perpendicular to the spatial axis of the slit:
• to subsample the spectral Line Spread Function (LSF) by stepping a fraction of a pixel along the dispersion direction;
• to map out a two-dimensional region of the sky by using larger step sizes equal to or greater than the slit width.

In first-order spectroscopic modes, improved S/N ratios can be achieved by stepping the target along the slit, taking separate exposures at each location. These separate exposures will subsequently be shifted and added in post-observation data processing. This dithering smooths the detector response over the number of steps, in a manner analogous to that for imaging. For echelle modes, stepping is only possible using the long echelle slit (6x0.2 arcseconds). Note that in the high dispersion echelle modes the Doppler shifting due to spacecraft motion will cause the counts from any output pixel to have been sampled at many independent detector pixels in the dispersion direction (for exposures comparable to an orbit visibility period and targets well away from the orbital pole of HST).

In slit-less or wide-slit mode, stepping along the dispersion would allow independent solutions for spectrum and flat-field, bearing in mind however the increased complexity due to the convolution of the spectrum with the spatial structure in the source. This technique is likely to be useful only if the constituent spectra have a good S/N ratio (perhaps 10 or better), so that the shifts between spectra can be accurately determined.

A variation on this technique involves using one of the contingent of fixed-pattern, or FP-SPLIT slits. These slits are designed to allow the wavelength projection of the spectrum on the detector to be shifted such that the fixed-pattern noise in the flat-field and the spectral flux distribution of the target can be computed simultaneously using techniques that have been successfully applied to data taken with GHRS. Note that this approach is likely to work best if the spectra have a good S/N ratio. More detailed information on the use of FP-SPLIT slits is provided in the STIS Instrument Handbook (Leitherer et al. 2001).

In many configurations the spectral line FWHM is less than two detector pixels. Possible solutions include stepping the target along the dispersion direction in a wide slit or slit-less aperture to subsample the LSF by displacing the spectrum. This technique can also be used to increase the S/N ratio. To employ this strategy, the observer will have to trade off the benefits of improved sampling with the negative impact of increased wings in the LSF when using a wide slit, particularly for MAMA observations. The use of high resolution (default) for MAMA observations may provide 15-30% better sampling, but flat-field variability may make it difficult to realize the benefits, particularly if high S/N ratio spectra are needed.

There are several pre-defined dither patterns that are available for observers to use, these include:

• STIS-PERP-TO-SLIT: This is normally used with a spectroscopic slit. It produces a scan along the POSTARGX-axis of the aperture; this is used to map a two-dimensional region of the sky (see Chapter 11 of the STIS Instrument Handbook). The target is moved perpendicular to the slit along the AXIS1 (dispersion)
• STIS-ALONG-SLIT: This is also normally used with a spectroscopic slit. It produces a scan along the POSTARGY-axis of the aperture; this is used to step a target along the long slit to dither bad pixels or improve spatial resolution (see the STIS Instrument Handbook). The target is moved along the slit in the AXIS2 (cross-dispersion or spatial) direction.

2.5.5.5 WFC3

   

WFC3/UVIS

WFC3/UVIS images are in many ways similar to ACS/WFC images. The detector comprises two rectangular CCD chips separated by a gap approximately 35 pixels wide, so that a gap-stepping dither is needed to avoid having a gap across the center of the field of view. The projection of the pixels on the sky is in the shape of a rhombus, with an angle between the X and Y axes of 86 degrees. As with the ACS/WFC, a POSTARG in Y is along the Y axis of the aperture (along columns), and a POSTARG in X is perpendicular to the Y axis (not quite along rows). The plate scale is 0.04 arcseconds/pixel on each axis, and the FWHM of the point spread function is between 1.6 and 2.3 pixels, depending on wavelength. WFC3/UVIS images will thus benefit from half-pixel dithering, but not as much as WFC3/IR images. Non-linear distortion causes the projected area of the pixels to vary by +/-3% relative to that at the center of the detector, so POSTARGs and patterns will produce shifts in pixels that vary with location on the detector.

Five patterns have been installed in the phase 2 software to dither and mosaic WFC3/UVIS images:

• WFC3-UVIS-DITHER-LINE dithers the UVIS aperture by (2.5, 2.5) pixels to sample the point spread function with fractional pixel steps.
• WFC3-UVIS-DITHER-BOX samples the point spread function with fractional pixel steps and produces spacings of more than one column to move hot columns. The relative steps in pixels are (0, 0), (4.0, 1.5), (2.5, 4.0), and (-1.5, 2.5).
• WFC3-UVIS-MOS-DITH-LINE has a primary pattern that dithers over the gap between the two chips of the detector with relative steps of (-4.5,-60.25), (0, 0), and (4.5, 60.25) pixels. A secondary pattern adds a dither of (2.5, 1.5) pixels to the primary pattern.
• WFC3-UVIS-MOS-BOX-LRG produces a UVIS mosaic that can be executed with a single set of guide stars. It dithers the gap between the chips so that no region lies in the gap more than once. The relative steps in pixels are approximately (-1000, -997), (1000, -1001), (1000, 997), and (-1000,1001).
• WFC3-UVIS-MOSAIC-LINE is designed for observations using the full WFC3/UVIS detector for primary exposures and the full ACS/WFC detector for parallel exposures. It dithers over the inter-chip gap on both detectors. The relative steps on the WFC3/UVIS detector are (0, 0) and (36.5, 71.5) pixels.

Other patterns can be created by using POSTARG offsets or generic patterns, or by changing the spacings in the defined patterns. For programs requiring high precision small aperture photometry, observers should see WFC3 ISR 2008-10 for a discussion of features called "droplets", caused by contamination on the outer window of the UVIS detector. Dithers ~100 pixels are recommended to improve the photometry.

The WFC3 pipeline produces cosmic ray rejected (CRJ) images from input FLT images for CR-SPLIT exposures. When MultiDrizzle is run in the pipeline, it will use the FLT images as input, tagging cosmic rays in those images with a different value of DQI (4096) from the value used by CALWF3 (8192). Observers are generally encouraged to use dithers instead of CR-SPLIT exposures for a number of reasons: to change the placement of hot pixels on the field, to resample the point spread function and to reduce the impact of errors in the pixel-to-pixel flats.

   

WFC3/IR

The WFC3/IR pixels are projected as rectangles on the sky, with X and Y plate scales ~0.14 and 0.12 arcseconds per pixel. A POSTARG in Y is along the Y axis of the aperture (along columns), and a POSTARG in X is along the X axis (along rows). The FWHM of the point spread function is between 1.0 to 1.25 pixels, so sub-pixel dithering is needed to recover spatial resolution. Non-linear distortion causes the projected area of the pixels to vary by +/-4% relative to that at the center of the detector, so POSTARGs and patterns will produce shifts in pixels that vary with location on the detector.

Three patterns have been installed in the phase 2 software to dither and mosaic WFC3/IR images:

• WFC3-IR-DITHER-LINE takes steps large enough for photometric accuracy and samples the point spread function with fractional pixel steps. The relative steps in pixels are (0, 0) and (3.5, 3.5).
• WFC3-IR-DITHER-BOX-MIN takes steps just large enough for photometric accuracy and samples the point spread function with fractional pixel steps. The relative steps in pixels are (0, 0), (4.0, 1.5), (2.5, 4.0), and (-1.5, 2.5).
• WFC3-IR-DITHER-BOX-UVIS is a four-point box pattern that produces an IR mosaic covering the same area as the UVIS detector. The IR imaging is intended to be accompanied by a UVIS exposure (or small dither pattern) using the aperture UVIS-CENTER.

Other patterns can be created by using POSTARG offsets or generic patterns, or by changing the spacings in the defined patterns. Note that there is a ~45 pixel diameter dead spot near the lower edge of the WFC3/IR detector, centered at ~[358,54]. A dither larger than this diameter should be used if imaging in that area is required.

WFC3/IR exposures are made with predefined timing sequences of non-destructive reads. As in NICMOS, up-the-ramp fitting of the fluxes in the sequence is used to identify and remove cosmic ray flux from each pixel. The accuracy of the procedure depends on the timing sequence and the number of frames specified in the proposal, just as the accuracy of traditional cosmic ray rejection in CR-SPLIT exposures on a CCD detector depends on the number of exposures and the exposure time. The cosmic ray rejected FLT image is used as input to MultiDrizzle. As for WFC3/UVIS images, DQI values of 4096 and 8192 are used to tag pixels with cosmic rays identified by MultiDrizzle and by CALWF3, respectively.