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DrizzlePac 2012 Handbook
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The DrizzlePac Handbook > Appendix C: Observational Dithering Options for Drizzling Data > C.2 Selecting the Right Dither Strategy

C.2 Selecting the Right Dither Strategy
ACS
 
The dithering strategies outlined in this section are guidelines, not solid rules. There will likely be science programs that do not neatly fit into any one of these dithering categories. If answers to your question are not found in this document, the Phase 2 Proposal Instructions, instrument web pages, and the Astronomer’s Proposal Tool (APT), please get in touch with your Contact Scientist or send an e-mail message to the STScI Helpdesk.
C.2.1
During the Phase II proposal writing stage, users are faced with the challenge of crafting the best possible observing program within the allocated telescope time. For instance, a long observation broken into multiple dithered exposures comes at a cost: increased readout noise and less total science exposure time (due to observational overheads). How much of that cost can be incurred without compromising science goals? That depends on the purpose of the observations: is it to detect an unknown underlying structure in the field? Is high spatial resolution a priority? Is there a requirement for highly accurate photometry?
Designing an observing program to get the best quality data depend on how to deal with cosmic rays, hot pixels, spatial sampling, and signal-to-noise.
Cosmic rays: a minimum of two exposures, preferably three or more, is the most effective way to reduce the number of cosmic ray hits at the same detector location in each exposure (according to the binomial distribution). Even with two exposures, it’s possible to get overlapping cosmic ray hits in the two images. In the example below, generated using the WFPC2 Exposure Time Calculator, a 3000 second exposure for a 24 magnitude point source in F122M with gain of 7 is broken into several sub-exposures to show how the number of overlapping cosmic ray pixels is reduced as more sub-exposures are used for the combined image, but at the cost of decreased signal-to-noise. (Items in parenthesis are additional comments). A 3000 second exposure would lose about 61,000 pixels per chip to cosmic ray hits. If two 1500 second images were combined, the number of cosmic ray-affected pixels drops dramatically to 1400 per chip. If three 1000 second images were combined, only 21 pixels per chip would be affected by cosmic rays.
Table C.1: WFPC2 Exposure Time Calculator Shows Changes in SNR and Cosmic Rays Based on Number of Split Exposures
Hot Pixels: flat-field calibrated images (flt.fits) from the Archive are processed with dark reference files that contain hot pixel information for a time period during which the observation was obtained. (It usually takes a few weeks for the most up-to-date dark reference files to catch up with the science observations; if you retrieve images taken within a month to six weeks of execution, chances are that the dark reference file used to calibrate the data does not match the observation date.) Since some hot pixels are variable on very short timescales, they’re not flagged in dark reference files. Therefore, the easiest way to remove hot pixels is to dither the images. A two-point dither with small integer shifts is enough to remove most hot pixels.
Undersampling: HST cameras, with exception of the ACS/HRC, have detector pixel widths comparable to the FWHM of the point spread function (PSF). Drizzle-combining images that are shifted by subpixel amounts can improve PSF sampling, (in other words, increase spatial resolution). Generally, subsampling by a small shift with a 1/2-pixel offset provides the best improvements over non-dithered images. In some cases, observers may wish to further explore the limits of the instrument and spacecraft pointing accuracy by considering small shifts with 1/3-pixel offsets. 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 vary in sensitivity across each individual pixel; this is referred to as intra-pixel sensitivity. For an undersampled PSF, this can complicate photometric analysis of dithered images. Therefore, programs requiring highly accurate photometry measurements may not always benefit from dithering.
C.2.2
Decisions on how to implement dithering in your observing proposal depends on many factors, some of which were discussed in the previous section, others that will be explained later in this chapter. With the exception of mosaic dithers, dither step sizes are kept small to minimize differential geometric distortion between the images but also need to be large enough to remove chip gaps for detectors like WFC3, WFPC2, and ACS/WFC. This keeps the step size at each position in each image more nearly the same so that every pixel gets as close to the same level as possible of subpixel sampling as intended by the dither pattern.
At a top level, there are several dithering categories:
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Very Short Exposures: if each target is observed for less than a few minutes, extra overhead from dithering could significantly impact the overall signal-to-noise (S/N) that may offset advantages gained from dithering.
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Critical photometric measurements: for high-precision time-dependent photometric monitoring, dithering may introduce additional complications due to intra-pixel sensitivity variations. Therefore, some observers may prefer to obtain all the images at a single pointing location.
Simple Dithering: dithering each exposure by integer pixel shifts reduces the impact of hot pixels in the final combined image. Furthermore, spatial sampling can be improved with two- or three-point subpixel dithering. It is possible to do cosmic ray rejection with a single image at each dither point but for a more robust rejection, two or more exposures at each pointing is recommended. For programs allocated about one orbit per target, at least two to three exposures should be obtained to facilitate cosmic ray rejection. If one is interested in targets throughout the field, rather than one single small target, cosmic ray removal will need to be more rigorous, and a larger number of exposures will be required. The instrument handbooks give expected cosmic ray rates for each of the imaging instruments.
Full Dithering: for improved spatial sampling, a “full” four-point dither, with 1/2 pixel subsampling along both detector axes, is recommended. Most of the subpixel information in an image can be recovered by a four-point dither. Deep programs may benefit from an even larger numbers of dithers. Obtaining a four-point dither across the field of view limits the user to small dithers because of the distortion of many HST cameras. At the same time, the user may want to remove features such as the slit between the two chips on ACS with a large dither. The user may want to combine several sets of four-point dithers in this case. In addition, in cases where there are small objects with high signal-to-noise, image quality can be improved by using dithering patterns sampled finer than four points.
Dithering for Parallel Images: it is not always possible to obtain optimal dithers simultaneously for primary and parallel instruments due to the large separation between detectors, and different pixel scales. Uniformly-spaced dithers for the primary instrument generally yield non-uniform dithers for the parallel instrument. In most cases, we recommend that users select their dither pattern to obtain the best possible data from their primary instrument.
Dithering in WFPC2: the Planetary Camera (PC) and Wide Field Cameras (WFC) have different scales; therefore, a dither pattern was developed to implement subpixel dithering in both camera types. (WFPC2 has been decommissioned.)
C.2.3
Dithering requires a noticeable amount of spacecraft overhead, with each dither offset typically adding about two to three minutes of overhead to the total observing plan. Outlined below are recommendations for various observing goals.
Integer-Spaced Dither Steps
Two to three integer-spaced dither steps will, in most cases, correct the effects of hot pixels; if the flux from an object fell on a hot pixel in one image, chances are good that it will fall on a normal pixel in the other dithered image.
Subpixel Dithering
Strategies and issues for subpixel dithering are covered in the remainder of this section. The number of subpixel dithers for an observation depends on the amount of available observing time and project goals.
The simplest type of subpixel dither is a two-point dither offset along only one axis; this is used in STIS long-slit spectroscopy for subsampling along the (spatial) slit direction. For example, one exposure would be obtained at the original pixel position of (0, 0) and a second obtained at (0, n+1/2) pixels where n is an arbitrary integer value.
For imaging, a two-point subpixel dither starting at the original pixel position of (0,0), followed by a second image shifted by (n+1/2, m+1/2), where n and m are arbitrary integer values, will provide a substantial increase in information over non-dithered data. For square detector pixels, this dither pattern results in sampling that would be produced by an array with a pixel size that’s smaller than the original array, rotated by a 45 angle from the original orientation. Setting n and m to a small integer value, around 5 to 10, will also allow the removal of hot pixels. Figure C.1 shows the sampling by the WFC3 IR detector on the sky (note the slightly rectangular pixels1), and Figure C.2 shows the sampling produced by introducing a two-point dither. The original placement is shown in black, the second dither is in red.
Figure C.1: The Sampling of the WFC3 IR Detector on the Sky
Figure C.2: The Sampling Produced by Introducing a Two-point Dither Using the WFC3 IR Detector.
A four-point dither yields a total of 4 images that have 1/2-pixel offsets in x and y, as well as small integer shifts (n, m) to reduce the effect of hot pixels: (0,0), (0,m+1/2), (n+1/2,m+1/2), (n+1/2,0). This yields uniform tiling along the x- and y-axis with half-pixel offsets, providing a more robust and powerful sub-sampling of the PSF. In fact, given the native sampling of HST instruments, an accurate four-point dither recovers nearly all of the information available in an image (see Figure C.3).
Figure C.3: A Four-point Dither
Use of a three-point dither may arise for cases where the available observing time breaks down more naturally into blocks of three exposures, instead of two or four. However, the best placement for a three-point dither is not obvious because there is no natural way to tile the plane using three placements of a rectangular CCD grid. Two- and four-point dither patterns described earlier minimize the largest distance of any point on the image plane to the nearest dither location. Therefore, what kind of three point dither pattern would have the same characteristics? Based on a (computer) calculation, this can be done with offsets along the diagonal of (0,0), (1/3,1/3), and (2/3,2/3) pixels. Again, additional integer offsets of a few pixels should be added to help remove detector defects. Figure C.4 shows a three-point dither applied to the WFC3 NIR detector.
Figure C.4: A Three-point Dither Applied to the WFC3 NIR Detector
If the goal is to obtain extremely accurate PSFs from observations spanning several orbits, users may consider an even finer subsampling of the pixel. An eight-point dither could be performed by crossing a four-point dither with a two-point dither; in other words, a secondary dither pattern at the location of each point in a primary dither pattern. That secondary dither should be a two-point dither of the form (m + 1/4,n + 1/4) which would place a point in the center of each “square” created by the primary four-point dither pattern. Note, however, 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 where the distortion will result in a dither pattern that varies significantly from the center of the chip. The four-point dither, if performed accurately with the loss of few pixels to cosmic rays or other defects, recovers nearly all the spatial information in an HST image. Therefore, users of instruments like ACS/WFC 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 because they find that three exposures fit well into a single orbit. One option2 is to create a nine-point dither by dividing the original pixel with a 3x3 grid.
Forming a six-point dither3, however, is less clear; a calculation suggests that crossing the linear three point dither, described above, with a (1/2,0) two-point dither is the optimal strategy. For square pixels, the half-pixel dither could be taken in either direction. But WFC3 IR pixels are slightly longer in the x-direction, so the dither should be performed along the x-axis. In Image:6pt_small.jpg, 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 C.5: A Six-point Dither
C.2.4
On rare occasions, pointing errors may occur during guide star re-acquisitions within a visit. As a result, images in the same visit cannot be aligned based on their WCS information. This will be evident in pipeline drizzle-combined images that may show double objects, elongated psfs indicating sub-pix misalignments, and artifacts like “chopped” psfs. Tasks such as tweakreg can be used to measure and correct the offsets between images, so they can be properly aligned and reprocessed with astrodrizzle.
C.2.5
In general, most cosmic rays can be removed with one image at each dither pointing. It’s the best approach for small programs (one orbit per target) that require subpixel dithering, and for programs that require low read noise (such as narrow-band imaging of extremely faint sources). For larger programs, or for programs where read noise is not a serious issue, users can opt for slightly improved sampling by executing a small secondary subpixel dither at each pointing of a larger primary dither pattern or they could choose to obtain multiple exposures at each primary dither pointing. Implementing multiple exposures at each dither position insures that cosmic ray rejection can be performed in all pixels of each image, whereas dithered observations will result in only one image on the edges of the combined image and making identification of cosmic rays by AstroDrizzle impossible in those regions.
C.2.6
WFC3
Summarized below are WFC3 dither strategies for UVIS and IR channels. Additional information is available in the Phase II Proposal Instructions, Section 8.4.4, as well as Appendix C in the WFC3 Instrument Handbook.
WFC3 dither patterns designed to subsample pixels can be used as secondary patterns to complement primary WFC3 patterns with larger steps. It is also possible to use WFC3 patterns as secondary patterns within a primary pattern based on generic BOX, LINE, or SPIRAL pattern types. When combining patterns, the smaller dither pattern should be the secondary pattern to minimize time spent in moving the telescope.
WFC3/UVIS
WFC3/UVIS images are in many ways similar to ACS/WFC images. The detector is comprised of 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. As with the ACS/WFC, a POS TARG in Y is along the Y-axis of the aperture (along columns), and a POS TARG 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 POS TARGs and patterns will produce shifts in pixels that vary with location on the detector.
Seven patterns are available for Phase 2 dithering and mosaicing of 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-LINE-3PT dithers the UVIS aperture by (2.33, 2.33) pixels to sample the point spread function with fractional pixel steps.
WFC3-UVIS-GAP-LINE dithers over the gap between the two chips of the UVIS detector with relative steps of (-2.25,-30.25) and (2.25,30.25) pixels.
WFC3-UVIS-DITHER-BOX samples the point spread function with fractional pixel steps and produces spacings of more than one column to remove 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.
For programs requiring high precision small aperture photometry, observers should see (Brown 2008) 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 photometry.
The WFC3 pipeline produces cosmic ray-rejected (CRJ) images from input flt.fits images for CR-SPLIT exposures, but these have not been corrected for geometric distortion. When AstroDrizzle is run in the pipeline, it will use the flt.fits images as input, tagging cosmic rays in those images with a different data quality flag value (4096) from those cosmic rays found by CALWFC3 (DQ value of 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 pixel-to-pixel errors in 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 POS TARG in Y is along the Y axis of the aperture (along columns), and a POS TARG 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 subpixel 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 POS TARGs and patterns will produce shifts in pixels that vary with location on the detector.
Note that there is a ~45 pixel diameter dead spot near the lower edge of the WFC3/IR detector, centered at about (358, 54). A dither larger than this diameter should be used if imaging in that area is required, such as the WFC3-IR-DITHER-BLOB pattern.
Five 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-LINE-3PT 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 (3.33, 3.33).
WFC3-IR-DITHER-BOX-MIN 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), (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.
WFC3-IR-DITHER-BLOB dithers over the IR blobs,described in WFC3 ISR 2010-09, using relative steps of (-14.25,-14.25) and (14.25,14.25) pixels.
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. This cosmic ray rejected IR flt images for WFC3/IR and NICMOS data is used as input to AstroDrizzle, so for most cases the final drizzle step would be necessary while sky subtraction may be performed depending on the data. As for WFC3/UVIS images, DQI values of 4096 and 8192 are used to tag pixels with cosmic rays identified by AstroDrizzle and by calwfc3, respectively. These DQ values may be reset when running AstroDrizzle to insure that only a successful run of AstroDrizzle based on proper alignment and parameter usage will be used to update the DQ arrays with properly identified cosmic rays.
ACS
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.
The relatively large distortion, up to 8% across the WFC camera, is an important consideration in designing a dither strategy. Each detector pixel, when projected on the sky, corresponds to a parallelogram. Interior angles of these parallelograms differ from 90 by as much as 5, depending on pixel location in the detector. As a result, a shift of several pixels will produce noticeably different subpixel offsets in the distorted (i.e., raw.fits or flt.fits) image. The two WFC chips are separated by about 2.5 arcseconds (about 50 WFC pixels). Therefore, many ACS/WFC dither strategies use offsets large enough to overlap this gap, which results in different subpixel shifts effects in the distortion-corrected image.
Since dither offsets are executed as POS TARG shifts along the detector x and y axes, this means that each POS TARG shift on the sky follows the edges of a parallelogram. These shifts have been defined such that displacements in rectilinear sky coordinates are aligned along the y-axis of the detector (Mutchler and Cox 2001). For example, a displacement of one WFC pixel along the x- and y-axes of the detector is represented in sky coordinates as follows: one pixel displacement along the detector y-axis is a 0.0497 arcsecond offset along the Y-POS direction; however, a one pixel displacement along the detector x-axis requires a 0.0496 arcsec offset along the X-POS direction and 0.0038 arcseconds along the Y-POS direction, due to the non-orthogonality of the pixels on the sky. (X-POS and Y-POS are the undistorted POS TARG reference frame.)
Figure C.6: ACS POS TARG Shifts in Sky and Detector Coordinates
XPOS = x. a11 + y. a10
ypos = x. b11 + y. b10
Pointspacing=SQRT(XPOS2 + YPOS2)
pattern orient = atan((YPOS)/(XPOS))
Distortion coefficients (just the first two terms of the full 4th-order polynomial)
A number of pre-defined dither patterns that cover a wide range of observing requirements have been created for ACS detectors (Mutchler and Cox 2001), and are incorporated in the Phase II Astronomer’s Proposal Tool (APT) software. These patterns are summarized below, more details are available in the Phase II Proposal Instructions.
DITHER-LINE: observations are taken along a “line” with integer pixel shifts in the detector x- and y-axis to remove most detector artifacts like hot pixels. For WFC, the shifts are 5 pixels in x and 60 pixels in y to cover the inter-chip gap. The SBC shifts are 10 pixels in x and y. (HRC, now inoperable, had 5 pixel shifts in x and y.) This pattern could be augmented by a secondary dither pattern at each DITHER-LINE pointing for PSF subsampling using half-pixel offsets (i.e., [2.5, 1.5]) or even one-third pixel offsets (i.e., [0, 0], [2.3, 1.3], [4.6, 2.6]).
MOSAIC-LINE: large offsets, comparable in size to the detector, taken along a line to increase the field of view. By default, this is a 2-point dither. For WFC, the default offset size is 1948 pixels along the y axis (about 47% of the y-dimension for the combined WFC detectors as projected on the sky) which gives a 200 x 300 arcsec field of view. This configuration, in most instances, allows the same guide star pair for the two pointings and will cover the inter-chip gap. For the HRC and SBC, this is a shift of about 95% of the y dimension of the detector (973 pixels) as projected on the sky, which nearly doubles the field-of-view. Up to nine pointings are allowed for this dither pattern. Sub-pixel dithers, as described above, may also be used at each pointing for better sampling.
DITHER-BOX: a set of four pointings using integer-pixel and half-pixel offsets at each pointing to provide better PSF subsampling. WFC, SBC, and HRC have the same relative pixel offsets: (0, 0), (5.0, 1.5), (2.5, 4.5), (-2.5, 3.0).
MOSAIC-BOX: a four-point dither pattern with large offsets, comparable to the size of the detectors. This pattern cannot be used for WFC because it requires the use of two guide star pairs, and therefore has to be manually implemented as POS TARG special requirements. For SBC and HRC, the default pattern uses shifts that are 95% the detector dimensions to create a mosaic roughly four times the field of view.
These predefined patterns should cover the needs of the vast majority of scientific program. Other patterns can also be created using a combination of POS TARG offsets.
STIS
STIS is used to obtain images and spectra; therefore, the best dithering method depends on the science goals for the observing program. Those goals may require increased spatial resolution, removal of hot pixels, and minimizing uncertainties in pixel-to-pixel sensitivity with respect to the reference flat fields.
Additional information about STIS dithering strategies are available at Section 11.3 of the STIS Instrument Handbook. A summary is provided below.
Image 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 effectively smoothens the detector response over the number of steps, achieving a reduction in 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, the spatial resolution may be somewhat improved with a dither pattern that includes subpixel shifts. Images obtained with the STIS/CCD (0.0508 arcsec/pixel)4, have nearly the same spatial scale as those obtained by the WFPC2/PC camera (0.045 arcsec/pixel); spatial resolution improvements from dithering would be similar for both cameras. The spatial scale of MAMA images is half that of the CCD images, so the gain in spatial resolution from dithering MAMA images would be more modest, and probably insignificant for 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 about 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 subpixel shifts, the effects of bad columns, hot pixels, and other detector artifacts on the CCD can be reduced or eliminated if the dither pattern is greater than a few pixels. Predefined dither patterns are available for observers to use, which include:
STIS-CCD-BOX: A four point parallelogram scan designed for dithering across the CCD pixels. The default setting produces relative pixel shifts of (0, 0), (10, 5), (15, 15), and (5, 10) to compensate for hot pixels and small-scale detector non-uniformities.
STIS-MAMA-BOX: Like its CCD counterpart, this pattern produces a four point parallelogram with the same relative pixel positions.
STIS-SPIRAL-DITH: A spiral dither pattern, starting at the center and moving outward counterclockwise. When this pattern uses four points, the result is a square pattern. For a 4 point dither, this is not the optimum strategy. Users will get better results, such as enhanced resolution, by using the STIS-CCD-BOX or STIS-MAMA-BOX patterns.
Spectroscopic Mode Dithering
Dither patterns can be used with STIS spectroscopic modes to do the following:
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 (6 x 0.2 arcseconds). Note that in the high dispersion echelle modes, 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 slitless 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.
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-res mode (which is the default) for MAMA observations may provide 15 to 30 percent 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 POS TARG X-axis of the aperture; this is used to map a two-dimensional region of the sky. The target is moved perpendicular to the slit along the AXIS1 (dispersion) direction.
STIS-ALONG-SLIT: This is also normally used with a spectroscopic slit. It produces a scan along the POS TARG Y-axis of the aperture; this is used to step a target along the long slit to dither bad pixels or improve spatial resolution). The target is moved along the slit in the AXIS2 (cross-dispersion or spatial) direction.
Additional information about these spectroscopic dither patterns are available in the STIS Instrument Handbook.
NICMOS
NICMOS has been decommissioned. The information below is provided as a reference for archival data users.
A wide variety of pre-defined patterns has been created for NICMOS, to allow an easy implementation of both integer-pixel and subpixel 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 orbits 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 subpixel 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 arcseconds, may prevent one from obtaining an optimal dither pattern in NIC1 and NIC2, where 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. Please see the section on HST pointing accuracy and stability for more information.
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 (Sosey 2003). 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 subpixel dithered images. If you plan to use subpixel 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.
WFPC2
WFPC2 has been decommissioned. The information below is provided as a reference for archival data users.
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
Pixels near the edge of the CCD differ in size on the sky from those near the center. For instance, a shift of (10,10) pixels at detector coordinates (400, 400) corresponds to a shift of about (10.2, 10.2) pixels at location (700, 700).
Default shift values for the DITHER-LINE pattern, in x and y, are 2.5 pixels for the WF detectors, and 5.5 pixels for the PC detector. For this scenario, over nearly the entire field of view, the difference in offset - even on the PC - is less than 0.1 pixels; the shift is essentially optimal across the whole field.
However, for the standard DITHER-BOX pattern, spacing offsets are as much as 0.75 arcseconds (15.5 PC pixels). This results in a shift difference of about 0.3 pixels in x and y between detector location (700,700) and the detector center (400,400). While the drizzle software is able to remove geometric distortion, it cannot change the fact that the sampling will not be optimal across the entire field of view. DITHER-BOX pattern default values were chosen to avoid the overlap of detector defects such as bad columns and hot pixels in the final combined image. However, for those willing to risk the possibility that a target area of interest could repeatedly fall on one of several bad chip columns, they could specify smaller offsets to produce a box that would have smaller shift differences across the entire chip, like, for instance, a square 2 x 2 box with sides of 2.5 WF pixels or 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 have small rotational offsets (less than 0.5) from their nominal alignments. Thus, the POS TARG 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 POS TARG 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 (less than 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 x on WF3 would cause spurious motion in y 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 Phase II software that is used to process 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: the default setting is a two-point dither along a 45 degree diagonal with respect to the pixels of the primary camera, with points spaced by 0.3535 arcsec. This is equivalent to offsets of 2.5 pixels in x and y for the WF, and approximately 5.5 pixels in x and y for the PC, providing an offset with half-pixel increments along both the x and y axes on all the chips. 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 four-point parallelogram dither with points spaced 0.559 arcsec apart that’s equivalent to these POS TARG offsets, in arcseconds: (0.0, 0.0) (0.5, 0.25) (0.75, 0.75) (0.25, 0.5). This default setting was designed to improve resolution in the final combined image. 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.
 

1
WFC3/IR pixels are not square pixels, but slightly elongated in the x direction.

2
A three-point dither with another three-point secondary dither at each point:(0,0), (0,a+1/3), (0,a+2/3), (m,m), (m+a+1/3), (m+a+2/3), (n,n), (n+a+1/3), (n+a+2/3), where (0,0), (m,m), (n,m) is a three-line dither with integer steps, and a is a small integer added to the fractional shift.

3
The six-point dither: (0,0), (0,m+a+1/2), (m,m), (m+a+1/2), (n,n), (n+a+1/2) where (0,0), (m,m), (n,m) is a three-line dither with integer steps, and "a" is a small integer added to the fractional shift.

4
http://www.stsci.edu/hst/stis/documents/handbooks/currentIHB/c13_specref03.html#922126


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