Dithering is necessary for MIRI medium-resolution spectrometer (MRS) observatfcrossions to improve spatial sampling and mitigate bad pixels.

See also: MIRI MRS Mosaics

Ideally, the MRS point spread function (PSF; Figure 1) should be Nyquist sampled with at least 2 spatial element per PSF FWHM. However, the IFU is significantly spatially undersampled by design in order to maximize the field of view. As illustrated in Figure 2, the slice width (orange dashed lines) and pixel size (blue dashed lines) are roughly a factor of 2 larger than the ideal sampling (dashed black line) at the shortest wavelengths within each spectral channel. Dithering is therefore necessary to improve this spatial sampling and mitigate bad pixels by sampling the image with redundant detector locations.

The MRS consists of 4 separate IFUs, each with a different wavelength range, pixel size, and slice width (see Table 1 on the MRS main page). Since all 4 IFUs observe a scene simultaneously, the MIRI dithering strategy must simultaneously achieve half-integer offsets in sampling for all 4 channels. The MRS slice widths of 0.177, 0.280, 0.390, and 0.656 arcsec (channels 1–4, respectively) were designed to accommodate such a strategy; an offset in the across-slice direction of 0.97" for instance corresponds to a move of 5.5, 3.5, 2.5, and 1.5 slices, respectively, in channels 1–4. Similarly, offsets in the along-slice direction of 2.058" correspond to nearly half-integer offsets of 10.50, 10.50, 8.43, and 7.54 pixels, respectively, in channels 1–4.

Even when observed with such a half-integer dithering strategy, the MRS is not diffraction limited. As illustrated in Figure 2, both the measured along-slice (α; blue squares) and across-slice (β; orange diamonds) PSF FWHM is slightly broader than the theoretical diffraction limit (solid red line), due to a combination of sampling effects and internal scattering within the MRS detectors (see discussion by Argyriou et al. 2023).  Likewise, a significant cross-artifact (see MIRI MRS Known Issues) on the detector produces non-local PSF structure on the sky which to first order is modeled and removed by the pipeline. Additionally, the undersampling of the PSF gives rise to resampling noise (see MIRI MRS Known Issues) in the reconstructed data cubes that can bias spectra extracted from regions smaller than the PSF.

Dither patterns for MIRI MRS observations can be implemented in the Astronomers Proposal Tool (APT) with the JWST APT MIRI MRS template. A dither pattern is defined as a sequence of small (less than 5" in the case of the MRS) moves from the starting position near the center of the MRS field of view. There are 2 kinds of dither patterns available for MRS science observations; patterns optimized for Point Source observations, and patterns optimized for Extended Source (or mosaicked) observations. These patterns differ in the size and purpose of their dither offsets; point source-optimized patterns maximize the offset distance to provide large point source separation at the cost of decreased common field of view, whereas extended source-optimized patterns minimize the offset distance to provide the greatest common field of view at the cost of decreased point source separation. Both sets of patterns provide improved spatial sampling and detector pixel redundancy. New since Cycle 3, there is also a dither pattern optimized for Background observations to improve simultaneous imaging.

The sequence is fully specified in APT by choosing:

1. The Primary Channel for the pattern (i.e., whether the pattern and MRS pointing origin are optimized for MRS ALL wavelengths, for a particular channel: Channel 1, Channel 2, Channel 3, or Channel 4, or whether the target should be placed on the Imager).
2. Either a 2-Point or a 4-Point pattern.
3. Whether the pattern is optimized for Point Sources, Extended Sources, or Background observations.
4. The Direction of the pattern on the sky.

The default dither pattern for MRS is a 4-Point pattern that is optimized for Point Source observations at ALL wavelengths. As such, it provides an offset large enough to move the channel 4 PSF significantly (offset ~3 times the FWHM of a point source in channel 4) while keeping the channel 1 images comfortably within the field of view (channel 4 has larger field of view than channel 1). This pattern is illustrated in Figure 3 (middle panel).

For observers who wish to increase the separation between the point source locations in successive exposures, variations on this basic pattern are provided that further increase the separation distance. These variations are channel-specific, in the sense that they achieve the greatest separation in a particular wavelength channel at the cost of poorer spatial sampling and smaller common field of view in other channels. The pattern optimized for Channel 1 is identical to the default pattern optimized for ALL wavelengths. In contrast, the pattern optimized for Channel 4, achieves a point source separation of 8 times the FWHM in channel 4 at the cost of moving the target entirely out of the field of view in channel 1 (see Figure 3, right panel).

Additionally, point source dither patterns can be specified with either of 2 Directions on the sky. The "positive" orientation repeats the pattern of the default "negative" orientation but with the offset directions swapped in order to rotate the movement on the sky by 43º, giving some flexibility in accommodating source geometry for a given spacecraft roll angle.

The locations of the 32 total Point Source dither patterns are illustrated in Figure 3 (left panel).

Dither patterns optimized for extended sources 

In cases where the science target is spatially resolved (or when mosaicking large areas of sky), the Point Source optimized patterns may be undesirable since a portion of the target may fall outside the shared field of view of the dithered observations or otherwise contaminate the annular regions typically used for background subtraction in point source observations. The Extended Source dither patterns therefore provide half-integer sampling offsets that maximize the shared field of view of each band at the expense of reduced PSF separation between successive exposures.

The basic Extended Source dither pattern is optimized to provide improved sampling for ALL wavelengths by applying the across-slice offset of the Point Source ALL pattern but with a smaller along-slice offset (see Figure 4, middle panel). Dither patterns specific to Channel 1, Channel 2, Channel 3, and Channel 4 are also provided that further maximize spatial overlap in a given channel at the expense of data quality at other wavelengths. As an example, the Extended Source pattern optimized for Channel 3 provides a ~35 arcsec² common field and good sampling for channel 3 at the expense of degraded sampling and pixel redundancy in channels 1, 2, and 4 (see Figure 4, right panel).

The locations of the 20 total Extended Source dither patterns are illustrated in Figure 4 (left panel). Since the offsets of the extended source patterns are substantially smaller than the point source optimized patterns, the Direction of these patterns need not be specified as both are identical.

Note that when using an Extended Source pattern, a dedicated sky exposure should be linked within APT in order to provide a reference background image free of source contamination.

Dither patterns optimized for background observations 

When the MRS is observing a dedicated background exposure, it is common to use the MIRI imaging field to observe the MRS science target or some other nearby region. The MRS Point Source and Extended Source patterns however do not provide ideal sampling or image separation for the MIRI imager dithering. As a result, the MRS Background dither pattern (Figure 5) has been designed to optimize data quality in the MIRI imager at the expense of having sources fall outside the MRS field of view (which is irrelevant when the MRS is observing only empty sky) and is available since Cycle 3.

As for the Point Source and Extended Source patterns, there are 2-pt and 4-pt variations of the Background dither pattern to accommodate different needs for the background depth and number of dither points within the imaging field.

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2-Point vs 4-Point dithers

As described above, the MRS slice widths and pixel scales are designed such that a simple 2-Point extended-source or point-source optimized dither pattern will nominally allow the MRS to achieve half-integer sampling in all 4 channels. In practice, however, optical distortions and discontinuities in the mapping of adjacent optical slices to detector pixels (see Figure 1 on the MRS main page) means that this half-integer sampling is not achieved for all locations within the MRS field. A simple modification of the 2-Point patterns to corresponding 4-Point patterns is therefore required in order to achieve optimal sampling throughout the MRS FOV (Figure 6).

Analysis of in-flight MIRI data has confirmed that 4-Point dither patterns achieve significantly better performance than 2-Point patterns, which are recommended only for background observations. As discussed in detail by Law et al. (2023) for instance, the curvature of the MRS spectral traces on the detector leads to wavelength-dependent variations in pixel sampling phase that produce coherent amplitude modulations in one-dimensional spectra (in addition to the fringing signature seen due to interference patterns within the detector substrate). As discussed in MIRI MRS Known Issues, the amplitude of such artifacts is reduced significantly with the use of a 4-Point dither pattern.

4-Point dither patterns should thus be used for all science observations with the exception of dedicated backgrounds. If programs require integration on-source for longer than the amount of time covered by a simple 4-Point pattern, they may wish to employ both Negative and Positive versions of that pattern in order to further improve sampling and redundancy.

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Which pattern should I use?

The best dither pattern to use for a given set of observations depends strongly on the science case.

In the majority of cases, programs observing either point sources or compact sources (less than about 0.5" in extent) should use the 4-Point, Point-Source optimized ALL-channel dither pattern. This provides robust sampling performance at all wavelengths and adequate point source separation in all channels such that dedicated background observations are not required. In cases where the scientific focus is on a specific wavelength channel, greater PSF separation can be achieved using the channel-specific dither patterns at the cost of poorer sampling in the non-primary channels and (potentially) no longer having the source in the field of view at short wavelengths.

Similarly, most programs observing extended sources (0.5"–1" or larger) or using the MRS to mosaic large areas of sky should use the 4-Point, Extended Source optimized ALL-channel dither pattern as this is the only extended source pattern that achieves ideal sampling at all wavelengths. If a particular science program wishes to maximize the common field of view in one particular channel (e.g., mapping extended emission from a specific spectral line), channel-specific options may be used at the expense of spatial sampling and/or detector pixel redundancy at other wavelengths.

For dedicated background observations dithering is not required, although at least a 2-Point is recommended (4-Point if intending to use a pixel-based background subtraction method).  The background-specific pattern is not required, but a 4-Point Background pattern will give the best sampling for simultaneous imager observations during the MRS backgrounds.

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References

Argyriou, I. et al. 2023, A&A, 675, 111 
JWST MIRI flight performance: The Medium-Resolution Spectrometer

Law, D. et al. 2023, AJ, 166, 45L
A 3D Drizzle Algorithm for JWST and Practical Application to the MIRI MRS

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