MIRI MRS Dithering

See also: MIRI MRS Mosaics

The MIRI medium-resolution spectrometer (MRS) is spatially undersampled at all wavelengths, particularly at the shortest wavelengths within each channel (see Figure 1). Ideal sampling of a point spread function (PSF) should provide at least two samples per spatial resolution element in order to avoid loss of information. Dithering is therefore necessary to (1) improve this spatial sampling, (2) mitigate bad pixels by sampling the image with redundant detector locations, and (3) allow for sufficient PSF separation that pairs of exposures can be used as background exposures for each other. 

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General Theory


The MRS consists of four separate IFUs, each with a different wavelength range, pixel size, and slice width (see Table 1 on the MRS main page).  Since all four IFUs observe a scene simultaneously, the MIRI dithering strategy must simultaneously achieve half-integer offsets in sampling for all four channels.  The MRS slice widths of 0.176, 0.277, 0.387, and 0.645 arcsec (Channels 1-4 respectively) were designed to accommodate such a strategy; an offset in the across-slice direction of 0.968" 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.

In theory, optimal sampling can therefore be achieved at all wavelengths with a simple two-point dither pattern.  However, due to optical distortions the effective pixel size is not constant across the MRS FOV, nor is the along-slice pixel phase matched between adjacent slices.  Such a two-point dither pattern therefore only achieves half-integer sampling offsets at some locations in the FOV, and is closer to integer at other locations.  A simple modification of the two-point pattern to four points is therefore required in order to achieve optimal sampling throughout the MRS FOV.

Figure 1. MRS spatial resolution and ideal vs. actual sampling as a function of wavelength

Spatial FWHM of an isolated point source as a function of wavelength based on simulations and ground tests data. The solid black line indicates the diffraction limit; reconstructed data cubes are nearly diffraction limited longward of 8 μm, while the along-slice FWHM is approximately 0.31" shortward of 8 μm (dashed black line). The dotted black line represents the ideal sampling, defined as one half of the diffraction limit. The solid and dashed colored lines illustrate the actual sampling of the MRS optics in the across-slice and along-slice directions respectively in each of the four channels (blue, green, yellow, red lines). MRS is roughly a factor of two undersampled at the shortest wavelengths in each channel. 


Available dither patterns

JWST dithering allows for moves specific to MIRI MRS. Dither patterns for the observation 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 two kinds of dither patterns available for MRS; patterns optimized for point source observations, and patterns optimized for extended source (or mosaicked) observations. These two kinds of 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.

The sequence is fully specified in APT by choosing:

  1. The Primary Channel1 for the pattern (i.e., whether the pattern and MRS pointing origin are optimized for ALL wavelengths or for a particular channel: Channel 1, Channel 2, Channel 3, or Channel 4).
  2. Either a 2-Point or a 4-Point pattern.
  3. Whether the pattern is optimized for Point Sources or Extended Sources.
  4. The Direction of the pattern on the sky.

Dither patterns optimized for point sources

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 separate channel 4 images for accurate background subtraction (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 2 (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, for instance, achieves a point source separation of eight 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 2, right panel).

Additionally, point source dither patterns can be specified with either of two 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 thirty-two total Point Source dither patterns are illustrated in Figure 2 (left panel).

Figure 2. MRS point source dither patterns

Left panel: MRS FOV in the JWST V2/V3 coordinate frame, the field borders are drawn as solid lines (sub-band A), dashes (sub-band B), and dots (sub-band C) for channels 1 (blue), 2 (green), 3 (yellow), and 4 (red).  Colored + symbols represent the Point Source optimized dither locations for the Channel 1/ALL pattern (blue symbols), Channel 2 pattern (green symbols), Channel 3 pattern (yellow symbols), and Channel 4 pattern (red symbols).

Middle panel: Example sky coverage (assuming zero spacecraft roll angle) for the 4-Point, Channel 1/ALL point-source optimized dither pattern. The blue/red circles indicate two times the PSF FWHM at 8/28 μm respectively.

Right panel: Example sky coverage (assuming zero spacecraft roll angle) for the 2-Point, Channel 4 point-source optimized dither pattern. The blue/red circles indicate two times the PSF FWHM at 8/28 μm respectively.  Note that the Channels 1-3 FOV do not overlap the science target.



Dither patterns optimized for extended sources 

In cases where the science target is larger than about an arcsecond in size (or when mosaicking large areas of sky), the Point Source optimized patterns may be undesirable since a portion of the target will fall outside the shared field of view of the dithered 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 3, 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 3, right panel).

The locations of the twenty total Extended Source dither patterns are illustrated in Figure 3 (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.

Figure 3. MRS extended source dither patterns

Left panel: MRS FOV in the JWST V2/V3 coordinate frame, the field borders are drawn as solid lines (sub-band A), dashes (sub-band B), and dots (sub-band C) for channels 1 (blue), 2 (green), 3 (yellow), and 4 (red).  Colored + symbols represent the extended-source optimized dithers locations for the ALL pattern (black symbols), Channel 1 pattern (blue symbols), Channel 2 pattern (green symbols), Channel 3 pattern (yellow symbols), and Channel 4 pattern (red symbols).

Middle panel: Example sky coverage (assuming zero spacecraft roll angle) for the 2-Point, ALL extended-source optimized dither pattern. The blue/red circles indicate two times the PSF FWHM at 8/28 μm respectively.

Right panel: Example sky coverage (assuming zero spacecraft roll angle) for the 2-Point, Channel 3 extended-source optimized dither pattern. The blue/red circles indicate two times the PSF FWHM at 8/28 μm respectively.


2-Point vs 4-Point dithers

As described above, the MRS slice widths and pixel scales are designed such that a simple 2-Point dither pattern will nominally allow the MRS to achieve half-integer sampling in all four 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.

The final image will therefore be both better and more uniformly sampled if the 2-Point pattern is repeated with a small (~0.1") offset to minimize the impact of field-dependent distortion.  This 4-Point variation is available for both the point source and extended source optimized dither patterns.

The level of impact on the resulting image quality of poor spatial sampling due to 2- vs 4-point dithering is still under study, as are the impacts of no dithering (which may be desirable for certain science cases). In the worst case, (e.g., an undithered observations of a point source that falls at the boundary between adjacent slices), however, the reconstructed profile of a point source may be distorted by as much as 50% in the along-slice direction, the across-slice direction, or both.


Which pattern should I use?

The best dither pattern to use for a given set of observations depends strongly on the science case.  Figure 4 summarizes the advantages and disadvantages of each of the available MRS dither patterns as they affect the point source separation, common field of view, and image sampling quality (Figure 5) in each wavelength channel.

In the majority of cases, programs observing either point sources or compact sources (less than about an arcsec in extent) should use the Point Source, 4-Point ALL dither pattern. This provides robust performance at all wavelengths and adequate point source separation in all channels such that dedicated background observations are not required. In cases where additional PSF separation is desired at longer wavelengths (due to a particularly bright source, or some extended structure surrounding the source), channel-specific options may be used at the cost of no longer having the source in the field of view at short wavelengths. 2-Point patterns are not recommended at the present time due to their poorer spatial and spectral sampling.

Similarly, most programs observing extended sources or using the MRS to mosaic large areas of sky should use the Extended Source, 4-Point ALL dither pattern. Although this has the least common field of view of any of the extended source patterns, it is the only pattern that simultaneously achieves ideal half-integer sampling at all wavelengths.  If a particular science program wishes to prioritize field of view at one wavelength at the expense of other wavelengths (e.g., mapping an emission line region with a specific spectral line), channel-specific options may be used at the cost of spatial sampling and/or detector pixel redundancy at other wavelengths. 2-Point patterns are not recommended at the present time due to their poorer spatial and spectral sampling.

Figure 4. Expected relative performance of MRS dither patterns (pre-flight)

Relative performance of the MIRI MRS Point Source and Extended Source dither patterns as a function of their Primary Channel and number of points (2-Point or 4-Point). The table gives the image separation between exposures in units of the channel PSF FWHM, the common field area of overlap of the exposures in each channel, and the quality of the spatial sampling in each channel. Spatial sampling marked as ‘GOOD’ indicates half-integer sampling throughout the common field of view, ‘POOR’ indicates near-integer sampling, and ‘FAIR’ is intermediate between the two.
Figure 5. Typical image quality expected from dither patterns

Mock images illustrating the impact of incomplete dithering on reconstructed image quality.


References



Published

 

Latest updates

     Significant revisions to all sections and figures.

  •  
    Revisions for MRS optical distortions from simulated and ground test data


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