What sorts of dynamic range will ALMA be able to achieve? =====================================================

The image dynamic range which an interferometer can achieve will be limited by various errors. Important among these are the closure errors, which may be assumed to be small and independent on each baseline. Achievement of these small independent errors will require baseline-based calibration. For an interferometer with the large number of baselines which ALMA achieves (2016) baseline based calibration may not be the default. Slopes and ripples, over the maximum channelwidth that the correlator will use when employed in high-fidelity imaging, must be limited. Bandpass structure on frequency scales larger than this should be calibratable (which then requires that such structures remain stable over periods many times longer than that required to measure the effects).

What does the VLA do?

The VLA is able to achieve very high dynamic range in images of bright point-like objects. While thermal noise should permit dynamic ranges in excess of 1e+6 on some objects, dynamic range is often limited by other factors, including:

* non-closing errors due to bandpass mismatch among antennas; This is largely addressed by using the full spectral line calibration even for continuum observations. Images of sources dominated by point sources can achieve dynamic range in excess of 1e+5.

* deconvolution algorithmic deficiencies: if the source is very extended, typically the dynamic range is limited to about 1e+4. Marginally resolved sources once presented a significant problem, often falling short of the potential resolution by a large factor, but this problem has been solved via the non-linear least squares deconvolution algorithm, permitting dynamic range of order 1e+5.

* mosaicing poses difficulties, as a whole host of errors (beam errors, pointing errors) which usually don't bother single pointing observations begin to limit the image quality. However, if the brightest features in the object are limited in number and are simple shapes (ie, a half dozen sources which are points or marginally resolved), one can accurately remove these sources (and their errors) from the visibility data and basically produce an image in two "channels", one of which is the extended emission, largely unaffected by the errors from the bright simple sources, and the other of which is those bright simple sources. Primitive (ie, "by hand") versions of this sort of algorithm produced VLA images with dynamic ranges ranging from 1e+3 to 1e+4. ALMA algorithms will make this sort of algorithm easier, more automatic, and more accurate.

What is the eVLA specification?
Closure Considerations

A spatial(??-AW) dynamic range goal of 70 dB is reasonable to plan for. This is based on reaching the thermal noise in the presence of a 10 Jy object in a 12-hour integration. This will be an uncommon, but not rare situation.

Under the assumption that each baseline will have an independent and small residual 'closure' error, one can show that the typical error in closure needed to reach this dynamic range is about $5\times10^{-5}$.

ALMA, like the VLA, will be very sensitive and will have the potential of achieving very high dynamic ranges. For example, in only 60~s of observing at 90~GHz, the image plane noise will be about 3e-5~Jy in continuum. As there are a number of quasars that weigh in at 3~Jy, this indicates that it should be very simple to make an observation with a potential dynamic range of 1e+5. In fact, there are brighter quasars, and ALMA can observe for longer times, so it is easy to imagine a potential dynamic range in excess of 1e+6, as with the VLA or eVLA.

What actual scientific goals might require such large values? We consider first the continuum case, and then the spectral line case. Examples of continuum science where high dynamic range is needed include: extended dust emission around a quasar, extragalactic supernova explosions which appear first at high frequencies, and free-free emission from HII regions. For ALMA in spectral line mode, noise per channel will be higher (by a factor between about 30 and 300, depending on the spectral resolution), and the potential dynamic range should be decreased correspondingly. There are accurate algorithms for subtracting the continuum emission from the visibilities prior to spectral line imaging, but the electronics still need to be linear and permit the high dynamic range. Spectral line observations near a bright continuum point source like a quasar may require at least 1e+4 in dynamic range.

ALMA Continuum

The ALMA Design Reference Science Plan (DRSP) solicited example proposals to carry out science projects described in the proposal for ALMA construction. These proposals tend to require more observing time than expected for the average proposal; the intent of the DRSP was to populate three years of ALMA time with proposals. As a result, the proposals tend to focus on faint objects. Keeping this in mind, examination of the DRSP can suggest a range of dynamic ranges expected for proposals within its scope. In the DRSP, potential observing proposals listed the maximum expected continuum flux by band, along with the required noise level of the images. By this measure, imaging experiments near a new supernova (DRSP 3.5.3) require dynamic range of >100,000::1 at 3mm to 40,000::1 at .85mm wavelength; imaging to measure depletion in cores (DRSP 2.3.2) requires a continuum dynamic range of 100,000::1 at 0.85mm; a similar dynamic range at 0.85mm is required by DRSP 1.7.10 to image super star clusters in the 'Antennae' galaxy pair. In the far submillimeter, DRSP 2.1.9, Envelope Structure of Intermediate-mass YSOs, requires continuum dynamic range of 5000::1.

ALMA Spectral Lines

Spectral dynamic range: A spectral dynamic range specification was established for the ALMA baseline correlator at the Correlator PDR as 10^4::1. This needs specific reference, and to be established above and beyond the capabilities of the baseline correlator.

Some spectral line sources requiring high dynamic range: In the submillimeter, thermal sources like compact HII regions can be extremely bright (1000~Jy), but extended. The noise level in the submillimeter will be much higher too (up by a factor of 100 or more from the 90~GHz noise calculation). The shortest baselines will see much of that flux (and all ALMA configurations possess some short baselines). The spectral line targets will include recombination lines (which are fairly faint) and molecular gas interacting with stars (ie, what is left of the molecular cloud after ionization; infall, outflow). These will be very demanding sources, made more demanding by the fact that many will be extended enough to require mosaicing, but possibly complicated enough in the bright continuum to preclude the "two channel" trick used to image high dynamic range mosaics with the VLA. Some of these sources might not require mosaicing (or at least will have a bright core that can be imaged in single field observations), and could require a dynamic range of 3e+4.

Again, we can consult the DRSP to guide our discussion. Here again potential observing proposals listed the maximum expected line flux by band, along with the required noise level of the images in those bands. At all ALMA bands, DRSPs 2.3.3 (Chemical differentiation in star-forming regions) and 2.4.8 (Structure of disks around high-mass protostars) require dynamic range of several thousand to one. At 1.3mm, DRSP 2.2.8 (Survey of the central fields in massive molecular outflows with the ALMA interferometer), 2.3.3 (Chemical differentiation in star-forming regions), 1.2.2 (A ultradeep galaxy survey through clusters using ALMA) and 1.2.1 (Weak lensing using ALMA) all require dynamic ranges from several thousand to ten thousand to one. Terrestrial planetary atmospheric dynamics (DRSP 4.1.1, imaging the dynamics of the middle atmospheres of Mars and Venus) also require high dynamic range. DRSP 4.1.3, investigating chemistry in the atmospheres of these neighbor planets also demands high dynamic range.

Mosaics:
As aluded to above, mosaics will be limited in dynamic range by various errors, such as beam errors, surface errors, and pointing errors. In rough terms, the dynamic range limitation will be about 1e+3, though as mentioned above, there are demonstrated techniques which should be able to extend that dynamic range to 1e+4 or even approaching 1e+5 for cases where the only bright source features are simple and easy to image (ie, if one is dominated by a point source on top of low level extended emission).

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Ideally, one should go backwards now and figure what the requirements are on the electronics based on the image dynamic range requirements. For an image of desiered dynamic range DR_{I}, we require that there be no systematic uncalibratable errors due to the electronics in the visibilities at the level of DR_{I}/sqrt(64). Noise-like errors in the visibilities (ie, things that average down) could be tolerated at a higher level: DR_{I}/ sqrt(64 * N_{int}) where N_{int} is the number of integration intervals. If there are non-systematic errors in the visibilities due to electronic limitations, one could get around them in part by going to more (ie, shorter) integrations, each of which would have higher noise -- ie, one would be making the thermal noise larger than the electronic errors.

Bottom line: I believe we should target being able to achieve 50,000::1 on a bright point source in the millimeter spectral region.

-- AlWootten - 16 Oct 2004
Topic revision: r1 - 2004-10-16, AlWootten

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