I had a conversation with Wesley Frazer about trailed asteroid photometry. He points out that if we know an asteroid’s velocity (and maybe position) then we can do a better job of the trailed-object photometry than if we have to estimate both the trail length and the flux from the data.
Currently I believe that LDM-151 doesn’t distinguish between measurements in DiaSource from AP (where we usually don’t know the asteroid’s orbit) and DRP (where we usually (or often) do). In principle, this means that we need to do orbit fitting early enough in DRP processing that it’s available when we redo the snap processing; as @jbosch points out, we may be able to defer the careful trailed-photometry until the forced photometry which may not require us to estimate orbits early.
It is also possible that we’ll decide that the trailed photometry isn’t important enough to worry about, but that’s a decision that probable needs to go to the SAC.
Two minor points: we could potentially have some orbit knowledge available during AP from NightMOPS, and I believe MOPS represents a global sequence point, so if that has to happen before forced photometry, it will (further) constrain handling of intermediate data products such as processed visit images.
I have a related, but slightly different concern as well. When we do DiaSource measurements in AP, these are on difference images and with preliminary zeropoints and other calibration products.
I had assumed that when we do photometric measurements at DRP, we would do measurements on images (not just diaimages) and thus they would be Source measurements. Is this true? I think you’ve told me in the past that there would not be appreciably different errors or photometric measurements between the two, but has that been tested?
If the plan would be to do diasource measurements at DRP, get the orbits, and then do Source measurements on images after the orbit is established, this seems like you could actually get all of it at once (and do the trailed photometry the way Wes wants to).
In DRP we’ll be doing forced photometry on both difference images and direct images. The photon noise in the difference image measurements will indeed be somewhat higher, but the deblending should be easier.
However, I’m not certain whether we had plans to do forced photometry on solar system objects at all (I don’t think that was in the DPDD, but I’m not looking at right now). That’s a lot trickier than regular forced photometry for three reasons:
the objects are trailed (not really a hard problem)
we’d need to do MOPS before we finish all the pixel processing, introducing a global sequence point (as @ktl noted)
the images we’d want to forced-photometer for a given object are not all in the same place on the sky.
The last one is the one that scares me the most, just because it implies a very different organization of the data than anything else we’re doing, but I don’t have a good sense for how problematic that is for I/O and data flow.
Some of this might be ignorant, simply because I am ignorant of the internal systems and processes. But the way my groups have ensured maximum and unbiased (more important) moving object photometry was to first determine a rate+angle of motion of an object on an image from its ephemeris, then determine the appropriate pill aperture and corresponding PSF. This is the approach for the Outer Solar System Origins Survey on the CFHT. We first find objects, get circular aperture photometry (biased because of trailing). Once orbits are known, I then go back with trippy and redo the photometry.
Fitting to determine trailing length on image will improve astrometry, but produces biased flux measurements when SNR is moderate to low, even beyond the accuracy of the measurement. So while it seems from Jim’s comment that going back and redoing forced photometry is somehow really expensive, IMO it is the only way to do the job correctly.
Some of this is talked about in my recent paper. For what isn’t, I’d be happy to help sort out the importance of.
I think you want measurements on the difference images. As Jim says there’s a little more noise (but it’s probably negligible – that depends on how we build templates), but the systematics are much reduced – at LSST depths there’s a lot of confusion noise, especially down towards the plane.
I think it’s clear that the optimal solution is to know the position and velocity of the asteroid; if we don’t know the orbit well enough we may need to centroid (in 1-D, or 2-D depending on whether the orbit or just the phase is uncertain); this is what Wes points out.
The rest is mechanics, and whether the improvements are important enough for enough people.
Many thanks to Wes for pointing out that we could do better with asteroid
photometry! We looked at a few numbers to gauge how important these
effects are in practice.
An upper limit on the photometric bias is the bias obtained when using psf
flux instead of flux computed with correct trailed profile. This bias was
computed in Jones et al. (2017): https://jira.lsstcorp.org/browse/PUB-39
In case the above JIRA link cannot be accessed, please send email to either
of us and we will send you pdf (the paper will be submitted in a few days).
Also, all the computations are reproduced in this ipython notebook
(the plot from the paper that we are referring to is the last plot in this notebook).
As Fig. 5 shows (the photometric bias is equal to the difference between
blue and red curves, see text to notebook for numerical expressions), at
0.5 deg/day photometric bias is about 0.03 mag. At 1 deg/day, the bias
increases to about 0.2 mag, and to about 0.4 mag for 2 deg/day (for the
fiducial seeing of 0.7 arcsec and 30 sec exposure; note that paper by Fraser
et al. referenced by Wes shows plots for ten times longer exposures).
Fig. 15 (page 40) from LDM-156, see http://ls.st/LDM-156
shows that about 99% of main belt asteroids and 80% of NEOs never
move faster than 0.5 deg/day. For them, the bias is at most 0.03 mag
and probably much smaller for flux computed for DIASources with (fitted)
trailed source profile. In the low SNR regime, random errors are several
times larger that 0.03 mag so this bias doesn’t seem catastrophic.
About ~5% of NEOs can move faster than 1 deg/day (but essentially none
of MBAs move that fast), and about ~1% of NEOs can move faster than
2 deg/day. According to the LSST Science Book, Table 5.1, LSST will
detect about 100,000 NEOs. Assuming they are all in the low SNR regime,
we could thus appreciably improve photometry for several thousand NEOs.
Given that we can preselect NEOs (or even individual visits) with large
velocities, and that the expected sample size is not large,
*** these computations could probably be done as a Level 3 project. ***
That said, it would be prudent to generalize the forced photometry code a
bit and allow for the source motion (convolve psf with known linear motion).
If so, DM could take a middle road and account for trailing above some
appropriate velocity threshold when doing forced photometry in DRP
** for objects where orbits are already known prior to that DR. **
This way the impact on DRP processing system is minimal, and we get
unbiased photometry for the majority of cases where we care the most
(it’s hard to imagine that we’d care about this biases in cases where we
cannot even constrain the orbit; there will be some objects whose orbits
will not be known from AP processing and will be determined in DRP
for the first time, but I am guessing that their fraction must be small).
We will take it as our action item to talk to Mario and others from DM
about this proposal in detail.
Lynne and Zeljko
PS
Wes, do you have any quantitative estimates of what happens in the low
SNR regime when the trail length is also a free fitting parameter? We can
see that the photometric error would increase, but we don’t see how to
induce a photometric bias. We haven’t done any studies of covariances
between free parameters when fitting trails yet but we do have the tools
for doing so (it’s a matter of prioritization of many different studies).
I haven’t actually studied in detail the fitting part yet. The only thing I really studied was aperture stuff, as you could probably tell from my paper. Though I would be happy to throw my hand at it. As Zeljko pointed out, I have been focused on much longer exposures than what LSST will involve. So if you have suggestion for what sorts of parameters to use (FWHM, or better alpha/beta for a moffat profile) I can jig something up for an LSST specific case.
A couple notes on the stuff above:
I agree this could/should be an L3 project. It’s a pretty straight forward thing, at least in concept. So why not? This sounds like something right up my alley…
For a low cost alternative, and once we know basic rates of motion (through linkages probably) we could generate a bias correction, either as a lookup table, or direct calculation from a PSF on an image-by-image basis. Then just apply that correction to the flux, and shove out the door. Both for PSF fit and aperture photometry.
As long as we know what the correction applied is, then if a use doesn’t like it, they can have the crappier version.
The only remaining penalty would be in SNR, but that’s not going to be so detrimental IMO.