making Fourier fitting super fast

At the request of Conor Sayres (UW), I have been looking at distortion patterns in the SDSS-V Focal Viewing Camera (FVC), which is the part of the system that looks at whether the focal-plane fiber robots are where they need to be. The distortions are extremely bad; they are large in amplitude and vary on extremely small scales on the focal plane. So I have to fit an extremely flexible model. Here are my comments:

First, you should use mixtures of sines and cosines for problems like this. Not polynomials! Why? Because sines and cosines do not blow up at the edges.

Second, you should punk fast Fourier transform (FFT) codes to speed up your regressions. I wrote code to do this, which wraps the finufft best-in-class non-uniform FFT code in scipy.sparse linear-algebra code. This wrapping makes the FFT operators into linear-algebra operators and permits me to do solve() operations. That move (wrapping FFT in linear algebra) sped up my code by factors of many!

what is a transmission function?

Mike Blanton (NYU) and I agree and disagree on almost everything about fundamental astronomy. As my loyal reader knows, I am writing something on how apparent magnitudes work, and also absolute, bolometric, reddening-corrected, and so on. The apparent magnitude of star depends (among other things) on a filter bandpass or a transmission function. There are two possible definitions of this. One is the fraction of light (as a function of wavelength or frequency) that makes it through the system, from the top of the atmosphere to stimulating the detector. The other is the mean contribution to the total counts read out by the detector of a photon (of a particular wavelength or frequency) impinging on the top of the atmosphere. These might sound similar—they are identical when your detector is a photon counter. But they aren't identical if your detector is, say, a bolometer. I struggled with how to simply communicate all this today.

re-scoping a paper on spectrograph calibration

In a long conversation, Lily Zhao (Yale), Megan Bedell (Flatiron), and I looked at a possible re-scope of our new paper on spectrograph calibration. Zhao is finishing one paper that builds a hierarchical, non-parametric wavelength solution. It does better than fitting polynomials independently for different exposure groups, even in the full end-to-end test of measuring and fitting stellar radial-velocities. But the paper we were discussing today is about the fact that the same distortions to the spectrograph that affect the wavelength solution also (to the same order) affect the positions of the spectroscopic traces on the device. That is, the relationship between (say) x position on the detector and wavelength can be inferred (given good training data) from the y position on the detector of the spectral traces. We have been struggling with how to implemnent and use this but then we realized that we could instead write a paper showing that it is true, and defer implementations to the pipeline teams. Implementation isn't trivial! But the result is nice. And kind-of obvious in retrospect.

calibrating a fiber spectrograph

I had my weekly call with Ana Bonaca (Harvard) this morning, where she updated me on our look at systematic effects in the radial-velocity measurements we are getting out of Hectochelle. We see very small velocity shifts in stellar radial velocities across the field of view that seem unlikely to be truly in the observed astrophysical stellar systems we are observing. At this point, Bonaca can show that these velocity shifts do not appear in the sky lines; that is, the calibration (with arc lamps) of the wavelengths on the detector is good.

All I have left at this point is that maybe the stars illuminate the fibers differently from the sky (and arc lamps) and this difference in illumination is transmitted to the spectrograph. I know how to test that, but it requires observing time; we can't do it in the data we have in hand right now. This is an important thing for me to figure out though, because it is related to how we commission and calibrate the fiber robot for SDSS-V. Next question: Will anyone give us observing time to check this?

forecasting tools; beautiful spectrograph calibration

Our five-person (Bedell, Hogg, Queloz, Winn, Zhao) exoplanet meeting continued today, with Winn (Princeton) working out the elements needed to produce a simulator for a long-term EPRV monitoring program with simple observing rules. He is interested in working out under what circumstances such a program can be informative about exoplanets in regimes that neither Kepler nor existing EPRV programs have strongly constrained, like near-Earth-masses on near-Earth-orbits around near-Sun stars. And indeed we must choose a metric or metrics for success. His list of what's needed, software-wise, is non-trivial, but we worked out that every part of it would be a publishable contribution to the literature, so it could be a great set of projects. And a very useful set of tools.

Zhao (Yale) showed me two-dimensional calibration data from the EXPRES instrument illuminated by their laser-frequency comb. It is astounding. The images are beautiful, and every single line in each image is at a perfectly known (from physics!) absolute wavelength. This might be the beginning of a very new world. The instrument is also beautifully designed so that all the slit (fiber, really, but it is a rectangular fiber) images are almost perfectly aligned with one of the CCD directions, even in all four corners of the image. Not like the spectrographs I'm used to!

Math+X Houston, day 1

Today was the first day of the 2019 Math+X Symposium on Inverse Problems and Deep Learning in Space Exploration, which is a meeting to bring together mathematicians and domain scientists to discuss problems of mutual interest. I learned a huge amount today! I can't summarize the whole day, so here are just a few things ringing in my brain afterwards:

Sara Seager (MIT) and I both talked about how machine learning helps us in astrophysics. She focused more on using machine learning to speed computation or interpolate or emulate expensive atmospheric retrieval models for exoplanet atmospheres. I focused more on the use of machine learning to model nuisances or structured noise or foregrounds or backgrounds in complex data (focusing on stars).

Taco Cohen (Amsterdam) showed a theory of how to make fully, locally gauge-invariant (what I would call “coordinate free”) deep-learning models. And he gave some examples. Although he implied that the continuous versions of these models are very expensive and impractical, the discretized versions might have great applications in the physical sciences, which we believe truly are gauge-invariant! In some sense he has built a superset of all physical laws. I'd be interested in applying these to things like CMB and 21-cm foregrounds.

Jitendra Malik (Berkeley) gave a nice talk about generative models moving beyond GANs, where he is concerned (like me) with what's called “mode collapse” or the problem that the generator can beat the discriminator without making data that are fully representative of all kinds of real data. He even name-checked the birthday paradox (my favorite of the statistical paradoxes!) as a method for identifying mode collapse. Afterwards Kyle Cranmer (NYU) and I discussed with Malik and various others the possibility that deep generative models could possibly play a role in implicit or likelihood-free inference.

There were many other amazing results, including finding seismic pre-cursors to landslides (Seydoux) and using deep models to control adaptive optics (Nousianinen) and analyses of why deep learning models (which have unimaginable capacity) aren't insanely over-fitting (Zdeborová). On that last point the short answer is: No-one knows! But it is really solidly true. My intuition is that it has something to do with the differences between being convex in the parameter space and being convex in the data space. Not that I'm saying anything is either of those!

writing

I spent the day writing in the spectroscopic-parallax project. I wrote six or seven paragraphs, and that's about it! (Actually, that's a great day: My goal is two paragraphs per day.)

But in addition to the writing, I did have an interesting conversation with Tom Herbst (MPIA), Thomas Bertram (MPIA), and Kalyan Radhakrishnan (MPIA) about adaptive optics. The idea is to think about using the science data (the imaging you care about) to update the adaptive mirrors. What new things might be unlocked by that, especially if used in concert with the wavefront sensors? This reminds me of old conversations I have had with Matthew Kenworthy (Leiden). I also asked what kinds of science you might do with the wavefront sensors. Just as the imaging detector gives wavefront information, the wavefront sensors give imaging information!

I also was present for presentations by Eilers (MPIA) and Birky (UCSD) on their stellar projects in the MPIA Stars Group Meeting.

mixture of factor analyzers; centroiding stars

On this, day four of my Hunstead Lectures, Andy Casey (Monash) came into town, which was absolutely great. We talked about many things, including the mixture-of-factor-analyzers model, which is a good and under-used model in astrophysics. I think (if I remember correctly) that it can be generalized to heteroskedastic and missing data too. We also talked about using machine learning to interpolate models, and future projects with The Cannon.

At lunch I sat with Peter Tuthill (Sydney) and Kieran Larkin (Sydney) who are working on a project design that would permit measurement of the separation between two (nearby) stars to better than one millionth of a pixel. It's a great project; the designs they are thinking about involve making a very large, but very finely featured point-spread function, so that hundreds or thousands of pixels are importantly involved in the positional measurements. We discussed various directions of optimization.

My talk today was about The Cannon and the relationships between methods that are thought of as “machine learning” and the kinds of data analyses that I think will win in the long run.

crazy space hardware

I spent today at JPL, where Leonidas Moustakas (JPL) set up for me a great schdule with various of the astronomers. I met the famous John Trauger (JPL), who was the PI on WFPC2 and deserves some share of the credit for repairing the Hubble Space Telescope. I discussed coronography with Trauger and various others. I learned about the need for coronographs to have two (not just one) deformable mirror to be properly adaptive. With Dimitri Mawet (Caltech) I discussed what kind of data set we would like to have in order to learn in a data-driven way to predictively adapt the deformable mirrors in a coronograph that is currently taking data.

With Eric Huff (JPL) I discussed the possibility of doing weak lensing without ever explicitly measuring any galaxies—that is, measuring shear in the pixels of the images of the field directly. I also discussed with him the (apparently insane but maybe not) idea of using the Sun itself as a gravitational lens, capable of imaging continents on a distant, rocky exoplanet. This requires getting a spacecraft out to some 550 AU, and then positioning it to km accuracy! Oh and then blocking out the light from the Sun.

Martin Elvis (CfA) gave a provocative talk today, about the future of NASA astrophysics in the context of commercial space, which might drive down prices on launch vehicles, and drive up the availability of heavy lift. A theme of his talk, and a theme of many of my conversations during the day, was just how long the time-scales are on NASA astrophysics missions, from proposal to launch. At some point missions might start to take longer than a career; that could be very bad (or at least very disruptive) for the field.