New Paper on Precise Doppler Velocities: To Stabilize or To Modulate?

High-precision Doppler spectrometers are all the rage right now.  With the success of NASA’s Kepler Mission, transiting exoplanets vastly outnumber those with Doppler velocity measurements.  Without Doppler measurements, we can't know a transiting planet’s mass, which is necessary to determine a planet’s mean density and surface gravity, which is in turn necessary to interpret atmosphere measurements.  Many current and future sub-meter-per-second Doppler spectrometers are trying to fill that need: HARPS, HARPS-N, Minerva, Minerva-RedCHIRONAPFHPF, CARMENES, NN-EXPLORE EPDS, NRES, ESPRESSO, EXPRES, G-CLEF, and MAROON-X.  That’s a lot of spectrometers, but we’ll need each and every one!

What do all of these Doppler spectrometers have in common?  They are stabilized.  In order to achieve less than 1 meter-per-second of Doppler precision with a spectrograph, you need to measure the motion of a spectrum across a few atoms within a detector pixel.  That’s hard, so stabilization is important.

Or is it?  Back in the 1930s, C. R. Cosens, a scientist at the Cambridge Scientific Instrument Company, published a paper in the Proceedings of the Physical Society of London describing an instrument that can measure faint electronic signals.  In 1941, Walter Michels and Norma Curtis of Bryn Mawr College further developed the idea and published a paper entitled "A Pentode Lock-In Amplifier of High Frequency Selectivity.”  The paper caught the attention of Robert Dicke, then at MIT, who developed the lock-in amplified approach as a way to measure any faint or slightly changing signal.  Using the lock-in amplifier, Dicke revolutionized microwave and radio astronomy, measuring radiation from the sun and moon and developing the "Dicke Switch,” still used to this day in radio astronomy.  (Robert Dicke is often credited with inventing the lock-in ampler, though he admitted to getting the idea from Michels & Curtis in an interview in the 1980s.)

Figure from Michels & Curtis (1941).

How does it work?  Basically, you take a signal, forcibly modulate that signal at a high frequency upstream to your measuring instrument, either by turning it off and on or by mixing it with a oscillator, then “lock-in” to that frequency in the data to isolate it from instrumental variations which occur at different frequencies.  The common implementation for visible light is a chopper wheel.  

Can we use this for Doppler velocities?  Yes!  Back when I was a postdoc at Caltech, I worked with a graduate student named Rebecca Jensen-Clem to investigate the benefits of forcibly modulating a spectrum with an interferometer.  Rebecca was taking a class on Bayesian statistics with John Johnson at the time, and for her class project she calculated whether a lock-in approach to radial velocities could get us to 10 centimeters-per-second of Doppler precision: what we need to measure the masses of Earth-like transiting planets orbiting sun-like stars.  The combination of an interferometer and spectrometer is not new, David Erskine pioneered the idea at Lawrence Livermore National Laboratory, even receiving a patent.  I worked on an implementation for my thesis.  But no one had investigated the benefits from a Bayesian perspective or investigated whether it could get us to 10 cm/s.

In her investigation, Rebecca found that, indeed, modulating a spectrum by an interferometer does provide the benefits of a lock-in amplifier: it removes instrumental variations that occur at frequencies other than the modulating frequency.  She submitted her work to Publications of the Astronomical Society of the Pacific, where it was recently accepted:

That’s Figure 2 from the paper showing how a fast-scanning interferometer imprints time variable fringes onto a spectrum.  A Doppler velocity change causes a change in the phase of the fringes.  Implementation is tricky.  Lock-in amplification only works if you know your modulation frequency accurately and precisely.  To get to 10 cm/s, we need to know the interferometer optical path difference to 1 part in 10^10.  Hard, but not impossible.  We also need to read out the detector at a furious speed, but recent advances in electron-multiplying CCDs make that possible as well.

In summary, we find that modulating a spectrum can give you all the benefits of stabilizing.  It sounds ironic, but it’s nothing new to radio astronomers.  If signal processing interests you, I encourage you to check out our paper!

-Phil Muirhead