Ball Scramblers for Precise Doppler Work

A big issue in precise Doppler work — measuring the radial velocity of a star to one meter per second precision or less, is how to account for the fact that the image of the star moves around.

When we take a spectrum, we are essentially spreading the image of the star out into many images of the star, one for each wavelength (color) of light.  What we think of as a spectrum, or rainbow of light, is really a continuous line of images of the star as seen by the telescope, each in a different color.

At Keck and Lick, we pass the starlight through a slit first, so if the star image is blurry it fills the slit and we image that. If the star image is sharp, it is smaller than the slit and you image the star itself.  Either way, the size of the image of the star on your detector sets the resolution of the spectrum — a big fat stellar image will blend with the neighboring stellar images, and make your spectrum blurry.  Narrowing your slit produces better spectral resolution.

Each row of this spectrum is a continuous series of images of a vertical slit (a tall rectangle).  Each image has a very slightly different color.  The image is stacked so that you read across until you get to the end of a row, then start at the next row (light reading a book).   The dark "lines" are actually images of the slit where the star (the Sun in this case) is darker because of elements in the solar atmosphere.  The whole Sun is dimmer at those colors, and so less light is collected there.  Those colors can move left and right for two reasons: you could move towards and away from the Sun, which would change the colors (wavelengths) those dark spots are at (via the Doppler effect) OR you could move the light illuminating the slit back and forth (shine more sunlight on one side than another).  Controlling for the latter effect is the point of using optical fibers.  Double scrambling makes this control almost perfect.

Each row of this spectrum is a continuous series of images of a vertical slit (a tall rectangle). Each image has a very slightly different color. The image is stacked so that you read across until you get to the end of a row, then start at the next row (light reading a book). The dark vertical “lines” are actually images of the slit where the star (the Sun in this case) is darker because of cool gasses in the solar atmosphere. The whole Sun is dimmer at those colors, and so less light is collected there. Those colors can move left and right for two reasons: you could move towards and away from the Sun, which would change the colors (wavelengths) those dark lines are at (via the Doppler effect) OR you could move the light illuminating the slit back and forth (shine more sunlight on one side than another). Controlling for the latter effect is the point of using optical fibers. Double scrambling makes this control almost perfect.

But if the star underilluminates the slit, then you can confuse motion of the star on the slit (due to imperfect guiding of the telescope) with a Doppler motion.  If the star moves from the left side of the slit to the right side, this moves the images on the spectrum, which changes the wavelength you think you are seeing a feature at, which changes the radial velocity you measure.  This effect introduces systematics at the km/s level, 3 orders of magnitude above our intended precision.  We correct for this by passing the light through an iodine cell.

Sam Halverson

Sam Halverson

Another way to do this is to use a fiber optic cable.  By focusing the starlight with the telescope on the input end of an optical fiber, and having your spectrograph image the output end of the fiber, you can get a nice, uniformly illuminated image of the fiber cross section.  The fiber “scrambles” the light so that if the star moves from the left to the right side of the fiber, the image of the star does not move on the spectrograph.

Almost.  This scrambling is not perfect.  One way to help is to use an octagonal fiber, which scrambles light better.  Another way is to perform “double scrambling”, where you join two fibers together, but swap the near and far optical fields between them.  That is, you use the nice, nearly uniform output of the first fiber to illuminate the input of the next fiber in a uniform way.  The scrambling from the second fiber brings you almost perfectly to a uniform output, independently of how the star is illuminating the input end of the first fiber.

The problem is that double scrambling is “lossy” — these fiber optics are tens of microns across, and it’s very hard to build, align, and stabilize tiny optics that can join the two fibers together properly without losing a lot of the light.

Arpita Roy

Arpita Roy

Enter Arpita Roy (she of the Lunar Farside Highlands Problem fame), Sam Halverson, and the Mahadevan HPF team.  Arpita has shown that you can use a single optical component — a sphere — to do the reimaging.  Even better, if the sphere has index of refraction n=2.0 — that is, it’s made of just the right kind of glass — then the foci are at the surfaces of the sphere.  That means that the proper way to align the sphere is so that it is touching both fibers.  This is important because it makes alignment almost trivial: just abut the sphere to the fibers.  It also makes stabilization easy: keep the sphere abutted to the fibers.

The efficiency is fantastic: 85%.  The scrambling is nearly perfect: a “scrambling gain” of over 10,000 using octagonal fibers and 20,000 if you use one octagonal and one circular fiber.  The spheres are cheap, the construction is relatively simple, and the stability and performance are basically perfect.

We’re using this for HPF.  You can read the paper here. Other fiber optic spectrographs should use them, too!

2 thoughts on “Ball Scramblers for Precise Doppler Work

  1. jtw13 Post author

    Most Chile and Hawaii telescopes are research telescopes, and so almost never have eyepieces affixed. When public tours are available, they are usually just in visitor’s centers, with windows that let you look at the telescopes. There might be public viewing on some of the smaller telescopes at those sites, but I’m not aware of it. Both locales are also very difficult to get to, requiring acclimation on the way up. At those elevations, the low oxygen levels dim your eyesight and color perception, so even if you did use an eyepiece, you would be at a disadvantage unless you brought an oxygen tank.

    My favorite telescope for eyepiece viewing is the Great Refractor at Lick Observatory on Mount Hamilton outside of San José, California. It is a 36″ telescope that was once the largest in the world. It was/is used for research for over 100 years (I don’t know if the last research programs have ended or not). It is the largest telescope I have ever looked through, and the dome and observatory itself are amazing.

    So that’s my recommendation for you.

  2. Kurt Rodeghiero

    Hi Jason. I came across a link to your post on SETI beyond the Milky Way via the Nova article on Searching for Advanced Alien Engineering. Great site – I look forward to exploring it more, especially as a PSU alum.

    Sorry that this is slightly off-topic but I didn’t see a general contact for you. I’m wondering if there is a telescope in Chile or Hawaii (or somewhere) that is considered the single best one that pedestrians like me are allowed to look through? I ‘m planning a trip and would like to plan it around visiting one of the best observatories.

    Thanks so much.
    Kurt

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