Reagan Herman
Amarillo Astronomy Club of Texas &
NASA's Night Sky Network

Introduction: Planets and fringes Seeing interference fringes at home Seeing fringes with your telescope

Anyone with a telescope wishing to get a sense of interferometric measurements can easily construct a mask and turn a telescope into a simple interferometer. It will show the fringes that spacecraft like SIM PlanetQuest will measure. A much more elaborate system is necessary, on the ground or in space, to actually make "delay" measurements similar to those SIM PlanetQuest will make to accomplish its mission of finding planets around other stars and making numerous astrophysical studies of the Milky Way and beyond.

Any type of telescope can be used for this project. Aperture size is not a driver, though 100 - 125 mm (4 - 5") is probably the practical lower limit. Using a larger telescope makes more light available and more manipulation can be done as part of the observing and experimenting. However, more magnification may be required to see fringes with more widely spaced apertures because they are closer together, indicating higher resolution.

As an example, consider a 200 mm (8") or 250 mm (10") telescope aperture. Build a mask to completely cover the front, sky end of the telescope (Figure 1). You can even use the dust cover of the telescope as long as you can plug the holes when the cover is intended to seal the telescope (film canisters or medicine bottles can be adapted for this purpose). The mask should have two holes on a diameter, separated as far apart as they can be over the aperture of the optic, not the diameter of the telescope tube.

Figure 1. Looking from above down on a telescope aperture, the outer circle is the telescope tube. The larger inner circle is the full aperture of the telescope's objective lens or mirror. The two small circles at the edges of the objective are the openings allowing light into the telescope for interference pattern observations. The rest of the objective is covered so no light goes through. The dashed circle and lines represent a secondary mirror and its supports.

Hole size only matters in that a larger aperture lets in more light. If you make a mask with apertures whose separation is adjustable (Figures 2 and 3), the hole size will limit the center-to-center separation possible and how much you can vary the separation. Aperture diameters of 35 to 50 mm (1.5" - 2") are a good compromise (smaller for smaller telescopes, larger for larger ones). Additional sliders with smaller apertures can also be built for further experimentation.

Figure 2. This prototype wooden mask has adjustable aperture separation. It is mounted on a Newtonian telescope.

Figure 3. The as-built mask's adjustable apertures are removed on the left and in place on the right. The slots permit light to come through the apertures wherever the sliders are positioned. The white marks make it easy to repeat the placement of the apertures. The apertures are offset in the sliders (made of kitchen counter laminate) so that they can be inserted to allow both the minimum separation and be reversed for maximum separation without unwanted light going through the slots.

With the mask mounted on the telescope, a first look through an eyepiece at a bright out-of-focus star shows a pair of illuminated circles. Getting closer to focus, the circles move closer together in the field of view and become twin, bull's-eye-like Airy patterns of disk surrounded by one or more rings (Figure 4a). The patterns are more prominent than you are used to because you are looking through a small aperture (making the disk larger) combined with high magnification provided by your eyepiece.

(The rings you see around the Airy disc are an interference phenomenon but not the one we are looking for. They are caused by the circular aperture of the telescope itself. Make a small, square aperture out of cardboard to put over your telescope and look at the "rings" then, just for fun.)

At this point you are close to focus. As those patterns come together with final focusing, fringes (stripes) start to be visible when the seeing merges the first rings of the Airy disks. When the Airy disks merge, the fringe pattern is easily visible (Figure 4b). The fringes will be oriented perpendicular to the line between the out-of-focus, separate star images.

Figure 4. These interference patterns were made with a laser but illustrate a highly magnified view of a star, as described below. In the telescope the patterns will appear white or only slightly tinted. Seeing these patterns is much easier than photographing them. (a) This single aperture interference pattern was made with a laser and a pinhole. It illustrates the Airy pattern seen by astronomers in their telescopes. (b) This is an interference pattern made with a laser and a pair of pinholes. Note how there are additional maxima and minima of brightness caused by the interference of light coming through the two holes. The single aperture pattern modulates the brightness of the double aperture pattern.

The eyepiece should provide 200x or more (divide your telescope's focal length by the eyepiece's focal length to compute the magnification). Use a Barlow lens to increase the magnification to 200x or more. Keep playing with the focus, watching the Airy disk carefully for closely-spaced stripes - the fringes - to pop out in the star image's Airy disc. Steady seeing (little twinkling or image motion and small star images) will make it easier to see fringes.

Now that you know what to look for, experiment with different stars in the sky. You may see little or no variation between them, but the exploration is part of the intrigue. Larger interferometers do measure differences.

Some observations to make include comparing giants and main sequence stars like Betelgeuse and Rigel, Arcturus and Spica or Vega, Antares and Altair or Deneb or Vega, and Aldeberan and Capella. Try changing the separation of the apertures for these observations.

Look at Capella with different position angles of the aperture pair (it's an unresolved binary). Antares and Castor might show the influence of their companions on their fringes. Look for qualitative changes in the fringe pattern, especially contrast in the fringes and spacing between them. Careful notes of what you observed and how are required to keep track of results. Changing the spacing of the apertures will change the spacing of the fringes, which the measurements would display. Don't be surprised if you don't see much difference between stars. Such observations are usually made with larger interferometers and far more complex instrumentation.

Fringe visibility (contrast) gives an idea of the size of the object, i.e., whether the interferometer (or telescope) can resolve it. Albert A. Michelson demonstrated measuring the size of a star with his interferometer mounted on the Mt. Wilson 100" Hooker Telescope in 1921: he determined the aperture spacing that produced fringes and the largest spacing that didn't and from that could deduce the angular diameter of the star.

You can mimic Michelson's star measurements by looking at Jupiter's Galilean satellites. With your masked telescope, look for fringes from Jupiter's satellites (you won't see them because the satellite disks are large enough to be resolved by the telescope) and compare that observation to the appearance of fringes from stars of similar brightness (similar brightness to remove that variable; you will see fringes). This will be challenging, because neither satellite nor star will be very bright. In fact, your observations copy experiments Michelson made with the 12" refractor at Lick Observatory in 1891. He got very good measurements of the diameters of the satellites this way.

If you have a crosshair eyepiece you can make fringe spacing measurements by timing. Let a star's interference pattern drift across the hair and time the separation from minimum to minimum or maximum to maximum for different star colors. You may want to tape record yourself with radio time signals in the background, use a lap counting stopwatch, or have an assistant watch a second hand and write down the timings. You can also simply start a stopwatch and count a number of fringes and then stop the watch to get a measure of fringes/second.

It is easy to convert fringes/second into an angular measurement. Since Earth rotates 360 degrees in 24 hours, this can be converted to 15 seconds of arc/1 second of time, 15"/s. Divide: ([number of fringes]/[time interval used])/15 = [fringe spacing in seconds of arc]. A correction is necessary if the star you are observing is not on the celestial equator: divide your result by the cosine of the star's declination for the final answer. I.e.:

fringe spacing [arc seconds] =

([number of fringes]/[time interval used]) (15 x cos[dec])

Compare this to Dawe's Limit, the predicted resolution of your telescope. The Dawe's Limit resolution in seconds of arc is:

Resolution [arc seconds] = 114.3/[telescope diameter in mm] or, equivalently, Resolution [arc seconds]= 4.5/[telescope diameter in inches].

The spacings of the fringes should be about the same as the resolution of your telescope.

If you have an eyepiece with measuring marks (like Celestron's Micro Guide or Meade's Astrometric eyepieces), or a real micrometer eyepiece, try measuring fringe spacing as functions of star color, star type, and aperture separation, separately. The reticle markings should be finely etched but probably there will be several fringes between the closest markings, even with a Barlow lens in to increase the magnification of the star image (the Barlow won't affect the magnification of the reticle). You will have to use the procedure above, timing the duration of a star's drift between reticle marks, to calibrate the angular spacing of the marks with your telescope (and Barlow lens, if used).

With professional instruments, on the ground or in space, there is a variety of astrophysics problems that can be solved using interferometry. These range from the shapes of stars (fast spinners get squashed, like Jupiter) to their masses (measuring orbits of binary systems, including star-star, star-brown dwarf, and star-planet systems) to orbital motions of stars in the Galaxy (and therefore determine the Galaxy's mass and dark matter content).

Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not constitute or imply its endorsement by the United States Government or the Jet Propulsion Laboratory, California Institute of Technology.