**Document ID**: 09_21_05_2

**Date Received**: 2005-09-21 **Date Revised**: 2006-06-19 **Date
Accepted**: 2006-06-19

**Curriculum Topic Benchmarks**: S15.4.4, S15.4.5, S15.4.6, S17.4.1,
S17.4.2, S17.4.3, M4.4.9 (primarily for Extension activities)

**Grade Level**: \[9-12\] High School

**Subject Keywords**: interferometer, interference fringes, telescope

**Rating**: Advanced

Seeing Interference Fringes with a Telescope

**By**: Stephen J Edberg, Jet Propulsion Laboratory, California
Institute of Technology, 4800 Oak Grove Drive, M/S 301-486, Pasadena CA
91011 and Reagan Herman, Amarillo Astronomy Club of Texas & NASA's Night
Sky Network

e-mail: Stephen.J.Edberg@jpl.nasa.gov

**From**: The PUMAS Collection http://pumas.jpl.nasa.gov

©2005, Jet Propulsion Laboratory, California Institute of Technology.
ALL RIGHTS RESERVED.

Astronomers build larger telescopes not only to collect more energy but
also to resolve finer detail in the objects to be studied. While
groundbased optical telescopes with "filled" apertures of up to 10 m
have been built, and 30 m and larger-aperture designs are being studied,
another method of observations permits equivalent apertures spanning
tens to hundreds of meters to be used. Radio astronomers have used these
instruments, called interferometers, for decades, with equivalent
apertures spanning thousands of kilometers. Optical astronomers have now
designed interferometer systems that rely on two (or more)
widely-separated telescopes to collect light, and combine the energy to
resolve detail that is equivalent to a filled aperture with diameter
equal to the separation of the telescopes.

With the fine detail resolved by professional instruments on the ground
or in space, a variety of astrophysics problems can be solved using the
brightness and spacing of interference "fringes." These range from the
shapes of stars (fast spinners get "squashed", like Jupiter), to their
masses (deduced by measuring orbits of both stars in binary systems,
including star-star, star-brown dwarf, and star-planet systems), to
orbital motions of stars in the Milky Way galaxy (which relate to the
total mass, including the amount of dark matter, in our galaxy).

Underlying principles of interferometry are explained in PUMAS Example
09_21_05_1, *Seeing Interference Fringes*. Additional activities with a
telescope are found in the Appendix.

**OBJECTIVE:** 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
(<http://planetquest.jpl.nasa.gov/SIM/sim_index.html>).

**APPARATUS:** (1) Any type of **telescope** can be used for this
project. Its aperture is not a limiting factor, though a light collector
100 -- 125 mm (4 -- 5") in diameter, is probably the practical lower
limit. A larger telescope admits more light, allowing more observing and
experimenting options. However, with more widely spaced apertures, more
magnification may be required to see fringes. They are closer together
due to the higher resolution possible with wider aperture spacing. A
telescope mount that automatically tracks objects in the sky will make
observations easier.

(2) A **mask** to completely cover the front, sky end of the telescope.
    The dust cover of the telescope can be used as long as the holes
    needed for this experiment can be plugged when the cover is intended
    to seal the telescope. Otherwise, cardboard, wood, or plastic are
    all suitable materials. The mask should have two holes on a
    diameter, separated as far apart as they can be *over the aperture
    of the light collector*, not the diameter of the telescope tube.

> Figure 1. Looking from above down on a telescope aperture, the outer,
> light grey circle is the telescope tube. The larger inner, dark grey
> circle is the full aperture of the telescope's objective lens or
> mirror. The two small, white 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
> enters. The dashed circle and lines represent a secondary mirror and
> its supports (may not be present in some types of telescope).

![](media/image1.jpeg){width="5.750694444444444in"
height="4.313194444444444in"}

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

![](media/image2.jpeg){width="2.870833333333333in"
height="2.1527777777777777in"}![](media/image3.jpeg){width="2.870833333333333in"
height="2.1527777777777777in"}

> 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 they
> can be inserted to allow both the minimum separation and be reversed
> for maximum separation without unwanted light going through the slots.
>
> Hole size only matters in that a larger aperture lets in more light.
> If the mask is made with sliding apertures whose separation is
> adjustable, the hole size will limit the center-to-center separation
> possible and how much the separation can be varied.  Diameters of 35
> to 50 mm (1.5\" -- 2") diameter are a good compromise (smaller for
> smaller telescopes, larger for larger ones). Additional sliders with
> smaller apertures can also be built for further experimentation.

(3) **Eyepiece yielding 200x or more.** Magnification is calculated by
    dividing the focal length of the telescope by the focal length of
    the eyepiece (both expressed in the same units):

> M = $\frac{\text{Ft}}{\text{Fe}}$ (1)
>
> If necessary, use a Barlow (negative relay) lens to increase the
> magnification to 200x or more if *Fe* is too large for M to be 200.

(4) **Cross hair eyepiece**, if desired, and Barlow (telemagnifying
    relay lens) to permit magnification to 200x or more with it, if
    necessary.

(5) **Stop watch**, if desired.

**PROCEDURE:** 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 (Fig. 4a).  The
patterns are more prominent than with the full aperture telescope
because, when a smaller aperture lets in light, the light bends
(diffracts) more sharply around the edges, making the disk larger. The
high magnification provided by the eyepiece also contributes.

(The rings visible around the Airy disc are an interference phenomenon
but not the one being demonstrated.  They are caused by the circular
aperture of the telescope itself.  Just for fun, make a small, square
aperture out of cardboard to put over the telescope and look at these
\"rings.\")

At this point the telescope+eyepiece+eye are close to focus. As those
patterns come together with final focusing, fringes (stripes) start to
be visible when the "seeing" (the image smearing and motion caused by
Earth's atmosphere) merges the first rings of the Airy disks.  When the
Airy disks merge, the fringe pattern is easily visible (Fig. 4b). The
fringes will be oriented perpendicular to the line between the initial
out-of-focus, separate star images.

Keep playing with the focus, watching the Airy disk carefully for
closely spaced stripes (fringes) to pop out in the star image\'s Airy
disc. Steady seeing (i.e., low atmospheric turbulence) will allow you to
see sharper images, making it easier to see fringes.

![](media/image4.jpeg){width="2.9180555555555556in"
height="1.9569444444444444in"}
![](media/image5.jpeg){width="2.9694444444444446in"
height="1.9569444444444444in"}

> \(a\) (b)
>
> 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.

Experiment with different stars in the sky. There may be little or no
variation between them, but the exploration is part of the intrigue.
Larger interferometers with complex instrumentation do measure
differences, important clues to the features of stars.

You might compare giants and main sequence stars, such as 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 the aperture pair in different position angles
(it\'s an unresolved binary of Sun-temperature, sub-giant stars). 
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.  Keep track of your
results by taking careful notes on what was seen and how. Changing the
spacing of the apertures will change the spacing of the fringes, which
the measurements would display.  Look for fringes from Jupiter's
satellites and from stars of similar brightness. If you have an eyepiece
with a reticle, you can make quite precise fringe measurements. See the
Discussion and the Extension in the Appendix below.

**DISCUSSION:** Light waves entering a telescope are brought to focus by
reflection off the curved, primary mirror or refraction (bending) of
light by the objective lens. All the rays entering come to focus at the
focal point. When they do, they interfere with each other and produce a
small, tight Airy (bull's eye) pattern. This pattern is the
two-dimensional analog of a laboratory single-slit, linear interference
pattern. When two smaller apertures are used in front of the telescope,
the interference pattern is a striped line instead of a bull's eye
pattern, and that line is modulated by the larger Airy pattern generated
by the smaller aperture(s).

The telescope interferometer system described thus far is analogous to
the classic double slit experiment done in the lab. The slits in the lab
and small apertures on the telescope are comparable. But the slits are
spaced close together, making the interference pattern large and easy to
see while the telescope apertures are widely spaced, making the
interference pattern tiny (hence the need for 200x magnification). In
both cases, light waves coming through the slits/apertures interfere
when they combine, due to the differences in distances the waves travel.

The star image shows striping (fringes) perpendicular to the line
between where the initial out-of-focus image disks appeared. More than
one fringe is visible because the star image has a small but appreciable
size due to its passage through the small aperture(s) at the front of
the telescope. Combining the images (Airy disks) allows light from
different portions of the disks to interfere across an area with a
measurable size. The light has taken two different paths, of different
lengths, to arrive at the same place. Because of the different path
lengths, the light waves interfere.

It is interesting to note the implication of the Airy disk's finite size
for a full aperture telescope or one with a reduced aperture. It means
that every telescope, no matter what its size, produces a small, but
larger than infinitesimal, star image. There are no true point images.
The physics of single aperture light wave interference requires an
infinite aperture (hard to build!) to produce an image of a point source
that is a mathematical point (infinitely small) at the focus of the
telescope.

The properties of an object affect the appearance of its interference
pattern. Equation (2) illustrates this:

For light passing through a double slit, the equation

sin θ = $\frac{n \times \lambda}{d}$ (2)

describes the angle, θ, from the direction of the beam to the local
brightness maxima, numbered *n* = 1, 2, ... outward on either side of
the maximum brightness spot (at the center, numbered zero) for a slit
pair separated by *d* and a light source of wavelength *λ*. The
wavelength is one factor determining the separation of the fringes so
star color will affect the separation of its fringes. Changing the
spacing of the entrance apertures changes the spacing of the fringes --
widely separated apertures reduce θ and the fringe spacing, while closer
apertures increase θ and widen the fringe spacing.

If a telescope-interferometer is close to resolving (separating) the
components of a binary star system, the fringe pattern will show
differences depending on the orientation of the apertures relative to
the orientation of the pair of stars. If the apertures are oriented in
the same direction as the star pair, the interferometer "sees" a larger
object and this can reduce the contrast of the fringes. If the apertures
are perpendicular to the orientation of the star pair the interferometer
cannot distinguish the two stars so the interference pattern matches
that of a single star. A detailed example of this is explored in the
Appendix.

Alternatively, varying the separation of the apertures permits the
observer to determine how point-like an object is for the telescope
(interferometer). An object presenting fringes with the same contrast
across the range of separation possible with the telescope is a point
source for that telescope.

The story is much more interesting if the fringe contrast changes, and
especially if the fringes disappear. When the fringes disappear, it
means the object is not point-like even if it seems so by eye. The
telescope's apertures demonstrate it to be so large that interfering
waves from across it wash each other out (peaks from some fall on
valleys of others). Knowing the separation where washout occurs permits
calculation of the object's angular size. See the Appendix.

**FOR MORE INFORMATION:** PUMAS Example 09_21_05_1, *Seeing Interference
Fringes*, gives instructions on making indoor observations of fringes.

There are links to the science, technology, and history of
interferometry at <http://planetquest.jpl.nasa.gov/SIM/sim_index.html>.

**ACKNOWLEDGMENT:** This publication was prepared by the Jet Propulsion
Laboratory, California Institute of Technology, under a contract with
the National Aeronautics and Space Administration.

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.

**[Appendix]{.underline}**

**EXTENSION:** Fringe visibility (contrast; for this purpose, the
difference between the maximum brightness of a fringe and the minimum
brightness between fringes) gives an idea of the size of the object,
i.e., whether the interferometer (or telescope) can resolve it.
Point-like objects emit all their light from an (almost) infinitesimal
source, so all the waves coming from them are "in step" and able to
interfere with each other to the maximum amount possible. An object with
some apparent size sends light from different parts of itself to the
instrument and the waves from different portions may arrive "out of
step" with each other to varying degrees so their interference is
different from other sets of waves. When all the sets of interfering
waves are added together, the fringe contrast is reduced.

Albert A. Michelson used this property to measure the size of a star. He
added optics to make an interferometer 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.

It is possible to mimic Michelson's star measurements by looking at
Jupiter's Galilean satellites. With the masked telescope, look for
fringes from Jupiter\'s satellites (they won\'t be visible 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 makes for easier comparison while
the star's unresolvable, nearly pinpoint image makes fringes visible). 
This will be challenging, because neither satellite nor star will be
very bright.  In fact, these 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, better
than with competing methods right up to the Space Age.

If a crosshair eyepiece is available, 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.  Tape record voice announcements of a fringe
crossing the hair 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. Or 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 = \[fringe spacing in
seconds of arc\] (3)

A correction is necessary if the star being observed is not on the
celestial equator: divide the result by the cosine of the star's
declination (the celestial equivalent of geographic latitude) for the
final answer. Specifically,

> fringe spacing \[arc seconds\] =
> $\frac{\text{number}_{\text{of}_{\text{fringes}}}\text{time}\text{\_int}\text{erval}_{\text{used}}}{\text{15} \times \text{cos}\left\lbrack \text{declination} \right\rbrack}$
> (4)

[]{.mark}

[]{.mark}

Compare this to Dawe's Limit, one method for predicting the resolution
of a telescope. The Dawe's Limit resolution in seconds of arc is

Resolution \[arc seconds\] = 114.3/\[telescope diameter in mm\] or (5a)

Resolution \[arc seconds\] = 4.5/\[telescope diameter in inches\] (5b)

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

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