SKY_July2014.pdf

SkyandTelescope.com July 2014 69

The Basics
The size of the Airy disk is determined by the telescope’s
aperture and the light’s wavelength. With green light
(555-nanometer wavelength) and aperture (D) measured
in millimeters, the angular diameter of the dark ring just
outside the Airy disk is 280/D arcseconds. In an optically
perfect, unobstructed telescope, 84% of a star’s light gath-
ered by the telescope objective is concentrated in the Airy
disk, with the rest distributed in the diff raction rings.
This simple mathematical formula easily shows why
larger apertures have an advantage. Double the aperture’s
diameter and your telescope collects four times as much
light. But the Airy disk’s angular diameter is halved, so
the light is now concentrated in one quarter the area. The
result is an Airy disk that is 16 times brighter. Illustra-
tions comparing the light distribution for star images in
diff erent-sized telescopes are often normalized (portrayed
with the same height), which obscures this advantage of
a larger aperture. Smaller Airy disks are also the rea-
son why larger telescopes have better resolution, which
translates into better views of double stars and lunar and
planetary detail.
The diff raction pattern of a fl awless in-focus star
image is lovely, but atmospheric turbulence (seeing)
often conceals it, especially when we’re observing with
large-aperture telescopes. Luckily, a star’s image slightly
inside and outside focus more readily helps us diagnose
problems, and it’s easier to discern details blurred by poor
seeing in this larger image.
In a telescope free of optical faults, with its optics
properly aligned, and at thermal equilibrium, a star’s dif-
fraction pattern just inside of focus will be identical to the
pattern at the same distance outside of focus. This is true
of any telescope design.
In a fi ne, unobstructed telescope, the expanded diff rac-
tion pattern seen just inside or outside of focus is a set of
concentric rings, with the outermost ring slightly brighter
and broader than the rest. The pattern is diff erent in
a telescope with a central obstruction. Other than the
very center, the area in the middle is quite dark, the ring
structure is coarser, and the inner rings are no longer of
uniform brightness. Nevertheless, the patterns at equal
distances inside and outside of focus are identical.

Preparing for a Star-Test
For star-testing, you should set your telescope outside
early and allow an hour or more for it to acclimate to the
ambient temperature. Although a star-test will quickly
reveal if your optics are out of alignment, it’s best to start
out with the telescope as well collimated as you can make
it ahead of time.
For moderate apertures, say 6 to 10 inches, select a 1st-
or 2nd-magnitude star. With smaller instruments use a

Stars seem like perfect points of light to our eyes, but they have

complex intensity profi les at the focal plane of a telescope. The 3-D

plots above by David E. Stolzmann are from this magazine’s Febru-

ary 1983 issue and show the intensity profi les for the diff raction

patterns created by theoretically perfect optical systems. Brighter

parts of the profi les are indicated by increased height of the plots

above the base. A star’s profi le consists of a sharply peaked central

Airy disk surrounded by a series of diff raction rings that fade

outward from the center. Introducing a central obstruction to an

optical system (such as the secondary mirror in a Newtonian or

Cassegrain telescope) increases the brightness of these rings rela-

tive to those formed by an unobstructed system.

Unobstructed

Refractor in focus Refl ector in focus

Obstructed

In an optically perfect telescope, the diff raction patterns for a star

seen the same amount inside and outside of focus will appear

identical. This is true even though the patterns will diff er for unob-

structed (refractors) and obstructed (most refl ectors) telescopes.

To a skilled eye, the distribution of light in the diff raction rings

can reveal a variety of common optical problems. The setup used

to capture these images (see box on page 71) introduced some

spherical aberration that is seen as a slight diff erence between the

inside- and outside-of-focus images for both telescopes.

Refractor inside focus Refl ector inside focus

Refractor outside focus Refl ector outside focus