Transcript Chapter 6 Telescopes The following section is from Ryden & Peterson, Foundations of Astrophysics.

Chapter 6
Telescopes
The following section is from Ryden & Peterson, Foundations of
Astrophysics. We will be getting a copy to put in the ISC.
The first camera was a camera obscura, Latin for ‘dark
room’.
Types of Reflecting Telescopes
Here are the main types of reflecting telescopes
Quality of Images
Chromatic Aberration occurs in a very cheap, single
component objective lens refractor when not all colors
come to a focus.
Quality of Images
Spherical aberration occurs when the spherical surface
of a lens or mirror does not bring all light rays to a
focus. It affects refractors and reflectors.
Quality of Images
Coma is the aberration that occurs when light rays
near the edge of a lens or mirror come to a focus at a
larger distance from the optical axis than the center of
the mirror. This is characteristic of off-axis images
formed by parabolic mirrors.
Quality of Images
Here is a photographic example of coma. Coma is
Latin for ‘hair’ and images with coma are fuzzy. The
word comet comes from coma.
Quality of Images
The Ritchey-Chretien is a type of Cassegrain telescope
that uses both primary and secondary mirrors that are
hyperboloidal in shape, eliminating both spherical
aberration and coma. CSM’s 20”telescope is of RitcheyChretien design.
Plate Scale
This chapter is taken from ch 6, Foundations of Astrophysics by Ryden and Peterson.
One can compute the separation, d between a pair of
stellar images on a chip when the stars themselves are
separated by an angle q on the celestial sphere. This
leads to s, the plate scale or image scale, s:
s(arcsec/mm) = q(arcsec)/d(mm)
(6.1)
Plate Scale
If the angular separation between the two stars is small, we
can use the small-angle approximation:
d
q (radians) =
F
where F is the telescope focal length and d is the distance
between a pair of images on a chip. Or,
Plate Scale
Converting q(radians) to q(arc sec), we get eq 6.3,
180 0
3600arcsec
d
q (arcsec) = q (radians)[
](
)
=
206,
265(
)
0
p radians
1
F
q(arc sec) = 206,265 (d/F)
Plate Scale
Here is how to get the image scale in terms of arcsec/mm –
Combining eqs 6.1 and 6.3, which are
s(arcsec/mm) = q(arcsec)/d(mm)
(6.1)
q(arcsec) = 206,265 (d/F)
(6.3)
we get,
s(arcsec/mm) = 206,265
F(mm)
(6.4)
Plate Scale
The smaller this value, s, the better detail on the image.
For example, your eye has a focal length of ~ 17 mm and
an image scale of s= 206,265/17 = 12,100 arcsec/mm or
s=3.4o/mm when you look at the full moon. This image
covers an area less than 0.15 mm across your retina.
Plate Scale
Astronomical telescopes have focal lengths expressed in meters,
rather than millimeters. For these giant telescopes, we may write:
s(arcsec/mm) = 206.265 = 206.265
F(m)
fD(m)
where f is the focal ratio and D is the aperture in meters.
Note 1: The comma in 206,265 has been replaced by a period to give
206.265. This is because the focal length is in meters, rather than in
millimeters.
Note 2: If f is the f/ratio and D is the diameter or aperture, the focal
length, F = fD
Plate Scale
Example for the 40” refractor at Yerkes Observatory.
Aperture, D =1.02 m
Focal ratio, f = 19
Plate scale of the Yerkes telescope is:
s = 206.265 = 10.6 arcsec/mm
19(1.02)
Rayleigh Diffraction Limit
Image quality is limited by diffraction. When light from
a point source passes through a circular aperture,
diffraction produces an image that looks like a central
bright disk surrounded by a series of alternating dark
and bright rings.
Rayleigh Diffraction Limit
The diameter of the central disk, known as the ‘Airy
disk’, after its discoverer, George Airy, is determined by
the aperture, D and the wavelength, l of the observed
light. Two point sources are said to be resolved when
the center of the Airy disk of one source falls into the
dark ring surrounding the Airy disk of the other source.
Rayleigh Diffraction Limit
This happens when the centers of the two light sources
are separated by a distance
This is known as the Rayleigh diffraction limit.
qmin(rad) = 1.22 l
D
Rayleigh Diffraction Limit
Observing at a l of 5000 A or 5 x 10-7 m, and resolving
two stars separated by an angular distance q = 1” =
4.8 x 10-6 rad, requires a telescope of minimum diameter
D = 1.22 l
q
D = 1.22 (5 x 10-7m) = 0.13 m
4.8 x 10-6
Space Astronomy Misconceptions
There are three misconceptions wrt advantages of
space-borne astronomy.
Misconception #1
• In space you can observe a celestial object continuously, not
just at night.
For a telescope in low Earth orbit (LEO), almost half of the
celestial sphere is blocked by the Earth at any given time.
Most objects can only be viewed for half an orbit at a time
(45 minutes on, 45 minutes off).
Space Astronomy Misconceptions
Misconception #2
The sky as seen from orbit is dramatically darker than the
night sky on Earth.
• Although the night sky is darker as seen from orbit, the
improvement is not as great as what you might expect. At
blue wavelengths, the sky is about half as bright as from the
ground. Much of the sky background is due to sunlight
scattered from interplanetary dust and distant unresolved
stars and galaxies.
Space Astronomy Misconceptions
Misconception #3
• Observations from space are not affected by weather.
The fact s there is ‘spaceweather’, generated by the sun and
manifest in solar magnetic activity. Instruments and
detectors deteriorate rapidly due to the harsh radiation
environment and broad temperature range through which
they are cycled.
Modern Observatory Telescopes
Large telescopes employ adaptive optics. In this
technique, atmospheric wavefront distortions are
sensed (by observing an artificial star) and
compensating for these measured distortions by
deforming the mirror with actuators.
Modern Observatory Telescopes
Why aren’t the largest telescopes mirrors monolithic?
The answer is thermal inertia. To perform well, the
mirror must be at the same temperature as the air
around it. If the mirror is warmer than its
surroundings, the mirror will radiate infrared light,
heating the air above the mirror and causing
turbulence and poor seeing.
Thermal Inertia
Thermal inertia is the measure of a mirror to store heat
during the day and radiate it away at night. It scales
with mass and the mass of a conventional mirror scales
as D3, since the thickness must increase
proportionately with diameter, to keep the mirror stiff.
Beating Thermal Inertia
Multiple mirrors – A large effective collecting area can
be achieved by combining the light collected by smaller
individual mirrors. An example is the Large Binocular
telescope (LBT) which has two 8.4 m mirrors.
Beating Thermal Inertia
Another example is the VLT telescope in Cerro Paranal
Chile. It consists of 4 telescopes, each with 8.2 m
mirrors. They can work separately or combined, using
interferometry.
Table of Large Observatory Telescopes
Beating Thermal Inertia
Segmented mirrors – Instead of a monolithic mirror
made from a single slab of glass, a mirros can be made
of many segments kept aligned through computer
controlled active supports. The two 10 m Keck
telescopes on Mauna Kea are prime examples. Each
mirror consists of thirty-six 1 meter segments.
Beating Thermal Inertia
Honeycombed mirrors – In this type of mirror, glass is
melted over heat resistant ceramic forms that leave the
back of the mirror with a honeycomb structure that is
stiff but still lightweight. The two mirrors of the LBT
are made this way. (Birds’ bones have a similar internal
structure, which is why they are so light but very stiff).
Seeing
The quality of the image of a stellar point source at a
given observing location at a specific time is know as
seeing. Due to Earth’s turbulent atmosphere, local
changes in atmospheric temperature and density over
distances ranging from centimeters to meters create
regions where the light is refracted in random
directions. This causes the image of a point source,
such as a star to become blurred or ‘twinkle’.
Seeing
Some of the best seeing is at Mauna Kea Observatory at 13,
800 feet above sea level. The seeing is routinely between
0.5” and 0.6” 50% of the time. On the best nights, it can
be 0.25”!
Other great observatory sites are
Kitt Peak National Observatory in Tucson, Az.
Tenerife and La Palma on the Canary Islands
Cerro Tololo Inter-American Observatory in the Chilean
Andes
Seeing
Why don’t planets twinkle?
Stars are point sources and are affected by our
turbulent atmosphere, causing them to twinkle.
However, a planet’s larger angular size make them
larger than the scale of atmospheric turbulence.
Distortions are averaged out over the size of the image.
The result is that planets don’t twinkle!
The exception occurs when a bright planet is viewed as
it rises or sets. One then looks through a very
turbulent atmosphere and distortions do not average
out, leading to twinkling.
Radio Telescopes (from BOB)
The strength of a radio source is measured in terms of
the spectral flux density, S(n), which is the amount of
energy per second, per unit frequency interval striking
a unit area of the telescope. To determine the total
amount of energy per second (the power) collected by
the receiver, the spectral flux must be integrated over
the telescope’s collecting area and over the frequency
interval, for which the detector is sensitive, which is
the bandwidth.
Radio Telescopes
If the efficiency of the detector at a frequency n, is
denoted by fn, then the amount of energy detected per
second becomes
P=
ò òn S(n )dn dA
A
Radio Telescopes
If the detector is 100% efficient over Dn, meaning that
fn =1, and if S(n) is constant over that interval, then the
integral reduces to P = SA Dn.
A is the area of the radio dish.
A typical radio source has a spectral flux density on the
order of one jansky (Jy), where 1 Jy = 10-26 W M-2 Hz -1.
Spectral flux densities are usually pretty weak ~ several
mJy. Large dishes are necessary to receive such weak
signals.
Radio Telescopes
Example 6.3.1
Cygnus A is the third strongest radio source, after the
Sun and Cassiopeia A. At 400 MHz (a wavelength of 75
cm), its spectral flux density, S(n), is 4500 Jy. Assuming
that a 25 m diameter radio telescope is 100% efficient
and is used to receive the radio energy of Cygnus A over
a bandwidth of 5 MHz, the power detected by the
receiver is:
P = S(n) p (D/2)2 Dn
Radio Telescopes
P = S(n) p (D/2)2 Dn where
S(n) = 4500 x 10-26 Wm-2Hz-1
D = 25 m
Dn = 5 x 106 Hz
we have that,
P = 4500 x 10-26 Wm-2Hz-1 p(25/2)2 m2 5 x 106 Hz
P = 1.10 x 10-13 W
Improving Resolution of Radio Telescopes
Rayleigh’s criterion when applied to radio telescopes
shows that resolution in the radio domain is much
worse than optical telescopes, due to the much longer
nature of radio waves. To obtain comparable
resolution, much larger dish diameters are needed.
Improving Resolution of Radio Telescopes
Example 6.3.2
To obtain a resolution of 1” at a wavelength of 21 cm, the
dish diameter must be:
æ
ö
l
21cm
D =1.22 =1.22 ç
÷ = 52.8km
-6
è 4.85x10 rad ø
q
In order to resolve an object 1” in diameter, a radio
telescope dish must be 52.8 km in diameter! The largest radio
telescope is that at Arecibo Observatory in Puerto Rico. Its
diameter is 300 m or 1000 ft.
Arecibo Radio Telescope
Arecibo Radio Telescope
Interferometry
A way to get higher resolution is to use a technique
called interferometry. Shown, is fig.6.22.
Interferometry
Figure 6.22 shows two radio telescopes separated by baseline, d.
Since the distance from scope B to the source is greater than the
distance of scope A from the source by an amount L, a specific
wavefront will arrive at B after it has arrived at A. If the two
signals are in phase, their superposition will result in a maximum
if L is equal to an integral number of wavelengths. In this case, L
= nl, where n = 0, 1, 2, … and we have constructive interference.
Similarly, if L is an odd number of wavelengths, L = (n--1/2)l,
where n= 0, 1, 2…, we have destructive interference.
Interferometry
The pointing angle q is related to d and L by
Sin q = L/d
By combining the signals from two radio telescopes,
one can determine the position of the source by using
the interference pattern produced by these scopes.
Antenna Pattern
Here is the pattern produced by a single antenna. The
narrowness of the main lobe is characterized by the
half-power beam width. The width can be decreased
and the side lobes reduced by the addition of more
scopes.
VLA
The Very Large Array or VLA consists of 27 radio
telescopes in a movable Y configuration with a
maximum configuration diameter of 27 km. Each dish
has a diameter of 25 m.
Atmospheric Windows
Our atmosphere blocks several regions of the EM spectrum from
the ground. Below is transparency of Earth’s atmosphere as a
function of wavelength.
Atmospheric Windows
Since water vapor is the chief absorber of IR radiation
from the ground, IR observations have to done in
space. Notable orbiting IR telescopes are:
IRAS, 0.6 m in diameter, launched in 1995, cooled by
liquid helium and operation ceased in 1998, due to He
depletion.
Spitzer Space Telescope, 0.85 m, f/12 mirror made of
beryllium, cooled to less than 5.5 K. Still operational.