. 3
( 28)


O3 stars and there are very few O3 and O4 would be the same for all the stars. For this pur-
stars. The hydrogen lines fall off very sharply pose, we use clusters of stars.
because of the high rate of ionization. The An HR diagram for over 40 000 nearby stars is
lines of singly ionized helium are still pres- shown in Fig. 3.11(a). These stars were studied by
ent, but there are very few lines overall in the Hipparcos satellite, which was designed to
the visible part of the spectrum. There are measure trigonometric parallaxes, so distances to
several lines in the ultraviolet. these stars are well known. So, apparent magni-
tudes can be converted into absolute magnitudes.
Some stars have emission as well as absorption
This allows us to compare, on the same basis, the
lines in their spectra. These stars are designated
properties of stars that are not all in a cluster. The
with an ˜e™ after the spectral class, for example,
first thing we notice is that stars appear only in
Oe, Be, Ae, etc. O stars with very broad emission
certain parts of the diagram. Arbitrary combina-
lines are called Wolf“Rayet stars. These stars proba-
tions of temperature and luminosity are not
bly have circumstellar material that has been
allowed. Remember, for a given temperature, the
ejected from the star. (Wolf“Rayet stars are not the
luminosity depends on the radius of the star, so
only stars with such outflowing material.)
the HR diagram is telling us that arbitrary combi-
nations of radius and temperature are not allowed.
Most of the stars are found in a narrow band,
3.5 The Hertzprung“Russell
called the main sequence. The significance of the
diagram main sequence is that most stars of the same tem-
perature have essentially the same luminosity,
Even though we cannot study any one star (except and hence essentially the same size. This close
for the Sun) in great detail, we can compensate relationship between size and temperature must
somewhat by having a large number of stars to be a result of the laws of physics as applied to stars.
study. From statistical studies we learn about gen- It gives us hope that we can understand stellar
eral trends. For example, if we find that brighter structure by applying the known laws. It also gives
stars tend to be both hotter and larger, then any us a crucial test: any theory of stellar structure
theory of stellar structure would have to explain must predict the existence of the main sequence.
that trend. Also, we think that any property that Not all stars appear on the main sequence.
is common to many stars must be telling us about Some appear above the main sequence. This
the laws of physics that are important in under- means that they are more luminous than main
standing the structure of stars. sequence stars of the same temperature. If two
One of the earliest statistical studies was car- stars have the same temperature but one is more
ried out in 1910 independently by the Danish luminous, it must be larger than the other. Stars
astronomer Enjar Hertzprung, and the American appearing above the main sequence are therefore
astronomer Henry Norris Russell. They plotted the larger than main sequence stars. We call these
properties of stars on a diagram in which the hor- stars giants. By contrast, we call the main
izontal axis is some measure of temperature (e.g. sequence stars dwarfs. We subdivide the giants
color or spectral type) and the vertical axis is into three groups: subgiants, giants, supergiants.
some measure of luminosity. We call such a dia- To keep track of the size of a star of a given
gram a Hertzprung“Russell diagram, or simply an spectral type, we append a luminosity class to the
HR diagram. spectral type. The luminosity class is denoted by a
If a random group of stars is chosen, all at dif- roman numeral. Main sequence stars are lumi-
ferent distances, a comparison of apparent mag- nosity class V. The Sun, for example, is a G2 V star.
nitudes is not very meaningful. The apparent Subgiants are luminosity class IV, giants are
magnitude must be corrected to give the absolute luminosity class III. Luminosity class II stars are

somewhere between giants and supergiants.
Supergiants are luminosity class I. We further
divide supergiants into Ia and Ib, with Ia being
larger. When we look at the spectral lines from a
star we can actually tell something about the
size. Stars of different sizes will have different
accelerations of gravity near their surface. The
surface gravity affects the detailed appearance of
certain spectral lines.
MV [mag]

There are also stars that appear below the
main sequence. These stars are typically 10 mag
fainter than main sequence stars of the same
temperature. They are clearly much smaller than
main sequence stars. Since most of these are in
the middle spectral types, and therefore appear
white, we refer to them as white dwarfs. (Do not
confuse dwarfs, which are main sequence stars,
with white dwarfs, which are much smaller than
ordinary dwarfs.)

Example 3.3 Size of white dwarfs
B - V [mag] Suppose that some white dwarf has the same
(a) spectral type as the Sun, but has an absolute mag-
nitude that is 10 mag fainter than the Sun. What is
Temperature (K)
the ratio of the radius of the white dwarf, Rwd, to
that of the Sun, R ?
Absolute Visual Magnitude

The luminosity is proportional to the square of the
Luminosity / Solar

radius, so

L wd>L 1R wd>R 2 2

We use equation (2.2) to find the luminosity ratio
for a 10 mag difference:

L wd>L 101M Mwd 2>2.5


Combining these two results to find the ratio of
Spectral Type
the radii yields
R wd>R 1L wd>L 2 1>2
Fig 3.11. (a) HR diagram for over 40 000 nearby stars
4 1/2
studied by the Hipparcos satellite, designed to measure (10 )
trigonometric parallaxes, so distances are known for all of
these stars. In this ¬gure, the color represents the number of
stars in each category, with red being the most and blue
The radius of a white dwarf is 1% of the radius of
being the least. (b) A schematic HR diagram, showing the
the Sun!
main features of the actual diagrams. Luminosity classes are
indicated by roman numerals. [(a) Michael Perryman, ESA, For any cluster for which we plot an HR dia-
Hipparcos] gram, we only know the apparent magnitudes,

scopic parallax. The word ˜spectroscopic™ refers to
not the absolute magnitudes. If we know the
absolute magnitude for one spectral type, then the fact that we use the star™s spectrum to deter-
we can find the distance modulus for stars of that mine its absolute magnitude. The word ˜parallax™
spectral type in the cluster. The distance modulus refers to the fact that this is a distance measure-
is the same for all the stars in the cluster, so we ment (just as trigonometric parallax was a dis-
can calibrate the whole HR diagram in terms of tance measurement using triangulation).
absolute magnitudes. To obtain a reliable calibra-
Example 3.4 Spectroscopic parallax
tion, we would like to carry it out for many stars.
For a B0 star (M 3), we observe an apparent mag-
We have already seen that there is a growing
nitude m 10. What is the distance to the star, d?
group of nearby stars for which trigonometric
parallax can give us a good distance measure-
ment. In Chapter 13, we will see how we can
The distance modulus is
improve on this sample by looking at the motions
m M 10 ( 3) 13 mag
of clusters.
Once we know the absolute magnitude for a We use equation (2.17) to find the distance:
given spectral type, we have a very useful way of
5 log10(d/10 pc) 13 mag
determining distances. For any given star, we
measure m, the apparent magnitude. We take a log10(d/10 pc) 2.6
spectrum of the star to determine its spectral
Solving for d gives
type. From the spectral type we know the
absolute magnitude, M. Since we know m and M, d/10 pc 400
we know the distance modulus, m M, and there-
d 4000 pc
fore the distance. This procedure is called spectro-

Chapter summary
In this chapter we looked at how spectral lines The distribution among ionization states is
are formed, and how spectral lines can tell us described by the Saha equation. In general, the
about the physical conditions in the atmosphere higher the temperature, the higher the level of
of a star. ionization and the more we find electrons in
We saw that stars were originally classified higher orbital states.
into spectral types before the nature of the tem- Finally, we saw what could be learned from a
perature sequence was understood. Hertzprung“Russell diagram, in which the hori-
We saw how an explanation of spectral lines, zontal axis is some measure of temperature and
in general, requires an atomic theory in which the vertical axis is some measure of luminosity.
the electrons can occupy only certain energy Most of the points representing stars on an HR
states. An atom can go from one state to another diagram fall along a narrow band, called the
by emitting or absorbing a photon with the main sequence. This tells us that, for most stars,
appropriate energy. We saw that a relatively sim- there is a simple relationship between size and
ple theory could explain the spectrum of the temperature. Stars that do not lie along the main
hydrogen atom. sequence are identified as being various classes of
In a star, the strength of a spectral line depends giants, for the brighter ones, and white dwarfs,
on the abundance of the particular atom, and on for the fainter ones.
the relative number in the appropriate ionization We saw how we can determine distances to a
and orbital states. The populations of orbital star using its apparent magnitude and a spectral
states is described by the Boltzmann equation. type to deduce its absolute magnitude.

binding energy is 13.6 eV. What happens to
3.1. What is responsible for the linelike appear-
the binding energy if the electron is not in
ance of spectral lines?
the ground state?
3.2. Arrange the standard spectral sequence “ O,
3.9. Explain how raising the temperature of the
B, A, F, G, K, M “ in order of decreasing H
gas increases the rate of collisional excitations.
3.10. (a) Explain how the H absorption strength
3.3. What are (a) the strong points (b) the weak
changes as we raise the temperature of a star.
points of (i) Rutherford™s atom and (ii) Bohr™s
(b) Explain how the Lyman absorption
strength changes as we raise the temperature
3.4. What evidence supports the idea of photons?
of a star.
3.5. What evidence supports the idea that elec-
3.11. Why do we not see helium absorption lines in
trons behave as waves?
stars like the Sun?
*3.6. Consider a neutral carbon atom that has six
3.12. Explain the advantage of studying the HR dia-
electrons orbiting the nucleus. Suppose that
gram for a cluster, as opposed to a random
five of the electrons are in their lowest states,
group of stars.
but the sixth is in a very high state. Why
3.13. What is the significance of the main
might the energy levels for the outermost
electron be similar to those for the single
3.14. (a) How do we know that giants are larger
electron in hydrogen. (Hint: Think of what is
than main sequence stars of the same tem-
exerting an electrical force on the outermost
perature? (b) How do we know that white
dwarfs are smaller than main sequence stars
3.7. (a) What do we mean when we say that a sys-
of the same temperature?
tem is bound? (b) If you looked at a electron
3.15. (a) Explain how the method of spectroscopic
moving near a nucleus, how would you
parallax works. (b) What are its advantages
decide if the system is bound?
and disadvantages relative to trigonometric
3.8. When we looked at the hydrogen atom, we
said that if it is in the ground state, the

ence between this case and hydrogen is that
3.1. Find the wavelengths of the H1 (Lyman-
the charge on the helium nucleus is twice
alpha), H1 and H2 transitions.
that for hydrogen. Ignore the difference in
3.2. What is the wavelength of a photon that will
reduced masses.)
barely ionize hydrogen in the ground state?
3.7. Using the de Broglie wavelength, h/p, show
3.3. (a) How much energy is required to ionize
that orbits whose angular momentum is
hydrogen already in the n 2 state? (b) At
quantized according to the Bohr quantization
what temperature would the average kinetic
condition ( J nh/2 ) correspond to orbits
energy of the particles in the gas equal that
whose circumference is an integer number of
3.4. Show that if we add a constant to all of the
*3.8. Rederive equation (3.6) without making the
energies in hydrogen, the energies of the vari-
assumption of an infinitely massive nucleus,
ous transitions are unaffected.
and show that one obtains the same expres-
3.5. An electron in a hydrogen atom is in a high n
sion except for the reduced mass replacing
state. It drops down one state at a time. What
the electron mass. (Hint: This problem is the
is the first transition to give a visible photon?
electrical analog of the gravitational problem
*3.6. What is the wavelength of the 2 transition
in binary stars, discussed in Chapter 5.)
in singly ionized helium? (Hint: The differ-

the ratio of the populations equal to the ratio
3.9. What are the radii of the n 2 and n 3
of the statistical weights, and (b) in what tem-
orbits in hydrogen?
perature range would you expect the ratio of
3.10. Consider only the two lowest levels in hydro-
the populations to be greater than the ratio
gen with g1 2, g2 6. (a) Find the ratio of
of the statistical weights?
their populations at a temperature of 5000 K;
*3.16. Assume that we are considering only the ion-
(b) at a temperature of 10 000 K.
ization of hydrogen, so that the electron den-
3.11. Consider only the three lowest levels in hydro-
sity is equal to the positive ion density, and
gen with g1 2, g2 6, g3 10. Find the three
the Saha equation simplifies to n2 /n0 F(T),
population ratios at a temperature of 5000 K. e
where F(T) is the right side of equation (3.10).
3.12. If the populations of two levels of energies Ei
Assuming that the total amount of hydrogen,
and Ej and statistical weights gi and gj(Ei Ej)
nTOT ne n0, is known and constant, find
are found to be ni and nj, respectively, find an
an expression for n2 /nTOT, the fraction of
expression for the excitation temperature of e
hydrogen ionized, in terms of nTOT and F(T).
this transition.
3.17. How much larger is an M0Ia star than an
3.13. Assuming that all the level populations are
M0V star? (See Appendix E for stellar
given by equation (3.9), derive an expression
for fi, the fractional population in the ith
3.18. For an A3 star, we measure an apparent mag-
level, defined as
nitude m 12. How far away is the star
ni (assuming it is a main sequence star)? (See
fi N
Appendix E for stellar properties.)
a nj 3.19. We observe a cluster, in the constellation
j 1
Orion, whose distance is 500 pc. We find a
where N is the highest populated level.
star whose spectrum is that of an A0, but we
3.14. At what temperature will the average kinetic
cannot tell the luminosity class from the
energy of the gas be equal to the hydrogen
spectrum. (a) If the apparent magnitude of
ionization energy?
the star is 9, what is its luminosity class?
3.15. For an atom whose populations are given by
(b) What if the apparent magnitude is 4?
equation (3.9), (a) in what temperature limit is

Computer problems

3.1. Tabulate the electron“nucleus reduced mass for 3.5. Make a table showing, for the mid-range tempera-
the nucleus being H, He, C, Fe. ture of each spectral type, the wavelength at which
3.2. Find all of the Hn transitions that fall in the visi- the blackbody spectrum peaks.
3.6. If we are limited to m 6 or brighter for making
ble part of the spectrum.
3.3. Consider only the three lowest levels in hydrogen naked eye observations, make a table of the maxi-
with g1 2, g2 6, g3 10. Plot the fraction of mum distance we can see a star for the mid-range
hydrogen in level 2, [n2/(n1 n2 n3 )] vs. T, for T of each spectral type (O5, B5, etc) for main
covering the range from the coolest M to the sequence stars.
hottest O stars discussed in this chapter. 3.7. For the mid-range temperature for each spectral
type, draw a graph of log B( , T) vs. for wave-
3.4. Make additional columns to Table 3.1 showing, for
each element in the table, the wavelength of a pho- lengths ranging from IR to UV.
ton that would just (singly) ionize the atom, and 3.8. For the mid-range temperature for each spectral
the temperature of the gas for which the average type, find the number of H ionizing photons emit-
kinetic energy is equal to the ionization energy. ted per second.
Chapter 4


The past decades have seen dramatic improve- second than the unaided eye. A telescope pro-
ments in our observing capabilities. There have vides us with a large collecting area to intercept
been improvements in our ability to detect visible as much of the beam of incoming photons as
radiation, and there have also been exciting possible, and then has the optics to focus those
extensions to other parts of the spectrum. These photons on the eye, or a camera, or onto some
improved observing capabilities have had a major detector.
impact on astronomy and astrophysics. In this
Example 4.1 Light-gathering power
chapter we will first discuss the basic concepts
Compare the light-gathering power of the naked
behind optical observations. We will then discuss
eye, with a pupil diameter of 5 mm, to that of a
observations in other parts of the spectrum.
1 m diameter optical telescope.

4.1 What a telescope does SOLUTION
Let d1 be the diameter of the pupil and d2 be the
diameter of the telescope. The collecting area is
An optical telescope provides two important
proportional to the square of the diameter. The
ratio of areas is
(1) It provides us with light-gathering power. This
d2 2 2
ab a b
1.0 m
means that we can see fainter objects with a
5.0 10 3 m
telescope than we can see with our naked eye.
(2) It provides us with angular resolution. This 104
means that we can see greater detail with a
This is the ratio of luminosities that we can see
telescope than without.
with the naked eye and with the telescope. We can
For ground-based optical telescopes, light-gathering express this ratio as a magnitude difference
power is usually the most important feature.
m1 m2 2.5 log10(4.0
4.1.1 Light gathering 11.5 mag
We can think of light from a star as a steady
This means that the faintest objects we can see
stream of photons striking the ground with a cer-
with the telescope are 11.5 mag fainter than the
tain number of photons per unit area per second.
faintest objects we can see with the naked eye. If
If we look straight at a star, we will see only the
the naked eye can see down to 6 mag, the telescope-
photons that directly strike our eyes. If we can
aided eye can see down to 17.5 mag. This illustrates
somehow collect photons over an area much
the great improvement in light-gathering power
larger than our eye, and concentrate them on the
with the telescope.
eye, then the eye will receive more photons per

A major advantage of film or a photoelectric
detector over the eye is its ability to collect light for
a long time. In the eye, ˜exposures™ are fixed at
about 1/20 s. With modern detectors, exposures of
several hours are possible. Therefore, the limiting

magnitude for direct visual observing is not as
faint as for photography or photoelectric detectors.

4.1.2 Angular resolution
We now look at resolving power. Resolution is
the ability to separate the images of stars that
are close together. It also allows us to discern the
details in an extended object. Screen
One phenomenon that affects resolution is
diffraction. Diffraction is the bending or spreading
of waves when they strike a barrier or pass
through an aperture. As they spread out, waves
from different parts of the aperture or barrier
interfere with one another, producing maxima
and minima, as shown in Fig. 4.1. As the aperture
size, relative to the wavelength, increases, there
are more waves to interfere, so the pattern is less
spread out. Most of the power is in the central max- D
imum, whose angular width (in radians) is
related to the wavelength of the wave and the
Incoming Radiation
diameter of the aperture, D, by
(rad) /D (4.1a)
Diffraction results in the images of stars being
smeared out by this angle. That means that if two
stars are closer than , their images will blend
together. We consider the images of two stars to
just be resolved when the maximum of one dif-
fraction pattern falls on the first minimum of the
other. This condition is called the Rayleigh crite-
rion. While equation (4.1a) is an approximation
good for all shapes of aperture, the actual size of
the diffraction pattern depends on the shape of (b)
the aperture. You may remember that, for circu- Fig 4.1. Diffraction. (a) A light ray enters from the bottom,
lar apertures, the resolution is given by and passes through a slit of length D. Diffraction spreads the
beam out and it falls on a screen.The intensity as a function
(rad) (1.22) /D (4.1b)
of position on the screen is shown at the top. Most of the
Example 4.2 Angular resolution energy is in the main peak, whose angular width is approxi-
Estimate the angular resolution of the eye for light mately /D (in radians). Smaller peaks occur at larger angles.
The effect in a real image. (b) [ESO]
of wavelength 550 nm.

We use a diameter D 5 mm for the pupil. We use
equation (4.1a) to find the angular resolution in
radians. We convert from radians to arc seconds to

convert the result to a convenient unit (1 rad

Sta direct

St com
2.06 105 arc sec; see Example 2.3).

r ap
ar in
lig g
12.06 105 2 15.5

pea n
¢ 1"2
10 m2

rs i

10 m2

23 arc sec
The eye™s resolution is not quite this good, since
the full diameter of the pupil is not generally used.
From equation (4.1a) we can see that we can
improve the resolution if we use a larger aperture.
A larger telescope will give us better resolution. A
10 cm diameter telescope (20 times the diameter
of the pupil of the eye) will give an angular reso- Ground
lution of 1 arc sec. However, diffraction is not the (a)
only phenomenon that limits resolution. The
Earth™s atmosphere also distorts images.
When light passes through the atmosphere
from above, it is passing through increasingly
dense air. As the density of air increases, its Moves
index of refraction increases. Therefore, the Around
light encounters an increasing index of refrac-
tion as it passes through the atmosphere. We
can think of the atmosphere as having a large
number of thin layers (as shown in Fig. 4.2) each Fig 4.2. Seeing. (a) Bending of a light ray as it passes through
with a slightly different index of refraction. As the atmosphere.We can think of the atmosphere as being
made up many thin layers, each with a slightly larger index of
the light passes from one layer to the next it is
refraction as you get closer to the ground. The amount of
bent slightly towards the vertical. The star
bending is actually much less than in this picture. (b) Effect of
appears to be higher above the horizon than it
changes in the amount of bending on the image of a star.
actually is.
This would not be a problem if the atmos-
phere were stable. However, variations on time
fraction limited images for telescopes with diam-
scales shorter than a second cause changes in the
eters from 1 to 2 m.
index of refraction in some places. The image
moves around. If we take a picture, we just see a
4.1.3 Image formation in a camera
blurred image. This effect is called seeing and usu-
To illustrate some basic points about the forma-
ally limits resolution to a few arc seconds. We
tion of images in optical systems, we look at the
refer to the numerical value of the blurring as
operation of a simple camera (Fig. 4.3). For astro-
˜the seeing™. At a good observatory site, on a good
nomical situations, we are dealing with objects
night, the seeing might be as good as 1/3 arc sec
that are ˜at infinity™, so the light rays from a
or better. This corresponds to the diffraction
point on the sky are traveling parallel to each
limit of a 30 cm diameter telescope. Building a
other. In the figure, we show bundles of rays
larger telescope does not help us past the seeing
coming from two different stars. The rays within
limitation on resolution, but it improves the light-
each bundle arrive at an angle with each other
gathering power. Hence our earlier statement that
equal to the angular separation of the stars on
light gathering is the main purpose of large
the sky.
ground-based optical telescopes. We will also see
For a camera with a lens of focal length f, the
later in this chapter that there are techniques for
rays in each bundle are brought together at a
overcoming the effects of seeing to produce dif-

Apart from image size, we are also concerned
Lens Film
with the brightness of the image. We can see that
the amount of light entering the camera is pro-
portional to the area of the lens. If D is the diam-
eter of the lens, then its area is D2/4. This means
θ θ
that the image brightness is proportional to D2.
The brightness of the image also depends on the
image size. The more the image is spread out, the
less light reaches any small area of the film or
detector. The linear image size is proportional to
f, so the image area is proportional to f 2. This
Fig 4.3. The optics of a camera. Bundles of rays from two
distant points enter, making an angle with each other. The means that the image brightness is proportional
focal length of the lens is f.
to 1/f 2.
Combining these two results, we find that the
image brightness is proportional to (D/f )2. The
distance f behind the lens. (The image is one focal
quantity f/D is called the focal ratio, so the bright-
length behind the lens when the object is at
ness is proportional to (1/focal ratio)2. We adjust
infinity. That is the definition of the focal
the focal ratio in a camera by changing f-stops.
length.) The images of all the stars in a field lie in
Since the focal length of the lens is fixed, we
a plane, called the focal plane. The images of two
change the focal ratio by changing the diameter
stars are at different points in the focal plane. We
of a diaphragm that controls the fraction of the
can locate the image of each star by following the
total lens diameter that is actually used. Each
chief ray of each bundle (the ray that passes
f-stop corresponds to a factor of 2 in the focal
through the center of the lens, undeflected) until
ratio, meaning that the image brightness
it intersects the focal plane.
changes by a factor of 2.
If stars have an angular separation on the
The discussions so far on image formation are
sky, then, as viewed from the lens, the two images
really only appropriate for thin lenses, as well as
have an angular separation on the focal plane.
optical systems where all of the angles are small.
This is simply the angle between the two chief
In real optical systems, rays that enter parallel do
rays. The camera provides no angular magnifica-
not all leave parallel to each other. Imperfections
tion. As viewed from the lens, the angular separa-
in the images formed by optical systems are
tion between the stars is the same as the angular
called aberrations. Some of the aberrations are
separation of the images.
reduced by using the central part. The less we use
We can also find the linear separation x
the edges of the lens the better the images. That
between the two images. From the right triangle
is why we might choose to use a diaphragm in a
in the figure, we see that
camera to block out the outer part of the lens. In
tan ( /2)
a real optical system there is a tradeoff between
image brightness and image quality.
If is small, then tan ( /2) is approximately /2, in
One type of aberration is called spherical aber-
radians. This gives us
ration. It arises from the fact that spherical curves
are the easiest to grind on glass surfaces. These
spherical shapes are close to the shapes required
Solving for x gives
for proper image formation, but differ slightly, so
x f (4.2)
the images are imperfect. Another type of aberra-
tion is called astigmatism. It occurs when the focal
This tells us that the linear size of the image
is proportional to the focal length. To obtain a length depends on where around the lens the
larger image, we use a longer focal length lens. light strikes.
(This is what we are doing when we put a tele- One aberration that occurs in lenses but not
in mirrors is called chromatic aberration (Fig. 4.4).
photo lens in a camera.)



Fig 4.4. Chromatic aberration.The focal length is different φ φ
φ φ
for different wavelengths.

This happens because a material™s index of refrac-
tion depends on the wavelength. The focal length
of a lens is therefore different at different wave-
lengths. The images at different wavelengths are
formed in different places. We can correct, some- fobj feye fcam
what, for chromatic aberration with a two-lens
Fig 4.5. Image formation in a refracting telescope. Light
system, called an achromat. The two lenses are
from a star enters from the left, making an angle with the
made of different materials, with different
axis, and leaves the eyepiece making a larger angle with the
indices of refraction, and different variations in
axis.The focal lengths of the objective, eyepiece and camera
the indices of refraction with wavelength. An
lens are indicated. For each lens, the ray that goes through
achromat only brings the images at two wave- the center unde¬‚ected (the chief ray) is indicated as a heavier
lengths together, but images for intermediate line. In a real telescope, the angles would be much smaller.
wavelengths are not far off.
Now that we have seen some of the basics of
optical systems, we can look at astronomical tele- The basic arrangement of the refracting tele-
scopes. Most current astronomical research is scope is shown in Fig. 4.5. We follow the forma-
done on reflecting telescopes. However, the basic tion of the images of two stars, just as we did
ideas of image formation in reflecting and refract- with the camera. Let™s assume that the focal
ing telescopes are the same. It is easier to visualize length of the objective is fobj. Since the stars are
refracting telescopes so we consider them first. at infinity, the objective forms their images this
distance behind the objective. The eyepiece has a
focal length feye. We place the eyepiece this dis-
4.2 Refracting telescopes tance behind the images formed by the objective.
(This means that the objective and eyepiece are
In a refracting telescope, the light first passes separated by a distance equal to the sum of their
through a large lens, called the objective lens. The focal lengths.) Since the initial images of the stars
are feye from the eyepiece, the eyepiece will focus
objective is the part that intercepts the incoming
light, so it determines the light-gathering power the light at infinity. This means that all of the
of the telescope. The larger the objective is, the rays in a given bundle emerge from the eyepiece
greater the light-gathering power. The light pass- parallel to one another.
ing through the objective is concentrated on a If you now look through the eyepiece, and
second lens, called the eyepiece. The eyepiece is focus your eyes at infinity (by relaxing the muscles
used to inspect the image formed by the objec- around your eye), the rays in each bundle will be
tive. The image formed by the eyepiece is viewed brought back together on your retina. Similarly, if
either by the eye or by a camera. In practice, you use a camera, you focus the camera at infinity,
either the objective or the eyepiece may be a and the images of the stars will fall on the film.
multiple lens, to correct for aberrations, but we The need to focus your eyes at infinity means that
will treat each as a single optical element. It is the best way to look through the eyepiece is to
also possible to just have a film holder with no relax both eyes and cover the unused eye, rather
camera lens. than squinting to close the unused eye.

angular magnification of a telescope by changing
Lets™s go back to the two bundles of rays
the eyepiece. There is a practical limit. You don™t
emerging from the eyepiece. Even though the
want to magnify the image so much that you blow
rays within a given bundle are parallel to one
up the blurring caused by atmospheric seeing.
another, the bundles make some angle with each
There are some limitations in the use of a
other. If the two stars are an angle apart on the
refracting telescope. One problem is the chro-
sky, then the two bundles will enter the objective,
matic aberration of the objective. Also, the objec-
making this angle with each other. The bundles
tive must be made from a piece of glass that is
leave the eyepiece, making a larger angle with
perfect throughout its volume, since the light
each other. We can find the angle by following
must pass through it. This is harder as you try to
the chief ray through the eyepiece. Note that the
make larger objectives. Larger objectives are also
chief ray at the eyepiece is not the same ray that
harder to support. The objective can only be sup-
was the chief ray at the objective. However, all
ported at its edges, since light must pass through.
rays in a given bundle will emerge from the eye-
Also, in many modern applications, we want to
piece parallel to the new chief ray.
place instruments near the eyepiece. However,
From the two right triangles in the diagram
the telescope must be supported closer to the cen-
with the common side x, we see that
ter of mass, which means far from the eyepiece.
Any instrument hung at the eyepiece will exert a
tan large torque about the mount, limiting the weight
of the instrument. As a practical matter, the
If the angles are small, we can replace the
largest refractors, such as that shown in Fig. 4.6,
tangent of the angle with the value of the angle
have objectives with diameters of, at most, 1 m.
in radians. If we also eliminate x in the equations,
we find
4.3 Re¬‚ecting telescopes
/ (4.3)
This means that we have an angular magnifi-
cation equal to the ratio of the value of the focal Many of the difficulties with refracting telescopes
lengths of the two optical elements. are avoided with reflecting telescopes. In reflec-
In general, when we want to do work with good tors, the objective lens is replaced by an objective
detail in the image, we use a telescope with a long mirror. With a mirror, there is no problem of chro-
focal length objective. Of course, we can change the matic aberration, since light of all wavelengths is

Fig 4.6. The 1 m refracting
telescope at the Yerkes
Observatory. Note the long
distance over which the observer
must move to keep up with the
eyepiece. [Yerkes Observatory

Fig 4.7. (a) The 5 m diameter Hale telescope on
Mt Palomar (California). For almost four decades it was the
largest useful telescope in the world.The caged part is the tel-
escope. It has an equatorial mount.The solid piece in the fore-
ground is part of the fork shaped support for the telescope.To
track an object, as the Earth rotates, the whole fork rotates in
the opposite direction.The prime focus cage is near the top of
the telescope. (b) The 4 m diameter Mayall telescope of the
National Optical Astronomy Observatory, on Kitt Peak,
Arizona.There is an identical telescope located on Cerro
Tololo, Chile.The Cassegrain focus is in a cage below the tele-
scope.The observer does not stay in that cage for observing;
that is done from a control room, where a television is used to
keep track of where the telescope is pointing. [(a) Palomar
Observatory/California Institute of Technology; (b)

aluminization. This is best done under very clean
conditions and under close to vacuum conditions,
to avoid impurities on the surface. The chamber
in which this is done is called an aluminization
chamber. Typically the effects of dust and oxida-
tion result in telescopes needing a new coating
every few years. So, large telescopes generally have
aluminizing chambers near the telescope.
reflected at the same angle. The mirrors are made Since the light doesn™t pass through the glass,
by shaping and then polishing a large piece of the requirements are for a good surface, not a good
glass. While the polished surface has some reflec- volume. Moreover, the glass can be supported from
tive ability, it is not enough for a good mirror. behind. It is therefore possible to make reflectors
Therefore a thin layer of reflecting material (usu- larger than refractors. For many years the largest
ally aluminum) is deposited on the surface. The reflector was the 5 m (200 inch) diameter Hale tel-
process of applying the reflective coating is called escope on Palomar Mountain (Fig. 4.7a).

One advantage of the wave nature of electro- Example 4.3 Blockage in prime focus
magnetic radiation is that the radiation is essen- Consider a 5.0 m diameter telescope, with a 1.0 m
tially unaffected by objects much smaller than diameter prime focus cage. What fraction of the
the wavelength. When electromagnetic waves incoming light is blocked by the cage?
reflect off a metal surface, they do it by inducing
an oscillating current in the surface. This oscil- SOLUTION
lating current then produces the reflected wave. The ratio of the areas will be the square of the ratio
If the surface is much smaller than the wave- of the diameters. The fraction of the mirror
length, there will not be enough room to produce blocked is therefore
a reflected wave at this wavelength. This means
(1.0 m/5.0 m)2
fraction blocked
that to have good image formation, the surface of
the mirror must be perfect to within approxi- 0.04
mately /20, where is the wavelength of the
This means that only 4% of the incoming light is
light being observed. For example, if you are
blocked. If we make the telescope smaller, but keep
observing with a wavelength of 500 nm, the sur-
the cage the same size, the blockage worsens.
face must be accurate to within 25 nm. (This is
Clearly, prime focus arrangements are only suitable
about 250 atoms.)
in larger telescopes.
Various shapes are possible for the mirror. It
turns out that spherical ones are the easiest to This problem was recognized by Newton, who
grind. You may remember that a parabola devised a mirror arrangement, called the Newtonian
focuses to a single point all rays coming in par- focus, in which a flat diagonal mirror is used to
allel to the axis. This means that a paraboloid, direct the image formed by the objective to the
where any cross section of the mirror will be a side. This is shown in Fig. 4.8(a). The eyepiece is
parabola, is a useful shape. Paraboloids are gen- then mounted on the side of the tube. There is
erally easy to grind, if you start with a spherical still some blockage but it can be kept small even
shape and then make a slight adjustment (taking for small telescopes. For a larger telescope, the
a little glass off the center). Current grinding Newtonian arrangement is difficult to use, since
technologies (discussed below) allow customized the eyepiece is at the top end of the telescope.
shaping of the mirror to optimize for various Also, the eyepiece is farther from the mount™s
applications (e.g. better imaging over a wide point of support, and equipment placed at the
field). focus exerts a large torque about the support.
We now look at what happens to the image An alternative solution is called the Cassegrain
formed by the objective. Replacing the lens with focus, shown in Fig. 4.8(b). The prime focus cage is
a mirror doesn™t change any of the basic ideas of replaced with a mirror that directs the rays back
image formation. There is, however, a problem through a hole in the center of the primary mir-
caused by the reflection of the light back along ror. Little light is lost by removing the center of
the direction from which it came. To examine the the mirror, since it would be blocked by the
image, the eyepiece (and observer) must be placed prime focus cage or the secondary mirror. The
between the stars and the mirror, blocking some secondary mirror in a Cassegrain arrangement is
of the incoming light. If an eyepiece is put at this diverging (convex), so the telescope seems to have
location, we call the arrangement a prime focus. a longer focal length than the objective. Since the
The advantage of the prime focus is that no more eyepiece is just behind the primary mirror, it is a
mirrors are required, so light is not lost (or convenient arrangement. Also, if you want to
images distorted) in additional reflections. It pro- place a lot of equipment at the eyepiece position,
vides for a ˜fast™ system (small focal ratio) with a this is not too far from the point of support of the
large field of view. However, there is some block- telescope.
age of the objective. If the telescope is very large, Sometimes an astronomer will want equip-
this blockage is a small fraction of the total col- ment that cannot conveniently be mounted on a
lecting area of the objective. telescope. It might be too large or it might require


(a) Newtonian

(b) Cassegrain

(c) Coude
Fig 4.8. Focal arrangements in (a) Newtonian,
(b) Cassegrain and (c) coud© telescopes. In each case the
light enters the telescope from the left.

a room in which the temperature can be kept con-
stant. It may also be necessary to have no mechan-
ical flexure of the instrument that moving it
would cause. For this purpose, some telescopes
have coud© focal arrangements (Fig. 4.8c). (The
term, pronounced coo-DAY, comes from the French
word for elbow, since the light beam is bent many
times.) A series of mirrors is used to direct the
image into a laboratory under the telescope
Fig 4.9. Stars act as true point sources, and their images
mount. One disadvantage of this arrangement is
have a diffraction pattern resulting from the supports for the
the large number of mirrors that must be used.
secondary mirror.The pattern is evident as a cross on the
No mirror is perfectly reflective, and a little light
brightest stars. [NOAO/AURA/NSF/Co.WIYN Consortium].
is lost at each reflection (see Problem 4.10).
A general problem with any of these arrange-
ments is that they all involve some blockage of observation. Often the goal is to provide a large
the objective. In addition to reducing the light field of view that is relatively free of aberrations.
striking the objective, the blocking element must For example, a Schmidt camera incorporates a glass
also be supported. Starlight passing by the ele- plate shaped to provide corrections for some aber-
ment and its supports is diffracted, creating rations. This plate is placed at the front end of the
unusual stellar images (as shown in Fig. 4.9). telescope and the light passes through it before
Some telescopes follow the basic layout of the striking the primary mirror. Schmidt cameras
Cassegrain system, but have some differences in are very good for wide field photography. Many
their optics to optimize them for a certain type of newer telescopes are of the Ritchey“Cretien design

(named after the two telescope designers who guiding, is done with the aid of a small auxiliary
came up with the idea in 1910), which incorpo- telescope and a control to adjust the position of the
rates hyperbolic mirrors as an alternative way for telescope about two axes to keep the object of
correcting for aberrations. interest in the center of your field. With the advent
While the 5 m telescope was the largest for of computers to control telescopes in real time (and
many years, there have been a number of break- television systems to fine tune the guiding), it is
throughs in telescope design and fabrication in the now easier to use alt-azimuth mounts, which move
past decade, and we have seen a progression of in azimuth and elevation, and are light and sym-
larger and more sensitive telescopes. For example, metric about the local vertical.
the old large telescopes are all equatorially There has been a growing realization that
mounted. This means that they keep up with the thermal currents in and just above the dome can
Earth™s rotation by rotating at a constant rate create bad seeing. Some telescopes built in the
about an axis parallel to the Earth™s rotation axis, 1970s had designs that tried to reduce these
the polar axis. This is convenient, but requires a effects by using massive mirrors and large domes,
large counterweight (Fig 4.6) or a fork to support to assure that they change temperature slowly.
the telescope on both sides of the polar axis Newer designs have mirrors that are very light
(Fig 4.7a). The alignment of the polar axis is not per- with good airflow, and minimal domes, so that
fect, and the motion of the telescope is not smooth. the systems quickly equilbrate with the outside
It is therefore necessary to make small corrections conditions when the dome is opened. The New
to the position of the telescope. This process, called Technology Telescope (Fig. 4.10) of the European

Fig 4.10. The 3.5 m New Technology Telescope of the European Southern Observatory, located at Cerro Paranal. It is
mounted in azimuth and elevation, and must move in two axes to track a source. As the telescope tilts to different elevations,
the shape of the mirror is adjusted with a grid of motors mounted on the back, visible in their casings in (a).The telescope is
placed in a small dome (b) that allows for quick equilibration with the outside air, reducing currents within the dome that pro-
duce bad seeing. [ESO]

Southern Observatory (Chile) was one of the first paraboloid. The mirror is cast so that most of the
to utilize that design. It is now becoming stan- glass on the back side is missing, leaving a hon-
dard for new large telescopes. eycomb pattern. This means that the mirror can
One potential problem with large telescopes be lighter than ones made using conventional
is that, as they tilt at different angles, gravity designs. Also, the honeycomb allows air to flow
acts at different angles relative to the surface of through the back of the mirror meaning that the
the telescope. This causes the surface to deform mirror can quickly reach the temperature of the
as the tilt is changed. To get around this prob- outside. As we just saw, this cuts down on air
lem, some newer telescopes have a grid of currents in the telescope, a major source of bad
remotely controlled motors on the back of the seeing.
telescope. These motors turn screws that adjust Even with the technology to build 8 m mir-
the shape of the surface, from the back, in a pre- rors, astronomers need even larger telescopes. A
programmed way. The NTT was also one of the different approach was pioneered by the Multiple
first to utilize this concept. An even more ambi- Mirror Telescope (MMT), in Arizona. Instead of
tious idea is to overcome some of the effects of one large mirror the telescope had six moderate
bad seeing by using real time signals from a sized mirrors. The images from all six mirrors
bright star to distort the third mirror in a coud© are brought together to produce an image that is
arrangement. This reshapes the wavefronts, com- six times as bright as the image from one mirror.
pensating for the distortions induced by seeing. While the multiple mirror approach sounds like
These processes are called active optics and adap- an obvious idea, a number of technical obstacles
tive optics. Together they are producing diffrac- had to be overcome before it could work. Among
tion limited images in telescopes up to 2 meters these are issues of aligning the mirrors, and
in diameter. combining the images properly. In the last few
Recently a group at the University of Arizona years a number of multiple mirror telescopes
has developed a technique for making high qual- have been developed with larger and larger col-
ity mirrors with diameters as large as 8 meters lecting areas.
(Fig. 4.11). It involves heating the glass and then The first of the newer generation multiple
spinning the glass while it cools. The surface of mirror telescopes is the Very Large Telescope (VLT)
the spinning molten glass takes on the shape of a operated by ESO on Cerro Paranal (2635 m) in

Fig 4.11. Polishing an 8 m
mirror in the University of
Arizona Mirror Laboratory.
[Steward Observatory Mirror

Chile (Fig. 4.12a, b). It has four telescopes, each in one direction. That direction changes as the
with an 8.2 m reflector. Eventually the light from Earth rotates, just as for radio interferometers,
all four telescopes will be combined into a single discussed in Section 4.8.
beam. Still under construction is the Large Another approach to large collecting areas is
Binocular Telescope, on Mt Graham in Arizona. It a variation on the multiple mirror approach.
uses two 8.4 m mirrors made in the Arizona The mirror is broken into a number of smaller
Mirror Laboratory (Fig. 4.11). It will have the reso- segments, all on the same mount. This seg-
lution of a single telescope with 23 m diameter, mented mirror approach allows all of the mirrors
to be pointed collectively, with fine tuning of
their positions as the telescope tilts. Located on
Mauna Kea (Fig. 4.12c, d) are the two Keck tele-
scopes, each 9.8 m, which utilize this design. The
Hobby-Eberly Telescope at McDonald Observatory,
also uses this design (Fig. 4.12e).


Fig 4.12. (a) One element of
the Very Large Telescope (VLT) on
Cerro Paranal in Chile, built by
ESO. (b) Exterior view of the four
domes.The telesopes are named
after the Mapuche (a pre-
Columbian tribe in northern
Chile) words for Sun, Moon,
Southern Cross and Sirius. (c) The
Keck telescope, located on Mauna
Kea in Hawaii. Its mirror consists
of a number of individually con-
trolled segments. It is operated by
the California Association for
Research in Astronomy, which is a
partnership among the University
of California, the California
Institute of Technology and NASA.


4.4 Observatories
4.4.1 Ground-based observing
In the past, the convenient location of observato-
ries was considered important. Observatories were
built near universities that had astronomers, and
those astronomers used whatever clear nights
were available. Today, the considerable investment
in large telescopes and sophisticated equipment
requires more regular utilization of the facilities.
Moreover, high quality telescopes are now built at
the sites that best allow them to take advantage of
their capabilities. Observatories are now built only
after there has been an extensive investigation of
the quality of the site.
Instruments have become more expensive; in
the 1960s and 1970s there was a trend away from
privately financed observatories to publically
financed national observatories. National observato-
ries are available to any qualified astronomer. An
astronomer who has a project will be required to
write a proposal, explaining the scientific justifica-
tion and the details of the observations. Generally,
there is not enough observing time for all of the
submitted proposals, and a panel of astronomers
decides which projects are to be done. More
Fig 4.12. (Continued) (d) An outside view of Keck. (e) The recently, with developments to cut the cost of tele-
Hobby-Eberly telescope at McDonald Observatory, also a scopes, there has been a trend back to private obser-
multisegment telescope. It is operated by the University of
vatories. Many of these are cooperative efforts by,
Texas,Austin, and Pennsylvania State University. [(a), (b), ESO;
typically, two to four universities with some public
(c), (d) W. M. Keck Observatory; (e) McDonald Observatory]
support. Keck is an example of such an effort.

The selection of an observatory site depends tory is built, seeing tests are done, with test obser-
on a number of considerations. Obviously, good vations being done over the course of a number
weather is important. However, clear weather is of years.
An additional consideration is light pollution.
not enough. The air should be dry, since water
vapor can attenuate signals. This suggests a Light from nearby cities is reflected up into the
desert. Also, the higher you go in altitude, the less sky, making the sky appear to glow. The brighter
air you have to look through. An altitude of 3 km this glow, the harder it is to see faint astronomi-
(10 000 ft) puts you above a significant amount of cal objects. Astronomers have found that certain
atmospheric water vapor. This suggests a moun- lights are better than others. For example, low
tain in the desert. Even with a mountain in the pressure sodium vapor lights, which have a yel-
desert, good seeing is not guaranteed. Seeing low appearance, give off most of their light in a
often varies with local conditions, depending on narrow wavelength range, and this range can be
air flow and terrain. Before an optical observa- filtered out at the telescope. For any light, a hood

(a) (b)

Fig 4.13. Observatories. (a) Kitt Peak National Observatory (operated by NOAO), southwest of Tucson, Arizona. Notice the
large number of telescopes.The 4 m telescope is in the background. (b) Mauna Kea, on the island of Hawaii. At 4.3 km
(14 000 ft), its summit is one of the best ground-based astronomical sites. (c) Cerro Tololo Interamerican Observatory
(operated by NOAO) in Chile.The largest dome is a twin to the 4 m telescope on Kitt Peak. (d) The European Southern
Observatory, located on La Silla in Chile, about 100 km from Cerro Tololo. [(a), (c) NOAO/AURA/NSF; (b) Richard Wainscoat,
Institute of Astronomy, University of Hawaii; (d) ESO]

Southern Observatory (ESO). ESO operates under a
that reflects light back to the ground rather than
letting it into the sky is very helpful. Such hoods treaty among member European countries. Its
also essentially double the brightness of the light primary location in Chile is on La Silla (Fig.
on the ground. 4.13d), which is about 100 km from Cerro Tololo.
Once a good site is found, it is likely that La Silla is the site of the NTT (Fig. 4.7a). ESO has
many telescopes will be built there. A good exam- recently gained another site, Cerro Paranal, fur-
ple is Kitt Peak in Arizona, operated by the National ther into the desert. It is the site of the VLT (Fig.
Optical Astronomy Observatory (NOAO), which is 4.12a). The third is Las Campanis, which is near La
shown in Fig. 4.13(a). This observatory has a num- Silla. All of these Chilean sites are quite far from
ber of different-sized telescopes, the largest being major population centers so that light pollution
the 4 m Mayall telescope (shown in Fig. 4.7a). To is virtually non-existent.
make maximum use of the site, there are even tel- The availability of spectacular sites in Chile
escopes on Kitt Peak operated by individual uni- has driven astronomers to make the best use of
versities or groups of universities, not directly those sites, by getting the best possible seeing.
affiliated with NOAO. As we have said, an important part of this is in
Surprisingly, one of the best observing sites is in the site selection. However, astronomers have
the middle of the Pacific Ocean. It is on the island long known that, at good sites, where the seeing
of Hawaii, at an elevation of 4.3 km (14 000 ft) on a is about 1 arc sec on a good night, about half of
dormant volcano, Mauna Kea (Fig. 4.13b). The that comes from air in and directly above the
island often has clouds, but they are generally telescope. Turbulence, caused by the ground,
below the altitude of the observatory, and the air dome and telescope are important contribu-
above the clouds is very dry. However, the lack of tions to seeing. As we mentioned above, new
oxygen at this altitude makes work very difficult. telescope and dome designs are improving see-
Many astronomers report headaches and other ing. For example, seeing at the NTT is frequently
discomforts. Clear thinking is also difficult, and better than 1 arc sec and, on really good nights,
there are many stories about simple mistakes is better than 0.5 arc sec.
made by experienced observers. For that reason, The lastest NOAO push to take advantage of
observing is conducted remotely, typically with excellent sites in the northern and southern
hemispheres is Project Gemini (Fig. 4.14). Both tele-
the observer at sea level.
The development of observatory sites in the scopes are 8.1 m in diameter. The northern tele-
Chilean Andes has had a major impact on astron- scope is on Mauna Kea, and started operation in
omy since the 1990s. First, it is important to have 1999. The southern telescope is on Cerro Pachon
telescopes in the southern hemisphere, since (2715 m) in Chile.
there are large parts of the sky that cannot be There is one other place that has recently
seen from the northern hemisphere. The north- been developed for astronomy. This is Antarctica.
ern part of the Andes runs next to the Atacama It is more than 2000 m above sea level, so it is at
Desert, which is dry even as deserts go. (There are a good altitude. The air is so cold that it is very
places in the Atacama Desert, some not too far dry. In fact, once you are more than 150 km from
from the Pacific, where there has been no the coast, you lose the ocean as a source of water
recorded rain in over a century.) There is precipi- in the air, and there is very little precipitation.
tation in the mountains, as is evidenced by the The snow that you see far from the coast is
snowy peaks, but a typical site in the Andes has blown there. This brings up one of the major
half the amount of water vapor overhead of a problems, wind. Telescopes would have to be put
comparable (in latitude and elevation) site in the in protective domes. This is reasonable for the
US. Three major observatories have been devel- infrared and millimeter parts of the spectrum.
oped in the Andes. One is the Cerro Tololo There is also an international science station,
Interamerican Observatory (CTIO) (Fig. 4.13c), which which is supported during the summer, so there
is operated by NOAO (in cooperation with the is logistical support. Astronomers are investigat-
University of Chile). Another is the European ing various sites near the South Pole.


We find the diffraction limit from equation (4.1a):
Fig 4.14. Project Gemini of the NOAO will have twin tel-
12.06 105 2 15.5 7
10 m2
escopes on Mauna Kea and in Chile. (a) The northern tele-
11 m2
scope has a moving weight of 342 tons, and the shape of the
mirror surface is controlled in real time using 120 actuators 1
1.1 10 arc sec
behind the mirror and 60 around the edge. (b) The southern
telescope dome on Cerro Pachon (2715 m) in Chile. A 1 m diameter telescope on the ground will
never realize this resolution because of the see-
ing limitations (typically worse than 1 arc sec and
sometimes as good as 0.5 arc sec). By putting a
4.4.2 Observations from space 1 m telescope in space we can realize a factor of
One of the major advances in observational
5 improvement over the best ground-based condi-
astronomy has been the ability to place telescopes
tions. With a 2 m telescope, we would have a fac-
in space. This is particularly important for observ-
tor of 10 improvement.
ing in parts of the spectrum that don™t penetrate
This is the reason for the development, by the
the Earth™s atmosphere. However, a telescope in
National Aeronautics and Space Administration (NASA)
space can even be important in the visible part of
and the European Space Agency (ESA) of the Hubble
the spectrum. It allows us to make observations
Space Telescope (HST), launched in 1990. HST, shown
free of the blurring caused by atmospheric seeing
in Fig. 4.15, has a 2.4 m diameter mirror providing
an angular resolution of about 0.05 arc sec. The
Example 4.4 Diffraction-limited optical telescope telescope is equipped with a full complement of
instruments so that it can carry out a full range of
What is the resolution of a 1 m diameter telescope
astronomical observations: imaging, photometry,
in space for observations at a wavelength of 550 nm?

tific support comes from the Space Telescope Science
Institute (STSCI), in Baltimore, MD. Observers can
view data at computer work stations at their
home institutions.
Shortly after HST was launched, astronomers
discovered a serious flaw in the optics, which
degraded the images. An error in fabrication
had produced a severe spherical aberration. This
resulted in a server degradation in the image



Fig 4.15. Views of the Hubble Space Telescope (HST).
(a) HST being deployed. (b) After deployment on service
mission. [STScI/NASA]

spectroscopy. It is an international facility, with
time available on the basis of proposals, just as (b)
with ground-based national observatories. The
Fig 4.16. Images of a shell around a star, taken by HST
telescope is controlled from NASA™s Goddard
(a) before and (b) after servicing. [STScI/NASA]
Spaceflight Center in Greenbelt, MD. The scien-

quality, and in the sensitivity. Astronomers were Since the servicing, HST has been so success-
excited about the successful completion of a serv- ful that astronomers are now planning a succes-
icing mission that compensated for the error. We sor, the Next Generation Space Telescope (NGST).
will come back to HST results throughout this
book, but in Figs. 4.16 and 4.17, we show images
4.5 Data handling
taken with HST before and after the servicing. In
2002 there was a scheduled servicing mission in
which many of the instruments were upgraded. In the previous sections we concentrated on
bringing as many photons to the eyepiece as pos-
sible. Now we will look at what we do with these
photons once they reach the eyepiece. We con-
sider three different types of observations:
(1) Imaging. This is probably the most familiar
type of observation. The goal of these obser-
vations is to obtain a picture of some part of
the sky.
(2) Photometry. The name implies the measure-
ment of light. The goal of the observations is
to measure the brightness of some object.
This may include measuring the brightnesses
through certain filters to measure colors. It
may also include measuring time variations
in brightness.
(3) Spectroscopy. The goal of these observations is
to obtain a spectrum of some object, generally
with sufficient detail to allow the study of
(a) spectral lines.

4.5.1 Detection
Whatever the type of observation, the data must
be recorded in some way. In the past, the most
common way was to use a photographic plate.
These plates contain an emulsion with light sen-
sitive grains. Each grain serves as a little detector
of radiation, or picture element (pixel). One advan-
tage of photographic plates is that there are many
pixels. We say that the plate has a panoramic qual-
ity. This means that we can simultaneously
record many parts of the image. There are some
disadvantages to photographs. One is that a very
small fraction of the photons that strike the plate
are actually detected. We call the fraction of pho-
tons that are detected the quantum efficiency of the
detector. For most emulsions, this efficiency is
only a few percent.
A much higher efficiency can be obtained
Fig 4.17. Images of the spiral galaxy M100 from HST
with photoelectric devices. A photon strikes a sur-
(a) before and (b) after servicing. [STScI/NASA]
face, causing an electron to be ejected. This is the

photoelectric effect that we discussed in Chapter value is the best estimate of the number of pho-
3. The electron is accelerated towards another tons detected in ten seconds, but the spread in the
surface, where more electrons are ejected. The gaussian “ the standard deviation “ tells you the
process is repeated many times, and eventually a uncertainty. For a counting experiment, in which
you measure N events, that uncertainty is N. So


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