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ASP2011 Measurement
Techniques
Lecture 1.
SCHOOL OF PHYSICS
Q: How do astronomers know anything about
astronomical objects that are too far away to visit?
A: We interpret the radiation (and sometimes particles)
emitted by astronomical objects using the laws of
physics that we know work well here on Earth.
"Cosmological principle"
Universe is isotropic and homogenous.
ie. looks the same to all observers and obey same
physical laws everywhere.
Sources of information
 Visible light (since antiquity)
 Other “invisible” electromagnetic (EM) radiation:
o Radio (1930s-)
o X-rays & -rays (1960s-)
 Cosmic rays (1912-)
 Neutrinos (1980s-)
 Gravitational waves (201?-)
Electromagnetic (EM) spectrum
Observational windows
The Earth's atmosphere is transparent to EM
radiation in the visible and radio frequencies.
Kutner M.L., Astronomy: Astrophysical Perspective. Harper & Row
Various processes contribute to the opacity of the
atmosphere in other bands:
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1. Gamma rays and "hard" X-rays are stopped by
collisions with gas molecules in the upper atmosphere.
2. X-Rays and UV C are absorbed in the ionosphere and
the van-Allen radiation belts.
3. UV A and UV B are absorbed by ozone layer.
4. Infrared is absorbed by CO2 and H2O in atmosphere.
Earth-based observational astronomy is thus restricted to
these two "windows".
 We can push the limits of infrared (IR) astronomy
by going to high altitude (Chile, Hawaii) or going to
places that are very cold and dry (Antarctica)
 For UV through X-rays, we must get above the
atmosphere, in rockets, balloons or (increasingly)
satellites
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The nature of light
Case 1. Light as a wave
Fig. 3.9
E. Hecht "Optics" 2nd Ed. Addison-Wesley; also Z&G ch 8
The figure shows that em waves are transverse waves,
with field vectors E & B perpendicular to the direction of
propagation. Frequency  the number of wave crests
passing a fixed point per second.
In a vacuum, speed c


c

=
=

2.99793x108 m/s
Case 2. Light as a particle.
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The modern quantum-mechanical picture of em
radiation: light is composed of individual elements
(quanta) of energy, and behaves like particles
"wave packets" called photons
Energy E = h
Both these explanations are equivalent!
Measurable quantities
Frequency (wavelength)
Arrival time
Polarisation
Intensity (flux)
Spectrum (flux vs. frequency)
Polarisation
Recall the wave picture for EM; the E-vector has two
orthogonal components Ex and Ey, both perpendicular to
the direction of transmission. For plane (linearly)
polarised light, the direction of E does not change.
Polarising films act as efficient filters, for example in
sunglasses. Polaroid film consists of long chain
molecules which readily absorb light with E field
parallel to the molecule's long axis.
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PHOTOMETRY
(measurement of light intensity)
Photometer (a device that measures the intensity of an
object in a part of the EM spectrum)
Today for optical astronomy we use charge-coupled
devices (CCDs, similar to those in digital still or video
cameras) to precisely measure source fluxes. We
sometimes quote the fluxes in units of photons or energy
per unit time; HOWEVER astronomers customarily use
a much older measure…
…which requires some historical background…
Astronomy is arguably the oldest science.
Ancients named constellations - proper names in Latin.
The eye is the oldest astronomical instrument (a highspeed but low efficiency photometer)
About 200 BC Hipparchus ranked the brightness of stars
by magnitudes. The brightest stars were described as
being of first magnitude, next brightest stars 2nd
magnitude, and so on until the faintest visible stars,
ranked at 6th magnitude.
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Unit of brightness: magnitude (Apparent or "visual"- how
bright is it seen from )
Because of the human eye's physiology (logarithmic), a
change of 1 magnitude  a doubling in brightness.
With modern detectors we find that 5 magnitudes  100
fold change in flux (unit energy per unit area per unit
time).
In 1856, N. Pogson defined a difference of 5 magnitudes
as equal to a 100 times change in brightness.
i.e. A decrease of 1 magnitude = 5100 = 2.512
times brighter.
With modern telescopes :
a) we can measure brightness more accurately
so we need divisions between magnitudes
m = 2.7, 5.3 etc.,
b) we can see fainter stars so we need
magnitudes greater than 6 and
c) some stars are very bright so they should
have negative magnitudes.
e.g. Sirius m = -1.4
Note: A large magnitude means a faint star! This can get
quite confusing…
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Converting magnitudes to fluxes
Take two stars m1, m2 : m2 > m1
Then the ratio of their brightness l1/l2 is...
m1  m2  2.5 log 10
l1
l2
Very important everyday practical astronomer's
equation since modern photometers give results in units
of luminosity.
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How to add magnitudes
Example: A certain binary is magnitude 4.1.
It is believed the 2 component stars are equally bright.
What is the magnitude of each?
Let m1 = combined magnitude = 4.1
Let m2 = separate magnitudes, so m2 > m1
m2 = 4.85
What about the effect of distance? For two identical stars
at different distances, how will the magnitudes differ?
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The Inverse-Square law
The apparent brightness of a star is inversely
proportional to its distance.
Apparent brightness  1/(distance)2
Knowing the distance to one star we can get a first
estimate of the distances to other stars from their
magnitudes.
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Sun's visual (apparent) magnitude m = -26.7
Take for example a 1st magnitude star mstar = 1
. m2 - m1 = 1-(-26.7) = 27.7 = 2.5 log10 (l / lstar)
. l / lstar = 1.2 x 1011
Assuming the difference in brightness is due to the
greater distance alone (that is we assume the other star is
identical to our sun),
. dstar = 3.47 x 105 x 150,000,000 km
= 5.2 x 1013 km  5.5 ly
Similarly a 6th magnitude star would be at 55 ly.
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ASP2011 Measurement
Techniques
Lecture 2.
SCHOOL OF PHYSICS
Units in Astronomy :
Physicists use the SI or MKS (metre, kilogram, second)
units system.
Astronomers and astrophysicists more commonly use
the cgs system (centimetre, gram, second), in addition to
a variety of specific units
Units of Distance:
Astronomical Unit (AU) Mean to
distance.
1 AU = 1.496  1011 m
Good measure within the solar system;
Mercury’s distance from the sun is at most 0.39 AU
Jupiter is 5.2 AU
Pluto is at most 39.4 AU
Light Year (ly) Distance light travels in a year
1 ly = 9.46  1015 m
= 6.324  104 AU
Parsec (pc)
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This unit illustrates the concept of (trigonometric)
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parallax
As the Earth orbits the Sun, nearby stars appear to shift
in position against the more distant background stars.
The further away the star is, the smaller the parallax
angle p. The star’s distance d (in parsecs) is found by
taking the inverse of p (in arcsecs), d = 1/p.
1 pc = 3.086  1016 m
= 3.26 ly
(note the typo in Z&G 4th ed. P225!)
This method is good to a few hundred parsecs; the
Hipparcos satellite, launched by ESA in 1989, obtained
milliarcsecond positions for 120,000 stars and thus
determined their positions to high precision out to
almost 1000 pc.
The parsec is effectively the standard distance unit in
astrophysics. For objects within our Galaxy, we
typically use the kpc (the Galactic center is ~8.5 kpc
away); for objects at cosmological distances, the Mpc
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Unit of brightness: Absolute Magnitude
We previously encountered the apparent magnitude of a
star (as viewed from Earth)
A star's absolute Magnitude is how bright the star would
appear if it were moved to a standard viewing distance
(defined at 10 pc).
Parallax = p "arc (seconds of arc  arcsec)
Distance = d = 1/p parsec
How much brighter (or fainter) would a star appear at 10 pc
compared to it’s real distance away from us, d?
Let l1 = luminosity (apparent brightness) of the star at
distance d, and l2 = luminosity at 10 pc.
Move the star from d to 10 pc then star becomes
 brighter using the inverse square law
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Now since for most stars the parallax angle is too small
to measure we will normally want to use this
relationship the other way around using:
d  10
 m M 5 


5


If we can determine a star's absolute magnitude M then
we can compute its distance.
Most stars are quite unlike the sun so before we can
estimate absolute magnitudes we must consider
differences in the distribution of stellar radiation.
Blackbody Radiation
As you heat up an iron bar you first notice "radiant heat"
being given off by the bar. The bar is actually "glowing"
in the infrared.
After further heating the bar will begin to glow a deep
cherry red, then bright red and finally a very bright
white. If you could continue to heat the bar (without
melting it!) would eventually glow with a blue colour.
Stars and iron bars are good approximations of
theoretical objects called blackbodies.
A perfect blackbody is in thermal equilibrium (constant
T) and it absorbs all EM radiation that strikes it. The
absorbed radiation adds heat to the body. The thermal
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motions of the charged particles in a body give rise to
the emission of EM radiation. As the temperature is not
increasing it follows that the blackbody must re-emit all
the energy it has absorbed. The temperature of an object
is a direct measure of the amount of motion of its
constituent particles. The blackbody curve is also known
as the Planck curve.
Fig 4-2 N.F. Comins & W.J.
Kaufmann III, Discovering the
Universe 5th Ed. W.H.
Freeman & Co. N.Y.
OR
Fig 8-14 Z&G
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Blackbody radiation laws
Wien's Law gives the relationship between wavelength
of the colour peak and temperature.
max
2.9  10 3

T (K )
Example: The Sun. The maximum intensity of sunlight
is at max = 500 nm
Stefan-Boltzmann law
An object emits energy at a rate proportional to the 4th
power of its temperature in Kelvins
or
Flux
F = T4
Luminosity L = T44r2
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Colour indices
The continuum spectra of stars approximate black body
curves; astronomers can estimate the temperature (and
hence spectral type) of a star by measuring its intensity
at two or more wavelengths.
Most photometers are equipped with a set of filters.
These filters are used to block out all starlight except that
which lies within a specific wavelength range.
Johnson, Morgan UBV standard filter system
Filter
Central Wavelength
U (ultra violet)
3600 Å
B (blue) {photographic} 4200 Å
V (visual) {human eye} 5300 Å
R (red)
6400 Å
Each filter has a band pass ~ 1000 Å wide.
Using these filters we can measure "colour magnitudes"
i.e. mU, mB, and mV or just U, B and V
From any two of these we can make a colour index
i.e. (U-B), (B-V) and (U-V) always "bluest" first.
There is also an important colour index value that links
the colour of stars to their spectral type ; e.g. for an A0 V
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star (B-V) = 0
(see Z&G Table A4-3; more in stars, week 7 onwards)
The Colour - Magnitude diagram
In 1910, Hertzsprung and Russell independently devised
a scheme to classify stars according to their colour and
absolute Magnitude.
Distance estimation
using the colourmagnitude diagram is
referred to as
spectroscopic
parallax.
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What can we discover from Photometry?
Just to name a very few!
Distance to stars
Types of stars (via colour indices)
Variable stars:Intrinsic variables, e.g. Cepheids
Eclipsing binaries
X-ray binaries
Microlensing
Temperatures of stars (Wien's Law)
If we can estimate a star’s radius, then we can determine
its absolute magnitude and distance. (Stefan-Boltzmann
Law)
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ASP2011 Measurement
Techniques
SCHOOL OF PHYSICS
Lecture 3.
Spectral types
O B
Hot
A
F
G
K
M
(R N
S)
Cool
or
Oh Be A Fine Guy/Girl Kiss Me (Right Now Smack)
Subdivisions
0 1 2 3
Hot
4
5
6
7
8
9
Cool
Table 13-1. Z & G
Luminosity Class
I(a b)
Supergiants
II
Bright giants
III
Giants
IV
Subgiants
V
Main sequence
VI
Dwarves
sd sub dwarf, w white dwarf, p peculiar
SPECTROSCOPY [Z&G sec. 9-4]
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The measurement and interpretation of spectra (plural;
singular is spectrum)
Spectrograph
1. instrument by which spectra may be
"photographed" (recorded) OR
2. a photograph of a spectrum (spectrogram)
Spectrometer
instrument to measure spectral intensity
A spectrograph or spectrometer disperses the light
collected by a telescope, using a prism or grating
Z&G
Fig.
9-14
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Spectrophotometer
spectrometer with photoelectric detector
Also there are task specific names used e.g.
Spectrohelioscope, Infrared spectrometer, microspectrophotometer.
"White" light, prisms, and simple spectroscopes
Ordinary sunlight can be decomposed (using a prism)
into a spectrum of colours; a lens and a second prism
can recombine the dispersed spectrum back into white
light.
I. Newton
Opticks (1704)
The index of refraction of glass is a function of
wavelength, thus so is the refracted angle, leading to
dispersion.
Bunsen 1856 noted that each element (compound),
when placed in a flame, produces a distinctive
fingerprint of bright lines.
Bunsen & Kirchoff built first decent spectroscope.
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Grating Spectrographs
Most modern spectrographs use a diffraction grating to
disperse the incident light. Both reflection and
transmission gratings are used
Constructive
interference at angles
sin   (n) /d

where  is the
wavelength, d is the
groove spacing and n is
the order of the spectrum
Z&G Fig. 9-13
Dispersion is
approximately linear, at the expense of having multiple
(overlapping) scattering orders
Spectrograph capabilities
Characterised by
 Bandpass
 Resolving power (E/E)
 Efficiency
 Resolution (for CCD detectors)
Kirchoff's rules
Fig 5.7 Chaisson McMillan Astronomy Today
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Fig 4.11 Comins & Kaufmann
1. A hot and opaque (optically thick) solid, liquid or
compressed gas emits a continuous (blackbody)
spectrum.
2. A hot, transparent (optically thin) gas produces a
spectrum of emission lines. Lines seen depend on
the composition of the hot gas.
3. If light from a continuous source passes through a
cooler gas then absorption lines appear. Lines seen
depend on the composition of the cool gas.
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Emission spectra
The “sample” is acting as the radiation source. The
spectral lines will appear as a series of narrow peaks at
the wavelengths characteristic of the elements present.
The sample is emitting energy preferentially at those
wavelengths; a continuum may also be present.
The nearby (z=0.1028) cluster of galaxies PKS 0745-191 is bright in X-rays and
contains a strong cooling flow. Such cooling plasmas are rich in X-ray line emission
and make interesting targets for the Chandra HETGS. PKS 0745-191 is, however, an
extended object making analysis of its spectrum more involved.
http://space.mit.edu/ASC
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Absorption spectra
The sample is between a radiation source (ideally a
source of continuous radiation) and the observer. The
sample absorbs energy at particular wavelengths which
are characteristic of the elements present in the sample.
A series of dark lines are observed at those wavelengths.
Example: The solar spectrum
J. von Fraunhofer 1814 counted over 800 dark lines
in the solar spectrum (mostly Fe).
Now named Fraunhofer lines.
Z&G sec. 10.2D
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ASP2011 Measurement
Techniques
Lecture 4.
SCHOOL OF PHYSICS
Bohr Model of Hydrogen atom
1st postulate;
"Only a discrete number of orbits (energy levels) are
allowed to the electron ... "
2nd postulate;
"a) radiation in the form of a single discrete quantum
(photon) is emitted or absorbed as the electron jumps
from one orbit to another
b) the energy of this radiation equals the energy
difference between the orbits"
fig 40-18 Giancoli General Physics; see also Z&G 8-2B
The energy levels for the Hydrogen atom can be found
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from
En 
 2.18  10 18 J
n2
for transitions
1 
 1
Et  En  Em  2.18  10 18  2  2 J
m 
n
and since
Et  h 
hc

the wavenumber (inverse wavelength) equals
 2.18  10 18  1
1 

 2  2  m-1

hc
m 
n
1
or
 1
1 
 R 2  2 
n m 

1
where
:R 
e 4
8 0 h 2 c
2
 109677 .759 cm-1

is the Rydberg constant
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Now calculate wavelengths
Lyman series
n=2
3
4
5
6
m=1
Lya
Ly 
Ly 
Ly 
Ly 
 1216 Å
Å


Å
Å


Å
Paschen series m = 3 .....
Balmer series m = 2
n= 3
4
5
6
.
n= 
H 
H 
H 
H 
 6564.6 Å
Å


Å

Å
note: converging series in ;
H
 = 3645.6 Å
Paschen series m = 3 .....
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Spectral - line Analysis
Line identification
By matching observed spectral lines with those found in
laboratory samples we obtain information regarding the
chemical composition of astronomical objects. This
analysis is complicated by the physical conditions at the
emitting source such as temperature and pressure.
Doppler Effect (non Relativistic version)
Lines emitted by objects moving relative to us will be
red- (blue) shifted.
z




v
c
where  is the shift in wavelength relative to the “restframe” value , v is the speed of the emitter relative to
the observer (us), and c is the speed of light.
The Doppler effect is a key phenomenon for the modern
study of cosmology, and objects at cosmological
distances are often characterised by their redshift z,
which is proportional to distance
e.g. A Calcium line has rest wavelength 3933 Å.
Measure this line in a star and find it shifted to 3972 Å.
How fast is the object moving towards or away from us?
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Doppler Effect (Special Relativity version)
vr

1

 
c
z

0  v r
1

c
1
2

 1


Line intensity (depth)
The intensity of a spectral line is proportional to the
number of photons emitted (or absorbed). The intensity
of the line depends only in part on the number (density)
of atoms that give rise to the line.
Line intensity is strongly dependent on the temperature
of the emitter as this determines what fraction of atoms
are in the right initial energy state to undergo any
particular transition.
In stellar atmospheres, the number of atoms in a
particular state relative to the number in another state
can be modelled using the Boltzmann and Saha
equations.
(See section 8-4 Zeilik & Gregory and 3rd yr ASP)!
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The relative population of electrons in the first excited
state N2 /N (Balmer lines) first increase with
temperature, reach a maximum then decrease. This
occurs for all elements.
Fig. 8-13 Zeilik & Gregory,
Introductory Astronomy &
Astrophysics
See also
Fig. 10-3 Comins &
Kaufmann, Discovering the
Universe
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Line Broadening (Z&G 8-5)
Natural line broadening
Heisenberg Uncertainty Principle. Energy of state may
not be specified more accurately than,
xp 
h
h

E

t

2 or
2
where t is the lifetime of the state hence,
 
1
2t
Thermal (Doppler) line broadening
Fig. 4.17 Chaisson
McMillan Astronomy
Today
Collisional (pressure)
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line broadening
Atomic energy levels are shifted by neighbouring
charged particles (Stark effect)
Zeeman Effect
Energy levels may split in a magnetic field. If the
Zeeman components are not individually resolved then
this looks like line broadening.
Rotational line broadening
Only detected for stars with very fast rotation
Fig. 4.18 Chaisson McMillan Astronomy Today
Spectral information from starlight
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Observed characteristic
Peak wavelength
Lines present
Line intensities
Line width
Doppler shift
Information obtained
Temperature (Wien's Law)
Composition
Relative abundance &
Temperature
Temperature, turbulence,
rotation speed, density,
pressure & magnetic field
strength
Radial (line of sight)
velocity, Distance
(Cosmological)
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ASP2011 Measurement
Techniques
Lecture 5.
SCHOOL OF PHYSICS
TELESCOPES I
A telescope comprises a focusing (or collimating) system
and a detector. The operating principles of each of these
components depends upon the waveband
Optical & IR
“Traditional” telescopes with lenses or mirrors
X-ray & gamma-ray
Grazing incidence optics, passive collimators, coded
masks etc.
VHE gamma ray & neutrinos
Using the Earth’s atmosphere or the Earth itself as a
detector
Radio & Interferometry
Combining signals from multiple detectors
Lenses and mirrors – optics review
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Light can be concentrated (focussed) either by a lens
(refraction) or a curved mirror (reflection).
See Z&G p154 & ch. 9
Law of reflection
When light is reflected at a mirror, the angle of
incidence (measured relative to the normal) equals the
angle of reflection
ir
NOTE wavelength independent!

Snell's Law
For a plane wave passing from a medium with refractive
index n1 into a medium with index n2, the angles
between the incident and refracted rays and the normal
to the interface obeys
n1 sin i  n2 sin r

(the speed of light in a medium is different from that in a
vacuum). Refractive indices also depend on the
wavelength of the light
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Thin lenses
Simple lens - spherical surfaces, one piece of glass
Positive lens - parallel rays converge
Double convex
Plano-convex Convex meniscus
Negative lens - parallel rays diverge
Double concave
Plano-concave
Concave meniscus
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The telescope produces an image of the object of interest
at the focus. The distance from lens to image for objects
at large distances is the focal length f
Note: incident rays are parallel for astronomical objects!
Point source and Extended objects
The figure depicts an extended object forming an image
in the image plane; an extended image can be thought of
as made up as an assemblage of point source images
Diameter (Aperture)
The primary lens typically forms the aperture; this
determines the maximum cone angle for a bundle of
rays to come to a focus in the image plane
The larger the aperture, the greater the light-gathering
power of the telescope
(proportional to d2)
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f ratio (Focal ratio) {f value, f number}
f = focal length / aperture diameter
written f/#, where we replace # with the value of f.
The “speed” of a lens or mirror system. A smaller f-ratio
delivers more light per unit time to the image plane.
There are other more practical advantages to building a
fast telescope!
Resolving power
A telescope cannot separate arbitrarily close point
sources. The resolving power is the inverse of the
minimum angle between two points in order for them to
be easily separated:
RP=1/min
This is a consequence of the diffraction pattern arising
from the (circular) telescope aperture. Airy (Astronomer
Royal mid 1800's) first to derive the solution
1.22min  206265 /d

Where  is the wavelength of the light and d the
telescope’s aperture (206265 is the number of arcseconds
in 1 rad). Such performance is rarely attained on the
ground, due to the atmospheric effects which blur the
image (seeing).
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Rayleigh’s Resolution criterion
Two star images are just resolved if the central
maximum of one falls on the first minimum of the other.
Dawes Resolution criterion
Empirical “rule of thumb”


 min 
11.6
D 
in arc seconds for D in cm.
Plate scale & Magnification
The size s of an image at the focus corresponding to 1
in the sky is
s=0.01745f
where f is the focal length of the lens (and 0.01745 is the
number or radians in one degree).
For small telescopes, an eyepiece is used to view the
image at the focal point.
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Magnification is the apparent increase in size of the
object compared to unaided visual observation.
Magnifying power is the ratio of focal length of the
objective (the lens or primary mirror) F to that of the
eyepiece f:
MP = F/f
upright image +ve, inverted image –ve
The shortest focal length eyepiece will not necessarily
allow you to resolve smaller details, if you are already
limited by the objective size. Furthermore, higher
magnification makes extended objects dimmer.
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When optical systems go bad: aberrations
We saw previously that the varying refractive index of
glass to light of different wavelengths can be exploited to
disperse the spectrum in a spectrograph. The same effect
causes chromatic aberration in a telescope. Two types:
Longitudinal colour (different wavelengths are focussed
at different distances from the lens)
Lateral or transverse colour (different wavelengths are
focussed at different positions in the focal plane)
Can use special glass or add an optical element
(“achromatic doublet” or “achromat”). Most common
type is Fraunhofer achromat, consisting of lenses made
to bring red and blue to same focus
Much worse for short focal ratios (“fast” lenses)
Spherical aberration
Rays striking spherical lenses or mirrors near the edge
do not come to the same focus point as rays near the
centre. Effect is worse for large and fast (again!) lenses.
Can use a non-spherical lens, but these are harder to
produce; alternatively add corrective optics.
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Large telescopes
As telescope diameter d increases, chromatic and
spherical aberration become more problematic, and the
weight (and optical depth) of the lens increases. To
avoid these problems most large modern telescopes are
reflecting designs. Several types, each with advantages
and disadvantages; Newton constructed the first
practical example around 1670.
Mirror equation - same as thin lens equation
Magnification - same as lens
Advantages:
Mirrors do not suffer from chromatic aberrations+++
- "apochromatic"
Only one surface of the mirror needs to be figured
correctly
Large lenses have to be supported at their edges, and can
sag; a mirror can be supported evenly (also allows
adaptive optics).
Disadvantages:
Spherical aberration (for non-parabolic primaries)
Comatic aberration or coma (variation in magnification
over the aperture)
The secondary mirror blocks the primary
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ASP2011 Measurement
Techniques
SCHOOL OF PHYSICS
Lecture 6.
Astronomical Telescopes
1608 Galilean Refractor
1611 Astronomical Refractor - Johannes Kepler
Advantages:
Disadvantages
Good for planets, double stars and
planetary nebulae.
Long tube, large f ratio, limited
max aperture
(1733 Achromatic refractor; see also apochromatic
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refractor)
1672 Newtonian Reflector - Isaac Newton
Paraboloid primary (or spherical for smaller
apertures/large f-ratio) and flat, angled secondary
Advantages
Disadvantages
Cheap, simple, achromatic,
low f ratio.
Central obstruction.
1672 Cassegrain Reflector - Guillaume Cassegrain
Paraboloid primary and hyperbolic secondary reflecting
the light through a hole in the primary to the focus
Advantages
Disadvantages
Most compact
Long F Ratio
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Schmidt-Cassegrain
Spherical primary and Schmidt corrector plate (an
additional lens placed in the optical path) to avoid
spherical aberration
Advantages
Disadvantages
No spherical aberration; no
coma.
Long F Ratio.
1911 Ritchey-Chrétien
Specialized Cassegrain with two hyperbolic mirrors
Advantages
Disadvantages
free of 3rd order coma and
spherical aberration at the focal
plane
5th order coma, astigmatism,
field curvature
Most modern reflectors!
Keck, Gemini, Hubble etc.
Light Grasp (Gathering) and Magnification
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Exit pupil
d
is an image of the objective seen in
the eyepiece. Its size depends on magnification

D 2
Light grasp  d 2
Brightness of a point source, limiting magnitude or
"What is the faintest star you can see with this telescope
?"
Here we will assume d = 0.7 cm
l1
l2
Use
m2  m1  2.5 log 10
then
D
m2  2.5 log 10    6.0
d
2
Note: for point sources the telescopic brightness increase
is not dependent on the magnification.
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Example. Limiting magnitude of a 20 cm telescope.
m2 =
Brightness of an extended object
For extended objects their light is spread by the telescope
over the viewed virtual image to cover an area M2 times
larger than it covers on the celestial sphere.
brightness of telescopic image
D 2
So, brightness of naked eye image  d 2 M 2
but magnification M = apparent field / true field
or
M
f objective
f occular

D
d
therefore the point (on the sky) to point (in the image)
relative intensity of an extended object is at best equal to
unity

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To obtain the maximum image brightness (richest field)
we need an exit pupil that just matches the pupil
diameter of the dark-adapted human eye
= 7mm.
Example. a) What magnification should be used to give
so called “richest field” views with a 15 cm
telescope?
b) If this is an F7 instrument, what focal length eyepiece
is required?
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Telescope Mounts
 To make pointing of a telescope in any direction
possible it must be movable in two planes, one
perpendicular to the other.
 A useful mount must have a high degree of stability
combined with smoothness and ease of movement
about both axes.
Altazimuth mounts
Move "Up and down" in altitude and "round and round"
in azimuth.
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A very popular sub type is the Dobsonian.
Advantages:
Compact, simple to
construct and highly
intuitive to point
Disadvantages:
Difficulty pointing at the
zenith; balance
Equatorial Mounts
Two axes perpendicular to one another, however, not
vertical and horizontal, but parallel to Earth's axis of
rotation (Polar axis or RA axis) and perpendicular to it
(Declination axis)
Advantages:
Even without a motor drive gives ease of following, ease
of re-finding after a pause in observations. With a motor
drive an equatorial mount will track the object making
long and continuous observations or long photographic
exposures possible.
German equatorial (inventor: Fraunhofer)
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Most common type
English mounting
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Horseshoe mounting
Fork mounting
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“Famous” Telescopes
School of Physics, Monash University
90 mm Maksutov
German equatorial mounting
Camera
30 cm Monash Automated Observatory
Schmidt Cassegrain F10 / F6.3
Fork mounting
CCD camera
45 cm Mt Burnett Newtonian F4 / Cassegrain F16
German equatorial mounting
Photoelectric (PMT) photometer & CCD
Australian Observatories
1.3 m "The Great Melbourne Telescope" Mt Stromlo
Newtonian, English equatorial mounting
Destroyed in the fire of 2003
2.3 m Advanced Technology Telescope
F7.85 Cassegrain Alt-Az mounting
Visible & IR imaging & spectroscopy
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3.9 m AAT Siding Spring F3.3 !!! 2 degree field
"Newtonian" Deep sky survey
Can record spectra from 200 stars at once!
International Observatories
8 m Gemini north (Mauna Kea) and south (Chile)
f/1.8 Altazimuth mount
Visible, near- & mid-IR imaging and
spectroscopywith AO
10 m Keck (I and II) Mauna Kea (Hawaii)
f/1.75 Altazimuth mount
270 tonnes of moving telescope!
Reading (browsing) list
http://www.mso.anu.edu.au
http://www.keckobervatory.org
http://www.gemini.edu
http://astro.uchicago.edu
http://www.aao.gov.au
http://www.eso.org
http://en.wikipedia.org/wiki/List_of_largest_optical_re
flecting_telescopes
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ASP2011 Measurement
Techniques
SCHOOL OF PHYSICS
Lecture 7.
TELESCOPES II
Beyond visible astronomy
X-ray/Gamma-ray units
E = h
= 4.13 18 keV
= 12.4/ keV
where 18 = /1018 Hz
where  is in Angstroms Å
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UV
Methods of light gathering and detection for UV
astronomy are similar to those of optical astronomy
BUT
The opacity of the atmosphere at these frequencies
necessitates a largely space-based approach
Example:
The Extreme Ultraviolet Explorer (EUVE); NASA,
1992-2001. All-sky survey in 4 bandpasses with 6x6’
resolution & spectroscopy of white dwarfs etc.
Energy range; 0.016-0.163 keV (760-70 Å)
http://heasarc.gsfc.nasa.gov/docs/euve/euvegof.html
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X-ray & gamma-ray
Non-imaging
Proportional counters
A sealed volume with one or more anode/cathode pairs
at high voltage, and filled to high pressure with a gas
(usually xenon). When an incoming X-ray interacts with
a xenon atom, it ionises the atom, ejecting an electron.
The strong electric field within the detector accelerates
the electron, causing it to knock the outer electron out of
another xenon atom. This cascade results in an electron
cloud which is registered in the detector electronics as a
pulse with amplitude proportional to the incident X-ray
energy.
Advantages: sensitive to high-energy X-rays
(typically up to a few hundred keV);
large area, high timing resolution
Disadvantages:
low-resolution or no imaging;
deadtime; high background
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Examples:
The ROSAT Position-Sensitive Proportional Counter
(PSPC); Germany/US/UK, 1990-1999
Energy range; 0.1-2.5 keV, EUV 62-206 eV
http://heasarc.nasa.gov/docs/rosat/rosat.html
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The Rossi X-ray Timing Explorer (RXTE) Proportional
Counter Array (PCA); NASA, 1995-present
Energy range: 2-250 keV, area ~6500 cm2, timing down
to 1s
http://heasarc.nasa.gov/docs/xte/rxte.html
ASTROSAT (India), proposed launch in 2008; very
similar to RXTE, plus optical monitor
http://www.rri.res.in/astrosat
Solid-state detectors
Scintillators are crystals (e.g. NaI) or organic liquids or
plastics which measure the visible light produced when
the X-rays interact with and are absorbed by the atoms
comprising the detector. The amount of light provides a
measure of how energetic the incoming X-ray was.
Another kind of detector, called a calorimeter, directly
measures the heat produced in the material when an
incoming X-ray is absorbed.
Imaging
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Coded-masks
Spatial (or temporal) “coding” allows simultaneous
measurement of multiple pixels in a field. The detector
records the shadow of a specially-designed mask
produced by the sources in the field of view. A
compromise between a scanning instrument (e.g. a
proportional counter) and a focussing instrument.
Advantages: low cost, moderate spatial resolution
Disadvantages:
inefficient, requires large detector,
thus high background
Examples:
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INTEGRAL (ESA) IBIS & JEM-X; 2002-present
Energy range: IBIS 15 keV – 10 MeV: JEM-X 3-35 keV
Angular resolution: IBIS 12’, JEM-X 1’
http://isdc.unige.ch
IBIS uses an array of scintillation (cadmium telluride or
CdTe) detectors, while JEM-X uses a position-sensitive
proportional counter detector
Grazing-incidence optics
Focussing of X-rays by mirrors or lenses is clearly
impossible; but focussing can be achieved by exploiting
narrow (grazing) incident angle interactions with
suitably-shaped mirror shells.
Advantages: can achieve high resolution (~1”) for
low-energy (<10 keV) X-rays
Disadvantages:
small effective area, requires very
precisely figured optics!
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Examples:
The Chandra X-ray Observatory; NASA, 1999-present
Energy range; 0.5-10 keV
http://chandra.harvard.edu
XMM-Newton; ESA; 1999-present
Energy range: 0.5-10 keV (RGS 0.5-2 keV)
http://xmm.vilspa.esa.es
XMM = X-ray Multi-Mirror; three mirror assemblies for
large surface area; sacrificing precision of the mirrors,
and hence resolution (only about 1’)
VHE Gamma-ray
Gamma-ray observatories use proportional counters and
solid state detectors, with coded-mask imaging, to reach
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up to GeV energies (e.g. INTEGRAL, GLAST etc.). But
ground-based observatories are also exploring the TeV
(1012 eV = 1027 Hz!!) band.
Emission mechanisms in this range are highly uncertain,
but are thought to be related to the production of highenergy cosmic rays, which can reach energies of 1021 eV
(see e.g. Z&G p407). Emitting sources are active galactic
nuclei, pulsars, X—ray binaries, and supernova
remnants.
TeV gamma rays do not reach ground level, but are
sufficiently energetic to produce a cascade of highenergy subatomic particles. These particles are travelling
very close to c, which is faster than the speed of light in
the medium (air). A “shock wave” of visible light, called
Cerenkov radiation, is emitted; this very short-lived
burst of light can be detected by ground-based optical
telescopes, and the direction and energy of the incoming
gamma-ray can be reconstructed.
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Example:
High Energy Stereoscopic System (HESS),
Germany/France/UK etc., array of four ~12m
telescopes in Namibia, f/1.2
Energy range: 0.1-10 TeV
http://www.mpi-hd.mpg.de/hfm/HESS
Neutrino
The number of neutrinos detected from nuclear
reactions within the sun are deficient by a factor of 2-3;
the solar neutrino problem. Solar neutrinos are abundant at
the Earth (1015/s/m2!) but interact very weakly with
matter, so detection is an enormous challenge.
Observatories (beginning with the Homestake mine in
South Dakota; 390 m2 of drycleaning fluid) have sought
to resolve this problem, and today observations seem
consistent with the deficiency arising from neutrino
oscillations.
These efforts also led to the detection of a handful of
neutrinos approximately 3 hr before the visible light of
SN 1987A (in the LMC, closest since SN 1604!) reached
the Earth. The largest detection was 11 events by
Kamiokande II (Japan, water Cerenkov detector).
Current goals include detection of neutrinos from
gamma-ray bursts.
Example:
Antarctic muon and neutrino detector array
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(AMANDA) 1996-; now part of IceCube (under
construction). Water ice Cerenkov detector
http://amanda.uci.edu
http://icecube.wisc.edu
Gravitational wave
Gravitational waves (GW) are a consequence of
Einstein’s general theory of relativity, and are thought to
travel through space at the speed of light (much like EM
radiation). Unlike EM they comprise periodic stretching
and compressing of spacetime itself, and arise from
motions of massive objects.
GW have never been detected, but have been indirectly
confirmed by observations of the Hulse-Taylor pulsar.
Currently several observatories around the world are
attempting to be the first to directly detect GW,
primarily via large laser interferometers
Example:
Laser Interferometer Gravitational Wave Observatory
(LIGO), Caltech/MIT, 2x 4km interferometers in the
US
http://www.ligo.caltech.edu
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Detectors
Quantum Efficiency
Zeilik & Gregory Fig. 9-10
Photographic
Photographic film (or plates) consists of a thin layer
of light sensitive emulsion on a celluloid or glass base.
The emulsion contains film grains that will become
"exposed" after receiving a sufficient number of photons.
After developing, the exposed grains become black and
the areas of the film containing the highest
concentrations of exposed grains become the darkest.
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Films are made with different ISO or ASA ratings
Fast for low light levels > ASA 1000
Slow for daylight
< ASA 100
Usually a film is made fast by increasing the surface
area of the film grains. This increases the likelihood that
a film grain will capture enough photons to become
exposed but it lowers the spatial resolution (and
information storage capacity) of the film.
Advantages of film - High storage capacity, cheap.
Disadvantages - Non-linear intensity response, Low QE
Photomultipier Tubes
A vacuum valve device that multiplies (amplifier)
the charge generated when the photons leaving the
telescope are directed onto a photocathode surface
where electrons are released via the photoelectric effect.
The invention of the photomultiplier tube allowed
astronomers to detect the arrival of individual photons at
the detector (photon counting) for the first time. CCD’s
have made photomultiplier tubes mostly obsolete .
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Advantages - Better QE than film and a linear intensity
response.
Disadvantages - Can't form image, expensive.
Charge coupled devices (CCD)
CCD’s are solid-state electronics devices (Silicon
chip manufactured using integrated circuit technology).
Consist of a large number of small light sensitive regions
called “pixels”.
When a photon is absorbed by a pixel a small
charge is generated and stored just below the pixel
surface. The charge is proportional to the number of
photons that have struck the pixel. The CCD is "read
out" digitally and this can be done very rapidly and
accurately. CCD cameras have revitalised the small
telescope in astronomical research as they have a very
high QE approaching 100%. The 30 cm MAO telescope
has demonstrated an ability to detect stars of 15th
magnitude in CCD images recorded in as little as 60
seconds in Melbourne’s light-polluted skies.
Advantages - Highest available QE, Images are digital
and hence ready for computer post-processing, a very
linear response.
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ASP2011 Measurement
Techniques
Lecture 8.
SCHOOL OF PHYSICS
Statistics and signal-to-noise
Observations almost always include some contribution
from background (aka noise)
Optical/IR: sky brightness, dark/bias current in
CCDs, light pollution etc.
X-ray:
charged particles, diffuse X-ray
Background
Spectroscopy: Continuum photons
As part of our data reduction process, we must account
for the background in our measurement, as well as
treating the resulting uncertainty appropriately.
If the number of expected counts from our source
(emission line) in a given time interval ∆t is S, and the
number of expected background counts in the same time
interval is B, our detector will measure in ∆t ON
AVERAGE S+B counts
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We want to know
i) what is the most probable value of S
ii) in what range are we likely to find the “true”
value of S (i.e. what is the uncertainty)
Counting statistics
The Poisson distribution gives the probability Px of
detecting a particular number of events x within a time
interval, given an expected rate m:
m x em
Px 
x!
where x! = x(x-1)(x-2)…2*1

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Note that this distribution is NOT symmetric about m
(except for very large values). The probability of
detecting precisely the mean rate m (even if it is an
integer) is rather low! The standard deviation of multiple
measurements xi is (for large m) just m1/2.
For large m, the Poisson distribution approaches the
normal (Gaussian) distribution
 (x  m) 2 
1
Px 
exp

2
 2
 2 
the conventional “bell curve” of probability

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Thus if we expect S+B counts in a measurement, the
standard deviation (uncertainty) is just (S+B)1/2.
Similarly, the uncertainty in the background counts is
B1/2.
Given these uncertainties, what is the uncertainty on S?
It can be shown that in adding and subtracting variables
x and y, each distributed normally with standard
deviations x & y, the variance (square of the standard
deviation) of the sum or difference of x is just the sum of
the variances
 x2y   x2   y2
So that the uncertainty on S is just
B  (S  B)  S  2B

We refer to the ratio of the source counts to uncertainty
S / S  S / S  2B

as the significance or the signal-to-noise (S/N) ratio

Example: the estimated count rate for an X-ray source
observed with Chandra is 0.1 count/s; the equivalent
background rate is 0.05 count/s. What is the signal-tonoise in a 1000 s observation?
How long would you need to observe to achieve a S/N
ratio of 10?
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Reddening
Light from distant stars is affected by scattering within
clouds of dust between the star and Earth. Bluer photons
are scattered preferentially, so the residual light that
reaches us is redder than when it was emitted by the
star. This effect is referred to as interstellar reddening or
interstellar extinction
Bradt, “Astronomy Methods”
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This effect is an important consideration for optical (and
even low-energy X-ray) observations, and (e.g.) limits
the range of visibility within the plane of the Milky Way
galaxy to only about 5000 ly (the Galaxy is ~105 ly in
diameter). Much less extinction is experienced for
directions out of the plane.
The extinction AV is the number of magnitudes by which
the light in the visible (V) band is dimmed by the
intervening dust:
AV = mV – mV,0
Where mV is the apparent magnitude of the star at
Earth, and mV,0 is the apparent magnitude that would be
measured IF there were no reddening. (Recall how this
is related to the absolute magnitude).
Example: In the Galactic plane the extinction is about
0.6 mag for every 1000 ly of distance (although this is
quite variable, depending upon the precise direction).
What fraction of intensity is lost in V-band for every
1000 ly of distance?
AV = mV – mV,0 = 2.5 log10 (l0/l) = 0.6
Since the scattering depends upon the wavelength of
light, it follows that AV  AB  AR …
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Bradt, “Astronomy Methods”
A consequence of this is that for a star of known
(intrinsic) colour (e.g. an A0 star, with B-V = 0) we
measure a colour excess because the reddening in B is
larger than the reddening in V. E.g.
AB = 1.324 AV
(Rieke & Lebofsky, ApJ 288: 618, 1985)
So that for the above example, for an A0 star at 1000 pc,
the colour will not be B-V = 0 but…
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Adaptive optics
A system to improve the resolution of Earth based
telescopes by mathematical removal of the atmospheric
blurring. A laser beam is used to generate a fluorescent
spot in the mesosphere and thus create an artificial star,
which is then observed with the telescope and analysed
by computer to determine how the telescope’s “figure”
should be altered (in real time) to correct for the
turbulence in the atmosphere.
The correction to the telescope’s figure is achieved with
a thin, flexible mirror in the telescope’s optical path that
changes shape about 1000 per second. Computer
driven piezoelectric actuators located on the back of the
adaptive mirror alter the mirror’s figure. Typically the
mirror surface moves by only a few tens of nanometers.
Reading list
http://cfao.ucolick.org/
http://www.ucsc.edu/news_events/press/photos/imag
es/distant_galaxies/Fig1.jpg
http://www.ifa.hawaii.edu/ao/
http://www.eso.org/outreach/press-rel/pr2005/images/phot-03-05-normal.jpg
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Bradt, “Astronomy methods”
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Timing
Many phenomena in astronomy are periodic, that is
they repeat on a regular timescale. Frequently we are in
the position of trying to determine, is a particular
phenomenon actually periodic? If so, what is the period?
This can be difficult to answer if the phenomenon is low
amplitude, the sampling is uneven, or the period varies
significantly.
For evenly-sampled data, the Fourier Transform allows
us to test for an excess of power at particular periods
(frequencies)
Example: the
first detection of
millisecond
oscillations in an
accreting
neutron star, 4U
1728-34
(Strohmayer et al.
ApJ 469, L9 1996)
This neutron
star is spinning
363 times every
second!
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For noisy astrophysical signals, the Fourier power
spectrum has some characteristic variation in the
absence of a signal. The usual approach is to identify a
significance (power) threshold such that it is exceedingly
unlikely that the Fourier power could exceed this value
from noise alone.
An important factor here is the number of trials. By
measuring the power spectrum within a range of
frequencies, we effectively make n trials, where n is the
number of (independent) frequency bins. Even though a
particular power threshold may be unlikely to be
exceeded by noise alone, it may be reached if we make
sufficiently large number of trials!
The situation for unevenly-spaced data (e.g. photometric
observations spanning more than one night, or in which
some portion of the night was clouded out) is more
difficult. We can use the Lomb-Scargle Periodogram, a
generalisation of the Fourier Transform, and set our
significance thresholds accordingly. There are a number
of other techniques commonly used.
Once the signal is detected, we need to precisely
determine the period (and its uncertainty). Typically the
statistics are too complex to treat analytically and we
must do simulations.
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In-situ Measurement Techniques in Space
Cassini-Huygens
http://saturn.jpl.nasa.gov/home
http://www.esa.int/SPECIALS/Cassini-Huygens
Full range of optical, IR and UV imagers and
spectrographs; plasma spectrometer; cosmic dust
analyser; mass spectrometer; magnetometer and
magnetospheric imaging instrument; and radar
Huygens “lander”: atmospheric structure instrument,
measuring the electrical properties of Titan’s
atmosphere; Doppler winde experiment to measure
wind speed; imager/spectrometer; GCMS; aerosol
collector and pyrolyser; and surface science probe to
measure the physical properties of the surface.
Mars Exploration Rovers
http://marsrovers.nasa.gov/technology/si_in_situ_instr
umentation.html
Miniature Thermal Emission Spectrometer (Mini-TES)
Remote investigation of mineralogy of rocks and soils.
Near infrared region of the spectrum.
Mineralogical information that Mini-TES returns is used
to select from a distance the rocks and soils that will be
investigated in more detail.
Can also provide temperature profiles through the
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Martian atmosphere.
Mössbauer Spectrometer
Placed directly on the target sample the spectrometer
illuminates rock surfaces with gamma particles emitted
by cobalt-57.
Detailed mineralogy of different kinds of iron-bearing
rocks and soils.
Microscopic Imager
Voyager I & II
http://voyager.jpl.nasa.gov
Launched in 1977, these RTG-powered instruments are
still operating and still returning useful science data!
Voyager 1 is now at the outer edge of our solar system,
at 100 AU (as of August 2006), in an area called the
heliosheath, the zone where the sun's influence wanes.
This region is the outer layer of the 'bubble' surrounding
the sun, and no one knows how big this bubble actually
is.
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Redundant material
Spitzer Space Telescope
http://www.spitzer.caltech.edu/technology/index.shtml
Infrared Array Camera (IRAC)
Imaging near- and mid-infrared wavelengths. (3.6, 4.5, 5.8,
and 8 m).
Infrared Spectrograph (IRS)
Spectroscopy at mid-infrared (5.3-40 microns) - the
fingerprint region of atoms and molecules.
Multiband Imaging Photometer for Spitzer (MIPS)
Imaging and limited spectroscopic data at far-infrared
wavelengths.
Chandra X-Ray Observatory
http://chandra.harvard.edu/about/science_instruments.html
Chandra Advanced CCD Imaging Spectrometer (ACIS)
X-ray images and measure the energy of each incoming Xray.
Makes pictures of objects using only X-rays produced by a
single chemical element such as a supernova remnant in
light emitted by oxygen ions, neon ions or iron ions.
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E=E0 cos  
Law of Malus



I  E2
I=I0 cos2 
Light emitted by "normal" stars is unpolarised.
Starlight may become polarised by interacting with
interstellar matter and magnetic fields.
Example 1. A photon may be absorbed by an interstellar
dust particle (molecule) and then re-emitted with a
polarisation characteristic of the particle's alignment and
elongation. Hence, the degree and direction of
polarisation can reveal information about :a) the size and density of the dust grains.
b) the orientation of the galactic magnetic field
responsible for the alignment of the grains.
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Example 2. In the Crab Nebula, high energy electrons
emit em radiation as a consequence of their acceleration
in a strong magnetic field. The direction of the electric
field vector E is perpendicular to the direction of the
nebular's magnetic field.
Fig. 3.20
E. Hecht "Optics" 2nd Ed. Addison-Wesley
True and Apparent field
Lens maker's equation
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f=
n=
R1 and R2 =
Some common approximations (exact for n = 1.5)
Double convex
if R1 = R2 then f = R
Plano convex f = 2R
Sign convention for lenses
Thin lens equation
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Graphical Ray Tracing
Required modifications for negative optical elements are
given in brackets
Lens
A ray passing through the
centre of the lens is not
deviated
Mirror
Rule 1
A ray passing through the
centre of curvature is
reflected back over the
same path
Rule 2 An on axis ray will (appear An on axis ray will (appear
to) pass through the
to have) pass(ed) through
far/(near) focal point
the focal point
Rule 3 A ray through the
A ray through the focal
near/(far) focal point will point will be reflected on
be refracted on axis
axis
The intersection of any 2 of the 3 rays will locate the image
Photographic image brightness (extended source)
Most astronomical photography is performed with the
film (or CCD) located at the real image at the prime
focus. Here the size of the image is directly proportional
to the focal length.
 D
1



or
Prime focus image intensity  f 2  F 2


since F = f / D.
Example. What is the ratio of the intensities of an image
of an extended object on the film of a) a SLR camera
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with 50 mm lens at F stop F2 to b) the Mt Palomar 5 m
telescope with a focal length of 1650 cm ?
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Resolution of telescopes
 The ability of a telescope to separate objects.
 Ideally, resolution is “diffraction limited”.
Airy (Astronomer Royal mid 1800's) first to derive the
solution for diffraction pattern produced by a circular
aperture.
min = 1.22 / D in Radians
Rayleigh’s Resolution criterion
Two star images are just resolved if the central
maximum of one falls on the first minimum of the other.
Dawes Resolution criterion


 min 
11.6
D 
in arc seconds for D in cm.
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