Download Telescopes—

Telescopes—
What will we learn?
„ Considerations for building telescopes for general and specific
purposes
„ Types of telescopes in common use for optical/infrared work
„ Some telescopes used for radio or x-ray work
What do we want a telescope to do?
1. Collect a lot of photons
2. Not lose any photons
3. Not add any background or noise
4. Treat all wavelengths with respect
5. Have a nice large magnification
6. Make the sharpest possible images
7. Cover a large area of sky
8. Point accurately
9. Not distort images
10.
Have a stable/calibratable throughput as a function of time,
temperature, position on the sky
11.
Not cost too much money
12.
Be easy to maintain and operate
As usual in engineering projects, any particular telescope is a
compromise between these goals, with #11 (cost) playing an important
role. Because some of the goals compete with one another, it is wise
to design different telescopes for different purposes, which include for
instance
1.
2.
3.
4.
5.
6.
7.
Wide field imaging
Wide field spectroscopy
Faint object spectroscopy
Astrometry
Bright object (e.g. solar) imaging
Polarimetry
…
One of the most common sets of trade-offs concern mirror-size, focal
length and field of view.
Just to show that what we learned a few weeks ago is stil useful, let’s start
the discussion with the wave-optics discussion of how a lens/mirror
works:
E (p ) ≅
ik
ikr
2
∫ E (x )e d x
r
kr = f + (x − p ) = kf 1 +
2
2
(x − p )2
f
2
≅ kf
+ k (x 2 − 2xp + p ) / 2f
2
− k (x 4 − 4 x 3 p + 6 x 2 p − 4x p + x 4) / 8f 3 + ...
2
3
Where (remember) x is the position in the aperture or pupil plane and p is
the position in the image plane. If I have a source, a long way away, at an
angle of θ , not too large, from the optical axis then the electric field from
/ 2 term with
this source E (x ) ∝ exp(ikxθ ) . If I cancel the
a lens, as I did a couple weeks ago, and ignore for now the higher order
kx2 f
terms, the integral looks like
exp(ik p / 2f ) , which I can ignore if I
2
only measure the power, and a Fourier Transform of E(x) with respect to a
variable kxp/f . For the point source this would yield a delta function
response at position p = fθ for an infintely large aperture, or an Airy
type function for a finite round aperture. We know that the angular size of
this diffraction pattern gets smaller as the aperture gets larger. I will
discuss the properties of Fourier Transforms in a lot of detail, probably
next week.
So we know that the magnification of the telescope is linearly proportional
to the focal length. The argues for large focal lengths, except when we
have to worry about noise from detector pixels.
Why did I write all the other terms above? Because if the aperture size
(maximum of x) gets large, or the field of view (max(p)/f in angular units)
we no longer get this clean Fourier transform. Effects arising from from
these ignored terms are called aberrations, and they lead to images that
are not sharp.
Various of the aberrations have historical names, that are worth knowing.
Consider the terms containing only x, the position in the aperture. These
can be corrected by using a lens that has a different form than the one I
assumed. In old-fashioned terms, the most important of these is spherical
aberration which arises when a spherical mirror is used. This type of
aberration can be corrected by using a more complicated mirror form. In
the old days such aspheric mirrors were very difficult to fabricate, but
with modern computer measurements of mirror form, this is not such a big
deal.
Terms that contain only p are no problem, no matter what the exponent,
because they don’t influence the integral, only the phase of the result.
The nastiest terms are those containing both x and p. These first show up
when you start considering the k(x-p)^4/f^3 term in the phase integral;
These are then called 4th order aberrations—the 2nd order aberrations
were corrected by putting in the lens. There are 6th order aberrations etc.
but by the time you get past 4th order there isn’t so much point in consider
the separate terms of the expansion. It is instructive to look at a couple of
the 4th order terms. The xp^3 term, for instance, still represents a term
which is linear in x, so that it doesn’t really alter the nature of the Fourier
Transform, but it changes the independent variable that measures angular
separation from p/f to p/f – (p/f)^3/2. So the result is a distortion in the
image plane. This is annoying but not terribly serious (except for
astronometry). The x^2p^2 term can be considered as a change of focal
length with respect to position. This can be fixed by introducing a curved
focal plane (not easy). The asymmetric x^3p term represents coma, a
progressive blurring of the image as you move away from the field center.
This is not easy to correct. If you add the 2nd dimension to the problem you
get a couple of new terms with xyp^2 etc, which introduce astigmatic
aberrations to the image.
Just to complete the series of classical aberrations, I should include
chromatic aberration. This does not usually occur in mirrors, but does in
transmitting lenses, where the delay in phase passing through the lens
varies with the wavelength of light. The result is that images in different
colors have different focal lengths, and are difficult to focus at the same
time. This is one of the reasons that reflective telescopes are more
popular than refractive telescopes.
So how can we deal with these aberrations in order to get sharp images?
1. Use aspheric mirrors (a little bit expensive)
2. Use long telescopes because most terms have 1/f type dependence.
This used to be (still is) a common solution but long telescopes are
expensive, have limited field of view, and require big detectors.
3. Add more curved reflecting surfaces. If you add lenses or figured
mirrors intermediate between the original pupil and the image you
can design them to eliminate some of the nasty phase terms. This
tends to be expensive, but has some side advantages in making the
telescope more compact. This is the most common current
approach to large optical telescopes that desire a reasonably large
field of view, i.e. the Ritchey-Chrétien telescope with a hyperbolic
primary and hyperbolic secondary.
Types and classifications of telescopes:
Telescopes can be classified in different ways, relevant to the engineering
choices that have been made and to the applications. For example:
Reflective versus Refractive
The earliest telescopes were refractive before the technique for silvering
of glass mirrors was invented. Refractive/lens telescopes have many
disadvantages. Very large lenses are difficult to make without internal
defects, and are difficult to support without blocking light (“vignetting”).
Medium size lenses show chromatic aberration unless very carefully made
with multiple surfaces. So most large telescopes are reflective. However
lens systems tend to be compact and are used for small telescopes, e.g.
binolulars, and as the last focus system in compact instruments.
Type of mechanical mounting/dimensionality
1. Zenith telescope—points up, e.g. mercury mirror telescopes. Very
limited field of view, but cheap to build, no moving parts.
Sometimes used for special calibration purposes. In a sense also
used for extremely large radio telescopes e.g. the Arecibo 305
meter telescope. Also used for extremely small radio telescopes,
e.g. the single element telescopes of LOFAR that are so small with r
espect to wavelength that they are essentially omnidirectional
.
.
2. Meridian—points only at one azimuth (usually the prime meridian),
and moves in altitude (declination) only. Has the great advantage
that you only need to build one movable axis. It used to be very
common for fundamental astronomy i.e. measuring positions of
stars and time. Then altitude->declination and meridian passage
time-> right ascension. Also occasionally used for very large (100
meters) radio telescopes, e.g. NRAO 300 foot (R.I.P.).
3. Telescope with two axes that can point (almost) anywhere on the
sky. The oldest of these (excluding hand-held telescopes) are
altitude-azimuth telescopes that are relatively easy to build because
of the symmetry of the bearings. Old hand long focal length, hand
steered telescopes were usually of this type.
There are two major disadvantages of alt-az telescopes that
supressed their usage during the early phases of tracking telescopes,
i.e. those with the convenient feature of following sources on the sky:
You need to steer two axes independently of each other.
The Image rotates as the object moves across the sky.
These are not considered major problems today because of the
development of computer controlled pointing systems and image rotating
systems. Before this time, however, when mechanical systems were
used, these problems led to the precedence of:
Equitorial Mounts
Location of focal plane/number of reflections:
It is common to add a number of reflecting mirrors, some of them flat, in
order to move the focus to the most convenient place. Each of these
configurations has it’s own name, and ad- +dis- advantages. There are
pictures in Bernard Brandl’s site, so I won’t include them here.
Some of the most important are:
• Prime-- The earliest choice, particularly for refractors. For
reflectors this has the major disadvantage that the – usually
heavy—observer and instrument have to be at the top end of the
telescope, which may be difficult to support. Nowdays the
observer is seldom near the focal plane, but this was not the
case for the 200” telescope. Prime focus is often used for wide
angle imaging, but suffers from aberrations. Prime focus is also
used in many radio telescopes because they only have one pixel
so most aberrations are ignorable.
• Cassegrain—Formally this is for telescopes with a flat secondary
and the instrument behind the primary, but the same name is
used for Ritchey-Chretien telescopes. This is probably the most
popular setup for general purpose, large telescopes. It has the
advantage of compactness, weight at the bottom, and relatively
few reflections, so not much loss of light. Disadvantage (shared
with Prime) is that it moves around a lot during observations, so
that it tends to deform with changing gravity forces (called
flexure and it is difficult to run cables, pipes… to instruments. A
lot of radio telescope use Cassegrain instead of Prima because
of the ease of mounting instruments and because the stray
radiation reaching the instruments comes mostly from the –
cold—sky instead of the –warm—earth.
• Nasmyth—Add another flat mirror to bring the light out of the
altitude axis (of an alt-az telescope). Now you have a flat, nontipping area to put your instrument, so flexure is less of a
problem. It still moves around in circles, so there are problems
with power, cooling, vibration, etc.
• Coude- Add more mirrors to get the signal a long way from the
telescope. This allows the construction of big, heavy
instruments requiring lots of connections, but has a long focal
length (good/bad) and lots of reflections.
Types of mirrors
•
•
•
•
Massive glass—used up to 5m (200 inch) telescopes until late 20th
century. Advantages: straightforward, mirror itself is reponsible for
accuracy of surface. Straightforward to polish and mount.
Disadvantages: very time consuming and difficult to cast. Very
heavy and difficult to support. Long thermal time constant and
sensitive to external temperature changes.
Segmented thick mirrors—New Technology Telescope (ESO), Keck
Telescopes. Advantages: small (1-2 meter) mirrors are relatively
easy to cast and mount. Can use active optics to align and control
individual segments. Disadvantages: Different segments have
different shapes. Difficult to polish edges of segments. Difficult to
align segments.
Thin mirrors—VLT Make the mirror very thin, too thin to support
itself, and support it with an active (motor driven) support structure.
Thinness makesit easy to cast and light and thermally quick.
Requires complicate active support to keep its shape.
Adaptive (Rubber) Mirrors (AO=Adaptive Optics). Extremely thin
and flexible mirror that is driven at kiloHz rates to follow
atmospheric oscillations. Not used for primary mirrors because too
difficult.
Mirror materials
•
•
•
•
•
•
First useful material was “speculum” a type of bronze about 2/3
copper and 1/3 tin with a little arsenic or antimony. Hard and
brittle,has a tendency to crack. Low reflectivity (30% absorption)
tarnishes quickly.
“Standard Glass” (silica+Na2O+CaO) is easy to polish and can be
covered with reflective metal coating. Chief problems are low
thermal conductivity (takes a long time to equilibrate to changing
surroundings) and moderate coefficient of thermal expansion:
1x10^-5 per degree (metals ~2 times higher)
“Pyrex” borosilicate glass: (Boron Oxide+Na2O..)coefficient 3x10^-6
Fused silica: 0.5x10^-6 but much higher melting point and difficult to
work with.
CerVit/ZeroDur Partily crystalline glasses. Near zero expansion
coefficient-2x10-8
Silicon Carbide—low coeff. Very hard and light, but very difficult to
fabricate
Coating materials
•
•
•
Vacuum or chemically deposited silver—good reflectivity (>90%)
especially in near infrared, corrodes quickly, may need to be coated
with SiO or other protections.
Vacuum deposited aluminum—better in visual
Gold—better in mid IR