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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