The size of the pinhole defines the sharpness and the brightness of the image.

Transcription

1 Chapter 4 Optical telescopes 4.1 Components of a telescopes Pin hole camera and image scale. In a pin hole camera an image is formed always, independently of the object distance z 1 and the screen distance z 2. The size of the image S 2 with respect to the object size S 1 is given by simple geometry: S 2 = z 2. (4.1) S 1 z 1 The size of the pinhole defines the sharpness and the brightness of the image. small pinhole: sharp but faint image (maximum sharpness limited by diffraction) large pinhole: bright but blurred image A sharp and bright image is obtained if the pinhole is replaced with a lens with a much larger aperture - this is the principle of a telescope. Image scale. The distance between pinhole and image screen z 2 defines the image scale. The image scale relates the angular size of an object θ to its geometric size S 2 in the image plane, for example as arcsec/mm or mm/arcsec. Simple geometry gives for a small field of view (small θ): θ tanθ = S 2 z 2. (4.2) and the relation between focal length f and plate scale (e.g. mm/arcsec) f[mm] = z 2 = S 2 θ = [arcsec] π S 2 [mm] θ[arcsec]. (4.3) The proportionality factor is /π = This relation holds for telescopes and other imaging systems if f is the effective focal length. 43

2 44 CHAPTER 4. OPTICAL TELESCOPES Mirror and Lenses Mirrors. The incident and reflected rays and the surface normal z lie in the same plane. The incident and reflected rays have equal angles with respect to z: θ r = θ i Not all light is reflected from a mirror surface. For example an aluminum mirror reflects in the optical only about 90 % of the light. Reflectivity of mirrors can depend strongly on wavelength. For example, gold mirrors are very good for the red and near-ir spectral range but they do not reflect blue light. Concave mirrors. Concave (converging) mirrors can form images at a point z 2 for objects located at a distance z 1. If z 1 and z 2 are located in the focal points of an ellipsoidal mirror then the two points are perfectly imaged. The focal ratio or F-number F of the mirror (or a lens) is given by the focal length f and the aperture diameter D: F = f D. (4.4) Spherical mirrors and spherical approximation. Spherical mirrors are special cases of the elliptical mirror where z 1 = z 2. Spherical mirrors can often be used as simple first approximation for an optical system if only rays close to the optical axis are considered (paraxial approximation). Paraboidal mirrors. This is a special case of an elliptical mirror where the object is located at infinity z 1 =. This shape has obviously some advantages for astronomical telescopes. Lenses. Refraction occurs for non-normal incidence at the boundary between two media with different refractory index n 1 n 2. Lenses use the refraction by a curved surface to focus light rays. Lens types: Light incident on a convex interface (n 1 < n 2 ) will intersect the optical axis and this interface acts like a lens. The location of the intersection point depends on wavelength due to the colour dependence of the refraction. Lenses can have different shapes depending on whether they are focusing or converging lenses or positive lenses (e.g. biconvex, plano-convex) or diverging or negative lenses (e.g. biconcave, plano-concave).

3 4.1. COMPONENTS OF A TELESCOPES 45 lens types: Lenses are characterized by the following quantities: diameter, focal length, detailed geometric shape: front and back focal length (distance from surfaces to the focal points), radii of curvature (first and last surface), center thickness, edge thickness Diffraction and telescope resolution Fresnel diffraction. The secondary wavelets from an aperture produce a diffraction pattern. Consider a parallel beam passing through a circular aperture where the wavefronts are in phase. A screen located a distance z behind the aperture will show a round illumination. In addition there will be an interference effect which may cause in the center C of the illuminated disk a bright or dark spot. The spot brightness is defined by the size of the aperture, in particular by the number of concentric circles in the aperture adding a positive or negative contribution depending on their distance z n to the central spot. The contribution is positive z n = z +n λ 2 n = 2,4,6,...

4 46 CHAPTER 4. OPTICAL TELESCOPES and negative for z n = z +n λ n = 1,3,5,... 2 The radii of these circles in the aperture are given by: r n = zn 2 z2 = 2 z nλ 2 +(nλ 2 )2 z nλ For λ z the area of each zone is πzλ. If the distance z of the aperture from the screen is such that the aperture produces an even number of zones then the cancellation of zones is nearly perfect and the central spot is dark. For an odd number of zones it is a bright spot (brighter than the straight through light). The same applies for a slit but instead of concentric circles bright or dark lines are formed. Frauenhofer diffraction. Frauenhofer diffraction applies for imaging systems using lenses and/or mirrors. We consider only a simple lens system. All secondary wavelets from the aperture are in phase at the focus C. For off-axis points the light from the opposite edges of the aperture travel different lengths so that alternating dark and bright rings are produced. The angular displacement from the axis is given roughly by sinθ θ = n λ/d for the bright rings and θ sinθ = (n 1/2) λ/d (n = 1,2,3...) for the dark rings. For a perfect lens about 84 % of the light is in the central maximum, and the peak flux in the center is 60 times higher than in the first ring. The width of the bright central spot or the diffraction limited resolution of the telescope is θ[rad] = λ D or θ[arcsec] = λ D. (4.5) The diffraction limit of some typical telescopes are: telescope λ D θ [arcsec] 8 inch (20 cm) visual 500 nm 20 cm m VLT visual 500 nm 8.0 m m VLT mid-ir 10 µm 8.0 m 0.26 Herschel IR-satellite 100 µm 3.0 m 6.9 Effelsberg radio telescope 20 cm 100 m Spectral dispersion The separation of a light beam into different colors, as function of of increasing or decreasing wavelength, is called dispersion. It results a spectrum of images of the aperture for every wavelength. Dispersive elements are for example diffraction gratings and prisms.

5 4.1. COMPONENTS OF A TELESCOPES 47 Diffraction grating. A diffraction grating consists of a large number of very fine, equally spaced parallel and periodic slits separated by a. The wavelets from each slit are strongly enhanced in a few directions θ n in which all the wavelets are in phase. θ 1 is the first order with a path difference of λ etc. For wavelength λ the angular displacement θ n is sinθ n = n λ a Because θ n depends on λ the light is dispersed and spectra are formed. The same effect is obtained for a reflection grating which has fine periodic rulings. Prisms. Prisms disperse light because the refractive index of glass varies with wavelength, n = n(λ). The dispersion of glass is usually expressed as n = n(486.1) n(656.3) = n f n c, where λ = nm and λ = nm are the wavelengths for the hydrogen lines Hα and Hβ. Examples: hard crown: n f = , n c = 1.515, n = , dense flint: n f = 1.635, n c = , n = Prisms usually give brighter spectra than diffraction gratings, while gratings spread the light into several orders. Gratings produce a nearly linear wavelength scale on the spectrogram. Grism spread well the short wavelengths but the dispersion decreases with wavelength Aberrations introduced by focussing optical components This paragraph discusses some important cases of optical aberrations. Chromatic aberrations. A simple lens produces chromatic aberrations in broad-band applications because longer wavelengths (e.g. red) are refracted less than short wavelengths (e.g. blue). Thus the focal length of a simple lens is colour dependent and the images of stars in an uncorrected astronomical refractor show a coloured limb or halo. The chromatic aberrations of lenses can be strongly reduced with a lens system composed of 2 or more components with different shapes and made from material with different refractive indices. Tilted glass plates in a converging or diverging beam also produce chromatic aberration. In this case the different colours are displaced in lateral direction. Reflecting optical systems (mirror telescopes) do not suffer from chromatic effects since reflections are colour independent.

6 48 CHAPTER 4. OPTICAL TELESCOPES. Spherical aberrations. This effect describes systems in which the peripheral rays are focussed closer or further away than the paraxial rays. It results in an image that is blurred along the optical axis. Spheres are only near the optical axis good approximations to paraboloidal mirrors and therefore all spherical mirrors (especially those with small F-ratio) produce spherical aberrations. An infamous example of spherical aberrations is the main mirror of the Hubble Space Telescope which was figured wrong due to an error in the optical test equipment. Adding correcting optics fortunately solved the problem for the HST. Coma. Coma is a radial displacement of the focal point for rays from different beam sections which produce radially elongated cone like image points. Centering errors within an optical system can produce coma. But also perfectly aligned simple optical systems produce a coma error for image points away from the optical axis in the outer regions of the field of view. We consider the image of an off-axis point formed by a paraboloidal mirror. The oblique rays reflected from the center or the periphery of the mirror will form focal points at different lateral places, but also at different z-distances (focal length) from the mirror, because these rays see a tilted paraboloidal mirror. The sum of all these displaced points then forms the typical coma shape. The coma aberration is a critical aberration in many reflecting systems. Oblique astigmatism. This is like coma another effect for off-axis points. The focus from the refraction or reflection of an off-axis point forms a line like for a lens with a cylindrical error. Further the focus line for a given plane of rays may be at a different distance on the optical axis when compared to a plane of rays oriented perpendicularly. Typically, oblique astigmatism is a less important effect than coma in telescope systems.

7 4.2. TELESCOPE TYPES Telescope types General principles. We first consider the astronomical refractor to explain the basic layout of telescopes. The astronomical refractor consists of: a converging (convex) objective lens or aperture lens, an intermediate focus with eventually a field stop, a collimating lens (often a converging eyepiece lens), a parallel beam section with an intermediate pupil, a converging lens (camera lens). The following quantities are used to describe a telescope: f 1 : focal length of objective lens L 1, f 2 : focal length of the collimating lens L 2 (or the eyepiece), f 3 : focal length of the camera lens L 3, y 1 : or D, the diameter of the entrance pupil or aperture, y 2 : diameter of the intermediate pupil, α: semi-angle of the field of view in the entrance pupil, θ: semi-angle of the field of view in the exit pupil. Some basic principles are: An image of the object is formed in the focal planes. The image plate scale is defined by the effective focal lengths f given by the F-ratio of the image forming lens L 1 or L 3 and the diameter of the entrance pupil D: f = F x D. (4.6) In a pupil plane the light from a distant object forms parallel rays. The information is in the angular direction of the rays. In the case of the astronomical refractor the collimating eyepiece refracts the light into a more or less parallel beam suited for observation with the eye. The magnifying power m (angular magnification) of the telescope is: m = f 1 = tanθ f 2 tanα = y 1. (4.7) y 2 The collimated beam section between L 2 and L 3 is the typical location for diffraction gratings or prisms for spectroscopy. The field stop in the first focal plane can be used for field selection (e.g. a spectrograph aperture) or for a coronagraphic mask. Well designed pupil and field stops can be very helpful in reducing the stray light and background of a system.

8 50 CHAPTER 4. OPTICAL TELESCOPES Newton telescope The Newton telescope consists of: paraboloidal primary mirror, inclined (45 ) flat mirror which deflects the beam, focal plane at the top of the telescope to the side. The main advantage of the Newton telescope is its simplicity. It is a convenient type for small telescopes < 1 m. For large telescopes the focus is at an inconvenient place and it is difficult to build fast telescopes with F-ratio < 4, because then the deflecting mirror must be large or the focus is in front of the primary mirror. Prime focus telescope. Instead of deflecting the beam to the side like in a Newton telescope one can also locate a detector directly in the focus of the primary mirror of a Newton or another telescope. Of course the focal plane instrument must be small with respect to the primary mirror diameter in order to avoid strong obstruction of the incoming light Cassegrain telescope. The Cassegrain telescope and its variants are very popular telescopes which consist of: paraboidal primary mirror with a central hole, convex, hyperboloidal mirror located in front of the primary focus, telescope focus behind (near) the hole of the primary mirror. The plate scale for the primary image can be changed with an exchange of the secondary mirror which can have different F-ratios. This was often made possible for the 3 5 m class telescopes in order to allow various types of applications. Ritchey-Chrétien telescope. This is an improved variation of the Cassegrain design providing a better image quality. With a combination of hyperboloidal concave primary mirror with spherical aberrations and a special shaped convex secondary mirror (which departs from hyperboloidal), both the spherical aberration and the coma can be minimized.

9 4.2. TELESCOPE TYPES 51 This is even possible for a short telescope. The shaping of the primary and secondary mirrors is more difficult but possible. The VLT is based on this design. Nasmyth telescope. A Nasmyth configuration is often combined with a Cassegraintype telescope. In the Nasmyth design the beam is deflected with a folding flat to the side. For telescopes with an alt-azimuth mounting the beam can be deflected conveniently through the altitude axis to an instrument platform on the side Schmidt telescope. Thisisaprimaryfocustelescopeusingacorrectingentrance lensat thetopof thetelescope tube. Due to the correcting lens the field dependent aberrations are strongly reduced. For this reason the Schmidt telescopes provide a large field of view which is ideal for sky surveys. Schmidt-Cassegrain telescope. This is a combination of the compact Cassegrain telescope with the conveniently located focus behind the primary mirror with a correcting lens as used for the wide-field Schmidt telescope. The correcting lens is used at the same time as holding device for the secondary mirror so that no secondary mirror spider structure is needed. The Schmidt-Cassegrain type telescope is a very popular telescope among amateur astronomers, because it provides a large field of view, is compact in size, and the optics is well protected from dirt due to the correcting lens in front of the telescope tube Other types Gregory telescopes. This telescope consists of: paraboloidal primary mirror with a central hole, concave, ellipsoidal secondary mirror located, after the primary focus focal plane behind (near) the hole in the primary mirror. The Gregory telescope is used for special applications. An advantage is the primary focus in front of the secondary mirror. The focus can be used as location for calibration components which is a significant advantage if the secondary is used as active or adaptive mirror. On the other hand the ellipsoidal secondary is difficult to manufacture and the telescope is relatively long. Coudé telescope. Many telescopes have a Coudé focus with a large F-ratio. In this case the beam is deflected through the telescope rotation axes to a stable focal station in a laboratory where large instruments can be installed. Examples for such instruments are high resolution spectrographs or interferometric laboratories in connection with adjacent telescopes (VLT interferometer or Keck interferometer). Off-axis telescopes. An off-axis telescope uses an off-axis primary mirror and a secondary which is not located in the beam. This has the advantage that the diffraction effects caused by the secondary and its support structure are avoided. On the other hand it is more difficult to make off-axis concave, primary mirrors when compared to symmetric mirrors. Image errors (e.g. coma and astigmatism) are more problematic for off axis mirrors when compared to symmetric mirrors of the same size.

10 52 CHAPTER 4. OPTICAL TELESCOPES 4.3 Mechanical concepts for telescopes The functions of the telescope mounting are simple in principle: hold the optical components in their correct mutual, alignment direct the optical axis towards the target. The problem is that the requirements for alignment and pointing are very demanding for astronomical applications. Therefore the mounting is a major cost item of large telescopes. Typically a telescope mounting has two axes of rotation. Alignment. Keeping the optics aligned is relatively easy for small telescopes because a rigid tube can be build. For large telescopes mechanical flexures become inevitable, and the structure must be designed so that the flexures for the mechanical alignment of the primary and secondary mirrors are identical. Flexures cause also significant deformation of the primary mirror shape for large telescopes D > 3 5 m. This can be solved with an actively supported primary mirror (e.g. ESO NTT and VLT or the Keck Telescopes) or a deformable secondary mirror (MMT, LBT). Pointing. Directing the telescope towards the target requires: pointing toward a new target for acquisition with a precision that allows to see the target within the field of view (typically a precision of an arcmin for large telescopes), center a target in the field to a predefined position in the focal plane with a precision of better than 1 arcsec (e.g. the width of an spectrograph slit), tracking the motion of the target on the sky with a precision of better than 1 arcsec during long integrations (up to an hour). This requires active guiding. Atmospheric refraction. If pointing with a precision of about 1 arcmin and tracking with a precision of about 1 arcsec should be achieved then the telescope control has to take into account the atmospheric refraction. The pointing offset due to atmospheric refraction is zero at zenith z = 0, less than 1 arcmin for a zenith distance z = 45, but then increases rapidly for larger zenith distances and reaches 30 arcmin (diameter of the sun!) for z = 90. The exact value depends on the altitude of the observatory, the air pressure, and the air temperature profile Equatorial mounts. Almost all older telescopes (build before 1980) have an equatorial mounting. One axis, the polar axis, is aligned with the Earth rotation axis. This axis is used to compensate for the steady rotation (with sidereal time) of the Earth. The second axis is perpendicular to the polar axis and it allows to point to objects at different declination. The guiding of these telescope is simple but the tilted rotation axes are mechanically challenging for large telescopes. Another disadvantage is that the orientation of the polar axis and therefore the whole mounting design depends on the geographic latitude of the telescope site Alt-Az Telescopes Most new telescopes are build as Alt-Az telescopes. Mechanically they are much simpler because they use a horizontal (altitude) and a vertical (azimuth) rotation axis. In Alt-Az telescopes the tracking of the targets requires a more complicated telescope control:

11 4.3. MECHANICAL CONCEPTS FOR TELESCOPES 53 both axis rotate simultaneously, the rotation speed is position dependent, the sky North direction (the image in the focal plane) rotates with respect to the telescope. The image rotation often requires that also the focal plane instrument has to be rotated during the observations. For high precision measurements the differential rotation between sky and telescope can cause additional problems, e.g. because the telescope diffraction pattern is not stable. The field rotation in the telescope pupil (primary mirror) with respect to N-sky is given by the paralactic angle p which defines the angle between the N-direction and the zenith direction for the center of the field (target). On the meridian the paralactic angle is p = 0 or 180. A Cassegrain instrument has to be rotated with the paralactic angle in order to have a stabilized field. Observations near zenith. For the planning of observations with an Alt-Az telescope one should consider that the azimuthal rotation speed for a target near zenith is very high. Therefore observations near zenith may not be allowed or they could be affected by tracking errors Special mountings HET and SALT: The 11m Hobby-Eberly Telescope (EBT) and the South African Large Telescope (SALT) have a primary mirror with a fixed zenith angle of 35. The primary mirror can only be rotated in azimuth. Pointing and tracking over large sky regions is still possible because the instrument position can be moved in the telescope primary focal plane so that a particular target can be followed. With this approach it is possible to observe objects with a declination in the range of 11 to +71 for HET (located in Texas) at least for certain hours during the night. HET and SALT are good examples of very large telescopes specialized for certain applications (e.g. spectroscopy). Thanks to the simplified telescope mount these large telescopes could be build for significantly less money.

12 54 CHAPTER 4. OPTICAL TELESCOPES 4.4 Examples for telescopes ESO 3.6m telescope The ESO 3.6m telescope is in operation since It is a typical example of the 3 5 m telescopes build before Basic characteristics are: 3.6 m primary mirror with interchangeable top end, F/8 Cassegrain focus, F/25 coude focus, equatorial mount, located in a huge dome 20 m above ground. The 3.6m telescope was the flagship of ESO for about 20 years. It had to fulfill a lot of needs of the European astronomical community and was therefore equipped with many different exchangeable instruments. Instrument changes required sometimes even an exchange of the secondary mirror to allow for example a switch between Cassegrain instruments with different F-ratio, the use of the prime focus plate holder, or the Coudé focus spectrograph. Since about 1995 the 3.6m telescope served also as test bed for new instrumental developments, like mid-infrared instruments and adaptive optics systems. The required support for running this multi-purpose machine was huge: instruments were exchanged (often on a weekly basis), the secondary mirror had to be realigned and many technical calibrations were required. A large staff of very experienced technicians and astronomers were required to allow a smooth operation. Now in the era of the VLT, the 3.6m telescope is since 2008 only available in conjunction with one single instrument, the HARPS high-resolution spectrograph for the RV-search of extra-solar planets. This is very cost effective and still provides a lot of first class science results ESO VLT The Very Large Telescope (VLT) array consists of 4 identical unit telescopes, UT1,..,UT4 with primary mirror diameters of 8.2 m and four movable 1.8 m Auxiliary Telescopes AT1,...AT4. The UT telescopes are mostly used alone with their individual instrumentation. For interferometry the beam of 2 or 3 telescopes can be combined in an underground interferometric laboratory. The ATs are only used for interferometry of bright sources, for projects where the large UTs are not required. The ATs can be moved in order to cover different baselines for interferometry. The 8.2m telescopes belong to the new generation of large telescopes which profit from the advances in technology made at the end of the 20th century. Special new features with respect to the old telescopes (e.g. ESO 3.6m telescope) are: primary mirror with short focal length or small focal ratio; the monolithic primary mirror was cast in a rotating oven in order to get a strongly curved paraboloidal shape, active support of the thin primary mirror with more than hundred actuators which push the mirror always into perfect shape, compact alt-azimuth mounting, small, co-rotating light-weight dome.

13 4.4. EXAMPLES FOR TELESCOPES 55 Thanks to the fact that each of the 4 telescopes has 3 focal stations for instruments, a large number of instruments can be installed permanently. In this way all kind of different instruments are available without time consuming and risky exchanges of instruments. The following list gives a short overview on the impressive suite of instrument available for the user (spring 2012). FORS2 (FOcal Reducer and Spectrograph) is a multi-mode instrument that can be used for imaging in the visible, for multi-object, low-resolution spectroscopy, and polarimetry. ISAAC (Infrared Spectrometer And Array Camera) is a cryogenic infrared imager and spectrometer, for the 1 to 5 µm range. UVES (Ultra-violet and Visible Echelle Spectrograph) is the high-dispersion spectrograph of the VLT, observing from 300 nm to 1100 nm, with a maximum spectral resolution of NACO is an Adaptive Optics facility producing images, spectroscopy, coronagraphy, and polarimetry in the 1 to 5 µm range with a diffraction limited spatial resolution of milli-arcsec. VIMOS (VIsible Multi-Object Spectrograph), a four-channel multi-object spectrograph and imager, allows obtaining low-resolution spectra of up to 1000 galaxies at a time. FLAMES (Fibre Large Array Multi-Element Spectrograph) offers the unique capability to study simultaneously and at high spectral resolution hundreds of individual stars in a small field of view. VISIR (VLT Imager and Spectrometer for the mid-infrared) provides diffractionlimited imaging at high sensitivity in the two mid infrared (MIR) atmospheric windows (8 to 13 µm and 16.5 to 24.5 µm). SINFONI is a near-infrared(1-2.5 µm) integral field spectrograph fed by an adaptive optics module. CRIRES (CRyogenic high-resolution InfraRed Echelle Spectrograph) provides a resolving power of up to in the spectral range from 1 to 5 µm. HAWK-I (High Acuity Wide field K-band Imager) is a near-infrared imager with a relatively large field of view. X-shooter is a wide-band, from UV to near infrared, spectrograph designed to explore the properties of rare, unusual or unidentified sources. Each unit telescope is equipped with instruments which are suited for bright time (full moon)anddarktime(newmoon). Inthiswayeach instrumentcanbeusedunderoptimum conditions. It is even possible to switch between different instrument on a given telescope during the night. For rare astronomical events, it is possible to ask for rapid response mode (RRM) in order to get an observation within a few minutes after an event has been detected. The rapid response mode is essential for Gamma Ray Bursts, which fade after the detection with a γ-ray satellite within very short time below the detection limit ESO E-ELT The European Extremely Large Telescope is a telescope project which shall revolutionize ground-based astronomy in the future. The planned telescope has a diameter of about 38 meters. For the realization of such a telescope new major technical challenges must be achieved:

14 56 CHAPTER 4. OPTICAL TELESCOPES the primary mirror made of about 1000 elements of about 1.5m hexagons must be in perfect shape, perfectly aligned, and maintenance (cleaning, re-coating) should not significantly impact the observations, the mechanical challenges for pointing and tracking are immense and thermal expansion/contraction as well as some wind should not impact on the telescope alignment and pointing, the size of the image in the focus must be small enough for optical components, the telescope must be operated in the diffraction limit using adaptive optics systems to correct for the atmospheric seeing. Without seeing correction the observation of faint sources would just be confusion limited (everywhere on the image is a faint galaxy). A novel telescope concept was developed for the E-ELT based on a 5 mirror system: a segmented concave M1 mirror, a convex M2 mirror, an intermediate focus in front of an concave mirrorm3, a flat adaptive mirror M4 with about5000 actuators, andaflat tip/tilt mirror M5. The design of the telescope was finished in 2010 together with feasibility studies for 8 focal plane instruments. In the best case the project will be approved in 2012 and the telescope might become operational around 2020.