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Telescopes Light Colletors Op#cal-infrared telescopes Light colletors Atualização: 4/5/18 AGA5802, Jorge Meléndez Ask students to mount telescope & discuss: - Diameter of the objec#ve - Angular resolu#on - Focal length (or focal distance) - Focal ra#o f/# - Angular size vs. Physical size - Field of view of CCDs - Problems with lenses and mirrors - Different loca#ons for focal plane - Mounts - Coa#ng Bibliography Kitchin – Astrophysical Techniques (5th Ed, 2009), Chap. 1 (par) Léna – Observational Astrophysics (2nd Ed, 1998), Chap. 4 (par) Birney – Observational Astronomy (2nd Ed, 2008), Chap.6 Smith – Observational Astrophysics (1995) Chap. 2 Walker – Astronomical Observations (1995), Chap. 2 e 3 www.das.inpe.br/~claudia.rodrigues/ www.if.ufrgs.br/~santiago/ www.astro.caltech.edu/~george/ ngala.as.arizona.edu/dennis/ Bibliography Roy & Clarke – Astronomy: Principles and Practice (4th Ed, 2003) Roth – Handbook of Practical Astronomy (2009), Chap. 4 Schroeder – Astronomical Optics (2nd Ed, 2000), several chaps. Lecture notes, Prof. Antonio Mário Magalhães Main characteris#cs collects energy ( ∝ collector area) image forma#on: ang ular resolu#on ● Increase in collec#ng area à detec#on of fainter object s beUer angular resolu#on Angular resolu#on Is the capacity to resolve fine details. The resolu#on is the smallest angle that could be discerned Angular resolu#on: diffrac#on of a slit Light diffraction imposes a limit on angular resolution The diffraction pattern of a slit of width d is: © Kitchin Angular resolu#on: diffrac#on of a slit -3λ/d -2λ/d -λ/d λ/d 2λ/d 3λ/d Angular resolu#on: diffrac#on of a circular aperture Diffraction pattern Lens Primeiro zero da função de Bessel Airy disk: central disk defined by the first Roy & Clarke minimum Angular resolu#on: circular aperture (c) Kitchin Airy function sets the resolution limit First zero of Bessel func0on Note: r = d/2 Roy & Clarke Angular resolu#on: Rayleigh criterium The resolu#on limit is when the maximum of one Airy disk is over-imposed on the 1st minimum of the other image The first minimum occurs at a radius α [rad]: α = 1.22 λ /d HST (2.4m) ~ 0,05” (c) Kitchin Rayleigh vs. Dawes criteria Rayleigh criterion: α = 1.220 λ / d Empirical Dawes criterion ~10% lower FWHM = 1.029 λ / d In prac#ce both limits are difficult to reach due to imperfec#ons of the instrument and the perturba#ons of the terrestrial atmosphere Roth Angular resolu#on: Rayleigh criterium α [rad] = 1,22 λ /d For V = 540nm: α[”] = 0,136 /d[m] A telescope with d = 13,6 cm reaches in the op#cal an angular resolu4on of 1”, about the same than the limit imposed by seeing (~ 1”) Angular resolu#on: Rayleigh criterium α [rad] = 1,22 λ /d For V = 540nm: α[”] = 0,136 /d[m] For K = 2,2μm: α[”] = 0,55 /d[m] In the K band (infrared), a telescope with d = 1 m reaches an angular resolu4on of 0,55” Focus, focal plane, focal distance F: focal distance, D: aperture of the lens/mirror Lens axis Principal focus Lens (a.k.a. focal point) Focal plane Principal axis D focal length is the distance to image an object at infinity www.antonine-education.co.uk/Physics_A2 www.antonine-education.co.uk/Physics_A2 F Focal length Focal ra4o f/# F: focal distance, D: aperture, focal ra#o f/# Lens axis Lens Principal focus Focal plane Principal axis D F www.antonine-education.co.uk/Physics_A2 www.antonine-education.co.uk/Physics_A2 Focal length Focal ratio ≡ f-ratio ≡ f-number ≡ f/# = F/D Short (low) f/ (e.g. f/5): faster: brighter: wider field of view Focal ra4o f/# = F / D F: focal distance, D: aperture, focal ra#o f/# Lens axis Lens Principal focus Focal plane D F Example: the 1,6m telescope at OPD has f/10 at www.antonine-education.co.uk/Physics_A2 www.antonine-education.co.uk/Physics_A2 the Cassegrain focus. Find the focal distance F Response: F/D = 10, D=1,6m à F = 16m Focal plane & focal length (or focal distance) study.com Focal plane & focal length mirror Light gathering power (LGP) LGP is the area of the objec#ve LGP = π (D/2)2 Young person in darkness: de ~7mm Ex. Telescopes rela0ve to the eye: 10 cm: 200 0mes ! 8m: 1.3x106 0mes ! Signal-to-noise ra#o (S/N) S/N = sinal/ruído S/N = 2 S/N = 4 S/N = 8 S/N = 16 simula#on of stars observed with a signal- to-noise ra#o ranging from 2:1 to 16:1 Integra4on 4me Joining the 4 ESO/VLT telescope (8m each) we can have a super-VLT with a diameter equivalent to 16m. If we can observe a galaxy in 1h with the super-VLT, how long would it take to achieve the same S/N if the observa#on is done with the 1,6m telescope at OPD? Rpta: 100 hours. Considering 2h of observa#on at OPD (near the meridian) by night, the observa#on may take 50 nights … 2 t1 = (D2/D1) t2 t1 , t2 : observing #me with telescopes of diametersD1 , D2 Physical size of the image F Focal distance Angular size of Image height image in radians Lens s D θ ircamera.as.arizona.edu Physical size s of image θ on the detector: s = F tanθ ~ F θ Example: if F = 8m, estimate s for θ = 1” 1 rad = 206265” à s = 8m*1/206265 = 3,9 x 10-5 m = 39 µm How large is the pixel of a CCD? m m m m m Physical size of the image, plate scale F Focal ra0o = F / D Focal distance Angular size of Image height image in radians Lens s D θ ircamera.as.arizona.edu Physical size s of image θ: s = F tanθ ~ F θ Plate scale p = dθ/ds = 1/F = 206265”/ F IAG: f/13.5; D=61cm. What is the plate scale? F = 13.5 x 61cm = 8235 mm p = 206265”/8235mm = 25”/mm = 0.5”/20µm (1mm=103 µm) Field of view F Focal distance Angular size of Image height image in radians Lens s D θ ircamera.as.arizona.edu Plate scale p = dθ/ds = 1/ F = 206265 / F Using the same CCD chip on two telescopes with different focal lengths affects the field of view and image scale, but not the display size (because the number of pixels is the same). CCD: 9-micron pixels, 765x510 array Telescope A: 500mm focal length A B Telescope B: 1000mm focal length Refractor telescopes: disadvantages ● Mechanical Lens must be supported on the edges. As there is no central support, it may get distorted ● Size of the tube In order to diminish distortions (chromatic/spherical) the focal distance must be large, increasing the cost $$$. Ex: huge domes ● Absorption by the lens Absorption of UV light ● Imperfections in the lens or air bubbles Longest refractor (1m) at Yerkes observatory Refractor telescopes: chroma#c aberra#on Refraction index n(λ) à focal distance f(λ) © Kitchin Refractor telescopes: chroma#c aberra#on Chromatic aberration Refraction index n(λ) à focal distance f(λ) Correction with achromatic lens” by fusing lenses (doublets, triplets, etc): but correction is not perfect Disadvantages of refractors: coma Coma can affect also reflector telescopes Coma affects parabolic mirrors. The rays parallel to the axis of the parabola are OK, but if the rays strike © Kitchin: The severity of the coma at at an angle, then a given angular distance from the there is coma op4cal axis is: 1/(f/#)2 In Newtonian reflectors a focal ra#o of f8 or larger gives acceptable coma for most purposes. At f3, coma will limit the useful field Roy & Clarke of view to about 1 of arc Disadvantages of refractors: as#gma#sm Astigmatism Rays that pass through the tangential (optical axis) & sagittal plane do not focus on the same point Can affect also reflectors Roy & Clarke Other aberra4ons ● Image curvature: flat object shows distorted image, i.e. focus is not on a plane ● Distortion: varia#on of the magnifica#on on the image plane Reflector telescopes I “Invented” by Newton (1668) At least the first working reflector ●Objec#ve: mirror Does not suffer chroma#c aberra#on Newton’s mirror was spherical, but a parabola is more common, because it focuses at a single point Roy & Clarke Spherical aberra4on Spherical mirror (spherical aberration) Parabolic mirror Types of focus: prime focus Smith Jesse P200 Palomar Greenstein at Prime focus: f/3,3 prime focus cage Anglo Australian Telescope Image © 1997, text © 2010, Australian Astronomical Observatory, photograph by David Malin (himself inside the prime focus cage) Prime focus of Subaru (8m) Smith f/1,8 Subaru http://oir.asiaa.sinica.edu.tw/subaru/pfs.php Prime focus of Blanco telescope (4m at CTIO) Installa#on of DECAM DECAM installed (September 2013) 2,2° FOV (62 CCDs) DECAM + 12 CCDs (guiagem e foco) (Dark Energy Camera) f/2,7 primary 153 pix 4096 pix 2048pix hUp://www.noao.edu/mee#ngs/decam/media/DECam_Data_Handbook.pdf DECam Fornax mosaic © Dark Energy Survey Collabora#on NGC 1365 is a barred spiral galaxy around 60 million light years from Earth, located in the Fornax galac#c cluster. © Dark Energy Survey Collabora#on Reflectors: Cassegrain focus adequate position to put instruments compact telescope: secondary increases the focal distance of the telescope Secondary: Primary: hyperbolic parabolic Kitchin Reflectors: Cassegrain focus Secondary: hyperbolic Primary: parabolic Palomar 5m: Last P200 big telescope of Palomar Cassegrain type Reflectors: Ritchey-Chré#en telescope Variation of Cassegrain with hyperbolic primary: better image quality Secondary: hyperbolic Kitchin George Ritchey's 24- inch (60cm) reflecting telescope, first RCT Primary: constructed in 1927 hyperbolic Reflectors: Ritchey-Chré#en telescope HST: 2.4m, fsys=57.6m, f/24 Cut through (comprimento do telescópio HST é de 13m) secondário hiperbólico primário hiperbólico SOAR: 4.1m, f/16 LNA: 1.6m, f/10 Nasa Refletors: focos Nasmyth & Coudé Nasmyth telescope with alta-azimutal mount flat mirror at the altitude axis position of the focus is fixed: independent of the movement of the telescope adequate for heavy instruments Keck Big telescopes have Nasmyth focus for big instruments, except Gemini … Reflectors: Coudé focus Coudé: similar to Nasmyth but for equatorial mount Example: Coudé spectrograph at OPD Coudé focus Kitchin Smith Refletors: problems similar to those of refractor telescopes ● Spherical ● Coma ● Astigmatism ● Image curvature ● Distortion ● Vignetting (is not a fault of mirror or lens.
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