Astro 500 A500/L-7 1

Transcription

1 Astro 500 1

2 Telescopes & Optics Outline Defining the telescope & observatory Mounts Foci Optical designs Geometric optics Aberrations Conceptually separate Critical for understanding telescope and instrument capabilities and preliminary instrument design Essential for detailed instrument design and for evaluating data. 2

3 Where we re headed Geometric Optics Ø Reflection Ø Refraction Ø Thin lens Ø Spherical optics Ø Conics Ø Stops Ø Pupils Ø Chief rays Ø Marginal ray Ø System design Optics Aberrations Chromatic Spherical Coma Astigmatism Distortion Field curvature Ø Telescope summary 3

4 The Thin Lens s parallel ray & marginal ray 1 f = 1 s + 1 s' m = s' s = h' h = magnification f ratio = f /D, D = clear aperture h focal ray chief ray f Image Object f h 1 f P = optical power s 4

5 The Thin Lens h s D 1 f = 1 s + 1 s' m = s' s = h' h = magnification f ratio = f /D, D = clear aperture f Image Object Object at f h s 5

6 Spherical Optics Focal Length Defined Definition 1 f = 1 s + 1 s' = 2 R Object at Infinity s C s 1 = s' 1 f 1 = s' f = R/2 is referred to as the paraxial focal-length 2 R R f 6

7 Snell s Law n and n depend on λ Index = n θ Q θ P Index = n B C 1 V = (n F n C ) /(n D 1) = dispersive power F,D,C: solar-spectrum Fraunhofer lines (486, 589, 656 nm). V vs n is called a glass table. Fermat s principle: least time 7

8 An Aside: Implications of Snell s Law α (n 1)θ z (n 1)t n % d t sinθ 1 cosθ ( ' * & n cosθ' ) t θ α z n n n θ θ d Impact of wedges and and plane parallel plates on an optical beam If beam is converging, astigmatism introduced. Can be eliminated with wedge. 8

9 The Thick Lens s parallel ray & marginal ray h focal ray chief ray n 1 n 2 f 2 Image Object f 1 h n 2 = n n 2 1 f 2 R = refractive power f 2 /n 2 = reduced focal length R = radius of curvature s 9

10 Optical Power, P Two surfaces separation d index n n R 1 P 1 f = P 1 + P 2 d n P 1 P 2 R 2 f Two-surface spherical lens in air or vacuum R 1, R 2 radii of curvature R>0: center of curvature behind lens Lensmaker s formula: P = 1 f = (n 1) # % $ R 1 R 2 units : dioptor (m 1 ) d(n 1) nr 1 R 2 & ( ' 10

11 Refractors: Chromatic Aberration 11

12 Chromatic Aberration Credit: Wikepedia 12

13 Two-lens achromat Two refractive indices Three radii of curvature More lenses, better correction over more wavelengths Difficult to make large achromats: Ø 300mm diameter challenging Ø Largest refractor: 1m Solution: Mirrors 13

14 Spherical Aberration-1 Object at Infinity C f f y y It is straightforward to show that f is a function of height, y, proportional to area. 14

15 Spherical Aberration-2 15

16 Spherical Aberration-3 Diameter of blur circle (of least confusion): β s = 1 (radians) Spherical ( ) 3 mirror 128 f /D So why do refractors work at all? Paraxial rays (optics): Ø Angles small (sin θ θ) What does this imply about f/d? 16

17 Conical Mirrors Cross-sectional cuts through a cone. Ø Ellipse, parabola, hyperbola All eliminate spherical aberration: Ø all rays passing through one focus form perfect image at other focus. Other aberrations present. Gregorian (Aplonatic Gregorian) Cassegrain (Ritchey-Cretien) F F F ellipsoid Paraboloid (ellipsoid) F F is common focus hyperbaloid paraboloid (hyperbaloid) 17

18 Parabola Parabola: Ø one focus at infinity suitable for astronomy Ø Off-axis aberrations: o Coma (negative) o Astigmatism (positive) '! β c = 3θ / 16 f $ ) # & () " D % 2 *, +, (radians) $ β a = θ 2 / 2 f ' & ) (radians) % D( through focus 18

19 Spherical Aberration: Parabola vs Sphere 19

20 Coma: Parabola vs Sphere y 2 < y 1 R Parabola y 1 y 1 z β c = 3 16 θ! f $ # & " D % 2 (radians) y 2 y 2 β c = 3 16 θ! f $ # & " D % f =R/2 2 Sphere ( 1-z / 2 f ) (radians) How can you eliminate coma (an off-axis aberration) from a spherical system? 20

21 Aberrations: 3rd order equations Imperfect images caused by geometric factors sinθ = n=1 θ n n! Seidel or third-order aberrations consider departures from first-order, or paraxial condition, i.e., going from to sinθ θ sinθ θ + θ 3 6 Chromatic Spherical Coma Astigmatism Distortion Field curvature 21

22 Aberrations: Zernike model Zernike polynomials: Orthogonal basis-set over circle of unit radius Aberrated wave-front fit with Zernikes Coefficients are linearly independent, and can be related to different types of aberrations 22

23 Meet the Zernike s 0 ρ 1: normalized pupil radius 0 θ 2π: azimuthal angle around pupil a 0 to a 8 : (fitting coefficients) wavefront errors in wavelengths 23

24 Spherical Aberration (revisited) 24

25 Spherical Aberration (revisited) Negative spherical aberration Paraxial lens Positive spherical aberration going through focus 25

26 Coma 26

27 Astigmatism 27

28 Astigmatism 28

29 Astigmatism ΔW=ρ 2 sinθ 2 29

30 Field curvature 30

31 Distortion 31

32 Why different designs? For a classical cassegrain focus or prime focus with a parabolic primary you need a corrector. The Richey-Chretien (RC) design has a hyperbolic primary and secondary designed to balance out coma and spherical in the focal plane. Gregorian and Aplonatic Gregorian (ApG) is another variant attempting to improve on the RC design. Ø In general, correctors are required to achieve good image quality over a wide field 32

33 Correctors Refractive (catadioptrics) o Singlet asphere + spherical mirror: can t correct spherical & astigmatism simultaneously o Achromatic spherical doublet + spherical mirror: can t correct spherical, coma and astigmatism simultaneously. o Triplet spherical meniscus + parabolic mirror: Wynne corrects coma, astigmatism, and eliminates field curvature o Multiplet: $$$ 7-lens design for 8.2m Subaru telescope: 0.5m diameter lenses, 30 FoV Reflective secondary: e.g., RC or ApG designs Reflective multiplet: HET and SALT 33

34 Ingredients in Telescope Design 1. Primary diameter - collecting area 2. Primary f-ratio - dome-size 3. Back focal-length - instrument volume 4. Final f-ratio - focal scale 5. Field of view - secondary diameter & distance (2)-(5) determine primary+secondary figures 34

35 Types of Telescopes Category Primary Secondary Corrector Name Principal Aberrations Singlet lens Spherical refractor spherical + chromatic Singlet mirror Paraboloid mirror Newtonian coma + astigmatism Doublet mirrors Paraboloid Hyperbaloid Cassegrain coma Hyperbaloid Hyperbaloid Ritchey-Chertien (RC) astigmatism (twice Cassegrain field) Parabaloid Ellipsoid Gregorian field curvature Ellipsoid Spherical Dall-Kirkham Ellipsoid Ellipsoid Aplonatic Gregorian (AG) Multiplets Spherical Aspheric lens or Schmidt achromate doublet Spherical Hyperbaloid Aspheric lens Schmidt-Cassegrain best images but large obstruction v. wide field Spherical Spherical Spherical meniscus lens Maksutov Spherical 4-mirror asphere HET, SALT Low cost 35

36 Two-mirror telescopes: Cassegrain focus Gregorian (Aplonatic Gregorian) Cassegrain (Ritchey-Cretien) f 1 f 1 D y D y x d e x d e Power: Focal scale: Back focal distance: Focal amplitude: f ratio f /D 1 f = d f 1 f 2 f 1 f 2 s = / D f ratio [arcsec/mm] ( ) $ e = f d f ' & +1) % f 1 ( Δe = ( 1+ m 2 )Δd, m = f 1 / f 2 Exit pupil distance: Exit pupil diameter: Focal-plan curvature: l = f 2 d /( f 2 d) = distance behind secondary D pupil = Dl /d 1 R Cass = 1 f f 2 36

37 Information Gathering Power A Ω or etendue name diameter FoV A Ω m deg m 2 deg 2 SDSS What s missing? CFHT WIYN PanStarrs 4x Subaru LSST SALT

38 Wide-Field Telescopes: A vs Ω Pan-STARRS SDSS LSST 38

39 Information Gathering Power name A Ω or etendue Effective diameter Used FoV Survey A Ω m deg m 2 deg 2 What s missing? SDSS CFHT WIYN PanStarrs Subaru LSST Ø Obstructions Ø Vignetting Ø Instrument FoV and what else? SALT