Class Note for ASTR 518 at UA
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Date Created: 02/06/15
Optics and Telescopes Geometrical ray optics Involves mapping of mular coordinates object to patial coordinates image Can be described by eg 1 Law of re ectionrefraction Snell s 2 Huygen s wavelets as modi ed by Fresnel 3 Fermat s principle Fermat s principle The optical pathlength through a system from a point on an object to the corresponding point on the image is the same for all neighboring rays ie the optical pathlength for hypothetical rays undergoes an in ection at the position of the true ray l s optical pathlength the product of physical distance times index of refraction A B C ds n dx Simple geometrical optics I 0 Law of refraction n1 sin 61 n2 sin 62 this implies for a thin lens 1 l 1 1 l i ir i 51 52 F 1 Law of re ection I W 91 92 I l Types of images Real Could place a detectors or a piece of paper at the position and record the image Virtual An image appears to exist at this location when looking through the optical system Either type of image can act as an object for a downstream omical element Stops Stop A limitng diameter Anything that limits which light rays can pass through an optical system Aperture stop A stop that limits the ray bundle from a given point on the object Objective mirrorlens of a telescope is usually the aperture stop Field step A stop that limits which portions of an object appear in the image Often the physical extent of a detector or detector array de nes the eld step Pupils Pupil The image of a stop In astronomy the pupil is almost always the image of an aperture stop Exit pupil The image of the aperture stop fanned by any optics that follow the stop Entrance pupil Tie image of the aperture stop formed by any 0 stics that might precede the stop Pupils and stops in a simple telescope gt i entrance pupil gt focus gt secondary primary Aperture stop at entrance pupil A Entrance pupil Aperture stop Canon 14mm f28 lens Field stops Photometer diaphragm Spectrograph slit Detector array Refraction in a thin lens A ray passing through the center of a thin lens is undeviated paraxial rays object chief ray S1 m xx1S2S1 Magni cation Re ection from a mirror A mirror acts like a thin lens With a reversal of coordinate Image scale of a telescope dxF d8 dBdxIF 206265F Equivalent mirror combination oftelescope fratio of an optical beam Speed of an optical system dB 2 L 0L4 ll alt ZS Z 31 E o D2 03639 Di ImF CI twigf2 A system with a smallerfnumber collects more photons per second per image element So it is faster Image formation by a sphere I By Fermat s Principle a sphere forms a perfect real image of a point source located at the center of the sphere The image is produced back onto the center of the sphere sphere locus of points equidistant from another point Image formation by a sphere II VVhatabouta source at 00 center of curvature sphere The spherical mirror at Are cibo Arecibo D N 1000 ft F 435 ft f 043 AFN 43 ft Image formation by an ellipsoid By Fermat s Principle an ellipse is a perfect imager for a point source located at one focus A real image is produced at the other focus ellipse locus of points Whose sum of distances from two other points the foci is a constant Image formation by a paraboloid I By Fermat s Principle a gt plane X2 parabola is a wuvel39rorii perfect imager for X 2 an onaX1s pomt Vertex source located at in nity A real X1 X1 image is produced on the aXis at a distance F here x from the vertex gt parabola of the parabola parabola locus of points whose sum of distances from a line and a point the focus is a constant Image formation by a paraboloid II 20F coma 3 1 3087 1087 comatic image formed by a parabola imaging offaxis x to 1 Q F if T Image formation by a hyperboloid hyperboloid xi xol 2 const By Fermat s Principle a hyperbola is a perfect imager for a Virtual object located at one focus Areal image is formed at the other inner uter focus hyperbole hyperbola the locus of points whose difference of distances from two points the foci is a constant Eccentricity VS conic constant Surface 3 If 131111130111 lt2 1 1 tn DC Sphere U D P 211 ahalnid 1 1 IIypnrhnlnid gt 1 lt1 1 K e2 The Cassegrain telescope gt paraboloid hyperboleid gt 3 gt secondary primary Unfortunately the hyperboloid preserves the inherent coma of the paraboloid limiting the net field of View Increasing the FOV the Ritchey Chretien design hyperbolmd hyperboloid gt secondary primary The 23m Bok RC 0726 primary achieves 45 arcmin FOV vs 10 arcmin with lt1 images The RitcheyChretien RC design uses two hyperboloids to simultaneously eliminate spherical aberration and coma This is one type of aplanat This maximizes the FOV for a given focal ratio Unfortunately the hyperboloidal primary must be matched with a specific hyperboloidal secondary for wide fieldof view TradeOffs with the RC design f12 primary 74 FM aquot 2m 194 Magi MED4 L H44 He 1 B 24 a x V 25u J 20 lt V De rm 4 7 I5quot ID IN 22c 4r VI 7 1 0 701 7 03 39 04 2 56 I Ive44 y 46 5A Fawn 2 r4 ca Unlcazzxtcrzp 2 Mill or IVs271 What limits the FOV of an RC focus Astigmamm 11w phenom when ray Yam approaching focus in di 39aml planes cross the axis A different focal dimm d ec 0 for R42 so mars zapidly 7 6F Increasing the FOV Correctors WT Focal Ratios 54 imaging f 58 spectroscopic 9 naked 15 05 degree 1 degree 10 arcmin adaptive venex heigmlmm a 25 m7 7 Z V 5 SamW 5 552 rs Securdary mum spedm pic EVBAMEimagi m EVWSSShare g i 55 Mary 17m 56ft diam 1466 55 mummy me an N mu v 5 sumsan s zsus mmq iswm mm 5 lt7 Fmermeh anener zzssuuHS 77 Fumipiane Corrected RC focus 9OPRIME 05 pixels 10 eld of View L1 052m 205in diam 429 9 mm 4X4096X4096 pix 134MBpicture gt5 inches
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