Introduction to telescope design

Introduction to Telescope Design

OpticsGeometric opticsRay tracing through optical systemsUsed to calculate important telescope parameters such as length, size of mirrors, and location of eyePhysical opticsAccounts for the wave nature of lightSources of image disturbancePolarizationInterferenceDiffraction

Physical Opticks & DiffractionImages are blurred by diffractionSets an absolute limit on resolving powerMost (84%) of light falls in a small circular region known as an Airy diskResolution is the smallest angular separation of two point sources (like stars) which allows both to be distinctCenter of the Airy disk of one point source just touches the outer edge of the other Airy disk (Rayleigh’s criterion)Limit of resolution:Depends on focal length, wavelength of light, and size of the primary mirror/lens

Geometric Optics - LensLight moves more slowly in lenses (glass, etc.) than air and this causes it to bendAmount of bend is the index of refractionSnell’s law relates indices of refraction and light ray anglesImage from http://commons.wikimedia.org/wiki/File:Refraction.PNG

Geometric Optics - MirrorsA light ray strikes a mirror at an angle relative to the surface normal and reflects at the same angle relative to the other side of the normalMirror shapes can be flat, spherical, or aspherical (hyperbolic, etc.)

Geometric Optics – Stops and PupilsAperture stop determines the amount of light reaching the image (end of the optical system)Can be a diaphragm or the edge of a lens or mirrorDetermines the total amount of irradiance availableIn telescopes, this is usually determined by the size of the primary mirror or lensField stop is an element limiting the angular size of an object being imagedIn astronomy this is usually determined by the size of film or CCD when creating astronomical images

Geometric Optics – Stops and PupilsEntrance pupil is the image of the aperture stop as seen from the axial point on the objectIn telescopes this is generally the unobstructed view of the primary mirror or lensIn catadioptric telescopes this may be changed slightly by corrective lenses before the primary mirrorExit pupil is the image of the aperture stop as seen from an axial point on the image planeDifferent eyepieces effect exit pupil size and can cause a loss in available irradiance

f/#Focal length is the distance from a mirror or lens where parallel rays meet at a single pointf/# (f-number, f-ratio, or relative aperture) is the focal length divided by the diameter of the entrance pupilThe entrance pupil for most telescopes is the primary mirror/lens (the objective)Unlike photography, f/# doesn’t effect the irradience at the eye since objects are essentially at infinite distance (only size of the objective matters)Focal length in telescopes determines the field of view and the scale of objects at the eye

Optical Ray TracingStart with parallel rays (point source at infinite distance) and trace the location and direction of rays at key points (edge of aperture, etc.)Trace rays through each elementSnell’s law for lensesUse equation for mirror shape (parabola, hyperbola, ellipse, etc.) to determine surface normalsStarting point of design is usually to place elements at the focal point of the previous element and adjust to account for aberrations

Chromatic AberrationEffects lensesCaused by wavelength dependence of index of refractionCauses different colors to focus at difference pointsColor blurringCorrected by using mirrors

Spherical AberrationSpherical lenses have a different focus on the edges and center of the mirrorCauses blurringCan be fixed by using convex and concave mirrors to zero out the spherical aberrationCan also be fixed by using aspheric lensesMain cause of early HST problems

Comatic AberrationOff axis point sources (located near the edge of the field of view) focus in a different location and on axis point sourcesCaused by parabolic mirrorsCauses a wedge shapeCan be corrected with aspheric lensesImage from http://en.wikipedia.org/wiki/File:Lens-coma.svg

GregorianConcave parabolic primary mirror and a concave elliptical secondary mirrorPrimary focus is before the secondaryEye point is behind the primaryAllows the observer to view behind the telescopeHas an upright imageUseful for solar observation since a field stop can be placed at the primary focusImage from http://en.wikipedia.org/wiki/File:Gregory-Teleskop.svg

NewtonianConcave parabolic primary mirror and a flat, angled secondary mirrorEye point is near the top of the telescope and on the sideLarge telescopes require the observer to sit on a platformEquitorial mounts can make viewing diificultCombined with short f/# can create a very compact telescopePopular with amateur astronomersSimple designInexpensive for a given apertureSingle parabolic mirror is easy to grind by handEasy to create a short f/# so a wide field of view can be obtainedGood for deep sky observation (galaxies, nebulae, etc.)Suffers from coma (serious with f/6 or lower)Secondary mirror causes a central obstructionRequires frequent collimationImage fromhttp://en.wikipedia.org/wiki/File:Newton-Teleskop.svg

CassegrainConcave parabolic primary mirror and a convex hyperbolic secondary mirror.Primary focus is aligned with the secondary’s focusEye point is behind the primaryLong focal length can be achieved with a short tubeSuffers from coma and spherical aberrations

Schmidt-CassegrainCatadoptric telescopeCassegrain with a Schmidt corrector plateAspheric lens which corrects spherical aberrationCan also be found in Schmidt-NewtonianCorrector also seals the tube keeping out dustImage from http://en.wikipedia.org/wiki/File:Schema_lame_de_Schmidt.svg

Maksutov-CassegrainCatadoptric telescopeA weakly negative meniscus lens corrects coma and spherical aberrationCorrector also seals the tube keeping out dustEasier to grind than a Schmidt correctorSecondary is integrated into the corrector (partially aluminized) which lowers manufacture costNot usually seen in > 7” telescopes as the corrector becomes large (heavy and requires long cool down times)

YoloOff axis telescopePrimary and secondary mirrors are concave and have the same curvatureSecondary doesn’t cast a shadowEliminates comaSignificant astigmatismPartially corrected by torroidal secondary mirror (different focal distance depending on mirror angle)Creates high contrast images with no obstructionImage from http://en.wikipedia.org/wiki/File:Off-axis_optical_telescope_diagram.svg

DobsonianAlt-az mount often used with Newtonian telescopesVery easy and inexpensive to buildVery easy to point by hand, especially for large (> 12”) portable telescopes“Light bucket” telescope with a large objective and low magnificationVery good for visual observation of large deep sky objectsLarge/heavy objective can be easily moved by handEasy to transport to remote, dark locationsNot easy to automatically trackNot a good design for camera/CCD useCan be computer assisted with adjustable alt-az marker wheels and/or computer position sensorsCan be placed on an equatorial platform for limited clock driven tracking

Introduction to telescope design

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Introduction to telescope design