INTRODUCTION TO TELESCOPE DESIGN

OPTICS

• GEOMETRIC OPTICS– RAY TRACING THROUGH OPTICAL SYSTEMS– USED TO CALCULATE IMPORTANT

TELESCOPE PARAMETERS SUCH AS LENGTH, SIZE OF MIRRORS, AND LOCATION OF EYE

• PHYSICAL OPTICS– ACCOUNTS FOR THE WAVE NATURE OF

LIGHT– SOURCES OF IMAGE DISTURBANCE

• POLARIZATION• INTERFERENCE• DIFFRACTION

PHYSICAL OPTICKS & DIFFRACTION

• IMAGES ARE BLURRED BY DIFFRACTION• SETS AN ABSOLUTE LIMIT ON RESOLVING POWER• MOST (84%) OF LIGHT FALLS IN A SMALL

CIRCULAR REGION KNOWN AS AN AIRY DISK• RESOLUTION IS THE SMALLEST ANGULAR

SEPARATION OF TWO POINT SOURCES (LIKE STARS) WHICH ALLOWS BOTH TO BE DISTINCT– CENTER 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 - LENS

• LIGHT MOVES MORE SLOWLY IN LENSES (GLASS, ETC.) THAN AIR AND THIS CAUSES IT TO BEND– AMOUNT OF BEND IS

THE INDEX OF REFRACTION

• SNELL’S LAW RELATES INDICES OF REFRACTION AND LIGHT RAY ANGLES

Image from http://commons.wikimedia.org/wiki/File:Refraction.PNG

GEOMETRIC OPTICS - MIRRORS

• A 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 NORMAL

• MIRROR SHAPES CAN BE FLAT, SPHERICAL, OR ASPHERICAL (HYPERBOLIC, ETC.)

GEOMETRIC OPTICS – STOPS AND PUPILS

• APERTURE 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

MIRROR– DETERMINES THE TOTAL AMOUNT OF IRRADIANCE

AVAILABLE– IN TELESCOPES, THIS IS USUALLY DETERMINED BY

THE SIZE OF THE PRIMARY MIRROR OR LENS

• FIELD STOP IS AN ELEMENT LIMITING THE ANGULAR SIZE OF AN OBJECT BEING IMAGED– IN ASTRONOMY THIS IS USUALLY DETERMINED BY THE

SIZE OF FILM OR CCD WHEN CREATING ASTRONOMICAL IMAGES

GEOMETRIC OPTICS – STOPS AND PUPILS

• ENTRANCE PUPIL IS THE IMAGE OF THE APERTURE STOP AS SEEN FROM THE AXIAL POINT ON THE OBJECT– IN TELESCOPES THIS IS GENERALLY THE

UNOBSTRUCTED VIEW OF THE PRIMARY MIRROR OR LENS

– IN CATADIOPTRIC TELESCOPES THIS MAY BE CHANGED SLIGHTLY BY CORRECTIVE LENSES BEFORE THE PRIMARY MIRROR

• EXIT PUPIL IS THE IMAGE OF THE APERTURE STOP AS SEEN FROM AN AXIAL POINT ON THE IMAGE PLANE– DIFFERENT 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 POINT

• F/# (F-NUMBER, F-RATIO, OR RELATIVE APERTURE) IS THE FOCAL LENGTH DIVIDED BY THE DIAMETER OF THE ENTRANCE PUPIL

• THE 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 TRACING

• START 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 ELEMENT– SNELL’S LAW FOR LENSES– USE EQUATION FOR MIRROR SHAPE (PARABOLA,

HYPERBOLA, ELLIPSE, ETC.) TO DETERMINE SURFACE NORMALS

• STARTING POINT OF DESIGN IS USUALLY TO PLACE ELEMENTS AT THE FOCAL POINT OF THE PREVIOUS ELEMENT AND ADJUST TO ACCOUNT FOR ABERRATIONS

CHROMATIC ABERRATION

• EFFECTS LENSES• CAUSED BY WAVELENGTH

DEPENDENCE OF INDEX OF REFRACTION

• CAUSES DIFFERENT COLORS TO FOCUS AT DIFFERENCE POINTS– COLOR BLURRING

• CORRECTED BY USING MIRRORS

SPHERICAL ABERRATION

• SPHERICAL LENSES HAVE A DIFFERENT FOCUS ON THE EDGES AND CENTER OF THE MIRROR

• CAUSES BLURRING• CAN BE FIXED BY USING

CONVEX AND CONCAVE MIRRORS TO ZERO OUT THE SPHERICAL ABERRATION

• CAN ALSO BE FIXED BY USING ASPHERIC LENSES

• MAIN CAUSE OF EARLY HST PROBLEMS

COMATIC ABERRATION

• OFF AXIS POINT SOURCES (LOCATED NEAR THE EDGE OF THE FIELD OF VIEW) FOCUS IN A DIFFERENT LOCATION AND ON AXIS POINT SOURCES

• CAUSED BY PARABOLIC MIRRORS

• CAUSES A WEDGE SHAPE

• CAN BE CORRECTED WITH ASPHERIC LENSES

Image from http://en.wikipedia.org/wiki/File:Lens-coma.svg

GREGORIAN

• CONCAVE PARABOLIC PRIMARY MIRROR AND A CONCAVE ELLIPTICAL SECONDARY MIRROR– PRIMARY FOCUS IS BEFORE THE SECONDARY

• EYE POINT IS BEHIND THE PRIMARY– ALLOWS THE OBSERVER TO VIEW BEHIND THE

TELESCOPE

• HAS AN UPRIGHT IMAGE• USEFUL FOR SOLAR OBSERVATION SINCE A FIELD

STOP CAN BE PLACED AT THE PRIMARY FOCUS

Image from http://en.wikipedia.org/wiki/File:Gregory-Teleskop.svg

NEWTONIAN

• CONCAVE PARABOLIC PRIMARY MIRROR AND A FLAT, ANGLED SECONDARY MIRROR

• EYE POINT IS NEAR THE TOP OF THE TELESCOPE AND ON THE SIDE– LARGE TELESCOPES REQUIRE THE OBSERVER TO SIT ON A PLATFORM– EQUITORIAL MOUNTS CAN MAKE VIEWING DIIFICULT– COMBINED WITH SHORT F/# CAN CREATE A VERY COMPACT TELESCOPE

• POPULAR WITH AMATEUR ASTRONOMERS– SIMPLE DESIGN– INEXPENSIVE FOR A GIVEN APERTURE– SINGLE PARABOLIC MIRROR IS EASY TO GRIND BY HAND

• EASY TO CREATE A SHORT F/# SO A WIDE FIELD OF VIEW CAN BE OBTAINED– GOOD FOR DEEP SKY OBSERVATION (GALAXIES, NEBULAE, ETC.)

• SUFFERS FROM COMA (SERIOUS WITH F/6 OR LOWER)• SECONDARY MIRROR CAUSES A CENTRAL OBSTRUCTION• REQUIRES FREQUENT COLLIMATION

Image from http://en.wikipedia.org/wiki/File:Newton-Teleskop.svg

CASSEGRAIN

• CONCAVE PARABOLIC PRIMARY MIRROR AND A CONVEX HYPERBOLIC SECONDARY MIRROR.– PRIMARY FOCUS IS ALIGNED WITH THE SECONDARY’S

FOCUS

• EYE POINT IS BEHIND THE PRIMARY• LONG FOCAL LENGTH CAN BE ACHIEVED WITH A

SHORT TUBE• SUFFERS FROM COMA AND SPHERICAL

ABERRATIONS

SCHMIDT-CASSEGRAIN

• CATADOPTRIC TELESCOPE• CASSEGRAIN WITH A SCHMIDT CORRECTOR

PLATE– ASPHERIC LENS WHICH CORRECTS SPHERICAL

ABERRATION– CAN ALSO BE FOUND IN SCHMIDT-NEWTONIAN

• CORRECTOR ALSO SEALS THE TUBE KEEPING OUT DUST

Image from http://en.wikipedia.org/wiki/File:Schema_lame_de_Schmidt.svg

MAKSUTOV-CASSEGRAIN

• CATADOPTRIC TELESCOPE• A WEAKLY NEGATIVE MENISCUS LENS CORRECTS COMA AND

SPHERICAL ABERRATION• CORRECTOR ALSO SEALS THE TUBE KEEPING OUT DUST• EASIER TO GRIND THAN A SCHMIDT CORRECTOR• SECONDARY IS INTEGRATED INTO THE CORRECTOR (PARTIALLY

ALUMINIZED) WHICH LOWERS MANUFACTURE COST• NOT USUALLY SEEN IN > 7” TELESCOPES AS THE CORRECTOR

BECOMES LARGE (HEAVY AND REQUIRES LONG COOL DOWN TIMES)

YOLO

• OFF AXIS TELESCOPE• PRIMARY AND SECONDARY MIRRORS ARE CONCAVE AND

HAVE THE SAME CURVATURE• SECONDARY DOESN’T CAST A SHADOW• ELIMINATES COMA• SIGNIFICANT ASTIGMATISM

– PARTIALLY CORRECTED BY TORROIDAL SECONDARY MIRROR (DIFFERENT FOCAL DISTANCE DEPENDING ON MIRROR ANGLE)

• CREATES HIGH CONTRAST IMAGES WITH NO OBSTRUCTION

Image from http://en.wikipedia.org/wiki/File:Off-axis_optical_telescope_diagram.svg

DOBSONIAN

• ALT-AZ MOUNT OFTEN USED WITH NEWTONIAN TELESCOPES

• VERY EASY AND INEXPENSIVE TO BUILD• VERY EASY TO POINT BY HAND, ESPECIALLY FOR LARGE (>

12”) PORTABLE TELESCOPES• “LIGHT BUCKET” TELESCOPE WITH A LARGE OBJECTIVE

AND LOW MAGNIFICATION• VERY GOOD FOR VISUAL OBSERVATION OF LARGE DEEP

SKY OBJECTS– LARGE/HEAVY OBJECTIVE CAN BE EASILY MOVED BY HAND– EASY TO TRANSPORT TO REMOTE, DARK LOCATIONS

• NOT EASY TO AUTOMATICALLY TRACK– NOT A GOOD DESIGN FOR CAMERA/CCD USE– CAN BE COMPUTER ASSISTED WITH ADJUSTABLE ALT-AZ MARKER

WHEELS AND/OR COMPUTER POSITION SENSORS– CAN BE PLACED ON AN EQUATORIAL PLATFORM FOR LIMITED

CLOCK DRIVEN TRACKING