Optical Telescope

Optical Telescope

Faint Light

• Astronomical objects are distant and faint.– Effectively at infinity

• Light collection is more important than magnification.– Refraction

– Reflection

• The Andromeda Galaxy (M31) subtends 3°.– 6 times the moon

– Only visible to the unaided eye in very dark conditions

Refraction

• Light is bent at the surface between two media.– Index of refraction n

• Refraction is governed by Snell’s law.

ttii nn sinsin

v

cn

i

rt

ri

Radius of Curvature

• Lenses shaped like parts of spheres are easy to make.– Easy to calculate rays

• Use Snell’s Law on a small part of a sphere.– Radius of curvature R

– Focal length f

– Index for air is 1

)1( nf

R

R f

Refracting Telescope

• A refracting telescope is designed to concentrate light from a distant object.– Object light rays nearly parallel

– Final image rays also parallel

objective focal point eyepiece

Aperture

• Lenses collect and concentrate light.

• The diameter (D) of the objective lens is the aperture.– Measured in m or mm

– Larger apertures for fainter objects

• The light gathering power (LGP) is related to the area of the lens.– Circular lens: A = (D2)/4

– Intensification relative to eye aperture 5 mm: LGP = D2/(5 mm)2

F-Stop

• The brightness of an image is measured by the focal ratio of the focal length to the aperture.– F-number or f-stop = f/d

– Dimensionless quantity

– Denoted by f/

• Lower f-numbers are “faster” and need shorter exposure times.

Fraunhofer Diffraction

• A single narrow slit creates diffraction.– No minimum for m = 0

ma sin

,2,1 m

Airy Disk

• Fraunhofer patterns are symmetric around the opening.

• A circular hole produces rings around a central maximum.– 84% of energy in center

Angular Resolution

• The limit of resolution is set by the aperture.

• The Rayleigh criterion is calculated from the first minimum of the Airy disk.– Aperture radius a

– Wavenumber k

– Bessel function J1

D

22.1

sin

)sin(2)( 1

0 ka

kaJII

0)(1 xJ ...02.7,83.3,0x

Daka

22.12

83.383.3sin

Tube Length

• The intermediate image at the focal point is a real image.– Long tube accommodates long focal length

– Parallel ray image related to the focal length

objective focal point eyepiece

o

O

oO

iOO s

f

s

sM

Magnification

• The eyepiece magnifies the intermediate image.

• The total magnification is the product from both lenses.

objective focal point eyepiece

E

i

oE

iEE f

s

s

sM

E

OEO f

fMMM

Yerkes Refractor

• The world’s largest refractor is in Wisconsin.

– 40 inch aperture, f/19

– 63 foot tube

Yerkes 40 inch

Chromatic Aberration

• The index of refraction depends on the wavelength.– Longer wavelengths - lower

indexes

– Blue light bends more than red

• Compound lenses can compensate for chromatic aberration.

• Air n(589 nm) =1.00029

• Crown glass 1.52

• Flint glass 1.66

Spherical Aberration

• A spherical surface does not focus all parallel lines to the same point.

• Aspheric lenses can be used to correct the aberration .

f

Curved Mirror

• Light that begins at one focus of an elliptical mirror converges at the other focus.– A parabola for a focus at

infinityfocus

focus

Parabolic Mirror

• A perfect parabolic mirror has a focal length like a lens.

• All wavelengths are focused to the same point.– No chromatic aberration

• The size of the mirror dish is the aperture.

focal lengthfocal point

Newtonian Reflector

• For viewing ray should be parallel on exit.– Combined primary mirror and eyepiece

• The reflecting telescope is cheaper, because a mirror is easier to make than a lens for a given size.

primary mirror

secondary diagonal mirror

eyepiece

Schmidt-Cassegrain Reflector

• A Cassegrain focus uses a flat mirror to make the tube up to three times longer.– Spherical aberration from extra mirror

– Aspheric Schmidt lens corrects aberration

eyepieceSchmidt corrector lens

Keck Reflector

• World’s largest reflector is in Hawaii.

– 400 inch aperture, f/1.75

– Focal length 57.4 feet.

– Telescope height 81 feet.

Keck Observatory

Coma

• Parabolic mirrors focus precisely for rays parallel to the central axis.

• The distortion for off axis objects is called coma.– Greatest for low f-numbers

• Lenses can correct for the coma. Starizona.com

Atmospheric Absorption

• The atmosphere absorbs radiation, except at visible light, infrared, and radio frequencies.

Adaptive Optics

• The moving atmosphere disturbs images.– Wavefront distortions

• Real time corrections are made by feedback to a deformable mirror.– Sample wavefront from beam splitter

– Measure distortion

– Compute necessary compensation for mirrors

Telescope Advantages

REFRACTOR

• Superb resolution

• Good for detail

• Rugged alignment

• Transports well

REFLECTOR

• Inexpensive optics

• Large aperture

• Good for dim objects

• Uniform treatment of colors

SCHMIDT-CASSEGRAIN

• Portable size

• Combines best optical qualities

• Good for photography

Altazimuth Mount

• Telescope mounts should permit two directions of motion.

• Altazimuth mounts directly control altitude and azimuth.

azimuth control

altitude control

Equatorial Mount

• Altazimuth mounts do not track with the star’s movement.

• Equatorial mounts are oriented to the pole.

• Allows control of declination and right ascension.

polar axisdeclination axis

Charge-Coupled Device

• The CCD is an array of photosensitive semiconductor capacitors.– Charge stored proportional

to light intensity

– Transfers charge as a shift register

– Amplifier on last capacitor converts charge to voltage

Hammamatsu.com

Telescope CCDs

• CCDs are sensitive to light from ultraviolet to infrared.

• CCDs are very efficient.– Can be sensitive to

individual photons

• Sensitivity to thermal noise and cosmic rays can blur an image.

• Multiple exposures are averaged to get correct image.– Dark frame closed shutter

Hubble Space Telescope

• The Hubble is an orbiting reflector telescope.

• It has no atmosphere to peer through.

• The onboard computer gives it enhanced optics.

• There are four different

cameras for different views.

Infrared and Ultraviolet

• Infrared is absorbed by water vapor.– Observe at high altitude

• Satellite telescopes avoid the atmosphere.– IRAS (1983) - first

evidence of planets around other stars

– Spitzer Space Telescope (2003-9).

• Ultraviolet is largely absorbed by the atmosphere.– Requires satellites

– HST, GALEX

M81 from GALEX