DEPARTMENT OF PHYSICS AND ASTRONOMY

Dr Matt Burleigh

3671 Multi-Wavelength Astronomy3671 Multi-Wavelength Astronomy

Lecture 3: TelescopesLecture 3: Telescopes

Dr. Matt Burleigh

In this lecture we will cover:In this lecture we will cover:

• Design of modern, large optical (& IR) Design of modern, large optical (& IR) telescopestelescopes

• Diffraction limited resolutionDiffraction limited resolution minmin=1.22=1.22/D/D

• Influence of atmosphere – “seeing”Influence of atmosphere – “seeing”• Adaptive opticsAdaptive optics

– Overcoming “seeing”Overcoming “seeing”

• Magnification and plate scaleMagnification and plate scale

Dr. Matt Burleigh

8m Gemini North on Hawaii8m Gemini North on Hawaii• Opened early 2001Opened early 2001

Dr. Matt Burleigh

8m Gemini North on Hawaii8m Gemini North on Hawaii• Opened early 2001Opened early 2001

Dr. Matt Burleigh

Diffraction limited resolutionDiffraction limited resolution

• A fundamental limit exists in our ability A fundamental limit exists in our ability to resolve objectsto resolve objects

• This limit arises by diffractionThis limit arises by diffraction

• Consider a single slit width DConsider a single slit width D

• Any ray passing through this aperture Any ray passing through this aperture and arriving at a specific point in the and arriving at a specific point in the focal plane is associated with another focal plane is associated with another ray passing through the aperture one ray passing through the aperture one half slit width away and arriving at the half slit width away and arriving at the same point.same point.

Dr. Matt Burleigh

Diffraction limited resolutionDiffraction limited resolution• If the two rays are one-half wavelength (If the two rays are one-half wavelength (/2) out of phase, /2) out of phase,

destructive interference occurs:destructive interference occurs:– (D/2) sin (D/2) sin – Or sin Or sin DD

• Now consider dividing the aperture into four equal segmentsNow consider dividing the aperture into four equal segments• A ray from the edge of the opening pairs up with one passing A ray from the edge of the opening pairs up with one passing

through a point one-quarter of a slit width awaythrough a point one-quarter of a slit width away• For destructive interference to occur:For destructive interference to occur:

– (D/4) sin (D/4) sin – Or sin Or sin DD

• This analysis may be continued by considering dividing the This analysis may be continued by considering dividing the aperture into 6 segments, then 8, 10 etcaperture into 6 segments, then 8, 10 etc

• In general, for minima to occur as a result of destructive In general, for minima to occur as a result of destructive interference from light passing through a single slitinterference from light passing through a single slit– Sin Sin m m DD– Where m = 1, 2, 3 … for dark fringesWhere m = 1, 2, 3 … for dark fringes

Dr. Matt Burleigh

Diffraction limited resolutionDiffraction limited resolution

• The analysis for light passing through a circular The analysis for light passing through a circular aperture like a telescope is more complexaperture like a telescope is more complex

• Due to the symmetry of the problem, the diffraction Due to the symmetry of the problem, the diffraction pattern appears as concentric rings:pattern appears as concentric rings:

Dr. Matt Burleigh

Diffraction limited resolutionDiffraction limited resolution

• The solution to this problem was first obtained in The solution to this problem was first obtained in 1835 by Sir George Airy1835 by Sir George Airy

• The central bright spot is known as an Airy Disk, the The central bright spot is known as an Airy Disk, the rings as Airy Ringsrings as Airy Rings

• A similar equation to our ideal slit describes the A similar equation to our ideal slit describes the location of diffraction minima, but m is no longer an location of diffraction minima, but m is no longer an integerinteger

RingRing mm IImax max / I/ I00

Central maxCentral max 0.000.00 1.001.00

First minFirst min 1.221.22

22ndnd max max 1.6351.635 0.01750.0175

22ndnd min min 2.2332.233

33rdrd max max 2.6792.679 0.00420.0042

Dr. Matt Burleigh

Diffraction limited resolutionDiffraction limited resolution

• When the diffraction patterns of two sources are sufficiently close When the diffraction patterns of two sources are sufficiently close together, the diffraction rings are no longer distinguishedtogether, the diffraction rings are no longer distinguished

• The two images are said to be unresolved when the central max The two images are said to be unresolved when the central max of one image falls inside the first minimum of the otherof one image falls inside the first minimum of the other

• This arbitrary resolution condition is called the This arbitrary resolution condition is called the Rayleigh CriterionRayleigh Criterion• Assuming Assuming min min is quite small, and invoking the small angle is quite small, and invoking the small angle

approximation:approximation:

min = 1.22 D• in radians

• note to convert radians to arcsecs x by 206265

• Resolution improves with increasing telescope size and at shorter wavelengths

Dr. Matt Burleigh

SeeingSeeing

• Unfortunately, the resolution of ground-based telescopes does Unfortunately, the resolution of ground-based telescopes does not improve without limit as the mirror size increasesnot improve without limit as the mirror size increases

• This is due to the turbulent nature of the Earth’s atmosphereThis is due to the turbulent nature of the Earth’s atmosphere• Local changes in atmospheric T and density over small distances Local changes in atmospheric T and density over small distances

create regions where the light is refracted in random directionscreate regions where the light is refracted in random directions• This causes a point source to become blurredThis causes a point source to become blurred• Since stars are effectively point sources, they twinkleSince stars are effectively point sources, they twinkle• The quality of the image of a star at a given observing location The quality of the image of a star at a given observing location

and time is called and time is called “seeing”“seeing” – A measure of resolution allowed by atmosphere A measure of resolution allowed by atmosphere

• The best seeing at major observatories like Hawaii & La Palma The best seeing at major observatories like Hawaii & La Palma can be below 0.5 arcsecondscan be below 0.5 arcseconds

Dr. Matt Burleigh

Seeing, image size & point spread functionSeeing, image size & point spread function• The light from a point source like a star spreads itself across the The light from a point source like a star spreads itself across the

detector (photographic plate, CCD, etc) in a roughly circular detector (photographic plate, CCD, etc) in a roughly circular patternpattern– Obviously in poor conditions or if the object is moving the image Obviously in poor conditions or if the object is moving the image

can become elongatedcan become elongated• This is called the This is called the point spread functionpoint spread function• A cross-section of the PSF is approximately gaussian A cross-section of the PSF is approximately gaussian • We measure the size of the image (PSF) in arcsecondsWe measure the size of the image (PSF) in arcseconds

– 1 arcsecond = 1/60 arcminute = 1/3600 degree1 arcsecond = 1/60 arcminute = 1/3600 degree– Human eye resolution ~1arcminuteHuman eye resolution ~1arcminute– Pair of car headlights 100km away ~1arcsecond apartPair of car headlights 100km away ~1arcsecond apart– A man on the moon ~1/1000 arcsecondA man on the moon ~1/1000 arcsecond– Size of Betelgeuse (red giant star) ~ 1/20 arcsecondSize of Betelgeuse (red giant star) ~ 1/20 arcsecond

Dr. Matt Burleigh

SeeingSeeing

• Betelgeuse seen with the Betelgeuse seen with the 4m William Herschel 4m William Herschel Telescope on La Palma Telescope on La Palma in about 1” seeingin about 1” seeing

Dr. Matt Burleigh

Choosing an observing siteChoosing an observing site

• A steady atmosphere to minimise times of poor seeingA steady atmosphere to minimise times of poor seeing• Away from sources of scattered light (ie street lights) and Away from sources of scattered light (ie street lights) and

sources of dust (industrial areas, sandy deserts)sources of dust (industrial areas, sandy deserts)• For infra-red astronomy, want atmospheric water vapour For infra-red astronomy, want atmospheric water vapour

content as low as possiblecontent as low as possible• Good weather!Good weather!

– Remote siteRemote site– High altitudeHigh altitude– Little rainfallLittle rainfall– Atacama, ChileAtacama, Chile– Oceanic islands – La Palma, HawaiiOceanic islands – La Palma, Hawaii– Poorer sites: Anglo-Australian Telescope Poorer sites: Anglo-Australian Telescope – Best site – Space!! (HST)Best site – Space!! (HST)

Dr. Matt Burleigh

HST + WFPC 2HST + WFPC 2

• HST / WFPC2 image of a multiple star system including a white dwarf

•Aa (solar-like star) – Ab (white dwarf) = 0.4”

• Image made in ultraviolet at 170nm

• Diffraction limited resolution of HST (2.4m) = 0.02”

• In reality, resolution is more like 0.08”. Why?

Dr. Matt Burleigh

Adaptive opticsAdaptive optics

• Advanced computers and new technologies now allow Advanced computers and new technologies now allow astronomers to compensate for the effects of seeing in real timeastronomers to compensate for the effects of seeing in real time

• It’s called Adaptive OpticsIt’s called Adaptive Optics• First AO systems designed by the military for use with spy First AO systems designed by the military for use with spy

satellites (and their own ground-based telescopes!)satellites (and their own ground-based telescopes!)• 1990s declassified material plus efforts within astronomical 1990s declassified material plus efforts within astronomical

community has led to AO systems being installed at world’s community has led to AO systems being installed at world’s major observatoriesmajor observatories

• Only now becoming really effectiveOnly now becoming really effective• AO system consists of 3 principle componentsAO system consists of 3 principle components

– A deformable mirror (wavefront corrector)A deformable mirror (wavefront corrector)– A wavefront sensorA wavefront sensor– Control system (real-time computer)Control system (real-time computer)

Dr. Matt Burleigh

Adaptive opticsAdaptive optics

Dr. Matt Burleigh

The wave front sensorThe wave front sensor

• Estimates the distortion of the atmosphere Estimates the distortion of the atmosphere along the line-of-sight to the targetalong the line-of-sight to the target

• Requires a bright source near the target Requires a bright source near the target – either a star (Gemini telescopes need stars either a star (Gemini telescopes need stars

brighter than 13brighter than 13thth mag) mag)

– Or a fake star created by a laserOr a fake star created by a laser

– Laser stimulates sodium atoms in a layer at Laser stimulates sodium atoms in a layer at an altitude of about 90km an altitude of about 90km

Dr. Matt Burleigh

The control systemThe control system

• Calculates the corrections required Calculates the corrections required based on inputs from the wave front based on inputs from the wave front sensorsensor

• Commands the actuators which deform Commands the actuators which deform the mirrorthe mirror

• Calculations are performed in sub-Calculations are performed in sub-millisecond range to keep up with millisecond range to keep up with changing atmospherechanging atmosphere

Dr. Matt Burleigh

The deformable mirrorThe deformable mirror

• Piezoelectric actuators deform the Piezoelectric actuators deform the mirror mirror

• The number of actuators required for The number of actuators required for near-perfect corrections in the optical is near-perfect corrections in the optical is several thousand – unrealisticseveral thousand – unrealistic

• AO works best in the IR, where fewer AO works best in the IR, where fewer actuators are requiredactuators are required

Dr. Matt Burleigh

Quantifying AO performanceQuantifying AO performance

• The Freid parameter, rThe Freid parameter, r00

– A measure of atmospheric turbulence A measure of atmospheric turbulence

– rr00 decreases as turbulence increasesdecreases as turbulence increases

– Also, rAlso, r00 is proportional to is proportional to **6/5**6/5

– rr00 can be viewed as the size of a telescope that would can be viewed as the size of a telescope that would

give the same resolution as the atmospheric seeinggive the same resolution as the atmospheric seeing• So if seeing = 1”, rSo if seeing = 1”, r00= 10cm in the optical (using = 10cm in the optical (using /D)/D)

• i.e. ri.e. r0 0 = = seeing in radiansseeing in radians

– Since rSince r0 0 -dependent, then if r-dependent, then if r0 0 = 10cm at 550nm it would = 10cm at 550nm it would

be 70cm at 3.4 microns in the IRbe 70cm at 3.4 microns in the IR– So it is easier to perform AO in the IR than in the opticalSo it is easier to perform AO in the IR than in the optical

Dr. Matt Burleigh

Quantifying AO performanceQuantifying AO performance• The Strehl ratio R is the ratio of the quality of the image The Strehl ratio R is the ratio of the quality of the image

obtained to that of a theoretically perfect point source obtained to that of a theoretically perfect point source image (Airy disk)image (Airy disk)

• R is proportional to rR is proportional to r00 and R improves (ie the image and R improves (ie the image

quality improves) with larger rquality improves) with larger r00

• 0 < R < 1; R=1 is a perfect image0 < R < 1; R=1 is a perfect image– For detection of extra-solar planets, need R>0.9For detection of extra-solar planets, need R>0.9

• As R increases, most of the light is concentrated in the As R increases, most of the light is concentrated in the central core and little in the Airy ringscentral core and little in the Airy rings

• Of course, R is Of course, R is dependentdependent– e.g. an AO system that gives an R of say 0.9 in the IR will only e.g. an AO system that gives an R of say 0.9 in the IR will only

give 0.1-0.2 in the visualgive 0.1-0.2 in the visual

Dr. Matt Burleigh

AO at the USAF AO at the USAF Starfire facilityStarfire facility

Binary Kappa Peg: Binary Kappa Peg:

Uncompensated on 1.5m telescope

756-actuators:

0.3” resolution

3D plot: uncompensated and with full AO (right)

Dr. Matt Burleigh

AO on Gemini NorthAO on Gemini North

Globular cluster NGC6934 observed with the 8m Gemini North telescope on Hawaii, in the visible (left) and in the IR (right) with the Hokopu’a AO system

Dr. Matt Burleigh

Magnification, resolution and plate scaleMagnification, resolution and plate scale• If F= focal length (mm) and D = diameter of telescope, then focal ratio f=F/DIf F= focal length (mm) and D = diameter of telescope, then focal ratio f=F/D• If If angular resolution in arcsecs thenangular resolution in arcsecs then

– Image size s = F tan Image size s = F tan or For F assuming small angles assuming small angles

• An increase in focal length increases the scale of a pattern, but not the An increase in focal length increases the scale of a pattern, but not the resolutionresolution

• Magnification – changes the size of an imageMagnification – changes the size of an image• Resolution – necessary to increase D to see more detailResolution – necessary to increase D to see more detail• Plate scale – no. of arcsec per mm in image planePlate scale – no. of arcsec per mm in image plane

– Plate scale dPlate scale d/ds = 1/F = 206265 / fD/ds = 1/F = 206265 / fD– Rem. 206265 arcsecs/radian Rem. 206265 arcsecs/radian

Dr. Matt Burleigh

Telescopes: summaryTelescopes: summary

• After this lecture you should know and After this lecture you should know and understandunderstand– The definition of diffraction limited resolution The definition of diffraction limited resolution = 1.22= 1.22/D/D– The limitations imposed by atmospheric seeingThe limitations imposed by atmospheric seeing– Overcoming seeing with Adaptive OpticsOvercoming seeing with Adaptive Optics

• Definition of Fried parameter and Strehl ratioDefinition of Fried parameter and Strehl ratio

– Definitions of image size magnification and plate Definitions of image size magnification and plate scalescale