Transcript LaPalma_2013_Hook

Telescope Optics
and related topics
http://www.eso.org/~rhook/NEON/LaPalma_2013_Hook.ppt
Richard Hook
([email protected])
ESO, Garching
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Introduction
• I will focus on general principles, mostly optics but also
some related topics like mountings
• Later in the week Michel Dennefeld will talk about the
history of the telescope and many topics will be covered in
more detail by other lecturers
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Some Caveats & Warnings!
• I have selected a few topics, lots of things are omitted
• I have tried to not mention material covered in other talks
(detectors, photometry, spectroscopy…)
• I am a bit biased by my own background, mostly Hubble
imaging. I am not an optical designer.
• I have avoided getting deep into technicalities so apologise
if some material seems rather trivial.
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Scope of Talk
From the sky and through the atmosphere and telescope, but stopping just before the detector!
•
•
•
•
Telescope designs
Optical characteristics
Telescope mountings
The atmosphere
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404 years of the Telescope
ESO VLT, 1999, d=8.2m (x4)
Galileo, 1609, d=2.5cm
E-ELT, 2024, d=39m
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Basic Telescope Optical Designs
Most modern
large telescopes
are variants of
the Cassegrain
design.
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Basic Properties of Telescopes Optics
Aperture = D, Focal Length=f, Focal ratio=F=f/D
For telescopes of the same design the following holds.
•
•
•
•
•
•
•
•
•
Light collecting power - proportional to D2
Theoretical angular resolution - proportional to 1/D (1.22 D)
Image scale (“/mm) - proportional to 1/f (206/f, “/mm, if f in m)
Total flux of an object at focal plane - also proportional to D2
Surface intensity of an extended source at focal plane - proportional to
1/F2
Angular Field of view - normally bigger for smaller F, wide fields need
special designs
Tube length proportional to fprimary
Dome volume (and cost?) proportional to f3primary
Cost rises as a high power (~3) of D
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Mirrors and Lenses
All optical telescopes contain mirrors and/or lenses:
Lenses:
• Have to be made of material with uniform optical properties for transmitted
light (expensive)
• Have refractive indices that are a function of wavelength - hence chromatic
aberrations
• Can only be supported at the edge
Mirrors:
• Fold the optical path so some designs are lead to vignetting
• Have to have surfaces with the correct shape, smoothness and reflectivity
• Can be made of anything that can be held rigidly, figured to the correct smooth
shape and given the right coating
In practice all large modern telescopes are mainly reflecting, with refractive
elements reserved for correctors and small components within instruments.
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Telescope Aberrations
Aberrations are deviations from a perfect optical system. They can be
due to manufacturing errors, alignment problems, or be intrinsic to the
optical design.
• There are five basic monochromatic (3rd order) aberrations:
–
–
–
–
–
Spherical aberration (~y3)
Coma (~y2)
Astigmatism (~y2)
Distortion (~3)
Field curvature
Where y is the linear distance away from the axis on the pupil and  is the
off-axis angle.
The last two only affect the position, not the quality of the image of an object.
• Systems with refractive elements also suffer from various forms of
chromatic aberration
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Spherical aberration
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Optical Aberrations - continued
Spherical
Aberration in action
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Zernike Polynomials
Aberrations may be represented as wavefront errors expressed as orthogonal
polynomial expansions in terms of angular position (and radial distance
( on the exit pupil
he first few are:
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Simplest case - one reflecting
surface
• A concave spherical mirror suffers from severe spherical aberration
and has limited use without additional optics (more about this later)
• A concave paraboloid focuses light to a perfect image on its axis but
suffers from coma (~1/F2) and astigmatism off-axis
• For long focal ratios (f/4 and greater), in the Newtonian design, this
leads to acceptable image quality and is widely used in smaller
telescopes
• For larger apertures a shorter focal ratio is essential and the field of
tolerable aberration becomes very small
• Large telescopes, if they have a prime focus, need correctors (more
later).
• Hyperbolic primaries can be easier to correct and occasionally appear
as “hyperbolic astrographs”.
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Two-mirror Designs
• The primary is concave.
• The secondary is either convex or concave and may be inside or
beyond the prime focus.
• Most common designs have the secondary acting as magnifier so that
the final effective focal length is greater than that of the primary
• If the primary is paraboloidal the secondary will be hyperboloidal
(Cassegrain) if convex and elliptical if concave (Gregorian). The
aberrations of the final image will be the same as those of a single
parabolic mirror of the same focal length - but the telescope will be
much shorter.
• The Cassegrain is more common as it is more compact but Gregorians
may be easier to make and can be better baffled in some cases.
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Two-mirror classical systems
www.telescope-optics.net
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Other two-mirror systems
• The primary does not have to be paraboloidal
• The conic constant (K= -e2) of the secondary can be
adjusted to correct for spherical aberration of the final
image
• Of particular interest is the case where coma is eliminated the aplanatic Cassegrain is the Ritchey-Chretien (RC)
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Why the Ritchey-Chretien?
There are many options for two-mirror telescopes:
•
Classical Cassegrain - parabolic primary, hyperboloidal secondary (coma)
•
Dall-Kirkham - elliptical primary, spherical secondary (easy to make, more coma)
•
Ritchey-Chretien - hyperbolic primary, hyperbolic secondary (free of coma)
•
All suffer from mild astigmatism and field curvature
The RC gives the best off-axis performance of a two mirror system and is used for most (but not all) modern large
telescopes:
ESO-VLT, Hubble, etc
Classical Cassegrain
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Three mirrors and more…
• Many three mirror designs are possible and, with more degrees of
freedom, wide fields and excellent image quality are possible.
• The main problems are getting an accessible focal plane, avoiding
excessive obscuration and construction difficulties.
• No very large examples have yet been built - but become attractive for
ELTs.
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A future large, widefield groundbased survey telescope with a
three mirror design plus corrector - the LSST
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The E-ELT
5 mirror design:
Segmented primary (39m)
Convex monolithic secondary (4m)
Concave tertiary (3m)
Adaptive flat M4 (2.5m)
Fast-moving flat M5 (2.7m)
Field - 10 arcmins (diffraction limited)
Final focal ration - f/16.
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E-ELT Optical Design
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Getting a wider field
• Two mirror designs work well for large general
purpose telescopes
• Typically the usable field is less than one degree
and the final focal ratio is f/8 or greater
• Aberrations rise quickly with off-axis angle and as
focal ratio decreases
• Survey telescopes need a wider field and faster
optics
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Schmidt Camera
•
Spherical primary
•
Stop at centre-of-curvature
•
No coma/astigmatism/distortion
•
Only spherical aberration and field curvature
•
SA is corrected by a thin correcting plate at
the radius of curvature
•
Excellent image quality at f/2 and 6 degree
field.
•
Tube length is twice focal length
•
Legacy - the sky surveys (DSS)
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The ESO 1-metre Schmidt at La Silla
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Catadioptric Systems
• There are many other possible systems with full aperture correcting
plates.
• Correctors can either be the thin/flatish Schmidt type, or a thick
meniscus in Maksutov designs.
• The corrector plate can be closer to the primary to make a more
compact design, with a narrower field.
• Very common as small telescopes as they can be compact and can use
spherical mirrors for ease of manufacture.
• Because of the difficulties in making and supporting large lenses these
systems, like Schmidts, are rarely much larger than 1m aperture.
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Sub-aperture Correctors
• Introducing refractive correctors close to the focus can
suppress residual aberrations and improve image quality
and field size.
• Different types:
–
–
–
–
Field flatteners
Prime focus correctors
Cassegrain focus correctors
(Focal reducers)
• Often part of instruments
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Prime focus correctors
• Wynne corrector (eg, WHT on La Palma):
–
–
–
–
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Expands useful field to around 1 degree at f/3
Spherical surfaces relatively easy to make
Works for paraboloidal and hyperboloidal primaries
Normally only slightly changes effective focal length
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More exotic Prime focus correctors:
• Suprime-Cam, on the Subaru 8m
Copyright: Canon
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An even more exotic corrector:
• Hobby-Eberly 11.1x9.8m, fixed altitude spherical
segmented mirror.
Penn State
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Cassegrain correctors
• A relatively weak corrector in front of the focus of a two
mirror telescope can flatten the field and improve image
quality
• If the original design of the whole telescope includes the
corrector, moderately wide (two degree) fields are possible
with excellent imaging
• Older examples are the f/8 focus of the JKT (with HarmerWynne corrector) and the 2.5m f/7.5 Dupont telescope at
Las Campanas.
• A new example, highly optimised is VISTA
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VISTA - ESO’s IR Survey
Telescope
4.1m, f/1 primary
Large integrated corrector/IR
camera
Modified RC optics
1.65 degree field
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VISTA in action: the
Flame Nebula (NGC
2024) and the
Horsehead Nebula in
Orion in the nearinfrared
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Atmospheric distortion correctors (ADCs)
The problem:
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Atmospheric Dispersion Correctors
• Need to be able to introduce dispersion opposite to that created by the
atmosphere - which varies with zenith distance (two counter-rotating
prisms).
• Want to reduce the image shift introduced, to zero at a given
wavelength - so need to make each component to be a zero deviation
pair of prisms of different glasses itself.
• Prisms can be thin and the wedge angle is small (typically 1.5 degrees)
and they are often oiled together in pairs to increase throughput.
• The design becomes more difficult in converging beams.
• An example - the ADC on the WHT.
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Telescope mountings
• Support the telescope at any desired angle
• Track to compensate for the Earth’s rotation
• Two main types:
– Altazimuth, axes vertical and horizontal
– Equatorial, one axis parallel to the Earth’s axis
• Desirable characteristics:
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–
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Rigid and free of resonances
Accurate tracking
Good sky coverage
Compact (smaller dome)
Space and good access for instruments
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Mountings: examples
• The German equatorial:
Jacobus Kapteyn
1m, La Palma,
1983. (ING/IAC)
Great Dorpat Refractor, 1824.
(Graham/Berkeley)
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Mountings continued:
• The English or “yoke” mount:
The Mount Wilson 100in. From a
book by Arthur Thomson, 1922
(Gutenberg project)
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More modern mounts:
• Pioneer: Hale 5m - horseshoe,
1948
• Also used for many 4m class
telescopes in the 1970s/1980s
(CAHA 3.5m, CFHT, ESO 3.6m,
AAT 3.9m, Kitt Peak 4m etc)
Hale 200in, (Caltech)
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The modern choice: altazimuth fork
• Very rigid and compact
• Access to Cassegrain and Nasmyth focii
• Needs variable rate tracking on both axes
• Field rotation compensation needed
• Dead spot close to zenith
1.2 Euler telescope,
La Silla (ESO)
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Mirror coatings
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The Atmosphere - transmission
J
H
K
A
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The Atmosphere - emission
(at a good dark observatory site, La Palma)
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A Few References
•
Astronomical Optics, D. Schroeder (good overview)
•
Reflecting Telescope Optics (2 volumes), R. Wilson
(comprehensive)
•
Telescope Optics, Rutten & van Venrooij (mostly for
amateurs)
•
The History of the Telescope, King (somewhat dated)
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Part II:
Astronomical Digital Imaging
(a very brief introduction)
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Topics
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•
•
•
•
•
•
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The imaging process, with detector included
The point-spread function
The pixel response function
Artifacts, defects and noise characteristics
Basic image reduction
Image combination
Undersampling and drizzling
FITS format and metadata
• Colour
• Software - the Scisoft collection
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Four Examples:
The power of imaging
HUBBLE: A supernova at z>1
VISTA Survey: Part of the VISTA VVV
survey of the Milky Way bulge and disc in
the infrared (JHKs).
ALMA mm:
Spiral structure
about R Scl
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ESO VLT NACO, nearIR, adaptive optics: the
centre of the galaxy
Image Formation in One Equation
I = SÄO ÄP + N
Where: S is the intensity distribution on the sky
O is the optical point-spread function (PSF, including atmosphere)
P is the pixel response function (PRF) of the detector
N is noise
is the convolution operator
Ä
I is the result of sampling the continuous distribution resulting from the
convolutions at the centre of a pixel and digitising the result into DN.
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The Point-Spread Function
• The PSF is the shape of the image of a point source (such as
a star) at the detector
• It determines the resolution and structure of an image
• The two main influences on the PSF are the optics and the
atmosphere
• PSFs vary with time, position on the image, colour etc
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Groundbased Point-Spread Functions (PSF)
For all large groundbased telescope
imaging with long exposures - without
adaptive optics - the PSF is a function of
the atmosphere rather than the telescope
optics,
The image sharpness is normally given as
the “seeing”, the FWHM of the PSF in
arcsecs. 0.3” is very good, 2” is bad.
Seeing gets better at longer wavelengths.
The radial profile is well modelled by the
Moffat function:
s(r) = C / (1+r2/R2)b+ B
Where there are two free parameters (apart
from intensity, background and position) R, the width of the PSF and b, the Moffat
parameter. Software is available to fit PSFs
of this form.
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The radial profile of a typical
groundbased star image.
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Lucky Imaging
Improving the
PSF – 1)
Lucky
Imaging
Wikipedia
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Lucky imaging (cont)
C14: 35cm, sea level with
lucky imaging (Damian
Peach)
Hubble: 2.4
metre, orbit
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Improving the PSF – 2) adaptive optics
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PSFs in Space
Mostly determined by diffraction and
optical aberrations. Scale with wavelength.
ACS, F814W - well sampled (0.025”
pixels)
WFPC2, F300W - highly undersampled (0.1” pixels)
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From Optics to the Point Spread Function
OPD = optical path difference = wavefront errors (often as Zernikes)
A = aperture function = map of obscurations in pupil (spiders etc)
Then, Fourier optics gives:
P = A e (2  I OPD / ) = complex pupil function
PSF = | FFT(P) |2 = point spread function
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Making Hubble PSFs
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Simple Measures of Optical Image Quality
• Full Width at Half Maximum (FWHM) of point-spread function
(PSF) - measured by simple profile fitting (eg, imexam in IRAF)
• Strehl ratio (ratio of PSF peak to theoretical perfect value).
• Encircled energy - fraction of total flux in PSF which falls within a
given radius.
All of these need to be used with care - for example the spherically aberrated Hubble images
had excellent FWHM of the PSF core but very low Strehl and poor encircled energy.
Scattering may dilute contrast but not be obvious.
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The Pixel-Response Function (P)
•
•
•
•
•
•
The sensitivity varies across a pixel
Once produced, electrons in a CCD may
diffuse into neighbouring pixels (charge
diffusion)
The pixel cannot be regarded as a simple,
square box which fills with electrons
The example shown is for a star imaged
by HST/NICMOS as part of the Hubble
Deep Field South campaign. The centre
of the NICMOS pixels are about 20%
more sensitive than the edges
CCDs also have variations, typically
smaller than the NICMOS example, but
very significant charge diffusion,
particularly at shorter wavelengths
Can affect photometry - especially in the
undersampled case
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Image Defects and Artifacts
• Cosmic-ray hits - unpredictable, numerous, bright, worse from space
• Bad pixels - predictable (but change with time), fixed to given pixels,
may be “hot”, may affect whole columns
• Saturation (digital and full-well) and resulting bleeding from bright
objects
• Ghost images - reflections from optical elements
• Cross-talk - electronic ghosts
• Charge transfer efficiency artifacts
• Glints, grot and many other nasty things
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Some real image defects (Hubble/WFPC2):
Bleeding
Ghost
Cosmic ray
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Charge Transfer (In)efficiency
CCDs are read out by
clocking charge along
registers. These transfers are
impeded by radiation damage
to the chips.
This effect gets worse with
time and is worse in space,
This image is from the STIS
CCD on Hubble. Note the
vertical tails on stars.
Can degrade photometry and
astrometry
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Noise
• For CCD images there are two main sources of noise:
– Poisson “shot” noise from photon statistics, applies to objects, the
sky and dark noise, SNR increases as the square root of exposure
time
– Gaussian noise from the CCD readout, independent of exposure
time
• For long exposures of faint objects through broad filters
the sky is normally the dominant noise source
• For short exposures or through narrow-band filters readout
noise can become important but is small for modern CCDs
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Geometric
Distortion
Cameras normally have
some distortion, typically a
few pixels towards the edges,
It is important to understand
and characterise it to allow it
to be removed if necessary,
particular when combining
multiple images.
Distortion may be a function
of time, filter and colour.
HST/ACS/WFC - a
severe case of distortion more than 200 pixels at
the corners. Large skew.
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Basic Frame Calibration
• Raw CCD images are normally processed by a standard pipeline to
remove the instrumental signature. The main three steps are:
– Subtraction of bias (zero-point offset)
– Subtraction of dark (proportional to exposure)
– Division by flat-field (correction for sensitivity variation)
• Once good calibration files are available basic processing can be
automated and reliable
• After this processing images are not combined and still contain cosmic
rays and other defects
• Standard archive products for some telescopes (eg, Hubble) have had
calibration performed with the best reference files and processed data
are available from the archive
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Image Combination
• Multiple images are normally taken of the same
target:
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–
–
–
–
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To avoid too many cosmic-rays
To allow longer exposures
To allow dithering (small shifts between exposures)
To allow mosaicing (large shifts to cover bigger areas)
To build contiguous images from multi-chip cameras
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Mosaic Cameras
• Detectors cannot be made larger indefinitely
• But larger images are vital for many purposes
• So, many recent imagers are mosaics of detectors
with gaps between the chips
• Examples:
–
–
–
–
–
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WFI @ 2.2-metre (La Silla) (8)
VISTA (16 – IR)
VST (32)
MegaCam @ CFHT (36)
…and many others.
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Dither patterns example: VISTA
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Combining mosaic camera images
• Basic reduction of each chip
• Astrometric calibration of each image against
reference catalogues (eg, 2MASS, GSC etc)
• Mapping and resampling each input image onto
the output grid
• Using appropriate weighting (so, ignoring bad
pixels)
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THELI - a general tools for mosaic reduction
A graphical interface to many
tools (mostly from the Astromatic
collection SExtractor/SWarp/WW/SCAMP
etc)
Can automate image reduction
very effectively.
Supports many instruments - from
Canon Digital SLRs to VLT
instruments.
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Sampling and Frame Size
• Ideally pixels should be small enough to well sample the PSF (ie, PRF
negligible). Pixel < PSF_FWHM/2.
• But, small pixels have disadvantages:
– Smaller fields of view (detectors are finite and expensive)
– More detector noise per unit sky area (eg, PC/WF comparison)
• Instrument designers have to balance these factors and often opt for
pixel scales which undersample the PSF.
– Eg, HST/WFPC2/WF - PSF about 50mas at V, PRF 100mas.
– HST/ACS/WFC - PSF about 30mas at U, PRF 50mas.
• In the undersampled regime the PRF > PSF
• From the ground sampling depends on the seeing, instrument designers
need to anticipate the likely quality of the site (so, typically 0.2 arcsec
pixels at a good site) – normally no special treatment needed
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Combining Undersampled Images
• Undersampled images present particular problems
• Sub-pixel stepping (as done by Hubble) can help
reduce the effects of undersampling
• Special combination tools are needed for best
results
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Undersampling and reconstruction
Truth
After pixel
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After optics
After linear reconstruction
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Drizzling
• A general-purpose image combination method – focussed on
undersampled images
• Each input pixel is mapped onto the output, including geometric
distortion correction and any linear transformations
• On the output pixels are combined according to their individual
weights - for example bad pixels can have zero weight
• The “kernel” on the output can be varied from a square like the
original pixel (shift-and-add) to a point (interlacing) or, as usual,
something in between
• Preserves astrometric and photometric fidelity
• Developed for the Hubble Deep Field, used for most Hubble imaging
now – as well as Herschel/LuckyCam etc etc.
• NOTE: for well-sampled images other, standard tools work as well.
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Drizzling
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Noise in drizzled images
Drizzling, in common with other
resampling methods can introduce
correlated noise - the flux from a single
input pixel gets spread between several
output pixels according to the shape and
size of the kernel. As a result the noise in
an output pixel is no longer statistically
independent from its neighbours.
Noise correlations can vary around the
image and must be understood as they can
affect the statistical significance of
measurements (eg, photometry) of the
output.
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The Effects of Resampling Kernels
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Implemented as MultiDrizzle for HST
- www.stsci.edu/pydrizzle/multidrizzle
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Cleaning Cosmics continued…
The LA-Cosmic
method (van
Dokkum)
Uses Laplace filter
and needs good noise
model - but works
very well.
IDL/Python/IRAF
versions exist.
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FITS format and Metadata
• FITS is an almost universal data exchange format in
astronomy.
• Although designed for exchange it is also widely used for
data storage, on disk.
• The basic FITS file has an ASCII header for metadata in
the form of keyword/value pairs followed by a binary multidimensional data array.
• There are many other FITS features, for tables, extensions
etc.
• For further information start at:
http://archive.stsci.edu/fits/fits_standard/
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FITS Header elements (Hubble/ACS):
SIMPLE =
T / Fits standard
BITPIX =
16 / Bits per pixel
NAXIS =
2
/ Number of axes
NAXIS1 =
4096 / Number of axes
NAXIS2 =
2048 / Number of axes
EXTEND =
T
/ File may contain extensions
ORIGIN = 'NOAO-IRAF FITS Image Kernel December 2001' / FITS file originator
IRAF-TLM= '09:10:54 (13/01/2005)'
NEXTEND =
3 / Number of standard extensions
DATE = '2005-01-13T09:10:54'
FILENAME= 'j90m04xuq_flt.fits' / name of file
FILETYPE= 'SCI
'
/ type of data found in data file
Fundamental properties:
image size, data type,
filename etc.
TELESCOP= 'HST'
/ telescope used to acquire data
INSTRUME= 'ACS '
/ identifier for instrument used to acquire data
EQUINOX =
2000.0 / equinox of celestial coord. System
……
CRPIX1 =
512.0 / x-coordinate of reference pixel
CRPIX2 =
512.0 / y-coordinate of reference pixel
CRVAL1 =
9.354166666667 / first axis value at reference pixel
CRVAL2 =
-20.895 / second axis value at reference pixel
CTYPE1 = 'RA---TAN'
/ the coordinate type for the first axis
CTYPE2 = 'DEC--TAN'
/ the coordinate type for the second axis
CD1_1 = -8.924767533197766E-07 / partial of first axis coordinate w.r.t. x
CD1_2 = 6.743481370546063E-06 / partial of first axis coordinate w.r.t. y
CD2_1 = 7.849581942774597E-06 / partial of second axis coordinate w.r.t. x
CD2_2 = 1.466547509604328E-06 / partial of second axis coordinate w.r.t. y
World Coordinate System (WCS):
linear mapping from pixel to
position on the sky.
….
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Image Quality Assessment: try this!
(IRAF commands in ())
• Look at the metadata - WCS, exposure time etc? (imhead)
• What is the scale, orientation etc? (imhead)
• Look at images of point sources - how big are they,what
shape? Sampling? (imexam)
• Look at the background level and shape - flat? (imexam)
• Look for artifacts of all kinds - bad pixels? Cosmic rays?
Saturation? Bleeding?
• Look at the noise properties, correlations? (imstat)
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A Perfect Image?
What makes a fully processed astronomical image?
•
Astrometric calibration
– Distortion removed (0.1pix?)
– WCS in header calibrated to absolute frame (0.1”?)
•
Photometric calibration
– Good flatfielding (1%?)
– Accurate zeropoint (0.05mags?)
– Noise correlations understood
•
Cosmetics
– Defects corrected where possible
– Remaining defects flagged in DQ image
– Weight map/variance map to quantify statistical errors per pixel
•
Description
– Full descriptive metadata (FITS header)
– Derived metadata (limiting mags?)
– Provenance (processing history)
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Colour Images
• For outreach use
• For visual scientific interpretation
The Lynx Arc
A region of intense star formation at z>3 gravitationally lensed and
amplified by a low-z massive cluster.
This image is an Hubble/WFPC2 one colourised with ground-based
images.
Hanny’s Voorwerp
Spotted because of its colour. Probably a
reflection of a now-switched off quasar.
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Making Colour Images
Developed by Lars Christensen and collaborators:
www.spacetelescope.org/projects/fits_liberator
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Original input images
from FITS files
Colourised in
Photoshop
Final
combined
colour
version:
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Software
Scisoft is a collection of many useful
astronomical packages and tools for Linux
computers. It can be downloaded from:
www.eso.org/scisoft
Most of the software mentioned in this talk
is included and “ready to run”.
There is also a Mac version.
Packages included:
IRAF, STSDAS, TABLES etc
ESO-MIDAS
SExtractor/SWarp
ds9,Skycat
Tiny Tim, CASA, THELI
Note – new 64bit version
coming soon!
July 2013
Python …etc, etc. +
VO tools (new in Scisoft VII)
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The End
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