Instrumentation Concepts Ground-based Optical Telescopes

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Instrumentation ConceptsGround-based Optical
Telescopes

• Keith Taylor
• (IAG/USP)
• Aug-Nov, 2008

Aug-Sep, 2008
IAG-USP (Keith Taylor)
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Adaptive Optics

• Optical Basics
• (appreciative thanks to USCS/CfAO)

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Turbulence changes rapidly with time
Image is spread out into speckles
Centroid jumps around (image motion)?
Speckle images sequence of short snapshots of
a star, using an infra-red camera
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Turbulence arises in many places
stratosphere
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Schematic of adaptive optics system
Feedback loop next cycle corrects the (small)
errors of the last cycle
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Frontiers in AO technology

• New kinds of deformable mirrors with gt 5000
  degrees of freedom
• Wavefront sensors that can deal with this many
  degrees of freedom
• Innovative control algorithms
• Tomographic wavefront reconstuction using
  multiple laser guide stars
• New approaches to doing visible-light AO

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Ground-based AO applications

• Biology
• Imaging the living human retina
• Improving performance of microscopy (e.g. of
  cells)?
• Free-space laser communications (thru air)?
• Imaging and remote sensing (thru air)?

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Aberrations in the Eye
and on the telescope
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Why is adaptive optics needed for imaging the
living human retina?

• Around edges of lens and cornea, imperfections
  cause distortion
• In bright light, pupil is much smaller than size
  of lens, so distortions dont matter much
• But when pupil is large, incoming light passes
  through the distorted regions
• Results Poorer night vision (flares, halos
  around streetlights). Cant image the retina very
  clearly (for medical applications)

Edge of lens
Pupil
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Adaptive optics provides highest resolution
images of living human retina
Austin Roorda, UC Berkeley
With AO Resolve individual cones (retina cells
that detect color)?
Without AO
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Horizontal path applications

• Horizontal path thru air r0 is tiny!
• 1 km propagation distance, typical daytime
  turbulence r0 can easily be only 1 or 2 cm
• So-called strong turbulence regime
• Turbulence produces scintillation (intensity
  variations) in addition to phase variations
• Isoplanatic angle also very small
• Angle over which turbulence correction is valid
• ?0 r0 / L (1 cm / 1 km) 2 arc seconds (10
  ?rad)?

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AO Applied to Free-Space Laser Communications

• 10s to 100s of gigabits/sec
• Example AOptix
• Applications flexibility, mobility
• HDTV broadcasting of sports events
• Military tactical communications
• Between ships, on land, land to air

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Levels of models in optics

• Geometric optics - rays, reflection, refraction
• Physical optics (Fourier optics) - diffraction,
  scalar waves
• Electromagnetics - vector waves, polarization
• Quantum optics - photons, interaction with
  matter, lasers

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Typical AO systemWhy does it look so
comlpicated?
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Simplest schematic of an AO system
BEAMSPLITTER
PUPIL
WAVEFRONT SENSOR
COLLIMATING LENS OR MIRROR
FOCUSING LENS OR MIRROR
Optical elements are portrayed as transmitting,
for simplicity they may be lenses or mirrors
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What optics concepts are needed for AO?

• Design of AO system itself
• What determines the size and position of the
  deformable mirror? Of the wavefront sensor?
• What does it mean to say that the deformable
  mirror is conjugate to the telescope pupil?
• How do you fit an AO system onto a modest-sized
  optical bench, if its supposed to correct an
  8-10m primary mirror?
• What are optical aberrations? How are
  aberrations induced by atmosphere related to
  those seen in lab?

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Review of geometrical optics lenses, mirrors,
and imaging

• Rays and wavefronts
• Laws of refraction and reflection
• Imaging
• Pinhole camera
• Lenses
• Mirrors
• Resolution and depth of field

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Rays and wavefronts
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Rays and wavefronts

• In homogeneous media, light propagates in
  straight lines

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Spherical waves and plane waves
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Refraction at a surface Snells Law
Medium 1, index of refraction n
Medium 2, index of refraction n?

• Snells law

n.sin? n.sin?
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Reflection at a surface

• Angle of incidence equals angle of reflection

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Huygens Principle

• Every point in a wavefront acts as a little
  secondary light source, and emits a spherical
  wave
• The propagating wave-front is the result of
  superposing all these little spherical waves
• Destructive interference in all but the direction
  of propagation

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So why are imaging systems needed?

• Every point in the object scatters incident light
  into a spherical wave
• The spherical waves from all the points on the
  objects surface get mixed together as they
  propagate toward you
• An imaging system reassigns (focuses) all the
  rays from a single point on the object onto
  another point in space (the focal point), so
  you can distinguish details of the object

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Pinhole camera is simplest imaging instrument

• Opaque screen with a pinhole blocks all but one
  ray per object point from reaching the image
  space
• An image is formed (upside down)?
• BUT most of the light is wasted (it is stopped by
  the opaque sheet)?
• Also, diffraction of light as it passes through
  the small pinhole produces artifacts in the image

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Imaging with lenses doesnt throw away as much
light as pinhole camera
Collects all rays that pass through solid-angle
of lens
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Paraxial approximation or first order optics
or Gaussian optics

• Angle of rays with respect to optical axis is
  small
• First-order Taylor expansions
• sin ? ? tan ? ? ? , cos ? ? 1, (1 ?)1/2 ?
  1 ? / 2

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Thin lenses, part 1

• Definition f-number ? f / f / D

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Thin lenses, part 2
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Ray-tracing with a thin lens

• Image point (focus) is located at intersection of
  ALL rays passing through the lens from the
  corresponding object point
• Easiest way to see this trace rays passing
  through the two foci, and through the center of
  the lens (the chief ray) and the edges of the
  lens

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Refraction and the Lens-users Equation

• Any ray that goes through the focal point on its
  way to the lens, will come out parallel to the
  optical axis. (ray 1)?

f
f
ray 1
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Refraction and the Lens-users Equation

• Any ray that goes through the focal point on its
  way from the lens, must go into the lens parallel
  to the optical axis. (ray 2)?

f
f
ray 1
ray 2
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Refraction and the Lens-users Equation

• Any ray that goes through the center of the lens
  must go essentially undeflected. (ray 3)?

object
image
ray 1
f
f
ray 3
ray 2
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Refraction and the Lens-users Equation

• Note that a real image is formed.
• Note that the image is up-side-down.

object
image
ray 1
f
f
ray 3
ray 2
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Refraction and the Lens-users Equation

• By looking at ray 3 alone, we can see
• by similar triangles that M h/h -s/s

object
h
s
image
hlt0
f
f
s
Note h is up-side-down and so is lt0
Example f 10 cm s 40 cm s 13.3 cm M
-13.3/40 -0.33
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Summary of important relationships for lenses
X
X
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Definition Field of view (FOV) of an imaging
system

• Angle that the chief ray from an object can
  subtend, given the pupil (entrance aperture) of
  the imaging system
• Recall that the chief ray propagates through the
  lens un-deviated

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Optical invariant ( Lagrange invariant)?
y1?1 y2?2
ie A? constant
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Lagrange invariant has important consequences for
AO on large telescopes

• From Don Gavel

L focal length
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Refracting telescope

• Main point of telescope to gather more light
  than eye. Secondarily, to magnify image of the
  object
• Magnifying power Mtot - fObjective / fEyepiece
  so for high magnification, make fObjective as
  large as possible (long tube) and make fEyepiece
  as short as possible

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Lick Observatorys 36 Refractor one long
telescope!
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Imaging with mirrors spherical and parabolic
mirrors
f R/2
Spherical surface in paraxial approx, focuses
incoming parallel rays to (approx) a point
Parabolic surface perfect focusing for parallel
rays (e.g. satellite dish, radio telescope)?
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Problems with spherical mirrors

• Optical aberrations (mostly spherical aberration
  and coma), especially if f-number is small
  (fast focal ratio)?

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Focal length of mirrors

• Focal length of spherical mirror is fsp ? R/2
• Convention f is positive if it is to the left
  of the mirror
• Near the optical axis, parabola and sphere are
  very similar, so that
• fpar ? R/2 as well.

f
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Parabolic mirror focus in 3D
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Mirror equations

• Imaging condition for spherical mirror
• Focal length
• Magnifications

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Cassegrain reflecting telescope
Parabolic primary mirror
Hyperbolic secondary mirror
Focus

• Hyperbolic secondary mirror 1) reduces off-axis
  aberrations, 2) shortens physical length of
  telescope.
• Can build mirrors with much shorter focal lengths
  than lenses. Example 10-meter primary mirrors
  of Keck Telescopes have focal lengths of 17.5
  meters (f/1.75). About same as Lick 36
  refractor.

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Heuristic (quantum mechanical) derivation of the
diffraction limit
Courtesy of Don Gavel
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Angular resolution and depth of field
Diameter D
?z

• Diffractive calculation ? light doesnt focus at
  a point. Beam Waist has angular width ?/D, and
  length ?z (depth of field)? 8f2/?D2

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Aberrations

• In optical systems
• In atmosphere
• Description in terms of Zernike polynomials

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Third order aberrations

• sin ? terms in Snells law can be expanded in
  power series
• n sin ? n sin ?
• n ( ? - ?3/3! ?5/5! ) n ( ? - ?3/3!
  ?5/5! )?
• Paraxial ray approximation keep only ? terms
  (first order optics rays propagate nearly along
  optical axis)?
• Piston, tilt, defocus
• Third order aberrations result from adding ?3
  terms
• Spherical aberration, coma, astigmatism, .....

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Different ways to illustrate optical aberrations

• Side view of a fan of rays
• (No aberrations)?

• Spot diagram Image at different focus
  positions
• Shows spots where rays would strike a detector

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5
3
4
1
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Spherical aberration
Rays from a spherically aberrated wavefront focus
at different planes
Through-focus spot diagram for spherical
aberration
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Hubble Space Telescope suffered from Spherical
Aberration

• In a Cassegrain telescope, the hyperboloid of the
  primary mirror must match the specs of the
  secondary mirror. For HST they didnt match.

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HST Point Spread Function plots
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Spherical aberrationthe mother of all other
aberrations

• Coma and astigmatism can be thought of as the
  aberrations from a de-centered bundle of
  spherically aberrated rays
• Ray bundle on axis shows spherical aberration
  only
• Ray bundle slightly de-centered shows coma
• Ray bundle more de-centered shows astigmatism
• All generated from subsets of a larger centered
  bundle of spherically aberrated rays
• (diagrams follow)?

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Spherical aberration the mother of coma
Big bundle of spherically aberrated rays
De-centered subset of rays produces coma
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Coma

• Comet-shaped spot
• Chief ray is at apex of coma pattern
• Centroid is shifted from chief ray!
• Centroid shifts with change in focus!

Wavefront
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Coma
Note that centroid shifts
Rays from a comatic wavefront
Through-focus spot diagram for coma
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Spherical aberrationthe mother of astigmatism
Big bundle of spherically aberrated rays
More-decentered subset of rays produces
astigmatism
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Astigmatism
Top view of rays
Through-focus spot diagram for astigmatism
Side view of rays
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Wavefront for astigmatism
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Different view of astigmatism
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Where does astigmatism come from?

• From Ian McLean, UCLA

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Concept Question

• How do you suppose eyeglasses correct for
  astigmatism?

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Off-axis object is equivalent to having
ade-centered ray bundle
Spherical surface
New optical axis

• Ray bundle from an off-axis object. How to view
  this as a de-centered ray bundle?

For any field angle there will be an optical
axis, which is ? to the surface of the optic and
// to the incoming ray bundle. The bundle is
de-centered wrt this axis.
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Zernike Polynomials

• Convenient basis set for expressing wavefront
  aberrations over a circular pupil
• Zernike polynomials are orthogonal to each other
• A few different ways to normalize always check
  definitions!

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Piston
Tip-tilt
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Astigmatism (3rd order)?
Defocus
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Trefoil
Coma
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Ashtray
Spherical
Astigmatism (5th order)?
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Units Radians of phase / (D / r0)5/6
Reference Noll
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Review of important points

• Both lenses and mirrors can focus and collimate
  light
• Equations for system focal lengths,
  magnifications are quite similar for lenses and
  for mirrors
• But be careful of sign conventions (argh....)?
• Telescopes are combinations of two or more
  optical elements
• Main function to gather lots of light
• Secondary function magnification
• Aberrations occur both due to your local
  instruments optics and to the atmosphere
• Can describe both with Zernike polynomials