Adaptive Optics: basic concepts, principles and applications Short course of lectures

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Adaptive Opticsbasic concepts, principles and
applications Short course of lectures

• Vadim Parfenov
• Res.Ctr. S.I.Vavilov State Optical Institute
• Birzhevaya liniay, 14, St.Petersburg, 199034,
  Russia
• vadim_at_optilas.spb.ru

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Contents

• Lecture 1
• Basic Concepts and Principles
• of Adaptive Optics
• Lecture 2
• Applications of Adaptive Optics.
• New Technologies. Future of AO.

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Lecture 1 Basic Concepts and Principles of
Adaptive Optics
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Light

• Wavelengths (color). Optics deals with the range
  of 10 nm to about 500 mm.
• Visible light occupies range of 350 to 700 nm.
• The speed of light is 300000 km/s and depends on
  the material. Light propagates slower in
  transparent dielectrics.

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Point source

• Point source is an infinitely small source of
  light.
• Point source produces a bunch of rays.
• As light propagates with the speed C in all
  directions, we can define a spherical surface
  indicating the current position of light, emitted
  at zero moment. This surface is a spherical
  wavefront of light source radiation.

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Geometrical optics
Refraction and reflection of light rays are
treated by geometrical optics
Refraction
Reflection
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Imaging optics
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Geometrical aberration
An ideal lens transforms a spherical wavefront
(WF) into a spherical WF image of a point is a
sharp point. In case of an aberration, the WF
deviates from sphere, resulting in a blurred
image of a point source.
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Aberrations

• Aberration can be described in terms of ray
  pointing (homocentric beams).
• Aberration can be described in terms of wavefront
  shape.
• Only spherical wavefront can form a good image of
  a point.

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Diffraction
?
Diffraction limits the resolution of optics !
Beam divergency depends on the beam diameter
(area) and on the wavelength. Another parameter
is the far-field distance, defining the
applicability of geometrical optics.
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Coherence
For spatial coherence all waves should be
statistically in phase over the cross section of
the beam. For temporal coherence the waves should
be statistically in phase over some time delay.
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Some definitions concerned
with Adaptive OpticsA
Wavefront is an abstract representation of the
phase of a propagating wave. It describes a
surface which joins points of equal phase. A
point light source may produce a spherical
wavefront which travels outward from the source.
A flat (or collimated) wavefront may be focussed
down by a telescope or other image-forming device
to a diffraction-limited image.
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In case of astronomical observations
atmospheric turbulence introduces distortions
into the wavefront arriving from an astronomical
source (guide). Such a distorted wave cannot be
focused into a diffraction-limited image unless
some sort of phase correction is applied. r0 is
a time-dependent parameter which entirely defines
the spatial statistics of phase fluctuations
occuring across a telescope aperture. It was
originally defined as the maximum diameter of
telescope which can support diffraction-limited
imaging under the particular conditions of
turbulence.At a good observing site one would
expect r0 to vary between about 1 cm and 20 cm,
depending on the how strong the turbulence is at
the time.
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The Diffraction Limit refers to the
smallest (angular) size of detail theoretically
resolvable by a telescope of a particular size
and shape. This is inversely proportional to the
diameter (D) of the aperture of the telescope, so
a 10m telescope should be able to see details in
the science object which are 100 times smaller
that a 10 cm telescope can. In fact, with
perfect optics, a telescope should be able to
resolve detail which is (wavelength/D) in angular
extent. Unfortunately atmospheric turbulence
blurs the image formed in a telescope so that the
diffraction limit of that telescope cannot be
reached without some sort of correction.
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A Reference Star (or guide star) is a light
source, which is used to provide a wave whose
phase geometry before encountering the atmosphere
is known sufficiently well in order to be able to
measure distortions introduced by the atmosphere.
It needs to be bright enough so that sufficient
photons are collected in order to make a good
estimate of the geometry of the wavefront
distortions. A natural guide star (i.e. an
astronomical source), or even the science object
itself, may be used as a reference star however,
if one is not available close to the science
object then a laser beacon may be manufactured.

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A Laser Beacon is an artificial reference
star which may be manufactured if a sufficiently
bright natural star is not available close to the
science object. It is made by shining a very
high-power laser into a small region of the
atmosphere and collecting and observing light
which is scattered back to the ground. The
Science Object is the astronomical object which
is under study this may or may not be the same
as the reference source used in adaptive optics.

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Phase Corrector is used in an adaptive optics
system to take out some of the distortions
introduced by the atmosphere (or any other
similar phenomena). It often consists of a mirror
(or other optical element) which can be rapidly
deformed to the equivalent shape of the wavefront
which must be subtracted out. A Wavefront
Sensor is used to measure the phase distortions
introduced by the atmosphere into a reference
wave (which are similar to those introduced into
the wave arriving from the science object in the
case of an adaptive optics system). Such a device
may also be used to perform seeing measurements.

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Open-loop is the mode of operation of an adaptive
optics system in which the phase aberrations are
measured but not corrected. In this situation,
the wavefront sensor observes the full
aberrations introduced by the atmosphere during
each cycle. The open-loop frequency is simply the
inverse of the time taken to detect the phase
distortions, calculate the signals required for
correction and drive the phase corrector.
Closed-loop is the mode of operation of an
adaptive optics system in which the phase
corrector is used to correct measured phase
aberrations. Once the loop is closed, the
wavefront sensor will only measure residual, or
uncorrected, phase distortions, i.e. the
difference between the actual phase aberrations
and the most recent position of the phase
corrector.
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A Pupil image is the intensity pattern which is
formed on the telescope pupil in other words it
might be what would be observed on a flat screen
placed just above the telescope, over a region
which corresponds to the shape of the telescope
aperture (usually an annular ring). Normally, one
might expect the pattern to be uniform, but
atmospheric turbulence diffracts the light from a
source above the atmosphere and causes
fluctuations in the pattern, rather like the
ripples seen on the bottom of a swimming pool.
Zernike Polynomials are a convenient set of
circular or annular basis functions which may be
used to represent an arbitary phase distribution
over a telescope pupil in a mathematical form. A
sum of a number of polynomials, each with its own
weighting, may be used to reconstruct an
atmospherically degraded wavefront the higher
the number of polynomials used, the better, in
general, will be the fit to the actual physical
phase distribution.
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History and Basic Concepts of Adaptive
Optics1953 - Horace Babcock, then director of
the Mount Wilson and Palomar Observatories, was
first who suggested how one can build an
astronomical telescope with compensation of
atmospheric seeing (H.Babcock, Publ.
Astron.Soc.Pac., 65, 229(1953)).
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1957 Vladimir Linnik, Russian Academician from
the Vavilov State Optical Institute,
independently described the same concept in
Soviet journal Optika i Spektoskopiya (
V.Linnik, (USSR), Opt.Spectosk., 3, 401
(1957)).  Linnik was first who suggested to use
an artificial beacon to compensate
aberrations of optical imaging systems. (He
proposed to place a portable light source at 8-
to 10-km altitude at the airplane or dirigible to
provide the reference wavefront).
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In 1950s realization of adaptive optical systems
was beyond the technological capabilities For
this reason  first fully operational adaptive
optics system was built and installed by
American military scientists only in the mid of
1970s on a surveillance telescope at Haleakala
Observatory in Maui, Hawaii, USA, where it
imaged satellites launched by the Soviet Union.
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1980 Nick Woolf Roger Angel recognized the
polychromatic nature of adaptive
optics Because the atmosphere is only weakly
dispersive, natural stars measured at optical
wavelengths can be used to correct wavefront
errors at infrared wavelenghts. (N.Woolf,
R.Angel, in Optical and Infrared Telescopes for
the 1980s, A.Hewitt, ed., Kitt Peak Natl.
Observarvatory, Tucson, Ariz. (1980), p..1062)
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1968 M.Kogelnik K.S.Pennington proposed a
concept of holographic correction of aberration
of optical systems. (M.Kogelnik, K.S.Pennington,
JOSA, 58, 273-274 (1968)) 1971 Russian
scientists Yu.Denisyuk S.Soskin carried out
first experiments on an aberrated telescope
primary mirror holographic correction
(Yu.Denisjuk, S.Soskin (USSR), Optika I
Spektroskopiya, 33, 992-993 (1971) ). Works of
M.Kogelnik, K.S.Pennington, Yu.Denisyuk,
S.Soskin beginning of Non-linear Adaptive
Optics.
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1980s beginning of the era of artificial laser
guide stars.   1983 Russian scientists V.Lukin
V.Matyukhin, from the Institute of Atmospheric
Optics (Siberian branch of the Russian Academy of
Sciences), renewed an idea of V.Linnik on the
use of reference light beacon for adaptive image
correction (V.Lukin, Vmatyukhin, (USSR),
Kvantovaya elektronika, 10, 2465-2473(1983) )
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1985 French astronomers Renaud Foy Antonie
Laberyie suggested that backscattered light from
a laser could be used to produce what now is
called a laser guide star ( R.Foy, A.Laberyie,
Astron.Astrophys., 152, L29 (1985) ).   1991
Declassification of the US military research
programs concerned with Star Wars US military
research groups stepped forward to announce that
they too had been investing in both adaptive
optics and laser-guide-star (LGS) researches and
independently devised LGS concept approximately
four years before Foy and Laberyie, but it was
not known in open literature.
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Whats now ?- Era of
building a number of large adaptive
astronomical telescopes.- There are a number of
non-astronomical applications of adaptive
optics
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Principles of Adaptive Optics    
An Adaptive optics system is optical system which
automatically corrects for light distortions in
the medium of transmission in real time. An
adaptive optics system measures the
characteristics of the aberrated wavefront of
incoming light and corrects for it either by
means of a deformable mirror controlled by a
computer or by means of nonlinear optics.
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Two alternative approaches  Linear Adaptive
Optics and Non-linear Adaptive Optics What is
difference ?
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Linear Adaptive Optics Real-time compensation
of wavefront aberrations by means of adjustable
optical elements.
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Non-linear Adaptive Optics Compensation of
wavefront aberrations by means of non-linear
optics phenomena.
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Linear Adaptive Optics deals with optical systems
operating in wide spectral range (astronomical
telescopes, imaging systems, etc.). Non-linear
Adaptive Optics deals with coherent optical
systems (high-power lasers, laser communication
systems, coherent optical imaging systems, etc.).
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Principles of Linear Adaptive Optics    
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Linear Adaptive Optics includes Active and just
Adaptive Optics Active Optics deals with
wavefront errors of rather low temporal (less
than 0.01 Hz) and spatial frequencies.
Adaptive Optics deals with
rapidly varying wavefront distortions (up to 1000
Hz).
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FREQUENCY DOMAIN OF WAVEFRONT ABERRATIONS
GENERATED BY VARIOSLY SOURCES. THE SPATIAL
FREQUENCY IS MEASURED IN TERMS OF D, THE
DIAMETER OF THE TELESCOPE.
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The simplest example for considering principles
of Adaptive Optics is case of astronomical
observations through distorted Earth
athmosphere    
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THE PRINCIPLE OF ACTIVE AND ADAPTIVE OPTICS
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Linear Adaptive Optics Systems work in a
conceptually very simple manner Light arriving
from a distant optical source (star or any
extended object) is essentially a plane (flat)
wave until atmospheric turbulence (or other
aberrant medium) deforms the wavefronts shape
or, equivalently, induces local phase delays
across the wavefront. These deformations or phase
delays in the wavefront can be monitored by
wavefront sensor and compensated by deformable
mirror in real time. Incoming light from an
astronomical source reflected off the deformed
mirror leaves the mirrors surface in its
original pristine state, as it had never
encountered any atmospheric distortions.
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• Principle 3. Wavefront sensing
• The wavefront sensor (WFS) measures the
  distortions in the wavefront of light incoming
  into adaptive optical system.
• Different approaches
• Hartmann method
• Interferometric methods (phase-shifting,
  shearing, two-wavelength
• interferometry)
• Curvature sensing
• Scene-based sensing (WFS operating on image of
  extended object).

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Hartmann Sensor
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The Shack-Hartmann method is the most commonly
used approach.
This approach is completely geometric in nature
and so has no dependence on the coherence of the
sensed optical beam. The incoming wavefront is
broken into an array of spatial samples, called
subapertures of the primary aperture, by a two
dimensional array of lenslets. The subaperture
sampled by each lenslet is brought to a focus at
a known distance F behind each array. The lateral
position of the focal spot depends on the local
tilt of the incoming wavefront a measurement of
all the subaperture spot positions is therefore a
measure of the gradient of the incoming
wavefront. A two-dimensional integration process
called reconstruction can then be used to
estimate the shape of the original wavefront, and
from there derive the correction signals for the
deformable mirror.
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• imager (CCD, CMOS imager)
• limited frame rate
• data-reduction algorithm

• position-sensitive detector matrix (PSD)
• fast readout
• direct spot position output

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Principle 4. Deformable mirrors and wavefront
correctors Deformable mirrors and wavefront
correctors are optical elements which are used to
compensate distortions of wavefront. Two types of
deformable mirrors - Large-size adjustable
mirrors (used to correct slow changes of WF) -
Small-size wavefront correctors (used to
compensate fast changes of WF)
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• Large-size adjustable mirrors
• Large primary mirror of astronomical (or imaging
  telescope) is flexible enough for mechanical
  devices (so-called actuators) to provide constant
  adjustment of its figure in accordance with the
  wavefront measurements.
• Three types of adjustable primary mirrors are in
  the use or under development of present
  technology
• - Continuous mirrors (which maybe moderately
  thin menisci)
• Segmented mirrors (typically structured
  honeycomb separate mirrors)
• Membrane-type (inflatable) mirrors manufacturing
  from thin polymer foil.

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Segmented mirror
Segmented mirror. General view
3-meter segmented mirror of adaptive imaging
telescope developed at the Vavilov State Optical
Institute (St.Petersburg, Russia)
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Small-size wavefront correctors Wavefront
correctors are small-size deformable mirrors (or
other types of adjustable optical elements),
which are used for compensation of
high-frequency (up to 1000 Hz) distortions of
wavefront. Because of the high bandwidth and the
small field, usually wavefront correctors have
diameter of 10 to 20 cm and are located within
the optical train of the telescope or in separate
box behind the focus of the telescope at an image
of the pupil.
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1. Segmented wavefront corrector  
developed at the Vavilov State Optical Institute
(St.Petersburg, Russia) for the space-based
NASA/CSA lidar ORACLE
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2. Bimorph Mirrors
Design of the bimorph mirror
General view of copper bimorph mirror (developed
by the Adaptive Optics group of Russian Academy
of Sciences)

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3. Micromachined Membrane Deformable Mirrors
The shape of tensed membrane is controlled by the
electrostatic attraction to the grid of electrodes
(developed by G.Vdovin, Delft Technical
University, Netherlands)
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4. Liquid-crystal spatial light modulators (LC
SLM)
First application of LC SPMs in Adaptive Optics
- D.Eskov, A.Onokhov, V.Reznichenko, V.Sidorov,
the Vavilov State Optical Institute, Russia
(reported at the SPIE Symposium on Astronomical
Telescopes for 21 century, Hawaii, USA, March,
1994)
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First civil Laser Guide Star System for Astronomy
 
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Lick Observatory of the University of California
on Mount Hamilton near San Jose, C.A., U.S.A
Laser Guide Star Laser Projection System of the
University of California's Lick Observatory
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Three views of the satellite Seasat from
the U.S. Air Force Starfire Optical Range
3.5 m adaptive optical telescope (AF
Kirtland Airbase, NM) (a) through the
turbulence, (b) real time correction using
adaptive optical system, (c) post-processed
with the blind deconvolution algorithm.  
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Principle 7. Multi-modular telescopes The main
idea using the set of separate small-size
telescopic modules one can achive the same
resolution, which can be obtained with
large-aperture primary mirror.      
Design of multi-modular telescopic system
1,2, 5 aspherical mirrors
3,4,6 flat mirrors 7
- spherical mirror 8
receiver of image
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Preliminary conclusions

• Linear AO is applicable to the optical imaging
  systems and can increase the resolution of its
  optics
• Key components of any AO systems include
• - a wavefront sensor to measure the
  distortions of the wavefront coming from a star
  or science object
• - a wavefront correction device (deformable
  mirror or wavefront corrector)
• - a control computer, which can be
  relatively slow for active optics, but must be
  extremely fast for adaptive optics.

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Principles of Non-linear Adaptive Optics  
Compensation of wavefront aberrations by means of
non- linear optics phenomena (phase
conjugation, four-wave mixing, dynamic
holography, etc.) You have to know everything
about it from course of lectures of Prof.
Andreoni !
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PHASE CONJUGATION OF CO2 LASER RADIATION DUE
TO FOUR-WAVE MIXING IN SF6 (?i ?1 mcs)
1 R.C. Lind et al.,1979 - FIRST EXPERIMENTS
WITH TEA CO2 LASERS 2 N.G.Basov, V.P.Kovalev et
al.,1982 - DEMONSTRATION OF HIGH PC FIDELITY 3
D.A.Goryachkin, V.P.Kalinin,N.A.Romanov et
al.,1983 -PCM REFLECTIVITY 100 4
D.A.Goryachkin, V.P.Kalinin, I.M.Kozlovskaya,
V.E.Sherstobitov, 1987 - FIRST EXPERIMENTS WITH
SF ON THE P20 LINE - REFLECTED BEAM PULSE ENERGY
ABOVE 2.5J
5 mm
210-3 rad
restored beam
aberrated beam
initial beam
aberrator
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Preliminary conclusions

• Non-linear AO is applicable to the coherent
  optical systems (including high-power lasers and
  laser optical communication systems)
• Researches in the field of non-linear AO also
  include its application in imaging optical
  systems
• Non-linear AO technology does not require
  investments comparable with linear AO (Lower
  costs) !

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Conclusions

• AO is very promising optical technology which can
  be applicable to the astronomical telescopes and
  optical imaging systems and can increase the
  resolution of its optics
• There are two alternative approaches to
  compensation of wavefront aberrations based on
  the use of Linear AO and Non-linear AO
• AO is a very research-intensive area
• Huge investments in AO technology are still
  necessary to get scientific results and to bring
  financial returns.