1. Instrumentation Concepts Ground-based Optical Telescopes
Keith Taylor
(IAG/USP)
Aug-Nov, 2008
Aug-Nov, 2008
Aug-Sep, 2008
IAG/USP (Keith Taylor)‏
IAG-USP (Keith Taylor) 1

2. Optical Basics (appreciative thanks to USCS/CfAO)
Adaptive Optics
Optical Basics
(appreciative thanks to USCS/CfAO)
Aug-Nov, 2008
IAG/USP (Keith Taylor)‏

3. 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

4. Turbulence arises in many places
stratosphere
tropopause
10-12 km
wind flow over dome
boundary layer
~ 1 km
Heat sources within dome
Ask class to suggest sources of turbulence

5. Schematic of adaptive optics system
Feedback loop: next cycle corrects the (small) errors of the last cycle

6. Frontiers in AO technology
New kinds of deformable mirrors with > 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

7. 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)‏

8. IAG/USP (Keith Taylor)‏
Aberrations in the Eye
… and on the telescope
Aug-Nov, 2008
IAG/USP (Keith Taylor)‏

9. 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 don’t matter much
But when pupil is large, incoming light passes through the distorted regions
Results: Poorer night vision (flares, halos around streetlights). Can’t image the retina very clearly (for medical applications)
Edge of lens
Pupil
Ask who has seen halos or flares around street lights when driving at night

11. 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

12. 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)‏

13. AO Applied to Free-Space Laser Communications
10’s to 100’s of gigabits/sec
Example: AOptix
Applications: flexibility, mobility
HDTV broadcasting of sports events
Military tactical communications
Between ships, on land, land to air

14. 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

15. “Typical” AO system Why does it look so comlpicated?

16. 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

17. 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 it’s supposed to correct an 8-10m primary mirror?
What are optical aberrations? How are aberrations induced by atmosphere related to those seen in lab?

18. 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

19. Rays and wavefronts

20. Rays and wavefronts
In homogeneous media, light propagates in straight lines

21. Spherical waves and plane waves

22. Refraction at a surface: Snell’s Law
Medium 1,
index of refraction n
Medium 2,
index of refraction n
Snell’s law:
n.sin = n’.sin’

23. Reflection at a surface
Angle of incidence equals angle of reflection

24. 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

25. 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 object’s 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

26. 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

27. Collects all rays that pass through solid-angle of lens
Imaging with lenses: doesn’t throw away as much light as pinhole camera
Collects all rays that pass through solid-angle of lens

28. “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

29. Definition: f-number  f / # = f / D
Thin lenses, part 1
Definition: f-number  f / # = f / D

30. Thin lenses, part 2

32. 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

33. 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

34. 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

35. 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

36. 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

37. 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
h’<0 f s f
Note h’ is up-side-down
and so is <0
Example: f = 10 cm; s = 40 cm; s’ = 13.3 cm:
M = -13.3/40 = -0.33

38. Summary of important relationships for lensesX X

39. 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

40. Optical invariant ( = Lagrange invariant)‏
y11 = y22
ie: A = constant

41. Lagrange invariant has important consequences for AO on large telescopes
From Don Gavel
L = focal length

42. 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

43. Lick Observatory’s 36” Refractor: one long telescope!

44. 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)‏

45. Problems with spherical mirrors
Optical aberrations (mostly spherical aberration and coma), especially if f-number is small (“fast” focal ratio)‏

46. 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

48. Parabolic mirror: focus in 3D

49. Mirror equations Imaging condition for spherical mirror Focal length
Magnifications

50. 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.

51. Heuristic (quantum mechanical) derivation of the diffraction limit
Courtesy of Don Gavel

52. Angular resolution and depth of field
Diameter D z
Diffractive calculation  light doesn’t focus at a point. “Beam Waist” has angular width /D, and length z (depth of field)‏ = 8f2/D2

53. Aberrations In optical systems In atmosphere
Description in terms of Zernike polynomials

54. Third order aberrations
sin  terms in Snell’s 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, .....

55. 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 1 2 3 4 5 1 2 3 4 5

56. Spherical aberration
Rays from a spherically aberrated wavefront focus at different planes
Through-focus spot diagram for spherical aberration

57. 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 didn’t match.

58. HST Point Spread Function plots

59. Spherical aberration “the 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)‏

60. Spherical aberration “ the mother of coma”
Big bundle of spherically aberrated rays
De-centered subset of rays produces coma

61. 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

62. Coma Note that centroid shifts: Rays from a comatic wavefront
Through-focus spot diagram for coma

63. Spherical aberration “the mother of astigmatism”
Big bundle of spherically aberrated rays
More-decentered subset of rays produces astigmatism

64. Through-focus spot diagram for astigmatism
Top view of rays
Through-focus spot diagram for astigmatism
Side view of rays

65. Wavefront for astigmatism

66. Different view of astigmatism

67. Where does astigmatism come from?
From Ian McLean, UCLA

68. Concept Question
How do you suppose eyeglasses correct for astigmatism?

69. Off-axis object is equivalent to having a de-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.

70. 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!

72. Piston
Tip-tilt

73. Astigmatism
(3rd order)‏
Defocus

74. Trefoil
Coma

75. “Ashtray”
Spherical
Astigmatism
(5th order)‏

77. Tip-tilt is single biggest contributor
Units: Radians of phase / (D / r0)5/6
Focus, astigmatism, coma also big
High-order terms go on and on….
Reference: Noll

78. 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 instrument’s optics and to the atmosphere
Can describe both with Zernike polynomials