Interferometra

1
Interferometría

• El caso más sencillo Interferómetro de Fizeau
• Una fuente puntual y monocromática en el infinito
• 2 pinholes (hoyitos de diámetro despreciable) en
  la pupila.

• Queremos conocer la intensidad en el punto r del
  plano focal de la lente (telescopio).
• En cualquier libro de óptica encuentran el
  desarrollo clásico (v.g. Hetch Optics).
• Con óptica de Fourier, verán que se hace en dos
  patadas.

D
F
r
2
El caso más sencillo
TF
D
TF
F
r
3
Y si el Objeto No Es Puntual ?
TF
D
TF
F
r
4
Y si el Objeto No Es Puntual ?
D
F
r
5
Y si el Objeto No Es Puntual ?

• Y la intensidad

GRADO DE COHERENCIA ESPACIAL Para un radiación
incoherente
Empezamos a adivinar franjas
6
Y si el Objeto No Es Puntual ?
FRANJAS TFOBJETO
FRANJAS VISIBILIDAD
Visibilidad
D
D
7
Llenando el plano UV

• Midiendo la visibilidad para distintos valores de
  u se va llenando el plano de la TF del objeto.
• Esto se logra con varios pares de telescopios,
  y/o variando la separación entre ellos, y/o l.
  Una manera es dejando que la tierra gire.

DBcos(q)
q
B

8
Llenando el plano UV

• En radio es más facil medir la visibilidad del
  objeto, ya que se mide la onda (amplitud y fase)
  proveniente de cada telescopio, mientras que en
  el óptico se mide la intensidad de la
  interferencia.
• Se demuestra que (Teorema de Zernike-Van
  Cittert)
• En radio se mide directamente G(u).

9
Radiointerferometría

• Como un telescopio con pupila en Y.
• Resolución dada por la separación máxima.
  Ejemplo para l7 mm y B 36 km,
• e0.04
• El plano de la pupila se va llenando gracias a la
  rotación de la Tierra.

Hasta 36 km
10
Fluctuaciones de Vapor de Agua

• Recordemos en l milimétrica, DH ?
  DN
• 
  ? Df

?
CN2(h) , v(h), L0(h)
Tropósfera lt 5 km
11
Función de Estructura en el VLA
?rms(?) ? ?(r) - ?(r?) 2 ? 1/2
5/6
1/3
For Kolmogorov Law ?rms(?) l-1 ? a
Para l1 mm, r0 cientos de metros
Carilli et al. 1998
12
Fast Switching para Corregir la Fase
HH47
El interferómetro mide ?(r) - ?(r?) de forma
natural. Esta información se usa para formar
imágenes. Al observar un objeto puntual, ?(r) -
?(r?) proviene de la atmósfera y de los
instrumentos. Tiempo del ciclo 1
a 10 s !!
r
El error depende de rh v Dt
rh
v
h
13
Review on Observational Methods for the Study of
Optical Turbulence
IAU Workshop Site 2000 Marrakech 2000
14
Outline

• History Before a quantitative description
• Parameters of optical turbulence a sketch
• Methods for profiling optical turbulence
• In situ measurements
• Scintillation
• Radar, Sodar, Lidar
• Methods for the study of integrated parameters
• Long exposure images, Scintillation
• Angle of Arrival, Centroid motion
• Reconstructed Zernikes
• Interferometry
• Speckle interferometry
• Curvature
• Perspectives

Only earliest references will be given
15
History Before a Quantitative Description

• Twinkling of stars has been noticed all over
  history
• One of the first references Aristotle in The
  Heavens
• Hooke (1665) Small moving regions of atmosphere
  having refracting power which act like
  lenses
• Newton (1730) The air in which we look is in
  perpetual tremor
• Danjon (1926) Semiquantitative visual scale of
  seeing
• Couder (1936) Photography of star trails
• Whitford Stebbins (1936) Photoelectric
  detection of scintillation
• Reviews of semiquantitative measurements of image
  quality
• Stock Keller (1960)
• Meinel (1960)
• Rosch, Courtes and Dommanget (1965)

• The era of quantitative measurements began with
  the description of Wave Propagation in a
  Turbulent Medium by Tatarskii (1961)

16
Parameters of Optical Turbulence
Fried 66, Roddier 1982, Fried Belsher 1994,
Borgnino 1990
17
Methods for Profiling In Situ Measurements

• Balloon-borne microthermal measurements (Coulman
  1973, Bufton 1973)

Azouit et al.

• Metheorological data numerical model
  (Coulman et al. 1973)
• In situ measurements of the average T, P, V
  profiles
• numerical model to estimate CN2(h)
• See review talk by E. Masciadri

18
Profiling Scintillation ( CN2(h) with Scidar )
?
Rocca et al. 1974, Tallon 1989, Avila et al. 1997
1
h
hgs
d1? ( h hgs )
Scintillation
19
Profiling Scintillation ( V(h) with Scidar )
?
Kluckers et al. 1998 Avila 1998
h
hgs
d? (h hgs)
d
instant t
instant t
instant t
instant t?t
20
The Instrument
D
hgsgt0
P
ftel
Lfield
Lcol
fcol
hgslt0
P
hgsgt0
hgslt0
Detector
Digitising card DSP C80
21
Data Processing
t
t20ms
t40ms
Profile
Power spectrum
Autocorrelation
TF
TF
TF
Maximum entropy
Cross spectrum 1
Cross correlation 1
Cross spectrum 2
Cross correlation 2
22
Profiling Scintillation ( Single Star )

• Spatio-temporal cross correlation (Rocca et al.
  1974)
• Peak position g V
• Peak width (lh)1/2 g h, Peak intensity g CN2
• But fluctuations of V (DV) spread peak and
  decrease its intensity
• Ambiguity can be broken with cross
• correlations at different Dt (Caccia
  Vernin 1990)

• Spatial filtering of scintillation (Ochs et al.
  1976)
• g CN2(h) with low vertical resolution
• New ideas for CN2 profiling using single-star
  scintillation
• See talks by M. Chun and A. Tokovinin
• Scintillation of uneclipsed sun measured with an
  array of photodiodes
• g daytime CN2(h) (Beckers Mason 1998) see talk
  by J. Beckers

23
Profiling CN2(h) with Other Techniques

• Radar (Ottersen 1969)
• Eddies of size lR/2 backscatter radar signal
• But influence of humidity is hard to remove
• Sodar (Wesely 1974)
• Thermal turbulence backscatters sodar signal
• Range up to 1.5 km
• Calibration resolved
• Lidar (Belenkii Gimmestad 1994)
• Proposed to measure the variance of laser beacon
  image jitter at different altitudes
• Angle of Arrival (AA) from Solar Limb
• Angular Structure function of AA (Bouzid et al
  1999)
• D(q) lta(x)-a(xq)2gt ? CN2(h) F(h,q) dh
• See talk by A. Bouzid

24
Integrated Parameters

• Long exposure images of point sources
• Telescope aberrations included
• Telescope vibrations and guiding errors included
• Scintillometer
• Simple
• Ambiguity variance depends on CN2(h) and on h
• sI2 19.12 l-7/6 ? dh h5/6 CN2(h)

eA eT
25
Angle of Arrival (AA) - Image Motion

• Shack Hartman sensor AA measurements
• Spatial studies (Dayton et al. 1992, Ziad et al.
  1994, )
• Structure function, spatial correlation
• g r0 , test of Kolmogorov turbulence, L0
• Temporal studies (Soules et al. 1989, Madec et
  al. 1993)
• Spatio-temporal structure function,
  spatio-temporal correlation
• g r0 , ?0 , test of Kolmogorov turbulence,
  Taylors hypothesis
• g Velocity of different layers (Gendron Lena
  1996)

Imperial College
26
Angle of Arrival (AA) - Image Motion

• Generalized Seeing Monitor
• ( Martin et al. 1994 )
• Angle of Arrival (?) in 1 direction
• Variance ? r0
• Spatial covariance ? L0
• Temporal cross-correlation ? ?0
• Scintillation ? q0
• 4 independent modules
• Any bright single star
• 6 baselines at a time in 2D
• See talks by F. Martin and
• A. Ziad

Photo Martin, Nice U.
27
Angle of Arrival (AA) - Image Motion

• Differential Image Motion Monitor DIMM (Stock et
  al. 1960, )
• Centroid spatial structure function
• g r0 , considering Kolmogorov spectrum
• Effect of exposure time (Martin 1987, Soules et
  al. 1996)
• Effect of outer scale (Ziad 1993 )
• Velocity of AA fluctuations (Lopez 1992 )
• g t0 , considering Kolmogorov spectrum

Washington U.
Washington U.
28
Angle of Arrival (AA) - Image Motion

• Extended objects
• Solar limb (Irbah et al. 1993)
• Moon edge (Ghedina et al. 1998)
• Angular structure function or correlation of AA
• g isokinetic patch
• differential measurements

Edge position g AA
columns
29
Interferometry

• Rotation Shear interferometer (Roddier 1976, )

• Fringe contrast at B2r
• r0
• model independent

-r


r
Pupil
Interferogram
Rotated pupil tilt
30
Other Techniques

• Speckle interferometry (Weigelt et al. 1986, Aime
  et al. 1986, )

• Autocorrelation
• g Atmospheric PSF, r0
• Spatio-temporal correlation g t0
• Spation-angular correlation g q0

Avila et al.
31
Perspectives

• Fundamental questions suited for experimental
  studies
• Horizontal extension of individual turbulent
  layers ?
• Characteristic time of individual turbulent
  layers ?
• Why L0 10 m while L0 25 m ?
• Needs of muticonjugate adaptive optics and ELT
• CN2 and v profiles monitoring in real time
• In 3-D ?
• Time for forecasting CN2(x,y,h) and v(x,y,h) ?
• Dual approach measurements forecasting