Coronagraphy with an apodized solar telescope

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Coronagraphy with an apodized solar telescope

• Claude Aime
• Université de Nice Sophia-Antipolis
• Laboratoire Fizeau

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Proposal a telescope with a variable
transmission aperture for high dynamic range
imaging of the Sun and its corona.
Clear aperture
Variable transmission aperture
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A telescope with a variable transmission gives a
apodized PSF with much lower diffraction feet
than a clear aperture. Example of apodization
using the  optimal  prolate spheroidal
function(this function is optimal for exoplanet
detection, not for solar studies)
PSF (linear and log-scales)
Aperture
Apodized aperture is a short cut for  aperture
with a variable transmission giving an apodized
point spread function 
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Apodized aperture vs Lyot coronagraph

• The objective is the same reduce as much as
  possible the halo of diffraction of the solar
  disk at the level of the corona (coronagraphs can
  do that and nothing else !).
• This result is obtained using completely
  different techniques.

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Lyot coronagraph a complex experiment
After an original drawing of Lyot
The principle of the experiment is simple, at a
first glance only. It belongs to the same kind
of experiment as the double diffraction technique
of Abbe and Porter (Fourier optics). The light
is rejected outside the instrument using a Lyot
mask and a Lyot stop.
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Principle of Lyot coronagraph illustrated for a
point source star
stop
mask
A full analytical description for the solar
case is difficult (Ferrari and Aime, ApJ
submitted).
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Apodized aperture (principle)
Focal plane
Center to limb variable transmission window
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Diffraction induces a halo much brighter than the
solar corona each solar point contributes
depending on its distance to the corona and the
PSF

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Diffraction halo Convolution Sun PSF
Airy goes as 1/?3

Too much diffraction light to see the corona
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Use a telescope with a better PSF Airy vs
Sonine (u1)
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Diffraction induces a Halo much brighter than the
solar corona each solar point contributes
depending on its distance to the corona and the
PSF

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Solar points contributing to the diffraction halo
for 2 different PSFs (not to scale, for
illustration only)
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Prolate are not the best functionsfor solar
coronagraphy, simple Sonine transmissions are
much better.
amplitude
intensity
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Comparison of diffraction halosSonine apodized
aperture vs a clear aperture
Limb
corona
Clear Aperture ( ? 0 )
? 1 throughput 1/3
? 1.5 throughput 1/5
?/D
7 arcsec lt 1 Rsun 500 nm 70 cm
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MTF for a Sonine apodization
Apodized aperture MTF
Clear aperture MTF
Amplitude transmission of the aperture
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An apodized window (15 cm, for tests) will be
made at OCA
Vacuum chamber
window
mask
Observatoire de la côte dAzur Nice
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Alternatives ?Dots ?
Produces image replications and very small steps
are needed
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What about shaped apertures ?
The PSF will present a high frequency tail
cannot be used for solar coronagraphy because of
the convolution with the Sun
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StilesCrawford effect
Figure 1 Schematic eye with a wide pupil showing
two identical bundles of rays from a distant
object focused on the retina that enter through
different pupillary regions A, the centre, and
B, near the edge.
Relative luminance efficiency for narrow bundles,
as a function of pupil location of the entering
beam. Data for two sets of measurements three
months apart in the left eye of W. S. Stiles
(Stiles Crawford 1933).
(From Directional sensitivity of the retina 75
years of StilesCrawford effect) Gerald Westheimer
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references

• P. Jacquinot and B. Roizen-Dossier,
  Apodisation, in Progress in Optics 3, E.Wolf,
  ed. (North-Holland, Amsterdam,
• 1964), Chap. 2, pp.29-186, 1964
• C. Aime, Apodized apertures for solar
  coronagraphy,Astron. Astrophys., 467,
  pp.317-325, 2007.
• C. Aime, Radon approach to shaped and apodized
  apertures for imaging exoplanets,Astron.
  Astrophys., 434, pp.785-794, 2005.
• Alexis Carlotti, Claude Aime, Jean Arnaud,
  Marianne Faurobert, André Ferrari, Catherine Grec
  and Gilbert Ricort  Apodized apertures for solar
  coronagraphy 
• SPIE Volume 7014, pp. 701415-701415-8 (2008)