Transcript Laboratory Validation of the Spergel Pupil (AAS Conf.)

An Optimized Pupil Coronagraph:
A New Way To Observe Extrasolar Planets
M. Littman, D. Spergel, N. J. Kasdin
Princeton University
Lyot Coronagraph Performance
To detect our earth around our sun as viewed
from a distance of ~60 lightyears requires the
ability to see two objects with an intensity
contrast ratio of 10-10 and an angular separation
of 50 milli-arc-seconds.
Gaussian Pupil Performance
Earth
Sun
Here we propose a new approach to terrestrial planet
detection using a pupil–based coronagraph and contrast
it to a conventional Lyot coronagraph.
Classical Circular Aperture
Wavelength (l)
Focal plane
The image in the
focal plane is the
spatial Fourier
transform of the
entrance field
The Lyot coronagraph is adjusted for contrast by choosing the
sizes of the Gaussian spot and the Lyot stop. A contrast ratio of
10-10 is achieved for a planet at 50 milli-arc-seconds from the star
with the planet at the half power point of the Gaussian apodizer,
and the Lyot stop at half the size of the entrance pupil. These
conditions give a total system throughput of 3%.
A Better and Simpler Way
to Reduce Diffracted
Light From the Star ...
Like the Lyot coronagraph, the Gaussian pupil coronagraph
is adjusted for contrast and throughput. Here adjustment is
the shape and size of the pupil. A contrast ratio of 10-10 is
achieved with the planet at 4 l/D (50 milli-arc-seconds for l =
0.5 m and D = 8 m) and the throughput is 30%. This figure of
merit is ten times better than that of the comparable Lyot
coronagraph.
The Optimized Pupil Coronagraph
Wavelength (l)
The Gaussian pupil is
optimal if the x
dimension is infinite. For
finite x one can look to
the signal processing
community for better
solutions. One such
solution is based on
prolate spheroidal
wavefunctions.
Focal plane
The Gaussian Pupil Coronagraph
Diameter (D)
Diameter (D)
Wavelength (l)
Entrance Pupil
Airy pattern (first
null at 1.22 l/D)
Focal plane
The clear area of the
pupil as a function of x is
a clipped Gaussian. The
“double hole” form of
the pupil allows for a
larger dark field.
Entrance Pupil
x
Diameter (D)
The Lyot Coronagraph
Modified Pupil PSF Intensities, Single Opening
10 0
Prolate Spheroidal
Kaiser
Gaussianl
Circle (Airy)
10 -2
Entrance Pupil
Focal plane
x
On Axis Performance
of Optimal Aperture
Improves Null by a
factor of 10 and
Improves
Resolution by over a
factor of two.
10 -4
10 -6
10 -8
10 -10
10 -12
10 -14
10 -16
+
before
Entrance Pupil
=
10 -18
•The Gaussian Pupil greatly reduces the
effects of star-light diffraction in a large
triangular field to the left and the right
of the star’s central image.
after
Gaussian
Apodizer
The apodizer (field occulter) blocks
most of the light from the star
Re-imaged Pupil
0
5
10
15
Image Plane Angle (lambda/D)
•The Gaussian Pupil achieves 10-10
contrast ratio in one step.
PSF Intensity of Prolate Spheroidal Aperture
50
•An X-shaped mask can be used to
prevent the bulk of the star-light from
entering the instrument, thereby
minimizing the effects of scattered light.
•Additional stages of filtering can
further improve the contrast ratio.
100
150
200
250
300
350
400
Camera Plane
First Focal Plane
450
500
50
100
150
200
250
300
350
400
450
500
Comparison with theory
PSF Image Intensity for Prolate Spheroidal Double Pupil, beta = 6
CCD
50
100
+
=
150
200
Entrance Pupil
Apodizer
Re-imaged Pupil
Lyot Stop
Post-stop Pupil
The Lyot Stop blocks diffracted light from star more than it
blocks light from neighboring objects such as nearby planets
250
300
The theoretical pattern to the right is the 2D FFT of a
Gaussian pupil. The experimental pattern was
obtained using a green single mode HeNe laser. The
pupil was recorded on a 35mm black and clear
transparency and tested using 25mm dia. optics.
350
400
450
500
50
100
150
200
250
This work was performed for the Jet Propulsion Laboratory, California Institute of Technology, sponsored by the National Aeronautics and Space Administration.
300
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450
500
Size of Dark Region
can be Adjusted by
Moving to Double
Pupil as Shown
Below. A Tradeoff
Exists between Size of
Dark Region and
System Throughput.