Download Pupil Mapping (aka PIAA)

Pupil Mapping (aka PIAA)
Robert J. Vanderbei
2007 March 16
What DO We Know Today
TPF-Lite Meeting
Princeton University
http://www.princeton.edu/∼rvdb
Pupil Mapping—Summary
• Create a nonuniform amplitude profile using a pair of mirrors
• Diffraction limits contrast to 10−5
• Pre- and post-apodizers restore desired contrast at expense of throughput and achromaticity
• High throughput and small iwa
• Sensitive to low-order aberrations
• Difficult to manufacture
The Pupil-Mapping Concept
2
Z
Ra
r
r
1.5
z
1
hr
0.5
0
r
a
a
Rr
−0.5
−0.5
0
0.5
a
h a
r
bottom.
0
4
10
3.5
10
3
10
−2
−4
Intensity Relative to Peak
Output Amplitude Relative to Input
High-Contrast Amplitude Profile
2.5
2
1.5
−6
10
−8
10
−10
10
−12
1
10
0.5
10
0
−0.5
−14
−16
0
Pupil−Plane Radius in fraction of Aperture
10
0.5
−60
−40
−20
0
20
Image−Plane Radius in L/D radians
Full Pupil-Mapping System
40
60
Fig. 2.— Left. An amplitude profile providing contrast of 10−10 at tight inner working
angles. Right. The corresponding on-axis point spread function.
Post-apodize here
Pre-apodize here
Occulter
f
Pupil Mapper
f
Reverse Pupil Mapper
– 21 –
Diffraction Analysis of Apodized
Pupil-Mapping
−5
2nd Pupil Amplitude Map
6
Target apodization
Pre−apodizer
Post−apodizer
Achieved apodization
3
2.5
2
1.5
1
0
0.002 0.004 0.006 0.008
Radius (m)
0.01
First surface
Second surface
4
3
2
0
0.012
0
2nd Pupil Phase Map
0.01
0.012
0
Intensity relative to peak
Phase
Phase smoothed
0.15
Phase in radians
0.002 0.004 0.006 0.008
Radius (m)
PSFs
0.2
0.1
0.05
0
−0.05
Lens/Mirror profiles
1
0.5
0
x 10
5
Lens/Mirror height (m)
Output Amplitude Relative to Input
3.5
0
0.002 0.004 0.006 0.008
Radius (m)
0.01
0.012
ideal PSF
achieved @ 632nm
achieved @ 442nm
achieved @ 822nm
−5
−10
−15
−20
0
5
10
working angle in units of λ/D
15
On-Axis PSF at 1st and 2nd Focus
0
first focus (same as ideal PSF)
second focus, no occulter
second focus, with occultor
−2
−4
Log10 Intensity
−6
−8
−10
−12
−14
−16
−18
0
2
4
6
8
10
12
working angle in units of λ/D
14
16
18
Off-Axis PSFs
tilt = 0.0009 λ/D
0.0144 λ/D
0.1155 λ/D
1 λ/D
2 λ/D
3 λ/D
4 λ/D
5 λ/D
0
1st
FOCUS
−1
−2
−3
−4
nd
2
FOCUS
−5
−6
−7
SHAPED
PUPIL
−8
−9
−10
Fig. 6.— Simulated responses due to off-axis sources in apodized pupil mapping and concentric rings. First row: pupil mapping, first focus, after the occulter. Second row: pupil
mapping, second focus (note the expected mirror flip). Third row: concentric ring coronagraph. The columns in this figure represent different off-axis source angles, labeled on the
Cross-Sectional Plot
Log
10
of Intensity relative to response with no obstruction
0
Tilt of 4 λ/D
2 λ/D
1 λ/D
−0.5
−1
−1.5
−2
−2.5
−3
−3.5
−4
0
1
2
3
4
5
6
7
working angle in units of λ/D
8
9
10
Throughput vs. Angle
1
Pupil mapping
Concentric ring shaped pupil
0.9
Total power throughput
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
working angle in units of λ/D
4
5
Sensitivity to Zernikes
Pupil Mapping
−4
(0,0)
(1,1)
(2,0)
−5
−6
(2,2)
(3,1)
(3,3)
−7
−8
−9
(4,0)
(4,2)
(4,4)
−10
−11
−12
Sensitivity to Zernikes
Concentric Rings
−4
(0,0)
(1,1)
(2,0)
−5
−6
(2,2)
(3,1)
(3,3)
−7
−8
−9
(4,0)
(4,2)
(4,4)
−10
−11
−12
Sensitivity to Zernikes
Radial Profiles
(1,1)
(0,0)
(2,0)
0
Ideal Apodization with no aberrations
Concentric Rings
Pupil Mapping (2nd focus)
−2
−4
−6
−8
−10
−12
(2,2)
(3,1)
(3,3)
(4,0)
(4,2)
(4,4)
Log10 of contrast
0
−2
−4
−6
−8
−10
−12
0
−2
−4
−6
−8
−10
−12
0
5
10
0
5
working angle in units of λ/D
10
0
5
10
Shaklan Plots
(1,1)
(2,0)
−5
Concentric rings, 4λ/D
Concentric rings, 8λ/D
Pupil mapping, 2λ/D
Pupil mapping, 4λ/D
Pupil mapping, 8λ/D
−5
10
10
−10
−10
10
10
−4
10
(2,2)
−2
10
0
−4
10
10
(3,1)
−5
0
10
(3,3)
−5
−5
10
10
Contrast
10
−2
10
−10
−10
10
−10
10
−4
10
−2
10
0
10
−4
10
10
−2
10
0
−5
−10
10
−10
−10
10
−2
10
0
10
0
10
−5
10
10
−2
10
(4,4)
−5
10
−4
10
(4,2)
(4,0)
10
−4
10
10
−4
−2
0
10
10
10
RMS of aberration in units of wave
−4
10
−2
10
0
10
Pupil Mapping Lab (Subaru Telescope)
Panels provide thermal, optical
and acoustic isolation
M1
Flat mirror
M2
Light source: He-Ne
laser + SM fiber
CCD
PIAA unit #1
Binary mask
is here
PIAA unit #2
Lens
DM
Wavefront control and a classical apodizer (binary
mask) have been included in the experiment..
Guyon’s Lab Results
Contrast ≈ 6 × 10−4