Nemati, Bijan

Stahl, Mark

Stahl, Phil

NASA Technical Reports Server

Effect of Space Telescope Primary 
Mirror Segment Errors on 
Coronagraph Instrument 
Performance
Bijan Nemati (U. AL. Huntsville), 
Mark Stahl (MSFC), Phil Stahl (MSFC)
SPIE Optics and Photonics
August 6, 2017
San Diego, CA
https://ntrs.nasa.gov/search.jsp?R=20170008789 2019-08-29T23:09:03+00:00Z
Outline
• Direct imaging of Earth like exoplanets will require a new generation of 
telescopes and coronagraphs
• Many of the proposed designs will involve a segmented primary mirror
• In the past we have studied the sensitivity of coronagraph raw contrast to 
segment errors
• Given the importance of the results, we have reviewed the approach and made 
corrections to the model
• Here we review what are the essential attributes and how we will be modeling 
the sensitivity to telescope errors, starting with the case of the ATLAST 
coronagraph.
• This is a work in progress!
ATLAST 9.2 m
segmented 
variant
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 2
Direct Imaging of Exo-Earths
• Relative to the star, the light from an exo-Earth is faint!
• Planet flux ratio is the fraction of the light arriving 
from the planet relative to the star
• The Earth seen from many parsecs away would have a 
flux ratio of approximately 2e-10
Observer
Exo system
𝛼𝛼
planet
𝑟𝑟𝑝𝑝
LOS
𝑎𝑎
phase 
angle
𝐶𝐶𝑝𝑝𝑝𝑝 = 𝐴𝐴 ⋅ 𝜙𝜙 𝛼𝛼 ⋅ 𝑟𝑟𝑝𝑝𝑎𝑎 2albedo
Phase law
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 3
Coronagraph Basics
• A coronagraph suppresses the starlight to allow 
the detection of the planet which is off-axis.
• There are numerous designs, but most involve 
controlling the diffraction of light by 
manipulating the phase and amplitude at a 
number of planes. Most typically, 3 masks and 
1-2 deformable mirrors are used.
• The result is a ‘Dark Hole’ within which starlight 
is suppressed strongly relative to planet light. 
• The inner and outer working angles are the 
radial limits of a dark hole:
– IWA is the angle below which the planet light 
throughput drops to < 0.5 of its peak value within the 
dark hole. 
– OWA the maximum angle where starlight suppression 
occurs, limited by the number of deformable mirror 
actuators.
IWA
~ 1~4 λ/D
OWA
Dark Hole 
with Speckle(u,v)
(0,0) 
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 4
Pupil Mask
Focal Plane Mask
Lyot Mask
Image Plane
ATLAST Pupil and Coronagraph
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 5
Key Coronagraph Performance Metrics
• The most important measure of a 
coronagraph’s performance is its contrast 
• Contrast is defined as the fraction of light 
leaking into the planet location relative to 
the light arriving if the star was located at 
the planet location
• Another important attribute is throughput. 
• Core throughput is the fraction of the 
entering light from a planet that ends up in 
the point spread function (PSF) “core”
IWA
~ 3 λ/D
OWA
Dark Hole 
with Speckle(u,v)
(0,0) 
𝐶𝐶𝐶𝐶𝐶𝐶(𝑢𝑢,𝑣𝑣) ≡ 𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢,𝑣𝑣; 0, 0)𝐼𝐼𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠(𝑢𝑢,𝑣𝑣;𝑢𝑢,𝑣𝑣)
sourceevaluate
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 6
Core Throughput Vs. Working Angle
• Core throughput drops off as 
we approach the line of 
sight. 
• The Inner Working Angle 
(IWA) is the angle at which it 
drops to half of its maximum 
value in the dark hole
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 7
What Contrast is Good Enough?
• We set the goal to be the direct imaging and characterization of 
an Earth clone at 30 parsecs. Earth flux ratio is about 2e-10.
• Contrast requirement is set by the need to avoid false positives.
• Direct detection needs to have systematic error small enough to 
avoid false alarms: for example, WFIRST requires SNR > 5
• Characterization would require SNR ( >10 for WFIRST) of at least 
10 per spectral element
• As a result, a coronagraph for Earth detection will need to have 
raw contrast in the 1e-10 regime, with stability in the few x 
1e-11 in the observation temporal band of interest
• We need to know what are the tolerances on instrument 
parameters, particularly maximum telescope wavefront errors 
that are allowable given these contrast requirements
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 8
Evaluating Contrast
• One challenge in evaluating contrast, both experimentally and in 
models, is that many pointings are needed 
• Pointings are expensive both in lab testing and in model
• Often, a surrogate for contrast is evaluated instead, 
called the Normalized Intensity (NI):
• NI underestimates throughput loss near the IWA
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 9
𝑁𝑁𝐼𝐼(𝑢𝑢, 𝑣𝑣) ≡ 𝐼𝐼𝐶𝐶𝐶𝐶 (𝑢𝑢, 𝑣𝑣; 0, 0)
𝐼𝐼𝑛𝑛𝑛𝑛 𝐹𝐹𝐹𝐹𝐹𝐹(0,0; 0,0)𝐶𝐶𝐶𝐶𝐶𝐶(𝑢𝑢, 𝑣𝑣) ≡ 𝐼𝐼𝐶𝐶𝐶𝐶(𝑢𝑢, 𝑣𝑣; 0, 0)𝐼𝐼𝐶𝐶𝐶𝐶(𝑢𝑢, 𝑣𝑣;𝑢𝑢, 𝑣𝑣)
Synthesizing A Good Contrast Estimate
• NI is a good estimate after a 
few lam/D so only a few 
pointings are really needed! 
• NI and C near IWA can be 
stitched together
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 10
The Context: An Observing Scenario
• Requirements on contrast need to into 
account the temporal structure of the 
observing scenario
• Speckle subtraction is a key step and 
affects the relevance of different errors
• Reference Differential Imaging Version 
(based on WFIRST):
– Generate dark hole on reference star 
nearby (bright and spectrally similar)
– Measure dark hole on reference star
– Slew to target star and settle
– Integrate on target star
– Chop back to reference start
• The integration is a low pass filter on 
errors, while the chopping is a high 
pass filter. The result is that only a 
limited band in frequency matters.
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 11
reference target targetreference
Sl
ew
 &
 se
tt
le
Sl
ew
 &
 se
tt
le
Sl
ew
 &
 se
tt
le𝜏𝜏𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
𝜏𝜏𝑐𝑐𝑐𝑛𝑛𝑝𝑝
rm
s d
ist
ur
ba
nc
e
time
~20 deg
Target star and planet
2
Bright star for 
acquisition of DH 
1
𝑉𝑉 ≤ 3𝑚𝑚𝑎𝑎𝑚𝑚 𝑉𝑉 ∼ 6𝑚𝑚𝑎𝑎𝑚𝑚
~ 100 available stars
𝑡𝑡𝑐𝑐𝑐𝑛𝑛𝑝𝑝 𝑡𝑡𝐿𝐿𝐿𝐿𝐿𝐿𝐹𝐹𝐿𝐿 𝑡𝑡𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠
How Instability Affects Contrast
• How does the error affect the speckle pattern?
• Instability is amplified by the existing field in the cross term
• However, the cross term is not positive-definite: it can be negative. An 
oscillating cross term can become attenuated if there are many oscillations 
during an integration.
– In that case, the Δ𝐸𝐸 2 term will be the next term to consider
𝐶𝐶 ∝ 𝐸𝐸 + Δ𝐸𝐸 2 = 𝐸𝐸 2 + Δ𝐸𝐸 2 + 2ℛ 𝐸𝐸∗Δ𝐸𝐸
existing field
(static field)
perturbation
(instability)
Cross term
Small oscillating 
perturbing field phase
Δ𝐸𝐸
𝐸𝐸
Small oscillating 
perturbing field amplitude
Δ𝐸𝐸
𝐸𝐸
0 500 1000 1500 2000 2500 3000
t
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
In
te
ns
ity
Intensities of E, E , and their sum
E
*
E
E
*
E
|E+ E |
2
2Re[E
*
E ]
Chopping
A
B
Small oscillating 
perturbing field phase
Δ𝐸𝐸
𝐸𝐸
Chop period
𝐶𝐶 ∝ 𝐸𝐸 + Δ𝐸𝐸 2 = 𝐸𝐸 2 + Δ𝐸𝐸 2 + 2ℛ 𝐸𝐸∗Δ𝐸𝐸
existing field
(static field)
perturbation
(instability)
Cross term
100 s frame 1000 s integration
Applying Segment Errors
• Segment errors evaluated in this study:
– Piston
– Tip/Tilt
– And the Next 15 Zernikes
– Global Aberrations: Tip/Tilt, Power, Spherical Seidel Coma, Bending
– Segment Aberrations: Piston, Tip/Tilt, Power, Astigmatism, Trefoil
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 14
Segment Piston
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 15
Segment Tilt
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 16
Segment Astigmatism
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 17
Summary
• The ATLAST coronagraph design for an obscured segmented 
primary has been modeled to find the sensitivity to various 
segment error modes. 
• Temporal processing and speckle subtraction are an important 
part of the story, and will be incorporated into the model next. 
• We will also be evaluating monolithic and unobscured telescope 
options and coronagraphs. 
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 18
BACKUP
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 19
Example: WFIRS Control Steps
1. Coarse Acquire Bright Star (𝑽𝑽 ≤ 𝟑𝟑)
1. ACS places the star within the imager FOV
2. CGI sends pointing error as sensed by imager to S/C for correction 
2. Preconfigure for Dark Hole
1. The LOWFS determines the tip tilt (T/T), focus (FOC), and LOWF modes
2. LOWFC actuates the FSM to zero out the measured T/T
3. LOWFC initially zeros out focus and LOWF using FocM and DM1
4. CGI configures masks and filters, and presets DM1 and DM2 
3. Generate Dark Hole
1. DM1 and DM2 generate probe fields for dark hole (DH) generation 
2. The system computer iteratively updates DM1,2, re-probes, and makes the DH deeper until delta 
Contrast is low enough
3. CGI sets target FOC, LOWF for LOWFS/C based on current state; T/T setting is stored (≡TTDH)
4. Slew to Science Star
1. ACS used to slew S/C to science star: FocM, DM1, DM2 frozen, TTDH saved
5. Acquire Science Star
1. Similar to Bright Star Acquisition, then:
2. LOWFC actuates the FSM targeting T/T  TTDH from best dark hole
6. Set Dark Hole and Integrate
1. LOWFSC maintains T/T FOC, LOWF at targeted values
2. DM1, DM2 are only modified to maintain LOWF 
20
~20 deg
Science star
2
Bright star for 
acquisition of DH 
1
𝑉𝑉 ≤ 3𝑚𝑚𝑎𝑎𝑚𝑚
𝑉𝑉 ∼ 6𝑚𝑚𝑎𝑎𝑚𝑚
~ 100 available stars
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph
The HabEx WF sensitivity paper
1. We are evaluating a number of options for the HabEx telescope. The baseline option currently is the monolith 
4m off axis
2. The dominant sensitivities of this design are to
1. LOS error (via beamwalk on secondary)
2. Seidel power and coma ?
3. Our plan is to ultimately create a feasibility assessment using integrated modeling of the HabEx instrument. For 
now we are taking initial steps. 
4. In the present paper, we are simply checking a few coronagraph design variations on the baseline design (4m 
monolith) [and possibly one segmented variation]
5. For each case, we start with
1. An amplitude of aberration
2. Existing surface power law or other aberration specification
3. (Temporal frequency of the aberration change)
6. We do EFC on the static error (contribution from Garreth Ruane)
1. This is our initial field in the dark hole
7. We then apply the deformation, and compute the delta field and mix it with the existing field
8. We then report the resulting contrast per amplitude of the delta aberration
9. What we are working on right now is implementing the nominal coronagraph for VVC charge 6 and above
10. The paper can include VVC 6 and 8 
11. It will be a work in progress
12. Later work will include the temporal analysis and observing scenario integration
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 21
Effects of Space Telescope Primary Mirror Segment Errors on Coronagraph Instrument Performance
Mark T. Stahl, H. Philip Stahl, NASA Marshall Space Flight Ctr. (USA); 
Stuart B. Shaklan, Jet Propulsion Lab. (USA). [10398-16]
Bijan Nemati, The University of Alabama in Huntsville. (USA)
Abstracts:
Long Version
Direct imaging of potentially habitable planets is challenging because of the relative proximity of the 
planet to the star and the low flux ratio (typically well under 1e-9 in the visible) of the planet relative to 
the star. Future exoplanet direct imaging telescopes like the Habitable Exoplanet Imaging Mission (HabEx) 
will hence require large collecting apertures with very low wavefront errors. The feasibility of these 
missions is in a large part dependent on the sensitivity of the achieved contrast at small working angles to 
imperfections and motions of the telescope optics. In past studies, we explored the effect of applying 
specific modes to segmented and monolith telescopes on the contrast leakage of a coronagraph. Here we 
extend the results to combined modes and incorporate some of the latest coronagraph designs.
Short Version
Direct imaging of potentially habitable exoplanets is challenging because of the small planet-star angle 
and the low flux ratio of the planet relative to the star. The feasibility of future direct imaging missions like 
HabEx is in a large part dependent on the sensitivity of the achieved contrast at small working angles to 
imperfections and motions of the telescope optics. In past studies, we explored the effect of applying 
specific modes to segmented and monolith telescopes on the contrast leakage of a coronagraph. Here we 
extend the results to combined modes and incorporate some of the latest coronagraph designs.
8/6/2017 B. Nemati SPIE 2017 Segment Errors & Coronagraph 22


Effect of Space Telescope Primary Mirror Segment Errors on Coronagraph Instrument Performance

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