# Presentation: 756835

## New Worlds OccultersWebster CashUniversity of ColoradoSeptember 29, 2006

- New Worlds OccultersWebster CashUniversity of ColoradoSeptember 29, 2006

## New Worlds Contributors

- Webster Cash	University of Colorado
- Jim Green
- Eric Schindhelm
- Jeremy Kasdin	Princeton University
- Bob Vanderbei
- David Spergel
- Sara Seager		Carnegie Institution – Washington
- Alan Stern		Southwest Research Institute – Boulder
- Steve Kilston	Ball Aerospace
- Tom Bank
- Charlie Noecker
- Jim Leitch
- Jon Arenberg	Northrop Grumman
- Ron Polidan
- Chuck Lillie
- Amy Lo
- Glenn Starkman	Case Western
- Sally Heap		Goddard Space Flight Center
- Marc Kuchner
- Keith Gendreau
- 				*and growing...*

## Important Caveats

- New Worlds is an emerging mission concept
- Rapidly developing with a small team
- Recent emphasis was on Discovery proposal, not a TPF-C class mission
- TPF mission under very active study
- There is no mission design or final concept
- We have found no obvious impediments to such a mission
- It is a major goal of this talk to inform the audience on how occulters do and do not work
- Given the limited time here, the results are sample of the work that has been done

## Overview of the Occulter Hour

- Development and performance of the occulter (Cash-CU)
- Occulter modeling (Lyon-GSFC)
- Overview of architecture trades (Arenberg-NGST)
- Alignment (Noecker-Ball)
- Summary (Arenberg-NGST)

## Origin:  2002-2003

- Maxim was stalled
-  Still is
-  Maxim was outgrowth of 1999-2001 NIAC
- Was there a way to apply Maxim technology to a more immediate problem?
- Noticed that TPF and Maxim were both driven by the need for high performance optics
-  Personally, the only thing I find as exciting as imaging a black hole is finding and imaging Earth-like planets
-  Decided to try my hand at the exo-planet game

## June 2003

- Came up with the Pinhole camera idea
-  It was not MAXIM, but a rather a refusion and reapplication of the Maxim approach

## A Pinhole Camera Meets The Requirements:

- 	Perfect Transmission
- 	No Phase Errors
- 	Scatter only from edges – can be very low

- Large Distance Set by 0.01 arcsec requirement
- 	diffraction: /D = .01”  D = 10m   @500nm
- 	geometric:  F = D/tan(.01”) = 180,000km

## Slide 8

## “Standard” Observatory Views Starshade

- ~1” resolution or somewhat better (not diffraction limited!)
- High efficiency, low noise spectrograph (e.g. COS)

## View Back Toward Starshade

## Starshade Aperture Shapes

## Focal Plane 

## View Dark Side of Starshade

## Planet Finding Mode

- Solar System at 10pc

- Survey to 7AU

- Survey Habitable Zone

- Jupiter

- Earth

- Venus

- Mars

- Venus

- Earth

## Why Pinhole Camera?Why Not Occulter?

- Because 

- Everybody knows that diffraction around an occulter is too severe

## Occulters

- Several previous programs have looked at occulters
- First look by Spitzer (1962)
- Marchal (1985) Used simple petal shapes
- Achieved 10-5 suppression across a broad spectral band
- With transmissive shades
- Achieved only 10-5 suppression despite scatter problem

- http://umbras.org/

- BOSS

- Starkman (TRW ca 2000)

## Extinguishing Poisson’s Spot 

- Simple Occulters Have Very Poor Diffraction Performance
- The 1818 Prediction of Fresnel led to the famous episode of:
- Poisson’s Spot  (variously Arago’s Spot)
- Occulters Often Concentrate Light!
- Must satisfy Fresnel Equation, Not Just the Fraunhoffer Equation
- Must Create a Zone That Is:
- Deep   	Below 10-10 diffraction
- Wide   	A couple meters minimum
- Broad    	Suppress across at least one octave of spectrum
- Must Be Practical
- Binary  	Non-transmitting to avoid scatter
- Size  	Below 150m  Diameter
- Tolerance   	Insensitive to microscopic errors

## The Vanderbei Flower

- Developed for Aperture in TPF focal plane
- Was to be only millimeters across
- Vanderbei had determined it would work for the pinhole camera but did not necessarily work for occulter.
-  Agreement that it was worth a look

## Breakthrough

-   From 11/17/04 to 4/12/05 worked on diffraction codes
-  Put the problem out there for whomever to solve
-  At one point had 3 professors, 2 engineers and 4 students
-  On April 12 last year (after Phase I, before Phase II due)
-  Had working code
-  Was trying functions  (as opposed to VDB generalized forms)
-  Tried OFFSET gaussian
-  Ten minutes later had a solution
-  In June discovered hyper-gaussians even better

## The Apodization Function

- for

- for

- and

- Found this in April.  Extended in June.
- This Function Extinguishes Poisson’s Spot to High Precision

## Performance

- A 50m diameter occulter at 50,000km will reveal Earths at 10pc

- a=b=12.5m
- n=6
- F=50,000km

***Arenberg and Cash (2005)***

## Occulters Are Fundamentally Fresnel(Never Ever Fraunhoffer)

- The central Fresnel zone and the eight inner half zones are shown schematically. The dark star in the centre represents a mask that is confined to the region where the Fraunhoffer approximation can be used.  It is clear that such a mask will integrate out to a net positive contribution in the focal plane.

## Suppression of Edge Diffraction Can Be UnderstoodUsing Fresnel Zones and Geometry

- The occulter is a true binary optic
- Transmission is unity or nil
- Edge diffraction from solid disk is suppressed by cancellation
- The power in the even zones cancels the power in the odd zones
- Need enough zones to give good deep cancellation
- Sets the length of the petals
- Petal shape is exponential
- b  is scale of petal shape
- n is an index of petal shape
- a is the diameter of the central circle

- a

- b

## Huygens-Fresnel Principle

## Fresnel Approximation

- Then, if circularly symmetric:

## Babinet’s PrincipleNecessary for Integration Across Shade

- We seek E2=0 or:

- or

- To simplify math we concentrate on the center of the shadow (s=0)

- We seek A() such that:

- or

## Now, Evaluate Candidate Apodization Function

## Dimensionless Natural Units

## Electric Field at Center:

## Integrate by Parts

- Yields  E = 1+R where R is small as desired
- And

- This closed-form integral represents the electric fieldat the center of the shadow

## Continue Integrating by Parts

- Drop Small Terms
- Dominant Term

**If  ********2 ****>> n**

## Binary Apodization

- Difference between petalsand circularly symmetricapodization.

## Tolerance Analysis

- Procedes by perturbation analysis
- Pitch or Yaw error – foreshortened to 1- in one dimension

- Reduces to:

- Proving

- Where z=x/(1-)

## Starshade Tolerances

- Position
- Lateral		Several Meters
- Distance		Many Kilometers
- Angle
- Rotational		None
- Pitch/Yaw		Many Degrees
- Shape
- Truncation		1mm
- Scale			10%
- Blob			3cm2 or greater
- Holes
- Single Hole		3cm2
- Pinholes		3cm2 total

## Fresnel Propagation from External Occulter

** ****Parallel “C/MPI” code to ****(512 node Beowulf):**** **
**    ****- Model occulter**
**    ****- Fresnel propagate to telescope**** **
** ****Current grids 32768 x 32768**
** ****Don’t yet get theorectical limit**
** ****Aliasing from small structure ?**
**     ****- No aliasing from Fresnel ripples (low Fresnel #)**
**     ****- from small scale structure ?**

- R. Lyon
- 09/29/06

- Real part of field at mask

## Occulter Systems Terrestrial Planet Finding

**Jon Arenberg**
**Amy Lo**
**Chuck Lillie**
**Richard Malmstrom**
**Ron Polidan**

## Occulter Based TPF Missions are Viable

**Occulter 101**
**Sufficient suppression of star light at the same time as achieving small IWA**
- Sizing and spacing of the occulter
- How does the occulter handle challenges to performance
**What would a mission look like?**
**How is occulter telescope alignment established and maintained (Charley Noecker)**

**Experimental Results; Leviton and Cash (In Prep)**

## The Basic NWO Architecture

**Occulters blocks on-axis star light **
**Telescope looks at off-axis star light to observe companion**

## The Occulter Parameters

| Parameter | Symbol | Affects.... |
| --- | --- | --- |
| solid disk radius | a | IWA, stellar suppression |
| Gaussian radius parameter | b | IWA, stellar suppression |
| the petal shape parameter | n | Observation wavelength |
| Occulter separation | F | IWA, stellar suppression |
| number of petals | P | Minimum needed |

## Two Effects of the Occulter

- Image at aperture:
- Diffraction pattern produced by occulter, color indicates the achievable stellar suppression

- Image at focal plane,
- the Occulter’s “PSF”, note that outside of the IWA, it’s dark!

- star

- occulter

- telescope

**LOG **
**Scale**

**LOG **
**Scale**

**R**

## The Occulter PSF

- Occulter acts as an optical element and focuses incident starlight to the entrance pupil
- The intensity of the starlight is greatly decreased, and the phase is distorted by the destructive interference caused by the occulter petals
- The telescope optics therefore produces a defocused residual stellar image at the focal plane, here called the stellar leakage
- Inside a certain radius on the focal plane, defined as the IWA, the stellar leakage is bright, and can be thought of as the occulter’s “PSF”

- These four points are artifacts of diffraction calculated with a square grid

**LOG Scale**

## The Occulter PSF

- Incomplete destructive interference produces gradual roll off of the residual stellar leakage
- The leakages decreases with radial distance from the occulter center, and is the chief source of the “background” signal OUTSIDE of the IWA
- Planet light compete with this background signal
- The correct figure of merit used to judge the NWO occulter is to measure the signal to noise of this background with incident, off-axis planet light

- These four points are artifacts of diffraction calculated with a square grid

**LOG **
**Scale**

## NWO Only Needs 10-8 Suppression

- In order for the planet light to be above the background, the occulter only needs to achieve 10-8 stellar suppression between the star and the planet
- We are in fact measuring the planet signals inside the wings of the stellar PSF, which gives us the extra factor of 100 reduction

**10****-10**** Suppression****	****	**** 10****-9**** Suppression ****	**** ****	****10****-8**** Suppression**

**Linear **
**Scale**

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 0 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 50 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 70 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 75 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 80 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 85 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 90 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 100 mas

- LOG Scale

- Linear Scale

## “Movie” of Planet moving Off-Axis Suppression at Suppression = 10-10

- 110 mas

- LOG Scale

- Linear Scale

## Occulters Capable of 10-10 Suppression

**Occulters that achieve the desired suppression**

**Occulters that do NOT achieve desired suppression**

**The following were generated using 1-D FrFT simulation**
**All numbers shown are real results, no approximations have been made**
**4 m telescope (on axis)**
**Maximum wavelength 800 nm**
**Order 6 occulter**

## Occulters IWA Less Than 100 mas

**Occulters with IWA smaller than 100 mas**

**Occulters with IWA larger than 100 mas**

## Intersection Identifies Viable Parameter Space

**Intersection Identifies Viable Parameter Space**

**There is a minimum size occulter for a given set of requirements**
- Different plot for hypergaussian order and maximum wavelength
**This size does not account for known liens on performance**

**Smallest Possible Occulter, 28m **

**Occulters with both suppression better than 10****-10**

**and  IWA smaller than 100 mas**

## Requirements Flow for Test Case

- Contrast ratio of 10-10, IWA of 100 mas
- 4 m diffraction limited telescope
- Maximum =800 nm
- Each source gets O(10-11)

- a, b, n, P, F,
- edge width, reflectance,
- Instrument

- a, b, n, P

- Operational
- constraint

- a, b, n, P, F

- a, b, n, P, F

- Operational
- constraint

- a, b, n, P, F

## Design Space Construction

**Occulter Too Far Away**

**Occulter Too Large**

**The allowed design space is continuous**

## Occulter Systems are Flexible

**An occulter can be located at any separation distance**
- Allows the system to mix and match suppression and IWA

## Full Scale Mission: 1 Telescope, 2 Occulters

**4 meter VIS/UV ordinary space telescope**
- Smaller telescope does allow the TPF-C science program to be accomplished
- 50% planet hunting duty cycle, 50% general astrophysics
**Survey occulter: quickly scan and discovery signatures of planets**
- IWA = 100 mas, Stellar suppression = 10-10 @ 800 nm
- Occulter size (theory) 28 m and separation 30 Mm
**Big Occulter: aligns with target star and provides deep integration**
- IWA = 50 mas, Stellar suppression = 10-11 @ 800 nm
- Occulter size (theory)  50m and separation 80 Mm

## Reference Mission Month

## Sample Full-Mission Orbit and V

**Lissajous orbit at Sun-Earth L****2**** point**
- 1.2M km wide
- Launch to C3 = −.68 km2/s2
**Telescope ∆V required****:**
- 70 m/s injection
- ~ 2 m/s/yr stationkeeping
**Survey occulter**
- Drift rate: 7.6 x 10-6 m/s2
- 1 m/s stationkeeping [1 day]
- 40 m/s slewing  [25°, 6 days]
- Total V = 304*41 = 12.5 km/s
**Big occulter**
- Drift rate: 1.7 x 10-5 m/s2
- 7.5 m/s stationkeeping [5 days]
- 70 m/s slewing [25°, 12 days]
- Total V = 80*77.5 = 6.2 km/s

**SEP is necessary for both the small and large occulters**

## New Worlds ObserverAlignment Sensing Concepts

- Charley Noecker

## The challenge

- Target star, telescope, and star-shade must be collinear within
- About 60-100 mas for the onset of occultation
- About 4 mas (TBR) during the observation
- During on-orbit checkout, allow alignment acquisition and calibration to take telescope time
- During normal operations, try to minimize telescope participation in alignment acquisition

## The Problem

- Four steps:
- (01) Find partner s/c on sky
- (2) Acquire occultation on new target	( accuracy)
- (23) Optimize alignment before observation	( calibration)
- (3) Maintain alignment during observation	( stability)

## Sensor options under consideration

- Red leak of occulter illuminates aperture edges; guide telescope to a minimum

- Acquisition

## Target acquisition requires accuracy

- Bearing vector (telescope  starshade) aligned with line of sight (LOS) within
- Arcsecond or more (close range) during initial checkout and calibration
- 60-100 mas accuracy operationally
- Bonus points: minimize telescope participation, for minimum impact on observing schedule
- Techniques
- On starshade, observe light from telescope against antipode stars
- Hipparcos limit ~30-50 mas (antipode vs. nearby stars)
- On starshade, observe light from telescope against retroreflected target star (camera/telescope with cubecorner in front)
- CC calibration pre-launch
- On-orbit calibration after first acquisition
- On telescope, observe light from starshade against target star
- Light sources:
- Scattered sunlight from other spacecraft
- Laser beacon

## Optimize alignment before observation

- Observe stellar occultation depth with telescope andsimultaneously watch the alignment sensor
- Map out target star’s occultation depth vs. alignment offsets
- Calibrate alignment sensor vs. peak occultation
- Hold the peak for the duration of an observation
- Maybe the detected image of diffracted starlight will help
- This calibration, carried from star to star, reduces the setup time needed to reach deep occultation

## Maintaining alignment during observation only requires stability

- Nominal control tolerance ~4 mas (TBR)
- 1 meter / 50,000km = 4 mas = 20 nrad
- For a 2 μrad pixel   20 nrad = 1%
- Stable for 4-16 hours (TBR) with few recalibrations
- During science observation, sensing of diffractive leakage at longer wavelengths (out of band) can help maintain centering and calibration without interruption

## Other spacecraft may be faint

- If telescope has 1 m2 total of lambertian scattering surface in direct sunlight, this gives 14 mag apparent brightness seen from 50,000 km
- Active source (laser) would need small divergence angle to keep optical power requirement low
- Large surfaces (starshade’s near side) could be turned deliberately into sunlight to boost visibility during acquisition

## Occulters Are Viable for TPF

**Occulters Are Viable for TPF**

**A mission design is being developed based on external occulters**
- No special telescope needed with multiple occulters
- Occulter sizes and distances reasonable
- Design space smooth
- System can be aligned
- Provide for flexible operations
- Can handle finite stellar size
- Are broadband
- Upper wavelength is the design parameter
- No outer working angle
**Engineering challenges to implementation exist, but technologies are of high TRL**
**External occulters need to be described by figures of merit that are different than other candidates **
**Current work continuing the rapid development of occulter based missions for exoplanetary science**