Exoplanet Program: Starshade Project

Research Goals

Fabricating, characterizing, and modeling Starshade and Coronagraph masks.
Optimizing and characterizing high-contrast, wide spectrum absorptive/reflective materials for optical instruments (ie. coronagraph masks for Wide Field Infrared Survey Telescope (WFIRST) mission).
Refining fabrication processes for back-etching of thick Si wafers via deep reactive-ion etching (DRIE), photolithography, and e-beam lithography, of Starshade scale-down optical test-bed masks for New Worlds Mission.
Develop MatLab scripts to stitch high-resolution microscope images of devices to detect micrometer defects in etching that would cause unexpected light scattering.
Perform modal analysis to model normal modes of bending for the Starshade truss segments to inform the optical error budgets of the mission.

Background on Starshade

Historically, direct imaging of exoplanets is a minority method for detection. However, other leading detection methods do not offer the same utility atmospheric spectroscopy among other advantages. Imaging exoplanets is challenging given that the stars they orbit are orders of magnitude brighter than the reflected light or heat radiation off the exoplanet's surface.

Blocking star glare with an occulter!

Shown to the right is the occulting of HR 8799 by Nexus for Exoplanet System Science (NExSS) at the Arizona State University (Christian Marois, NRC-Herzberg), demonstrating the capabilities of blocking out light from the star in order to see reflected and thermal light from the orbiting planets.

The principles behind these devices rely on manipulating the Fourier Transform (eg. by convolution) at each optical plane so as to filter out unwanted signal of the exo-star, leaving the signal of interest and noise. This process can in part be done by an occulter (coronagraph or Starshade).

Characterizing exoplanets and determining habitability requires spectra

Spectra require greater contrast! To maximize contrast, positioning the occulter outside of the telescope further improves contrast. A means of doing this was first proposed by Lyman Spitzer, a professor at Princeton, over 50 years ago. Using a Starshade, it became possible to form a shadow so that there would be no source of glare.

The Starshade modifies the diffraction pattern by removing the glare that surrounds an exo-star. This process is designed to increase contrast of the star-planet system to make observation of the exoplanet, whose point spread function represents a minor fraction of its host star’s reflected light, discernible.

Shade cannot just be a circular disk

In this case, the edge ‘bends’ or diffracts light toward the optical axis, forming a bright spot known as the “Arago/Poisson’s spot.”

Sunflower shape provides deeper shadow

The flower-shaped starshade has edges that diffract the light away from the axis. A deep shadow is formed without a bright axial spot.

Optical Test-bed Scaled Testing

High contrast Starshade imaging  (A. Harness and J. Kasdin of Princeton, S. Shaklan and P. Dumont of JPL) shows promise through optical test bed experimentation. This is possible because of maintenance of the Fresnel Number which preserves the math. The physics of a miniature and orbiting Starshade (despite their considerable size difference) is effectively identical.

Now the question of designing scale down models becomes relevant!

Fabricating optical test-bed starshade masks

Together with Victor White and Karl Yee in the Micro Devices Laboratory (MDL) at JPL, Starshade process flow was re-developed and optimized using nanofabrication techniques.

Plot of e-beam rendering for photolithography mask writing

Combined mask

Nanofabrication cross section of device (and released petals)

The final device is formed from fall-out of petals which leaves behind thin Silicon struts that support the inner Starshade.

SEM of deep back-etch forming aperture wall (at 20°)

Laser scan of Si back-etch cut into wafer

Cross section from laser scan plot showing wall verticality

Using both contact lithography (initial process flow) and direct write (improved process flow), masks could be prepared for Deep Reactive Ion Etching (DRIE) on front and back sides. Direct write improved resolution and accuracy of final mask, while reducing the previously observed absolute error in petal tip widths that were cause for diffraction effects.

Deep Reactive Ion Etching (DRIE) typically produces rough non vertical walls resulting in poor edge definition and light scattering
Thicker edges can also induce surface plasmon effects /waveguide effects at grazing incidence causing polarization effects and unwanted scattered light
A thin membrane defining the edges helped eliminate both problems, though involves fabrication challenges
In addition, a thinner device layer enabled better wall verticality, but at the cost of fragility

Note: SiN layer eventually removed from process flow for a variety of reasons in process flow simplification and optimization

Defect detection is imperative

Seen in the below microscope image (green backdrop) and MatLab scripted auto-detect, etching defects, punctures, tapering of dimensions along Z-axis, and minor un-etched overhangs severely impact the quality of the Starshade and impair it's usability for modeling exo-planet detection in the Princeton Frick Testbed.

Here the defect seen protrudes from the edge of 6th petal and while only ~450 μm2 in cross-section a significant defect on the mask, as shown in the contrast plots: experimental (top) and modeled (bottom). These minor defects imitate the expected response from planets, which frustrates true detections.

The mask was returned from Princeton for correction using a Focused Ion Beam, but demonstrates the significance of minor defects.

The near perfect mask!

Finally, from process flow optimizations, extreme care in the fabrication process (and handling), and a fair bit of being lucky, a near perfect mask was formed for testing. The mask below (DW-17) exhibited a deep, dark center, necessary for achieving extremely high contrast necessary for for detection as spectroscopic characterization of Earth-like exo-planets.

Scatter fainter than an Exo-Earth detectable, meaning detections of potentially habitable planets becomes possible.

From Micro to Macro: Modeling Truss Deformations for Optical Error Budget Calculations

The Starshade's petals sit on a truss composed of bay structures. While petal bending deformation modes had been determined, truss / truss bay deformation could also affect diffraction effects, shadow length, and shadow shape that could be the difference between finding habitable exo-planets (let alone seeing any exo-planets) or not.

Summary of Mechanical Deformation and Optics

The light scattering behaviour of Starshade changes when system deforms:

Exo-star’s light is predominantly distributed in the center peak (largest maxima). Contrast can be increased by cutting out a few of center most peaks of point spread function (PSF) using a filter that’s built to radially apodize the transmission.
The Starshade performs this task, as a binary apodization function, suppressing light at the center of the PSF, thereby increasing the relative brightness of the planet to enable the observer to discern the PSF of the planet in the airy disks of the star.
When system undergoes mechanical deformations in the truss, bays/petals can shift causing changes in light scattering, potentially restricting full-range of observation.

Building a mathematical model

For low-N polygons, by inspection:
- Triangle (limiting case) has 0 bending modes,
- Hexagon has 3 bending modes,
- Octogon has 5 bending modes
- etc...

The truss, being composed of individual bays, can be generalized "n-gon".

Treating the truss of N bays as a closed polygon with N discrete rigid segments of length L allows determination of the joint-bending modes ("low-stress bending modes").
- Note: low-stress indicates no Euler-Bernouille beam bending!

Truss has 24 bays – thus a 16gon or 24gon reflects Starshade interior (depending on size).
A pattern of joint-bending modes emerges: # joint-bending modes: nmode = Nbays - 3

Circular harmonics applied to the "closed string" of the polygon can solve this problem. Circular harmonic basis functions given by Fourier Series, with orthonormal basis functions.
To decompose a function into the set of normal modes that produce it, a weight projection is used that takes in the function being projected and the applicable circular harmonic function.
The value of this approach is that, taking together the translational and joint-bending modes, a basis set for the system is formed, from which any function of motion of the polygon (truss) can be composed by linear combination of one or more of those eigen modes in the set. Each of these modes is orthogonal, that is to say each harmonic is normal to another in the sense that each moves totally independently, so that the motion of one will never induce excitation of another.
For higher order N-gons of the type used in the Starshade design (16- and 24-gons), finite element analysis was used to model the bending modes.

ANSYS Modeling

Constraints

Lengths of bays (faces of polygon) are constant (rigid).
In plane motion only.
72 Degrees of Freedom (24x3) in X, Y, Θ.
48 coincident constraints at each endpoint of a bay/face.

Approximations

No spokes – easier to build in CAD and modes will be the same, spokes only increase internal resistance to torsion about joints and thus will shift modal frequencies but not change patterns, which are what is sought.
Polygon with wall thickness t and width z
Joints constructed as 2D Ball-Socket with adjoining spring

No Separation: Contact setting applies to regions of faces (3D solid male-female joint interface, see image). When no separation is applied, then no sliding or separation between faces or edges is allowed: the region is fixed in place!

This type of contact allows for a linear solution since the contact length/area will not change during the application of the load. Separation of the geometries in contact is not allowed (total constraint).

Longitudinal Spring: joint springs here are elastic elements that are used to store mechanical energy and retain original conformation (undeformed Ngon).

The stiffness, behaviour model (compression/tension spring) and other model parameters are controls to enable a clean solution, that does include beam-bending.

A total of one spring per joint adjoins the male and female components, totaling 24 springs.

This model version employs 24 named selections (inner edge of joint on male component of hinge) as a means to trace the nodes under deformation. Two model types were used, a programmed solution and a "physical" solution.

The centroid of these points was calculated. Allows tracing 1 “point” per vertex to know (X0,Y0 )→(Xfinal,Yfinal ) for each modal deformation.
The refined model used a separate part in the solidworks assembly file (which was meshed distinctly) to trace the XY-centroid under deformation using a node at the tip of the cone, as shown in the rending.

Each one of these cone tips is in alignment with the XY center of mass of the joint so that tracing this point is an accurate representation of each modal shape. Hence, the initial and final locations of this mode (equilibrium and maximum deformation positions) was represented in the data set exported, substantially minimizing the amount of post processing required by calculation of the centroid. This directly provided 24 XY directional translation vectors from the equilibrium/initial location to the position of maximum deformation for each mode (final location). These vectors in turn characterize the eigen modes and, within the linear regime, are easily scalable.

Starshade Truss Harmonics

Of the 30 solutions modeled, 24 were indeed rigid body solutions as expected from a Fourier treatment. Modes 4 through 24 corresponded to joint-bending solutions, having varying frequencies depending on resistance to the deformation. The larger the energy barrier to deform, the higher the frequency, and the greater the resistance to deformation. The probability of deformations occurring is inversely proportional to the energy of deformation and therefore to the frequency of the harmonic. The lower the frequency the higher the probability of deformation in that modal shape.

Note: appearance of stretching is an artifact of extending the results beyond the linear range for easier observation, these stretches are not real.

Modes 0-3 correspond to translation and rotation.
Modes 4-24 correspond to hinging/joint-bending modes (highlighted in orange)
Modes 25-30 correspond to Euler beam bending (highlighted in green)

The frequency of beam bending modes is more than twice that of the hinging modes, this is indicative of a substantially greater energy barrier for these motions.

Optical impacts of truss deformations

Collated data can be used in post-processing in MatLab to predict how modal behaviours will affect light scattering and diffraction, informing the error budget and setting specifications for mechanical performance. The optical error budget captures sensitivity to changes to the Starshade when in flight, where the predominant effect on Starshade mechanics is thermal from absorption of radiation. Predicting the motion is essential to determining the suppression characteristics and mechanical flow-down requirements for design.

While it is impossible to predict and assess the optical impact of every possible deformation the Starshade can undergo, any concerted motion of a system can always be broken down into weighted combinations of fundamental harmonic modes.

Starshade’s suppression capabilities will be sensitive to petal locations and deformations.

Modes can impact effectiveness of local approximation of the apodization function. This changes diffraction properties and can create artificially brighter or dimmer zones (ie. potentially reducing the suppression of exo-star light at the central maximum of the PSF, generating bright spots about the starshade which trigger false positive observations of exoplanets, or drowning any exoplanet signal in stellar glare).
Any systematic motion of the truss and its bays can be broken into fundamental harmonic modes.

The example of deformation above shows an exaggerated quadrilateral mode which causes pinching and spreading of petal formations. This makes the "effective corners” of the quadrilateral appear brighter.

Publications

Starshade Mask Poster SPIE 2018 v4.pdf

EXEP__Starshade_Modal_Analysis_for_Optical_Error_Budget_Determination_2017.pdf

Bonus material: Starshade Pumpkin carving at JPL!

Note: published information and released material is generally limited due to propriety, confidential, and ITAR restrictions. The scientific and technical information disclosed has been approved for release under the Universal Release System from the Jet Propulsion Laboratory (JPL). Note that images of Starshade Mechanical Subsystems, Cumulative Number of Detections (of Exoplanets), Exoplanet Brightness vs. Wavelength charts, Starshade Truss and New Worlds Mission rendering courtesy of NASA JPL/Caltech's publicly released material. Images of Optical Test Bed, Optical Vector Model, and Contrast vs. Fresnel Number plots courtesy of Princeton Frick Laboratory in partnership with NASA JPL/Caltech.

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