2.1.

Multi-Angle Scatterometer

The MAS was designed to measure scatter performance of coupon-scale components (roughly $25\mathrm{mm}\times 50\mathrm{mm}$, Fig. 2) over the full range of possible Sun angles.

Fig. 2

A 500-mm-long optical edge segment. The AM edge is sandwiched between graphite composite substrates. Inset: an AM coupon mounted in its holder.

The MAS optics are set up to emulate, in reverse, the illumination of the starshade by sunlight. A general schematic and image is shown in Fig. 3. To summarize, a collimated, calibrated 635-nm laser illuminates the terminal radius of an optical edge coupon that scatters light into a detector. The coupon and laser light can be rotated about 2 degrees of freedom to simulate the Sun moving to different positions relative to the starshade. Whereas in space the starshade edges are illuminated by the 30-arc min wide Sun and observed over the infinitesimal angle of the distant telescope aperture, for convenience in the laboratory the illumination is with a collimated laser beam and the detector integrates the scatter over a 30-arc min wide acceptance cone equivalent to the solar disk size. The signal scattered by the illuminated edge is compared to the signal of the illuminating beam shining directly into the camera with the edge removed. The ratio is the fractional scatter at the 30-cm distance of the detector. The SDF is the fractional scatter over the range of solar angles and edge orientations, scaled to a standard distance of 1 m. Every point in the SDF (Fig. 4) corresponds to the fractional scatter at the angle of the Sun from the starshade normal (vertical axis) and a position angle of the optical edge relative to the Sun and telescope (horizontal axis). Specular reflection is at 0° on the horizontal axis. The data from the SDF are read by the solar glint code in the SISTER simulations.

Fig. 3

(a) Simplified schematic of the MAS and (b) image of assembled instrument.

Fig. 4

Log-intensity display of the fractional intensity SDF, with edge orientation relative to the Sun on the horizontal axis and solar angle with respect to the starshade normal on the vertical axis. This SDF is formed from the average of 13 AM edge coupons (see Sec. 6). The intensity units are scaled to show the log of the fractional incident solar energy per meter of edge length, observed from a distance of 1 m.

We note that, unlike a bi-directional reflectance distribution function, the scatter from the starshade is always observed at 90° from the starshade axis (with a small inconsequential tolerance for wobble as the starshade spins). Thus, the SDF only considers the range of incident Sun angles, with the observer always at 90° to the reference plane.

The repeatability of the MAS over several months is the largest contributor to the uncertainty in the estimated level of glint. Measurements of the scatter of an AM coupon between February and October 2019 had a standard deviation of 10%. It is possible that some of this is due to changes in both the position of the measurement along the edge, as well as contaminants. However, we are not able to separate those effects from the instrument itself and therefore use the measured repeatability of 10% in our estimation of the MAS precision.

2.2.

Single-Angle Scatterometer

The SAS measures scatter along the length of an edge up to 1-m long but only over a fixed cone angle. Because the SAS has no means of measuring the unscattered beam, it has no absolute scatter calibration; it is used to determine the ratio of one scattering edge relative to another, e.g., etched coupons relative to razor blades and edge segments relative to coupons. The segment-to-coupon scatter ratio (SCSR) is the primary product that is used to link the MAS coupon measurements to SAS segment measurements, which together form the basis of the solar glint imaging simulation.

The optics of the instrument are composed of a 635-nm laser launcher, an alignment detector, and a camera tube. A test article is rigidly mounted while the instrument is fixed to two translation stages and one rotational stage, such that the camera can follow the edge and orient itself perpendicular to it. A final vertical stage is attached to the camera itself for focusing. As with the MAS, a laser illuminates the terminal radius and scatters light into the camera. A schematic of the major components and a picture of the device are shown in Fig. 5. Unlike the MAS, camera images the edge scatter so that the local scatter characteristics can be studied. Figure 6 shows a typical image. All detectors and the camera have narrow bandpass filters to remove the majority of room light. More detail on each component and the operation of the instrument follows.

Fig. 5

(a) Schematic diagram of fixed angle scatterometer setup and (b) image of assembled instrument.

Fig. 6

SAS image of scattered light from an optical edge segment. Axis units are in camera pixels. The field of view is $\sim 1\mathrm{mm}$.

A single-mode optical fiber and laser collimator expand a laser beam to a diameter of 10 mm. The beam is linearly polarized such that roughly equal power is produced in both S- and P-polarizations at the output. The polarized beam passes through a 10:90 (R:T) non-polarizing beamsplitter. The reflected light is then measured with a silicon detector to monitor power fluctuations. The majority of the light passes through the beamsplitter and is reflected toward the test article, illuminating the terminal edge from below.

An alignment detector is positioned above the sample and consists of a collecting lens, a neutral density (ND) filter, a bandpass filter, and a silicon detector. The alignment detector is used to ensure that the laser is centered on the edge.

The camera tube consists of a long working distance $10\times$ microscope objective with an acceptance angle of $\sim 30°$, a focusing lens, linear polarizer, bandpass filter, and a high-resolution CMOS monochrome camera. The scattered light from the terminal edge enters the objective and is focused through the filters onto the camera. The camera is able to image roughly 1 mm of edge at a time. At each measurement location, light is gathered over that length of edge from a range of incident angles between 45° and 75° from the edge normal.

The translation stages consist of a 1-m longitudinal stage, a perpendicular 200-mm stage for lateral movement, a rotation stage, and a small 15-mm vertical stage. The optics are held to the rotation stage with an aluminum bracket. The vertical stage is also mounted to this bracket and holds only the camera tube, as the other optics do not need a vertical range of motion.

The instrument is aligned to a test article by manually finding the corners of the terminal edge using a reticle on the camera output. Using this process, the instrument can be repeatably positioned within $50\mu \mathrm{m}$. The position of the edge is then interpolated by the software, which automatically re-centers and refocuses the camera on the terminal edge at each measurement location.

A sample set of SAS output data is given in Fig. 7. Each data point on the plot corresponds to a separate SAS measurement at 1 mm spacing along the edge. Each measurement is the integral of the light across the camera, an example of which was shown in Fig. 6. The vertical axis units are the fractional scatter at a distance of 1 m, for a 1-m length of edge, at a wavelength of 635 nm.

Fig. 7

Sample data taken with the SAS instrument.

The fractional intensity scale in Fig. 7 was determined by comparing the SAS segment scatter to the mean SAS scatter from a set of coupons (the SCSR). The coupons were also measured on the MAS where their absolute scatter characteristics were determined. The process of linking the SAS and MAS measurements is described in Sec. 2.3.

To verify SAS repeatability, a single edge coupon was measured over the central 90% of its length on six separate occasions during the six-week course of the data collection. The resulting repeatability of the mean scatter had a standard deviation of 0.9%. In practice, reference coupons are measured regularly to ensure that the instrument calibration is not drifting.

2.3.

Relating the SAS to the MAS

The MAS measures the absolute SDF of edge coupons at angles ($\theta ,\varphi$), spanning the full range of incident solar angles and edge orientations necessary to compute the solar glint lobe pattern. The SAS measures the integrated scatter of edge coupons relative to edge segments over a 15° radius of the SDF centered at a Sun angle of 60° and specular edge orientation (Fig. 8). The link between the SAS segment measurements and the MAS coupon measurements is the circular region of the SDF. For a given coupon edge, the ratio of the light within the SAS acceptance cone to the light within the full MAS rectangle is termed as the selection ratio, $\rho$. A perfectly specular edge will only reflect light at $\theta =0°$, leading to $\rho =1$. Razor blades are highly specular reflectors and we find $\rho =0.95$. AM blades are more diffuse and the selection ratio based on measurements of 13 coupons drops to $\rho =0.6$ with a standard error of the mean (SEM) of 0.029 (4.8%). The SEM of $\rho$ is one of contributing error terms in the glint lobe estimation accuracy detailed in Sec. 6.

Fig. 8

SDF, plotted on a linear scale, indicating the difference between a highly specular razor blade and a more diffuse AM edge between the two scatterometer testbeds. The circle represents the SAS acceptance cone. The ratio of light captured by the SAS to light at all edge orientations over the same range of solar angles is shown to the right of the acceptance cone circle.

With measurements of the relationships between the cone and the full range of edge angles, and between the segments and the coupons, the data are combined as shown in Fig. 9 to compute the SDF used by the imaging software. The MAS coupon measurements indicate the fraction, $\rho$, of the total scattered energy that the SAS is measuring. The measurement of coupons by both the SAS and MAS provides the relative calibration of the two instruments. The SAS measurements of the two instrument, and the SAS measurements of the segments and coupons yields the SCSR. The output product is the average SDF of the coupons multiplied by the SCSR; this then represents an estimate of the segment SDF.

Fig. 9

Flowchart of measurements and analysis. Solar glint is computed from the average coupon scatter heatmap multiplied by SCSR.

4.1.

Design Overview

The optical edge precisely defines the perimeter of each petal. It is not continuous but is made up of segments approximately 1-m long that are bonded to the structural edge of the petal, as depicted in Fig. 11. The structural edge is a continuous piece of CFRP defining the perimeter of the petal primary structure.

Fig. 11

Petal mechanical structure with placement of optical edge.

A cross section of an optical edge bonded to the petal is shown in Fig. 12(a). The substrate CFRP layup matches that of the structural edge. It provides structural support to a $38\text{-}\mu \mathrm{m}$-thick AM foil. The edge of the foil defines the terminal edge of the segment and therefore the petal. The components are bonded together with EA9394 epoxy, chosen for its relatively high strength across a broad and relevant temperature range, creep resistance, long pot life, and history of use in flight programs. Two bond operations are necessary to assemble an optical edge: first, the AM is bonded to the CFRP substrate to produce a segment, then that segment is bonded to the structural edge. The substrate is bonded to within 0.64 mm of the terminal edge to support the thin foil, whereas the structural edge is offset $\sim 12\mathrm{mm}$ inboard to prevent sunlight from illuminating the telescope side of the starshade. All bond line thicknesses are controlled using 0.005-in.-diameter glass beads. A detail of the terminal edge is provided in Fig. 12(b).

Fig. 12

(a) Cross section of optical edge flight and prototype designs, see section A-A in Fig. 13 and (b) detail of terminal edge showing the orientation with respect to the Sun and telescope.

AM is chosen to form the terminal edge due to the results of a previously performed trade study.¹⁶ The typically large grain structure found in most off the shelf metals and alloys creates large, irregular etched feature sizes, resulting in more scattered light reaching the telescope. In contrast, the glassy molecular structure of AMs results in a relatively smooth and thus sharp bevel well suited for this application. The specific alloy used is known by the trade name MBF23 and is manufactured by Metglas Inc. The alloy constituents include 60.5% Fe and 30% Ni by mass percent, along with small amounts of Cr, B, and Si.

4.2.

Test Articles

Two sets of test articles were fabricated: assembled 500-mm segments and standalone 50-mm AM coupons. The segments incorporate etched AM bonded between two pieces of carbon fiber as depicted in Fig. 12. The segments are too large to be measured in the MAS. Therefore, coupons manufactured in the same lot as the segments were used to characterize the performance of bare AM over all potential Sun angles as well as to establish the SCSR, as described in Secs. 2.2 and 2.3.

4.2.1.

Segments

A total of six prototype segments were constructed as part of the MS3 effort. The segments were subjected to a full battery of environmental tests. The segments are full scale in cross section and, at 500-mm long, are approximately half scale in length compared to the flight design. This section describes the design and manufacturing process for segments in detail.

The design of the segment test articles is derived directly from the flight design described in Sec. 4.1. The cross section is identical to that shown in Fig. 12, whereas the in-plane shape is a 500-mm-long sinusoid with a peak-to-peak amplitude of 20 mm, as shown in Fig. 13. This shape was chosen because it is consistent with the expected curvature of the petal and enables easy detection of in-plane shape changes with traditional data analysis tools. Although the length is about half that of full scale, all other dimensions (e.g., thickness and width) are full scale to preserve critical dimensions for manufacture and test. Additionally, all components are flight grade materials. The structural edge is included in the assembly and extends 25 mm beyond the ends of the substrate to mimic the continuous nature of the petal structure.

Fig. 13

Layout of an as-built optical edge segment. The cross section A-A is given in Fig. 12.

The purpose of constructing these segments was to demonstrate scatter performance before and after environmental tests, and separately to verify in-plane shape performance.

Construction of the optical edge segments is a multi-step process. The AM was photochemically etched using a commercial process to form the precision edge while the CFRP structural components were routed from fabricated panels. The edge components were then bonded together as described above to ensure the in-plane shape of the foil was preserved and the terminal edge was not damaged.

5.1.

Stow and Deploy Cycles

To stow a starshade, each petal is wrapped in a spiral pattern around the 2.25-m-diameter folded perimeter truss, although the spirally wrapped petal of the flight article takes a slightly larger curvature. To conservatively bound the worst bending case, the test articles were stowed to a 2.25-m diameter. Although a starshade is only deployed once in space, the flight system is expected to go through a series of on-the-ground test deployments. For the purposes of this study, 10 cycles were determined to encompass the likely number of ground deployments a petal would experience.

The desired radius of curvature was achieved with a fixed-displacement four-point bending fixture. The design of the fixture was driven by the desire to use the same fixture for stowed thermal testing, requiring it to fit inside an oven and to be easily transportable. A schematic and image of the bending fixture are shown in Fig. 14.

Fig. 14

(a) Schematic diagram of the four-point bending fixture and (b) fixture in use including loading weights, micrometers, and an installed edge (white).

The desired radius of curvature was achieved with a fixed displacement four-point bending fixture. The design of the fixture was driven by the desire to use the same fixture for stowed thermal testing, requiring it to fit inside an oven and to be easily transportable. A schematic and image of the bending fixture are shown in Fig. 14. The fixture was assembled using T-slotted aluminum framing and other off the shelf components. The top half of the fixture was constrained on two 19-mm-diameter bushings. Displacement, and therefore curvature, was set using three fine pitched 1/4-80 set screws on the ends of the fixture. The inner pins were set to be a distance of $L/4$ from the outer pins, where $L$ is the distance between the two outer pins. This configuration was chosen because it provides a sufficiently long region (250 mm) in the middle of the test article where theoretically constant curvature and zero shear are applied while also avoiding excessive shear in the outer regions compared to the expected flight values. The displacement-driven configuration is more representative of the boundary conditions of the flight hardware system and is more deterministic than a load-driven configuration. This in turn improves the overall ability to correlate our test configuration to our model.

The vertical displacement was set to achieve the desired radius of curvature of 1.125 m. Simple textbook equations and estimated bulk material properties were used to calculate the bending moment and shear in the test specimens under four-point bending:

After a test article was placed in the fixture, the raising and lowering rate was controlled with two motorized micrometers operating in tandem and programmed to move at a velocity of 0.5 mm/s, a sufficiently slow rate to simulate expected ground handling and flight deployment speeds.

The starshade petals can be bent in one of two orientations depending on where they are attached on the truss. Since the neutral axis of the optical edge assembly is slightly offset toward the substrate side, the metal foil can be put into either compression or tension depending on the bending direction. Therefore, half of the assemblies were tested with the AM in compression and the other half in tension.

5.2.

Deployed Thermal Cycle

The stressing condition for an optical edge in the deployed configuration is thermal loading resulting from the mismatch in CTE between the AM and CFRP components. The CFRP has a near-zero CTE while the AM has a measured value of $8.4\mathrm{ppm}/°\mathrm{C}$.

Deployed thermal cycling occurred in a nitrogen purged chamber at JPL. The edges were placed on a flat plate in an unconstrained state. A starshade system-level thermal analysis was used to determine test temperatures. The finite element model is detailed and incorporates all major components of the starshade, including petal structure, optical shield, and other blanketing. It assumes all CFRP surfaces, except the optical edges, are covered in single-layer insulation on the Sun side and a three-layer optical shield on the telescope side. The Sun-facing layer consists of a single layer of Kapton, doped with silicon on the Sun side and aluminized on the anti-Sun side for favorable thermal properties. The two remaining layers are composed of black Kapton XC for its low light transmissivity property.

The analysis assumed that the starshade would spin at 1/3 RPM. Because the spinning of the starshade equalizes the temperature of all like components on the starshade, the primary variable in determining the maximum and minimum temperature of the optical edge is the angle of the Sun relative to the starshade. During science operations, the Sun will fall between $\sim 40°$ and 83° relative to starshade normal. In addition, the starshade must also be able to survive a Sun angle of 0° as the starshade re-orients and maneuvers into position at next target star.

The maximum temperature of 80°C occurs when the starshade is normal to the Sun, $\varphi =0°$, and the minimum temperature of $-96°\mathrm{C}$ occurs with the Sun to the side of the starshade at $\varphi =83°$.

To provide temperature margin compared to the model predictions, we tested the edge assemblies over a temperature range of $+105°\mathrm{C}$ to $-125°\mathrm{C}$. Note that $\varphi =180°$ (Sun shining on the telescope side of the starshade), while not a mission design case, was also analyzed and found to have nearly identical results to the 0° case.

The number of thermal cycles in the deployed configuration for SRM is expected to be under 40. This is based on the number of target star re-orientations, a maneuver that results in the starshade changing orientation with respect to the Sun, and thus cycling the temperature of the starshade. For this test, a minimum of 25 cycles was performed on all edges, and 50 cycles on one edge assembly, as well as on the edge coupons.

6.1.

Experimental Error Budget

We estimate that the our glint lobe brightness predictions are accurate to $\pm 17\%$ $1-\sigma$. This is based on measurements of the instrument repeatability and accuracy, small sample size limitations of the coupons and segments, and the accuracy of the imaging code. These quantities are identified in Table 2. All values listed in the table and in the discussion below are the measured standard deviation or SEM, where appropriate, unless otherwise stated. The final $\mathrm{\Delta }\mathrm{mag}$ confidence of 95% at $1.65\sigma$ relies on the assumption that the combination of independent errors forms a normally distributed population.

Table 2

Sources of error in estimating solar glint lobe brightness.

6.2.

Final Glint Lobe Brightness Uncertainty

In addition to the instrument, coupon, and segment uncertainties, the analysis and lobe prediction by the SISTER software has been shown to be accurate to 1% (Sec. 3).

In total, these uncertainties combine to yield an estimated uncertainty of $\sim 17\%$ in the computation of the glint lobe brightness. Assuming the uncertainties are normally distributed, the 95% confidence level is an uncertainty of 28%, which can be expressed as an observational magnitude uncertainty of $\mathrm{\Delta }\mathrm{mag}=0.27$. In Sec. 7, we include this offset to report on the 95% confidence level in our estimate of the glint lobe brightness.

7.1.

Brightest and Average Photometric Pixels.

The visual magnitude of the solar glint lobes is summarized in Tables 3Table 4–5. The evaluation regions for the lobes are shown in Fig. 16. The magnitude of the integrated light in a lobe (column 2 of the tables) is computed by integrating the glint over half the plane, as shown in Fig. 16(a). Much of this light is at radii smaller than the IWA. Column 3 is the magnitude of the integrated light at and beyond the IWA [Fig. 16(b)] and is a full magnitude fainter. To identify a planet, a photometric aperture or matched filter would be used. In columns 4 and 5, and Figs. 16(c) and 16(d), we have convolved the image with a photometric aperture whose diameter is equal to $\lambda /D$, with $D=2.4\mathrm{m}$ for SRM and 4 m for HabEx, at the middle of each band (488.5 and 710 nm for the SRM blue and green bands, respectively, and 650 nm for HabEx). These images represent the signal that is measured in the photometric aperture at any point in the image plane. Column 4 and Fig. 16(c) show the magnitude of the brightest photometric pixel for radii $\ge \mathrm{IWA}$. Column 5 shows the magnitude of the mean brightness calculated at the IWA along the path shown in Fig. 16(d). This value represents the average signature of the glint lobes on the detection of planets at the IWA and is typically the value used in evaluations of starshade performance. In column 6, we subtract the measurement uncertainty of 0.27 magnitude from the values in column 5 to account for the 95% experimental confidence level in the experiment (see Table 2).

Table 3

Estimated glint lobe magnitude in Roman Space Telescope Rendezvous 425- to 552-nm band.

Table 4

Estimated glint lobe magnitude in Roman Space Telescope Rendezvous 615- to 800-nm band.

Table 5

Estimated glint lobe magnitude for HabEx 300- to 1000-nm band.

Fig. 16

Evaluation of glint lobe magnitude. SRM lobes are shown and HabEx is similarly analyzed. Each panel spans $500\times 500\mathrm{mas}$. Panels (a) and (b) are displayed with a linear intensity scale while panels (c) and (d) use a magnitude scale. (a) The lobe intensity is evaluated by integrating over half the plane. (b) The lobe intensity is evaluated only for $\mathrm{radii}>\mathrm{IWA}$. (c) The image has been convolved to the resolution of $\lambda /D$. Each point in the image represents the visual magnitude within the photometric aperture. The brightest pixel at the IWA is evaluated. (d) The average value of the scatter at the IWA is evaluated.

We also show how the magnitude of the mean photometric pixel values evolve with working angle for the SRM (Fig. 17). A vertical line marks the IWA radius: 72 mas for the 425- to 552-nm band and 104 mas for the 615- to 820-nm band. The curves show that the glint effect diminishes with increasing distance from the starshade. At a distance of $\lambda /D$ beyond the IWA (112 mas in the 425- to 552-nm band, and 166 mas in the 615- to 800-nm band), the average brightness has dropped by more than 2 magnitudes.

Fig. 17

Magnitude of the Roman Space Telescope average level of illumination per lobe within a photometric aperture as described in Fig. 16. Magnitude values at the IWA are in column 5 of Tables 3 and 4.

7.2.

Mission Performance Assessment

The levels of solar glint will significantly impact integration times for a planet appearing near the IWA. In fact, it is several times larger than any other instrument-related background contributor including stellar diffraction due to starshade shape errors, stellar and solar leakage through micrometeoroid holes in the optical shield, and reflection of the Milky Way and other astrophysical objects from the telescope-facing surface.¹⁵ The SRM’s focus on the closest stars, with planets appearing well beyond the IWA, gives ample habitable zone access with minimal interference from the glint lobes. Nonetheless, it is desirable to significantly reduce solar glint to provide the best possible SNR.

Fortunately, there is much of room for improvement. In addition to the potential to produce segments that are close in performance to coupons, the bare metallic edges can be coated with a hybrid interferometric/absorptive coating. The results of our preliminary testing and analysis of these edges show that they improve performance by about an order of magnitude, as reported in the companion paper.⁹

A second mitigating approach is to employ “stealth edges,” which is a term we use to describe serrated edges placed where the specular reflection is greatest.² The serration removes the specular component for all but the tips and valleys of the serrated portions and has been shown through MAS measurements to reduce scatter by up to an order of magnitude. The $\sim 1\text{-}\mathrm{mm}$ serration period has no effect on the starlight shadow. However, the stealth edges are not compatible with the baseline approach of spinning the starshade about its axis during an observation. If the starshade does not spin, there will be increased thermal deformation, which in turn would degrade the starlight shadow. This is a trade that is currently under consideration.