4.1.

Primary Mirror Physical Specifications

The AMTD Science Advisory Team specified that the minimum aperture diameter of interest was 4 m and that larger was better. A key specification derived from aperture diameter is areal density. Table 1 shows one potential allocation for the maximum mass of the primary mirror as a function of the mission’s launch vehicle and its resulting areal density. Note that current state-of-the-art areal density for UVOIR glass primary mirror assemblies is $35\mathrm{kg}/{\mathrm{m}}^2$ and state-of-the-practice is $50\mathrm{kg}/{\mathrm{m}}^2$.^20,21 The PSF of various segmentation architectures is another implication of aperture diameter that AMTD investigated as it relates to the coronagraph inner working angle (IWA).^15,22–24

Table 1

Maximum mass allocation as a function of launch vehicle.25

Derived from a desired telescope diffraction-limited performance of 500 nm, a nominal 7 nm rms specification was defined for the primary mirror’s SFE. This error was partitioned between low-, mid-, and high-spatial frequencies (Table 2) based on what is required to enable the creation of the coronagraph “dark hole” and minimize leakage into the dark hole from uncorrectable spatial figure errors. It is assumed that a DM will be used to create the dark hole and that it can correct errors up to 30 cycles per diameter. Therefore, to prevent leakage into the dark hole, the primary mirror must be smooth up to 90 cycles—because uncorrectable errors up to 90 cycles can “alias” energy into the dark hole. Finally, note that in Table 2 segmented mirrors have a smaller error specification. This is because, for a segmented mirror, error must be allocated to aligning and co-phasing the individual segments to each other to form an equivalent “monolithic” primary mirror. As shown in Table 2, AMTD assumed that segment co-phasing could be achieved at a 5-nm-rms precision. If better co-phasing can be achieved, then the fabrication error allocations can be increased.

Table 2

Primary mirror SFE as a function of spatial frequency.

4.2.

Primary Mirror Stability Specification

A fundamental tenet of systems engineering is the ability to decompose a system into its constituent parts to specify, in this case, the optical telescope performance independent of the science instruments. To do this for exoplanet science requires modeling and analyzing the telescope and coronagraph as an integrated system. Depending on a given coronagraph’s sensitivity, small dynamic perturbations of the input wavefront can produce speckles in the dark hole—contrast leakage—that might obscure a planet or lead to a false positive. The key challenge is understanding how to create a wavefront dynamic stability specification for the primary mirror. To this end, AMTD developed a series of increasingly sophisticated modeling tools to estimate the contrast leakage that occurs when dynamically aberrated wavefronts are propagated through candidate coronagraphs.^18,22–24

A summary finding of this study is that, to prevent unwanted contrast leakage into the dark hole, the telescope wavefront must be stable to better than 10 pm rms per 10 min.¹⁴ However, this specification is poetry. The actual specified maximum WFE amplitude depends on the spatial frequency of the error.^4,5,18,23,24 And, the actual specified time period is wavefront control cycle, which, depending on the size of the telescope aperture and the brightness of the target star, can vary from a few minutes to $>20\min$.

For example, Table 3 shows the sensitivity of a coronagraph published by N’Diaye²⁶ for use on a segmented aperture telescope similar to the James Webb Space Telescope with an IWA of $4.5\lambda /D$. In general, segment level errors are more important than global aberrations because segment level errors produce speckles at the same spatial frequency as the dark hole. For this system, global errors produce speckles that are inside the IWA. At the IWA, segment piston and tip/tilt errors are the most important because this is where their speckles are located. Higher order segment level errors (power, astigmatism, and trefoil) are less important at the IWA because, since they are higher spatial frequency errors, their speckles occur further into the dark hole. To illustrate the use of this analysis, if the primary mirror was the only error source in the telescope, then its SFE specification would be one half of the values in Table 3.

Table 3

Maximum random aberration amplitude as a function of contrast leakage.

5.1.

Large-Aperture, Low-Areal Density, High-Stiffness Mirror Substrates

Whether the PMA is monolithic or segmented, low-areal density high-stiffness substrates are an enabling technology. The easiest way to increase stiffness is to make the substrate thicker. Before AMTD, the state of the art for ULE^® mirrors was defined by the Advanced Mirror System Demonstrator (AMSD) and WFIRST. Both of these mirrors have a first mode frequency of $\sim 200\mathrm{Hz}$. The AMSD mirror is $1.4\mathrm{m}\times 0.06\mathrm{m}$, $10{\mathrm{kg}/\mathrm{m}}^2$ and was manufactured as a three-layer substrate (face/back sheet and core) via a LTF/LTS process. The WFIRST primary mirror is $2.4\mathrm{m}\times 0.2\mathrm{m}$, $50{\mathrm{kg}/\mathrm{m}}^2$ and was fabricated via LTF using curved components. At 21-cm thick, the WFIRST primary mirror represents the current state of the art for monolithic mirrors. This thickness is limited by Harris Corp’s ability to abrasive water jet (AWJ) cut core structures. By comparison, Schott AG has a maximum core machining depth of 28 cm.

AMTD partner Harris Corp. successfully matured the technology for low-areal density high-stiffness substrates by demonstrating a 5-layer, 4-cm-thick mirror manufactured via the new “stacked and fuse” process. To make thicker mirrors, multiple core elements were cut [Fig. 1(a)] and stacked between a face sheet and back sheet, then LTF’d together into a plano/plano substrate. The substrate was then LTS’d to a radius of curvature. Using this new process, a 43-cm diameter “cut-out” of a 4-m diameter, 40-cm-thick, $<45{\mathrm{kg}/\mathrm{m}}^2$ mirror substrate was fabricated [Fig. 1(b)]. Harris Corp estimated that this process significantly reduces the cost to fabricate mirrors, possibly by as much as 30%.^27,28

Fig. 1

A 43-cm diameter × 40-cm-thick mirror was manufactured by (a) fabricating individual core elements that were (b) stacked, fused to a plano/plano, and slumped to a 2.5-m radius.

In AMTD phase 1, Harris Corp tested the core-to-core LTF bond strength using 12 modulus of rupture (MOR) test articles (Fig. 2). Also in phase 2, Harris performed an A-basis test of the core-to-core LTF bond strength as a function of alignment using 60 MOR samples: 30 samples were assembled with nominal alignment and 30 samples were deliberately misaligned. Based on 49 of the samples, the A-basis Weibull 99% confidence strength allowable was found to be 17.5 MPa, which is $\sim 50\%$ higher than the most conservative design allowable value for margin of safety calculations at the core-to-plate LTF bond. The data on the 50 samples ranged from 60% to 250% above this design allowable value.²

Fig. 2

MOR test article fabrication: (a) in AWJ and (b) post-AWJ.

To demonstrate lateral scalability, Harris Corp. used the “stack and fuse” process to manufacture a $1.5\mathrm{m}\times 165\mathrm{mm}$, 5-layer, 400-Hz first mode mirror. This was a major milestone for AMTD phase 2. The reason that this mirror has three core element layers instead of one is because it is a subscale version of a 5-layer, $4\mathrm{m}\times 440\mathrm{mm}$ mirror in which each core element layer is 150-mm thick. The mirror consisted of a face sheet, back sheet, and 18 core elements (6 elements per core layer), which were first fused together to form a planar substrate [Fig. 3(a)]. The substrate was then slumped to a 3.5-m radius of curvature [Fig. 3(b)]. Note that this radius was selected because a slumping body was available. Also note that a single-core layer version of this 400-Hz mirror would meet the performance needs for a 12- to-16-m segmented aperture telescope.^29,30

Fig. 3

(a) LTF mirror substrate; (b, top) five-layer design; and (b, bottom) completed mirror assembly.

During AMTD-1, when the 43-cm deep-core mirror was slumped from a 5- to 2.5-m radius of curvature, there was noticeable deformation in the core walls. To quantify the magnitude of this bending, MSFC imaged the mirror’s internal structure via x-ray tomography. A small amount of bending was expected because slumping places the concave surface in compression and stretches the convex surface; this places the core elements in shear stress. To mitigate this effect, the design of the 1.5-m mirror was adjusted to increase the gap between core elements. The measured deformation exceeded that expectation. Fortunately, analysis indicated that such core-wall bending had a limited effect on the mirror’s strength. Using this lesson learned in designing the 1.5-m 1/3 scale model of a 4-m mirror, Harris Corp. used proprietary modeling tools to predict the viscoelastic performance of the mirror [Fig. 4(a)]. The spacing between the wedge-shaped core elements was specifically increased to prevent adjacent core walls from touching. Unfortunately, because of a fixture issue from an external vendor, when the mirror was assembled, some of the core elements were shifted toward the center of the mirror by up to 20 mm, reducing the gap size. As a result, when the core walls bent, they contacted in one location (but did not fuse) and got within $<0.25\mathrm{mm}$ at three other locations [Fig. 4(b)]. MSFC imaged the internal structure of the mirror via x-ray-computed tomography and used that data to create an as-built 3-D model of the mirror to predict its mechanical and thermal performance.⁵

Fig. 4

(a) Predicted viscoelastic deformation used to design mirror substrate; (b, three images) actual viscoelastic deformation; four-locations had gaps of <0.25 mm.

Core-wall bending is complicated. Previous to AMTD, the only mirrors fabricated via the LTF/LTS process were AMSD and Multiple Mirror Segment Demonstrator, neither of which exhibited core-wall bending. Preliminary analysis indicates that the effect depends on shear stress in the core. The greater the amount of shear stress is, the greater the amount of viscous flow of the glass during LTS is, and the greater the core-wall bending is. Preliminary analysis indicates that this shear stress is proportional to the unsupported radial core-wall length divided by the radius of curvature (independent of core thickness and whether the core is composed of a single layer or multiple layers). The AMTD-1 mirror (2.5-m ROC, $0.43\text{-}\mathrm{m}\text{diameter}\times 400\text{-}\mathrm{mm}\text{thick}$) had significantly larger core cells than the AMTD-2 mirror (3.5-m ROC, $1.5\text{-}\mathrm{m}\text{diameter}\times 165\text{-}\mathrm{mm}\text{thick}$) and thus less bending. If the 1.5-m mirror had been LTS’d to a 7.5-m ROC, it likely would have had negligible bending.

5.2.

Support System

Large-aperture mirrors require large support systems to ensure that they survive launch and deploy on-orbit in a stress-free and undistorted shape. Additionally, segmented mirrors require large structure systems that establish and maintain the mirror’s shape relative to the back plane.

AMTD used the AMM to design strut and launch support systems for candidate open- and closed-back 4-m class monolithic mirrors. Dozens of point designs were generated.^31–34 Additionally, AMM was used to investigate the stiffness of candidate 4-m class mirror designs for a nominal 720-kg mass constrained mission (i.e., launched via Delta-IV Heavy), as shown in Table 4, and mass relaxed designs enabled by the Space Launch System (Table 5). Dynamic and static analysis was performed on candidate mirrors to determine stress on internal structural elements and at the mount interfaces during launch. Several launch support system configurations were identified that keep internal stress below 600 psi (Fig. 5).

Table 4

4-m mirror point designs (with thin face sheets).

Table 5

4-m closed-back mirror point designs (with thicker face sheets).

Fig. 5

Potential launch support designs evaluated for stress distribution.

Dynamic WFE is particularly important for coronagraphy. Dynamic WFE at levels $>10\mathrm{pm}$ per control cycle can introduce speckle noise that can degrade exoplanet science. An important dynamic WFE is inertial deformation. Inertial WFE is produced when a mirror is accelerated by a mechanical disturbance, causing it to react (i.e., bend) against its mounts. Its simplest example is gravity sag. The acceleration of gravity causes a mirror to bend on its mount. On-orbit, assuming that no resonant mode is excited, a mirror’s inertial WFE has the same shape as its gravity sag with an amplitude proportional to the disturbance’s “G-acceleration.” AMTD studied inertial WFE for various mirror substrates on both 3-, 6-, 9-, and 18-point mounts and mounts attached to the substrate at the edge, 80% and 50% radial points (Fig. 6).^32,33,35 As to which mount configuration might be best, it depends on the application. The optimum configuration for an imaging application might be different from that for coronagraphy. For example, where to locate the mounts radially depends on the coronagraph’s sensitivity to power. Moreover, whether to use 3 or 6 mount points depends on its sensitivity to trefoil versus hexafoil.

Fig. 6

Static gravity sag and dynamic deformation of 180-Hz, 4-m diameter closed-back mirror on 3-point mount attached at edge, 80% and 50% radial locations. The first two columns show the mirror mount locations. The third column is the 1-G gravity sag for the mirror on its mount. The fourth column shows the resonant response of the mount system. It is at these frequencies that the mirror experiences its maximum acceleration and thus its maximum inertia deformation. The last column illustrates how the inertial deformation shape matches the mirror’s 1-G sag.

5.3.

Mid/High-Spatial Frequency Figure Error

High-contrast imaging requires mirrors with very smooth surfaces ($<10\mathrm{nm}\mathrm{rms}$). Although DMs can correct low-order errors, they cannot correct mid- and high-spatial frequency errors caused by the fabrication process or coefficient of thermal expansion (CTE) inhomogeneity. These errors are important because they can introduce artifacts into the dark hole.

AMTD partner Harris Corp. specifically designed the 43-cm deep-core mirror to have a pocketed face sheet to minimize the mid/high-spatial frequency quilting error from polishing pressure and thermal stress. However, as expected because the face sheet was thin, the 43-cm mirror did have quilting associated with the pocketing. Harris removed this quilting via ion polishing to produce a mirror with a 5.4-nm-rms finished surface (Fig. 7). AMTD assesses the ability to correct mid-spatial errors to be demonstrated (i.e., TRL-6).

Fig. 7

Harris Corp ion-polished the AMTD 43-cm to remove cell quilting, resulting in a 5.4-nm-rms surface.

Because on-orbit temperature can be different from the fabrication temperature, thermal stress, even for a low-CTE material such as ULE^® glass, can cause SFEs. To understand the impact of thermal deformation, it must be quantified. MSFC tested the 43-cm and 1.5-m ULE^® mirrors and a 1.2-m Zerodur^® mirror from 230 to 300 K (Figs. 8 and 9).^36,37

Fig. 8

Schott 1.2-m ELZM and Harris 1.5-m ULE^® mirrors under test in XRCF.

Fig. 9

XRCF thermal characterization: (a) test setup and (b) typical thermal profile.

As shown in Fig. 10, the cryodeformation of the 43-cm mirror exhibits no quilting signature similar to the pattern seen in Fig. 7. Its mid-spatial frequency error was $<4\mathrm{nm}$ rms.³⁶ Similarly, the Schott 1.2-m Zerodur^® mirror also displays no thermal-induced cryodeformation associated with its machined isogrid core structure (Fig. 11). Note that the fringe-shaped pattern is an artifact of the measurement algorithm because the mirror was only polished to about 100 nm rms to save money. By comparison, because the 1.5-m ULE^® mirror does not have a pocketed face sheet, it is not expected to have quilting. However, as shown in Fig. 12, its cryo-deformation does contain a mid-spatial frequency error which is correlation to the mirror’s core pattern.

Fig. 10

43-cm mirror 253- to 293-K cryo-deformation mid-spatial error is $<4\mathrm{nm}$ rms and shows no quilting pattern.

Fig. 11

1.2-m Zerodur^® mirror’s cryodeformation shows no correlation with core pattern.³⁸

Fig. 12

1.5-m ULE^® mirror’s cryodeformation has mid-spatial error, after removal of 36 Zernike terms, which increases with temperature change and, as shown in the left image, is correlated with the core.

There are several important lessons to be learned from Figs. 11 and 12. First, the spatial frequency of the cryodeformation for the Zerodur^® and ULE^® mirrors is different. Moreover, if uncorrected, their impact will be different. The ULE^® mirror has more mid-spatial frequency content than the Zerodur^® mirror. Fortunately, both deformations are in the capture range for state-of-practice computer-controlled polishing processes. Thus both could be corrected to the specified surface figure necessary to enable high-contrast imaging at a specific temperature. Second, the temperature sensitivity of both mirrors is similar. The Zerodur^® mirror has $\sim 0.2\mathrm{nm}/\mathrm{K}$ of surface deformation, and the ULE^® mirror has $\sim 0.3\mathrm{nm}/\mathrm{K}$. This is important because it places a constraint on the thermal stability specification for the mirror. For example, if the coronagraph that will be paired with the ULE^® mirror requires that the amplitude of the surface thermal deformation be $<0.003\mathrm{nm}$, then the temperature of the mirror must be stable to $<10\mathrm{mK}$.

Finally, in support of the WFIRST program, the 1.5-m ULE^® mirror was soak tested at 260 K for 12 days to assess the AMTD mirror mount interface’s thermal stability for potential use on WFIRST. The test indicated that the AMTD mirror mount design, which was designed to be athermal at 250 K, was stable within the metrology uncertainty, and there was no indication of mount effects printing through to the surface.

5.4.

Segment Edges

For a segmented primary mirror, the edge diffraction and the quality of segment edges impacts the telescope’s PSF, contributes to stray light noise, and affects the total collecting aperture.^39,40 All of these impact high-contrast imaging. One mitigation for these effects is edge apodization.

AMTD partner STScI successfully demonstrated an achromatic apodization coating. A glass grayscale prototype mask was fabricated using chromium microdots and tested at the Brookhaven National Laboratory beam line. When used at high $F/\#$, the synchrotron beam simulates collimated starlight. The purpose of the test is to use a Fourier transform spectrometer to measure the mask’s transmission (to an accuracy of $\sim 0.1\%$) from 500 to 1000 nm (Fig. 13). The coating provides a variable attenuation with uniform performance over a broad spectral band. Such a coating deposited on a segmented mirror enables a high-contrast imaging PSF by minimizing edge diffraction, straylight, and structure obscuration diffraction.⁴¹

Fig. 13

Microdot apodization coating attenuation is flat as a function of wavelength.⁴¹

5.5.

Segment-to-Segment Gap Phasing

Segment phasing is critical to achieving diffraction-limited performance. To achieve 500-nm diffraction-limited performance, the figure error of the primary mirror surface needs to be $<10\mathrm{nm}$ rms. For a segmented mirror to achieve this specification, it is necessary to co-phase its mirror segments to $<5\mathrm{nm}$ rms.

AMTD partner Harris Corp. designed, built, and characterized the “fine” stage of a low-mass two-stage actuator (Fig. 14), which could be used to co-phase mirror segments to the required tolerance. The “coarse” stage was previously demonstrated on a different project. Unfortunately, because of electronic noise, it was not possible to verify the actuator’s predicted resolution.

Fig. 14

Actuator and its performance test results.^2,30

Additionally, to avoid speckle noise, which can interfere with exoplanet observation, internal coronagraphs require a segment-to-segment dynamic co-phasing error of $<10\mathrm{pm}$ rms between wavefront sensing and control updates. Although active phasing control at this level is beyond the scope of AMTD, two passive approaches were investigated.

First, AMTD investigated the utility of correlated magnetic interfaces to reduce the dynamic co-phasing error. Although it was found that such interfaces increase dampening by $\sim 2\times$, they cannot achieve the required specification. It was also found that, while the correlated magnetic interfaces acted over a shorter distance than conventional magnets, their dampening was not significantly different from that provided by a conventional magnet. Therefore, given the inability of correlated magnetic interfaces to reduce dynamic segment-to-segment co-phasing error below the required level, investigation of this approach was stopped.

Next, AMTD co-investigator Jessica Gersh-Range conducted an analytical study that indicated that connecting segments at edges with damped spring interfaces provides potentially significant performance advantages for very large mirrors. With no edgewise connection, the segments behave independently. With as few as three damped spring interfaces, the segments start to act as a monolith (Fig. 15), provided that the interfaces are sufficiently stiff. Adjusting the spring stiffness tunes the assembly’s first-mode frequency proportionally to the square root of the interface stiffness but approaches monolithic performance asymptotically. By adjusting the stiffness and damping, a segmented mirror will stabilize faster after a force impulse than a monolith. A segmented mirror with low to intermediate interface stiffness does not propagate disturbance waves, and a segmented mirror with high damping reduces the propagating wave amplitude quickly.^42–44

Fig. 15

Segmented mirror with edgewise interfaces can be tuned to have different bendings.

5.6.

Integrated Model Validation

On-orbit performance is driven by stability (both thermal and mechanical). As future systems become larger, compliance cannot be fully tested on the ground. Thus performance verification will rely on results from a combination of subscale tests and high-fidelity models. With never-before-required performance specifications, integrated STOP modeling of candidate PMAs (including substrates, structures, and mechanisms) and complete OTAs is critical to their design and performance modeling. To provide confidence that integrated STOP tools can design systems with never-before-required specifications, they must be validated by tests of full- and subscale components in relevant thermovacuum environments.

AMTD generated STOP models for the 1.5-m ULE^® mirror (manufactured by AMTD partner Harris Corp.) and a 1.2-m Zerodur^® mirror (owned by Schott North American). These models were used to predict the static and dynamic performance of each mirror, including: gravity sag, modal response, and thermal deformation.^38,45

Both mirrors’ thermal performances were characterized in the MSFC XRCF thermal-vacuum test chamber from 250 K to ambient. To enable testing of short-radius mirrors, a pressure-tight enclosure was built to place at the mirror’s center of curvature: an interferometer to measure surface figure, an absolute distance meter to measure radius of curvature, and a thermal camera to measure front surface temperature distribution. The mirror and its mounting structure were extensively instrumented with temperature sensors (Fig. 16).⁴⁵

Fig. 16

(a) Short radius of curvature mirror test setup with pressure tight enclosure. (b) The test setup was extensively monitored via thermal sensors.

Mechanical and thermal models were made of the Schott 1.2-m ELZM mirror. The mechanical model predicted a gravity sag deformation of 125 nm rms. The gravity sag measured via a rotation test was 142 nm rms (31 nm rms difference between predicted and measured), as shown in Fig. 17. Because the ELZM model was not an as-built model, this gravity sag difference could have been caused by a 2-mm error between the model and the actual mount pad locations. Thus a lesson learned, given the importance of gravity sag for achieving diffraction-limited performance, is the need for as-built mechanical models.

Fig. 17

ELZM gravity sag predicted versus measured.

The mechanical model predicted a first free-free resonant bending mode of 207 Hz. ELZM first-mode frequency was measured via a roving tap test on foam blocks to be 196 Hz (5% agreement with prediction), shown in Fig. 18. The thermal model predicted a 9.6-nm rms total SFE consisting of contributions from its athermal mount through thickness thermal gradient and bulk CTE homogeneity. The largest contributor to this error is from an assumed CTE homogeneity of 5 ppb (based on internal Schott data). ELZM total thermal deformation measured from 294 to 250 K was 9.4 nm rms (Fig. 19).

Fig. 18

ELZM first free-free modal frequency predicted versus measured.

Fig. 19

ELZM thermal deformation predicted versus measured.³⁸

Finally, a CTE homogeneity distribution estimate was created by correlating the model with the measured ELZM soak temperature thermal deformation. AMTD estimates that the Zerodur^® boule from which the Schott 1.2-m mirror was manufactured had a slightly radial varying CTE distribution between 3.0 and $6.5\mathrm{ppb}/\mathrm{K}$ (Fig. 20). With this CTE distribution, the thermal model predicts the measured thermal deformation with an uncertainty of $<6\mathrm{nm}$ rms. Given the LTS induced core-wall bending experienced by the 1.5-m ULE^® mirror, the team decided to make an as-built model of its internal structure via x-ray tomography (Fig. 21). This model was used to predict the mechanical and thermal performance of the 1.5-m ULE^® mirror.

Fig. 20

ELZM estimated CTE distribution from measured thermal deformation.³⁸

Fig. 21

Internal dimensional structure of the 1.5-m AMTD-2 mirror was quantified via x-ray-computed tomography, and code was developed by MSFC to convert CT scan data into a finite-element model.

The MSFC as-built mechanical model predicted a gravity sag deformation of $2.5\mu \mathrm{m}$ pv (580 nm rms). The gravity sag measured via a rotation test was $2.6\mu \mathrm{m}$ pv (582 nm rms, a 55-nm rms difference between predicted and measured), as shown in Fig. 22. By comparison, the Harris Corp. “design” model predicted a $3.0\text{-}\mu \mathrm{m}$ pv (681 nm rms). The as-built mirror is stiffer than its design. This is because, during mirror assembly, due to a fixture issue from an external vendor, some of the hex core elements were shifted radially inward from their design location by up to 20 mm. In addition to producing a stiffer mirror, it decreased the gap between adjacent core elements and may have contributed to core-wall contact due to bending during slumping.

Fig. 22

1.5-m ULE^® mirror gravity sag predicted versus measured.

When the ELZM mirror was tap tested resting on foam, the 1.5-m ULE^® mirror and its support structure were tested suspended from a bungee. The mirror and structure were tapped at 42 locations with an instrumented modal test hammer. Each location was tapped 5 times, and results were averaged. Twenty-two of the 42 locations were on the back of the ULE^® mirror. Test results were deciphered to identify the modes associated with the ULE^® mirror. Those results were compared to predicted frequencies from the MSFC as-built model and the Harris Corp. design model (Fig. 23). Again, the as-built model is stiffer than the design model and more closely matches the test data. The as-built model predicted a first mode of 401 Hz, and the measured first mode was 414 Hz (3.3% agreement).⁴⁶

Fig. 23

Predicted versus measured modal frequencies of 1.5-m ULE^® mirror.⁴⁶

The 1.5-m ULE^® mirror thermal model was constructed by combining the x-ray computed tomography structure data, boule CTE maps provided by Harris Corp., and an MSFC CTE homogeneity correlation. The model was used to correlate the mirror’s estimated performance with its “as-measured” performance (Fig. 24). The measured thermal surface change (231 to 293 K) was 28.8 nm rms. The model estimated that the mirror would have 18.9 nm rms of mount deformation (caused by CTE of the aluminum delta frame relative) and 16.6 nm rms of CTE deformation (caused by ULE^® CTE distribution and homogeneity), for a total SFE of 22.8 nm rms. The difference was 13.4 nm rms. One explanation for the 13.4-nm-rms residual is uncertainty in the best-fit CTE homogeneity correlation. Another potential explanation is differential strain between the front and back face sheets. Introducing such an effect into the model by adding a uniform bias to the back sheet CTE reduced the uncorrelated error to 4.4 nm rms. However, it must be noted that at present we have no physical basis for how such a differential strain could arise.

Fig. 24

1.5-m ULE^® mirror thermal deformation predicted versus measured.³⁸

8.1.

Arnold Mirror Modeler

The AMM was developed to rapidly create and analyze detailed mirror designs. AMM can create a 400,000-element model in minutes. This tool facilitates the transfer of a high-resolution mesh to various mechanical and thermal analysis tools. AMM creates input decks for ANSYS, ABAQUS, and NASTRAN. It creates a complete analysis stream, including model, loads (static and dynamic), plots, and a summary file of input variables and results suitable for optimization or trade studies. The values of all settings in the program are archived and recalled to continue or redo any configuration. AMM supports a range of mirror architectures:

Supported strut configurations include hexapod, Hindle, axial, radial, and tangential. Struts can either follow the contour of the mirror to attach to a curved backplane or have variable length for attachment to a flat backplane (Fig. 25). For large segmented mirrors, AMTD used the curved backplane option. This provides more uniform strut stiffness for dynamic behavior. For ease of design, an algorithm aligns the mount pads to either the center of a cell or the intersection of cell webs (Fig. 26).

Fig. 25

Hexapod support system for large aperture—flat versus curved backplane.

Fig. 26

Algorithm locates mount pads at cell center or rib intersections.

8.2.

Sensitivity and Performance Evaluator for Coronagraph Leakage

AMTD developed a series of increasingly sophisticated modeling tools to estimate the contrast leakage that occurs when dynamically aberrated wavefronts are propagated through candidate coronagraphs.^18,22,23 The purpose of these tools is to help define a wavefront stability specification for candidate primary mirror architectures. The SPECL tool has the ability to study monolithic, hex segmented, and petal segmented primary mirror architectures (Fig. 27). It can apply global Seidel aberrations upon the whole aperture of power, astigmatism, coma, spherical, etc., or it can apply Zernike aberrations to individual segments, including piston and tip/tilt. It also models the effect of backplane bending on a segmented aperture. For each of these cases, it can introduce an error that is static, periodic, or randomly varying. Static errors determine the sensitivity of a coronagraph to a fixed amplitude of each aberration. Periodic models contrast leakage for a WFE that varies sinusoidally between ±peak amplitude values. This case represents periodic vibration, such as the rocking mode of a secondary mirror tower or of a primary mirror segment that is uncorrected (either no active control or active control is slow). Random models motion is not corrected by an assumed active control system. Following the definitions and methodology of Shaklan,⁴⁷ the contrast leakage is decomposed into radial (photonic noise) and azimuthal (systematic noise) components. Contrast leakage is calculated over an annual region of interest (ROI) and plotted as a function of aberration type and amplitude (Fig. 28).^22,23

Fig. 27

SPECL supports various apertures: monolithic and segmented (petal and hex).^4,22

Fig. 28

SPECL calculates contrast leakage over annular ROI as function of aberration.²³

8.3.

Thermal MTF

AMTD developed a methodology for understanding how a primary mirror responds to a dynamic thermal environment.¹⁹ Any thermal environment can be decomposed into a set of periodic thermal oscillations that cause wavefront figure errors on the primary mirror with a thermal time constant determined by the mirror’s thermal properties (e.g., mass and conductivity), as shown in Fig. 29. The magnitude of these figure errors depends on the amplitude and period of the input thermal oscillation. These T-MTF responses can be used to determine thermal boundary and control conditions for passive and active telescope thermal control.

Fig. 29

Primary Mirror optical performance depends the mirror’s response to thermal modulation as a function temporal frequency.

Integrated modeling shows that the RMS WFE range is inversely proportional to the mirror’s mass and specific heat and the RMS WFE range is linearly proportional to the mirror’s CTE. A closed-form derivation found similar relationships between thermal parameters and the thermal strain rate caused by a heat imbalance:

AMTD explored telescope thermal stability sensitivity for candidate 4-m-class mirrors. The required WFE stability can be achieved when the primary mirror is inside a thermally controlled environment with a period and controllability that meet the specifications shown in Fig. 30. Controllability is the maximum deviation of the shroud’s temperature from the average temperature. The period of the control system is the time it takes for an entire heater cycle to occur.

Fig. 30

For a given telescope, its wavefront stability can be kept below a specified value by varying shroud controllability and cycle period.

8.4.

Fast Response Simulator for Telescopes

From FY11 to FY13, AMTD partner GSFC developed a suite of MATLAB^®-based tools for using STOP and jitter-integrated models to calculate optical path length difference maps and line-of-sight errors called FaRSiTe (Fig. 31).² FaRSitE can be used to generate high-fidelity PSF simulations and compute standard metrics associated with imaging systems (MTF, EE, Zernike coefficients, etc.), as well as user-defined metrics. This represents an advance over the previous state of the art in which performance estimates from multiple independent sources were often combined via an error budget framework (e.g., via root-sum-squares of scalar quantities, where all terms are assumed to be independent whether this is actually the case or not).

Fig. 31

Fast Response Simulator for Telescopes.