1.1

Future Relative Importance of Mass Efficiency and Thermal Transient Resilience

As it was for the Webb Telescope, basic to mission architecture will be early mirror material selection for future great spaceborne observatories. This is especially true for large apertures in the domain being called for of monolithic or segmented apertures 4 meters diameter through 6 meters diameter or larger. With the advent of heavy lift vehicles available for the next generation of great observatories, there will be less emphasis on lightweighting of the telescope mirrors. Thus, the mass/stiffness efficiency, a classic predictor of gravitational deformation

is of less importance for launch. The main structural stability driver may be Eigenfrequency resonance to launch loads and to gyros, reaction wheels and cryo-coolers during operations. And the first Eigenfrequency is given by

Since this is a square root function, the differences in Young’s Modulus between very stiff materials and materials with excellent optical properties is less pronounced than in the gravitational deflection case η.

For these missions, perhaps even more crucial than mirror eigenfrequency response and mass considerations are the effects that define optical figure stability. While operational vibrational resonance is a factor in optical stability, technologies are advancing to decouple spacecraft vibration disturbance sources from the optical system. In Figure 1 below, we plot eigenfrequency response vs. the Thermal Transient Resilience Parameter. This is an expression of balance relating how rapidly the equalization of temperature field occurs after the introduction of a thermal transient, divided by the coefficient of thermal expansion (CTE) of the material. Later, we will discuss second order effects including how homogeneity of CTE(x_i Cartesian Tensor notation) throughout the volume affects stability, and also including how the variation of CTE with temperature ∂CTE/∂T also affects stability. Special problematic cases include:

Figure 1.

Both Specific Stiffness (E/ρ where E is Young’s Modulus and ρ material mass density) and Thermal Transient Resilience (Diffusivity = k/(ρ*cp where k is thermal conductivity) are commonly used in initial considerations of mirror material. They are expressed, one against the other, in this LINEAR-LINEAR room-temperature diagram. Contour hyperbolae denote constant utility as the product of the two axes. ZERODUR® performs favorably on this 2-dimensional metric. It may be argued that for ultrastability as required in the subject future great observatories that thermal transient resilience is the most important parameter. At presently expected operating temperatures of these missions (In contrast to InfraRed Webb, the likely operational range is expected to fall at temperatures of 250K to room temperature), the extremely low CTE of ZERODUR® is highly favorable to consideration. Later other thermal factors will be discussed.

1.2

Mission Characteristics will drive Mirror Material Considerations

For the large perspective missions of ESA and NASA, contemporary high performance mirror material considerations are summarized in Table 1. Wavelengths far shorter than those of Webb are being called for in the future of both ESA and NASA great observatory telescopes. Exoplanet coronagraphy is a highly desirable future tool for characterizing “Worlds around other Suns”. When this is a science flow-down, both wavelength and coronagraphy operations put a premium on the mirror’s ability to be polished to an extremely high smoothness and, perhaps more important to accurately maintain its figure over an operational temperature range. Since Webb was optimized to be “The First Telescope to see the First Light in the Emerging Universe”, This implies very large redshifts of light from early universe objects with the associated requirement to operate in the infrared. The infrared requirement in turn required the reduction of thermal noise from the telescope optics, necessitating very cold telescope operation at about 35K. The situation is different for next flagships of both ESA and NASA.

Table 1.

While future large observatory attributes are far from settled, we consider candidate operating environments and observational wavelengths. This Table is a top-level look at how suitable materials map into the underlying requirements, and a starting point for this discussion. Manifestations of the Coefficient of Thermal Expansion (CTE) ultimately include second level material requirements including homogeneity ∂CTE/∂xi, CTE = f(T), ∂CTE/∂T = f(T), radiation compacting stability will be considered together with heritage, TRL and infrastructure.

For mirrors of new large observatories working in Near InfraRed (NIR), Optical Ultraviolet (UV) domain, dimensional stability is crucial. Not only will the diffraction limited wavelength be much shorter than for Webb, in some cases, stabilities as challenging as 10 picometers (pm) over 10⁴ seconds may be required. The principal mechanisms driving such short-term optical surface perturbations usually relate to thermal transients. These may result from orbit and pointing driven solar view-factor changes, heat transfer from electronics and active devices, and any mixture of these effects.

2.1

Thermal Stability of ZERODUR®

ZERODUR®, in continuous production since 1968, exhibits the heritage and high TRL suitable for consideration for future extremely high performance spaceborne telescopes. The formulation is unchanged since inception. Since Ultrastable Materials have become critical enabling many dimensionally critical applications, including extensive applications in the semiconductor industry, production has been continuous, not only responsive to episodic astronomical demand, and accordingly, investment in IR&D and infrastructure ongoing. Presently ZERODUR® is made in monolithic single melt pours up to 4m. In the past, the VLT 8m mirror blanks were made at SCHOTT, and some of this large infrastructure remains as well as the methods.

2.2

Passive Stability (Topic D2) Ratio of (Thermal Diffusivity)/CTE should be large for low Transient Respose

Textbook material selection often describes plotting orthogonal material attributes, one-against-another [8]. Figure 1 is an example of this where the selection factors First Eigenfrequency Parameter and Resilience to Thermal Transients are treated. With the advent of heavy lift vehicles, mirror material selection is somewhat relieved from extreme lightweighting and now gives special emphasis on thermal stability. There are two classes of materials most commonly considered for mirror substrates:

Figure 2.

In this Log₁₀-Log₁₀ plot, the solid curve represents equal merit between the two axes. This assumes transient stability merit equally values thermal diffusivity and inverse Coefficient of Thermal Expansion (1/CTE). At operating temperatures of room temperature to perhaps 250K expected for a Visible/InfraRed mission, the extremely low CTE of ZERODUR® establishes this as the preferred material based on the thermal transient criterion.

There is no mirror-appropriate material that both has high thermal diffusivity and low CTE over a reasonable range of temperatures for space applications. Therefore, the telescope architect must choose from the above options. If the distinction in eigenfrequency is less important, the choice falls between the thermal attributes of heritage materials. Figure 2 addresses the trade between these materials room temperature to moderately cold (~260K to 290K). Webb was able to use Beryllium since at its very low temperatures (~35K), the CTE of Beryllium is nearly zero. However, at near room temperature, where the CTE of ZERODUR® is routinely less than 5ppb/K, or a factor of over 2000x smaller than that of Beryllium at 11400ppb/K and a factor of over 400x smaller than SiC at over 2200ppb/K. Figure 2 illustrates the differences between relevant mirror materials on the log-log plane.

We have considered a worst-case analysis as an illustration comparing the transient response of two mirrors:

Both were subject to the same telescope geometry; both were Low Earth nadir-looking telescopes. And both passed through the Earth’s umbra. As such, the telescope and mirror would see continuous change of solar view factor, continuous thermal transients. The result of this analysis is illustrative. To the left, the mirror of Boostec SiC exhibits nearly imperceptible temperature gradients to the full-scale resolution seen here at the moment in orbit this frame was taken while that of ZERODUR® shows apparent transient-induced temperature gradients across the mirror, also at full scale. However, to the right as we look at surface deformation across the mirror, Boostec SiC shows notable surface errors while surface errors are nearly imperceptible in ZERODUR® at the same scale. This illustrates in another manner the thermal advantage of ZERODUR®, a very low CTE, moderate Thermal Diffusivity material.

Figure 3.

This simulates the relative response of a ZERODUR® and a SiC primary mirror in telescopes, identical except for the material [9]. After 22 orbits, the temperature distribution on the primary mirror of each telescope is examined (Left), and as expected, temperature is notably smoother for SiC. However, the opposite is true for surface deviation (Right). This demonstrates that in comparison with an extremely low expansion material like ZERODUR®, high diffusivity fails to compensate for ZERODUR®’s low CTE in terms of surface □eviation

2.3

Homogeneity and Isotropy of CTE (Topic D3)

ZERODUR® is highly isotropic in thermal qualities. This is not necessarily true of other materials. For example, the beryllium crystal is anisotropic and there is some residual anisotropy in packing the powder and solidifying it. Improvements have been made by introducing quasi-spherical particles, and consolidation of the powder by hot-isotropic pressing (HIP). Nevertheless, some anisotropy remains. Isotropy is a valid consideration in material selection.

For ultrastability, the next incisive consideration is homogeneity. Comprehensive studies have been conducted at SCHOTT over the last decade demonstrating the extremely low inhomogeneity of ZERODUR® [10,11, 12]. Recently the 4.3m diameter mirror blank for the next generation solar telescope (DKIST) was produced by SCHOTT from a single casting for which perimeter readings determined that the CTE throughout the mirror (Secant 0C to 50C) averaged 0ppb/K +/-5ppb/K. SCHOTT has done frequent destructive testing exploring homogeneity on scales from 1cm to meter spatial frequencies. Unlike other materials, comprehensive ZERODUR® results are published.

ESA’s and NASA’s next generation large observatories will require ultrastability, even to the 10 picometer level! In 2015, a study was presented by Eisenhower et al: “ATLAST ULE mirror segment performance analytical predictions based on thermally induced distortions” [13]. SCHOTT has conducted a parallel study for ZERODUR®, using the well-established values for homogeneity of ZERODUR® [14, 15].

Figure 4.

The confirming study between ZERODUR® and ULE addressed first the assumption of perfect homogeneity, then actual measured inhomogeneity. Since Corning has not released homogeneity data, based on data at hand an inhomogeneity of 22 ppb/K was used for ULE. ULE, produced by deposition on a rotating platform, has been found to display a systematic CTE variation from the center to edge.

Figure 5.

Homogeneity drives achieving a 10-picometer rms surface in response to 1-mK, 10-mK and 100-mK. Measured inhomogeneities of several different batches of ZERODUR® were used, and all satisfied 10-picometer surface stability to up to a 100-mK perturbation. Thus, the superior homogeneity of ZERODUR® resulted in superior dimensional stability of ZERODUR® mirrors.

2.4

Cladding Mirror Substrate for Optical Finishing & a Mirror Substrate of Multiple Pieces (Topics D4, D5)

For smoothness of optical surfaces required for Optical and Ultraviolet wavelength observation, ZERODUR® is regarded as highly satisfactory. It polishes well with an extremely smooth microroughness, even to the Angstrom level.

If either beryllium or silicon carbide is to be used for telescope mirrors operating in the Optical and Ultraviolet wavelength regions, the natural microroughness of the polished surface is too large and will induce significant scattered light. Total Integrated Scatter is proportional to (microroughness/wavelength)². The specular surface must be clad with a material that polishes to a high smoothness. Webb mirrors are of bare polished beryllium which can only achieve a microroughness of the order of 4 nanometers rms. Thus, if beryllium was to be used, it would need to be clad with autocatalytic nickel, perhaps between 25 microns and 100 microns thick. ULE is polished to an order of magnitude better microroughness, and ZERODUR® up to another order of magnitude smaller. The same is true for SiC. To have a mirror surface clad in a manner it does not affect the optical figure, three conditions need to be addressed. Table 3 summarizes these considerations.

Table 3:

When ultraprecision is needed, what are the criteria for cladding a mirror surface to induce an acceptable instability. Often notional approaches of no-impact cladding are stated. Each of these requires detailed examination. Cladding materials typically exhibit a significant Modulus of Elasticity (E) and thus, the ability to impose a bending moment on the substrate in the presence of thermal transients and gradients. Furthermore, cladding induces a stress balance opposing the substrate material. Does this induce the propensity for microcreep and other temporal effects? Comprehensive studies are necessary if cladding is to be used for Ultrastable mirrors taking into account the entire thermal history of the mirror through optical fabrication, coating and operation.

Another potential instability is the fabrication of mirrors out of many roundels of material. In 2003, NASA’s 1.8m diameter Technology Demonstration Mirror (TDM) was being constructed out of ULE [16, 17]. At that time, the TDM substrate was to be fabricated by low temperature fusion out of 9 separate selected pieces of ULE. At the level of ultraprecision, it must be asked how the slightly differing characteristics of each piece affects the overall stability of the mirror. Similarly, ESA built the 3.5m Hershel Primary Mirror out of 9 pieces of Boostec SiC, brazed together in pie shaped segments. While Herschel has been highly successful, it operates in he sub-millimeter wavelength regime, 80 microns to 640 microns. There is little resemblance to the stability that will be needed for the upcoming large observatories.

2.5

Optimizing Mirror Transient Response by Tailoring CTE to Operational Temperature Range (Topic D6)

The ability to tailor the thermal expansion characteristics of ZERODUR® to various operational environment conditions simplifies the design requirements imposed on an Optical Telescope Assembly (OTA). The CTE of ZERODUR® may be optimally tailored over the relevant thermal range. There are three ways tailoring can help minimize thermally induced perturbations on the mirror optical surface. Four examples of many SCHOTT tailored ZERODUR® CTEs are shown as examples in Figure 4. Notice that there may be ZERO-CTE crossings at specific temperatures. If the operational temperature range that the mirror assembly will experience is:

Tailoring is done in the production process and does not alter the composition or Technology Readiness Level (TRL) of the material. Thus, the material itself may largely support required dimensional stability over orbital varying thermal boundary conditions. While this tailoring of ZERODUR® may be applied to optimally match operating conditions, in Figures we express four examples of CTE as a function of temperature for different factory applied tailoring, suggesting that a variety of thermal environments may be met with a high degree of passive stability.

A gradual slope of CTE with temperature is important. The larger the slope, the more homogeneous the material must be in CTE. Tailoring of ZERODUR®’s CTE provides a powerful tool to support optimization of ultrastability [11].

Figure 6.

Designations A,B,C,D are examples of actual CTE(T) tailoring. CTE can be both positive and negative, and that there are ZERO Crossings of CTE, as designated at -17°C for case D.

2.6

Evaluation of the Effect of Space Ionizing Radiation on Mirror Stability

While radiation compaction has been reported via laboratory testing of ZERODUR®, there is no evidence of any radiation induced dimensional instability on ZERODUR® experienced in telescopes at a variety of orbits. Well over 30 spaceborne missions have partially or totally depended on ZERODUR® mirrors [5, 6] and none have exhibited changes due to radiation. These include two NASA Great Observatories with enduring timelines…

While other parts of these systems have endured radiation damage, none is evident in the ZERODUR® mirrors. In an effort to close this ambiguity and provide actual data that can be used in error budgets, SCHOTT initiated a study under the direction of Dr. Antoine Carre. A comprehensive article is presently being prepared by Dr. Carre for JATIS. Figure 7 is a result of that study

Figure 7

gives one result of Dr. Carre’s study that begins to explain the dichotomy between actual flight experience and prior laboratory results. Literature extrapolations to realistic (lower TID) dosages far overestimate the measured values using the precision methods of the current study