Space environment factors:

Earth borne telescope environments are distinct from those in space. Some of the factors that a designer of spaceborne telescopes must consider and accommodate are expressed in Table 1.

Table 1.

The Space Environment Effects influencing the mirror material selection: two elements are rated as strongly relevant

Of these, #6 is typically the greatest challenge to the performance of the telescope. Since most optical surfaces are to be maintained to within nanometers of the prescribed form [2](with currently envisioned missions of HabEx, LUVOIR and LISA requiring surfaces constant to a few picometers), we are concerned with effects often ignored in less demanding engineering. Each material will be subject to both the innate material property, and also the process available to implement the mirror.

A Materials checklist:

There are two approaches to managing thermal transients innate to material selection. Any deficiency of the thermal solution to address surface stability through material properties must be augmented by sensing temperatures and proportionally adding heat. Innate material stability depends on the thermal expansion over the thermal range, and the thermal diffusivity. Unfortunately, practical materials for mirrors have either a High Coefficient of Thermal Expansion (CTE) with a high Thermal Diffusivity (TD), or a low CTE with a low TD. Metals and ceramics fall in the first category, and low expansion glass and glass ceramics fall in the second category. Later in this paper, the relative effectiveness of each approach will be illustrated.

Thermal expansion at different operating temperatures

Thermal stability is a key requirement for most spaceborne systems. Because attributes of ZERODUR^® have been extensively published by SCHOTT and others, we start by referencing our discussions to this available data. ZERODUR^®, a very low thermal expansion glass ceramic, illustrates critical attributes of materials in this class for thermal design. Figure 1 illustrates that modest thermal strain may be achieved even going between room temperature and LN2 temperatures. Furthermore, as we will describe later, the tailored expansion of ZERODUR^® closely matches expansions that can be realized for the common structural material Carbon Fiber Reenforced Polymer.

Figure 1.

Without changing the heritage composition of ZERODUR^® glass ceramic, the thermal expansion characteristics can be altered by process parameters in ceramization. In this example, dl/l at Room Temperature is identical to dl/l at ~40K. The dl/l curve can be further optimized depending on the operational temperature or operational temperature range [3].

Many telescope assemblies operate over a shorter temperature range than that expressed in Figure 1. 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 shorter thermal range than that expressed in Figure 1, a thermal range often encounter in OTAs operating in the Visible and Ultraviolet (wavelengths between 100 nm and 1100 nm). The 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 provide required dimensional stability over orbital varying thermal boundary conditions. While this tailoring of ZERODUR^® may be applied to optimally match operating conditions, in Figures 2 and 3 we express four examples of strain 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.

Figure 2.

Here we illustrate 4 different measured target thermal expansion curves for ZERODUR^®. Note designations A,B,C,D are for convenience here and not SCHOTT defined profiles. Thus, if the telescope was to operate between T=0 °C and T= - 30°C, ZERODUR D would be preferred. While if the telescope was to operate between 10 °C and 40 °C, ZERODUR A would be preferred.

Figure 3.

Designations A,B,C,D are converted into CTE. Note that the change of slope in Figure 2 implies that CTE can be both positive and negative, and that there are ZERO Crossings of CTE, as designated at -17°C for case D.

Because there are maxima and minima in the strain curves of Figure 2, the derivative with temperature, coefficient of thermal expansion (CTE), will be zero at these temperatures. Ultraprecision mirrors may be designed to maintain the mirror close to one of these ZERO Crossing Temperature. To do this, a gradual slope of CTE with temperature is important. The larger the slope, the more homogeneous the material must be in CTE.

ZERODUR^® is a monolithically cast material, distinct from a mirror substrate fabrication using multiple pieces, and from substrates built additively. As such, it is innately homogeneous as illustrated in the Figure 4 [A]. For a low expansion material like ZERODUR^®, characterization depends upon precision dilatometry at the part-per-billion/K (ppb/K) level [4]. CTE metrology accuracy to this level has been established at the ZERODUR^® factory floor. This qualifies the substrate material for high precision telescopes. The achieved homogeneity is crucial for minimizing surface deviations associated with taking the mirror from room temperature to a different operational temperature, and also for consistent performance over the operation range. Furthermore, the product of at the CTE ZERO crossing temperatures must be minimal if the mirror surface accuracy is to be actively maintained. The following figures illustrate measured homogeneity of mirror blanks at various spatial frequencies.

Figure 4.

The 1.5m disk, 2cm thick, is sampled in a polar coordinate sys tem exhibiting homogeneity of 5.3 ppb/K peak-to-valley, consistent with the mixing process associated with casting the blank

Figure 5:

Homogeneity measurements made on two ZERODUR® 1.554m diameter blanks produced three years apart further establishes the low level of inhomogeneities in the process [5]. The measures in Figure 4 and Figure 5 establish homogeneity on moderately large blanks. These are sampled at of the order of 20 cm average increment. Recently, measurements have been made of material around a full 4 m blank, exhibiting very small inhomogeneity. Smaller scales are highly relevant to critical stability. Sacrificial measurements have also been made of a 10 cm cube of ZERODUR^® sampling on the 1 cm spatial scale. Results are found in Figure 6. In summary, Table 2 summarizes homogeneity on various size blanks and sampling at various spatial scales.

Figure 6.

Homogeneity is established at the 1 cm scale for ZERODUR^®. 97 coupons fell within a peak-to-valley range of 1.3 ppb/K.

Table 2.

Measured CTE Homogeneity [5]

NASA MSFC conducted optical tests of a SCHOTT provided lightweighted mirror at the XRCF thermal vacuum facility. The mirror substrate was 1.2 in diameter, lightweighted 88% and prepared as a machining demonstration. The mirror was polished as a sphere, and kinematic mounts added. MSFC conducted interferometric tests at temperatures 295K, 270K, 250K and 230K [6]. The homogeneity maps were not available, NASA’s analysis attributed all the small changes in mirror shape to inhomogeneity, even though gradients and other systematic errors were known to be present. Even with this assumption, all models of homogeneity suggested that the inhomogeneity could be no larger than 5ppb, in agreement with SCHOTT dilatometry maps on 1.5m disks.

Relative thermal merit of various mirror materials

For optimal telescope optical performance, two conditions are to be met as the telescope or instrument assembly goes through gravity release, launch loads, and operating temperatures over a range often not including the fabrication temperature.

In most telescopes of moderate to large size range, there is a provision for focusing, and perhaps adjustments of other degrees of freedom once on orbit. Exoplanet coronagraphs and other critical narrow angle systems may even reimage the entrance pupil to restore low- and mid-spatial frequency errors to ideal form.

Our consideration is passive athermalization, the extent that the mirror material may minimize errors without mechanical intervention or proportional addition of heat at nodes. A common comparison is often evoked comparing CTE to thermal diffusivity (= thermal conductivity/(density*c_p)). Thermal diffusivity is a measure of the volume of material to come to a new equilibrium temperature. We consider three cases:

The thermal stability ideal might evoke mirror materials exhibiting both High Thermal Diffusivity and Low CTE over typical broad operational temperature ranges. Unfortunately, such materials are not available. Therefore, a trade is needed among available materials based on consideration of

Materials exhibiting High Thermal Diffusivity with High CTE can be made to work only if isothermal conditions are maintained. However, the sun and earth expose a heat load on part of the telescope, while cold space constitutes a thermal sink. Typically, this is a transient situation as well, depending on whether the observatory is earth observing or conducting astrophysics. For such a system, can the system become sufficiently isothermal rapidly enough or at all from spaceborne boundary conditions, even if heat is added? This is especially true for diffraction limited telescopes that operate in the visible and ultraviolet part of the spectrum. It is less true for telescopes at long wave infrared and sub-millimeter wavelengths that have much more forgiving optical tolerances.

Our focus is on Cases A and B above, which address most mirror material solutions currently being considered. Case C is an emerging solution being posed by Cordierites for cases that include high authority temperature control of the mirror, addressing the challenge of steep slope of CTE(T) at the temperature of CTE zero crossing, authority of control and CTE slope driven demands on homogeneity. The numerical simulation in Figure 7 examines the critical trade between Cases A and B above [7,8]. Intentionally, a thermally stressing orbit was modelled with identical telescopes, one with the primary mirror of SiC and the other with the primary mirror of ZERODUR^®. The analysis assumed an 100-minute low earth orbit, with the telescope nadir looking toward Earth. Furthermore, the orbit is made to pass through the earth’s umbra, inducing thermal perturbation in addition to a solar view factor rotating 360° per orbit. In this case, the Low Thermal Diffusivity, Low CTE selection performs substantially better than the SiC case.

Figure 7.

This simulates the relative response of a ZERODUR^® and a SiC primary mirror in telescopes, identical except for the material. 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 deviation. [7,8]

A number of mirror materials have been used in spaceborne telescopes, each with strengths and weaknesses. The attributes a designer considers are broad. First, the material must have the dimensional stability in the environment satisfying the imaging performance requirements. Principal among these is dimensional stability in the orbital environment. Heritage, Technology Readiness Level (TRL), and mechanical strength and mass attributes are all important, as is the ability of the material to take a smooth optical surface. Increasingly, telescope cost and manufacture schedule are becoming deciding factors, especially for moderate sized telescopes in the 0.3-1m diameter class.

Table 3 emphasizes the parameter maximum monolithic diameter. Also, a consideration is the ability to inspect for subsurface defects. If voids or inclusions manifest during machining a lightweight mirror, or optically finishing the mirror, the expense and lapse time of replacing the material in these operations may be considerable. For many materials, mirrors are made of joined sections of different material production runs. For example, the 3.5m Herschel Telescope primary mirror was made of 9 pieces of SiC, each brazed together. This piecing together of pieces of material made in differing batches introduces a number of uncertainties in response to thermal stimuli. In the case of Herschel, operation was between the wavelengths of 80 microns to 640 microns. Since the wavelength is approximately two orders of magnitude larger than telescopes operating at visible wavelengths, the error is proportionally more forgiving to effects of joining materials, and of any dissimilarities between the 9 parts in thermal response. In a different manner, large ULE mirror blanks may frit bond or low temperature fuse a number of pieces of ULE to make a single mirror (for example the 1.8m Technology Demonstration Mirror made for NASA joined by low temperature fusion 9 separate pieces of ULE to form the 1.8m diameter mirror [9]. This mirror was never completed, and the effects of joining pieces is not known.). In the case of aluminum, while castings can be made quite large, preferred materials for diamond turned mirrors require rapid quenching, as done by RSP Technology, and it appears that this quenching cannot be homogeneous for large mirrors.

Table 3.

Material Properties Comparison I: Glass ceramics, glass, cordierites and metals. Bold designates favored.

For materials that take an optical surface or can be clad with another material to take a smooth optical surface, considerations for spaceborne mirrors center on mass efficiency, and resilience to thermal transients. These are often plotted against each other (Figure 8). Mass characteristics have been important in situations when the space element mass is required to be limited to meet the capacity of launch vehicles reaching the desired orbit. A useful measure of this is the quotient of E, the modulus of elasticity divided by the density, r. High modulus materials can make thinner mirrors with the same degree of deflection in gravity. Beryllium has both a very high E and a low r, favorable from the structural point of view. This ratio is less critical presently with the emergence larger lift capacity launch vehicles. While E/ρ represents bending, once in space the eigenfrequency of vibration response to stimulus from cryocoolers or spacecraft reaction wheels may be more important. The fundamental eigenfrequency f₀ scales with √(E/ρ).

Figure 8.

Frequently, the first order figures-of-merit for candidate mirror materials are taken to be the material’s structural efficiency (Elastic Modulus divided by Density, the metric for gravitational or inertial displacement) and its Thermal Transient Resilience (Thermal Diffusivity D divided by CTE (=α in the chart) (where D = thermal conductivity divided by the product density times specific heat cp). Here, we show one plotted against the other. The hyperbolic contours are for (E/ρ)*(D/α) = constant implying these two metrics are of equal weight. Frequently today, the Abscissa giving the thermal figure of merit is favored. Here FS=Fused Silica, CO-720 = Cordierite, and Si = Silicon. ZERODUR^®, with both CTE and CTE homogeneity as low as 5 ppb/K, is in a favored position for thermal response. Since eigenfrequency relating to vibration response goes as √(E/ρ), the separation along the ordinate is less.

The resilience to thermal transients is expressed as Thermal Diffusivity D (D = Thermal Conductivity/(density ρ*specific heat at constant pressure c_p) divided by the CTE (or α).