2.1.

Mirror Segments

Mirror segments are the basic elements needed to build a mirror assembly. Once top-level parameters of a telescope, such as focal length, mass, and effective area, are decided based on science requirements, the total mirror surface area and areal density, i.e., mass per unit mirror surface area, are determined as well. Furthermore, once a material is selected, its density will determine the thickness of the mirror. What is left to be decided is how to realize the mirror surface area: a small number of very large mirror segments or a large number of small mirror segments or somewhere between the two extremes. See Sec. 3.1 for how we have decided on the mirror segment dimensions for Lynx.

Each mirror segment, together with its primary or secondary counterpart, must meet image and effective area requirements. They also have to meet structural integrity requirement as well so that they will be able to survive the launch.

2.2.

Mirror Modules

Each mirror module is composed of dozens of mirror segments precisely aligned and bonded onto a structural element, i.e., a midplate that is made of the same material as the mirror segments. In addition, for reasons of thermal control and minimization of mechanical blockage, we have chosen also to implement stray light baffles on each module. The module construction process must realize the full potential of each mirror segment. In the end, each module must pass x-ray performance tests before and after a battery of environmental tests, including vibrations, thermal vacuum, acoustics, and shock tests.

2.3.

Mirror Metashells

Each metashell is composed of a number of identical mirror modules, aligned and bonded onto two integration rings, one at the forward end and the other at the aft end of the module. The forward end of the module’s midplate is a precision-ground surface that serves as the reference from which its focal length is defined and measured. The forward ring, as such, serves as a reference for confocality of all modules.

The alignment and bonding of the module into its metashell, while a process demanding engineering precision, requires no special development. This is for two reasons. The first is that the module is a rigid body, consisting of a rigid midplate with dimensions of $\sim 200\mathrm{mm}$ in the optical axis direction by 100 mm in the circumferential direction by 10 mm in thickness or in the radial direction, and many mirror segments, which by some measure enhance the module’s structural stiffness. The second reason is that the precision required to align a module is relatively loose, much looser than that required for aligning and bonding a mirror segment in the process of constructing the module. For Lynx the required precision for each of the six degrees of freedom is as follows:

Therefore, the integration of a module into its metashell is a straightforward process, though requiring engineering precision and discipline. Substantially similar and even more demanding tasks have been performed for past missions. It should be noted that a significant feature of the module or the metashell is that, other than trace amounts of foreign materials such as mirror coatings and epoxy, they are made of a single material, which in the Lynx case is silicon. This uniformity in material offers significant advantages during their construction process and later during mission operations where the operating temperature of the mirror assembly can differ from the laboratory temperature where they were built and tested.

2.4.

Mirror Assembly

The 12 metashells are aligned and attached to a spider-web made of composite material or metal to bear the load of all metashells and to structurally interface to the rest of the observatory. The alignment of a metashell, which is treated as a rigid body, has requirements in $X,Y,Z$, pitch, yaw similar to those of the module alignment, but it essentially has no roll requirement because of its axial symmetry. The attachment of a metashell to the spider is via a number of titanium flexures, which serve as structural and thermal isolators between the metashells and the rest of the observatory. At the outer edge of the spider-web is a stiff flange that allows the mirror assembly to be mounted to the observatory.

3.1.

Mirror Segment Fabrication

We have chosen direct fabrication as the method for making mirror segments because of two considerations. First, of all techniques that have been used for making optics in general and x-ray optics in particular, direct fabrication, also known as grind-and-polish, makes the best possible optics. Second, direct fabrication technology has progressed by leaps and bounds in the last 20 years since the Chandra mirrors were fabricated in the 1990s. Many then-esoteric techniques have matured and become commercially available in the form of turnkey machines. In particular, ion beam figuring technology has become widely used in the semiconductor industry for making high precision wafers to meet ever more stringent device requirements. Perhaps most important of all, some of these polishing processes exert little to no shear stress or normal pressure that could fracture thin substrates, opening up the possibility of polishing thin optical components that were not possible before.

In conjunction with choosing the direct fabrication method, we have chosen monocrystalline silicon as the material because of several reasons. First of all, monocrystalline silicon is free of internal stress, unlike any other materials, especially glass, that are full of internal stress because of domain boundaries between crystal grains as in metals or because of supercooling as in glass. This lack of internal stress makes it possible to use deterministic material removal techniques of modern polishing technologies to make precision optics: any figure change is determined and only determined by the amount of material removed. In contrast, with a material with internal stress, the removal of material causes figure change in two ways: the disappearance of the material itself and the disappearance or appearance of stress as a result of the material removal. The figure change due to stress is unpredictable. The unpredictable stress-induced figure change is totally negligible for a thick ($\sim 10\mathrm{mm}$) substrate but not so for a thin ($\sim 0.5\mathrm{mm}$) substrate.

Second, silicon has highly preferred material properties. It has a relatively low density, $2.33\mathrm{g}/{\mathrm{cm}}^3$, lower than most glasses and aluminum. Its elastic modulus, $\sim 150\mathrm{GPa}$, is twice that of the typical glass and aluminum alloys, making it relatively stiff. Equally important is its high thermal conductivity, 130 W/mK at room temperature, more than 100 times higher than the typical glass, minimizing thermal gradients caused by a hostile thermal environment in space. Compounding the benefit of high thermal conductivity is its low coefficient of thermal expansion, 2.6 ppm/K at room temperature, lower than typical glass and much lower than typical metals. All of these material properties make silicon almost an ideal material for making x-ray mirrors for spaceflight. It would be ideal if its coefficient of thermal expansion were zero.

In addition, monocrystalline silicon is an industrial material. Very large blocks of it are commercially available at low costs. In conjunction with this, material availability is the availability of a large body of knowledge that has been accumulated in the last 50 years and industrial equipment for processing it. No other material enjoys these advantages. As a matter of fact, a key aspect of our technology development is to maximize the use of these advantages to make the best x-ray optics at the lowest possible cost.

Once the fabrication technique and material are determined, the thickness of the mirror segment can be determined by three parameters: mass allocated for the mirror assembly, mirror surface area, and density of the material. For Lynx, these three parameters lead to a thickness of 0.5 mm. The dimensions of the mirror segment are then determined by finite element analysis requiring that gravity distortion while the mirror is supported at four locations (see Sec. 3.2) and is sufficiently small to meet angular resolution requirements. All things considered, the dimensions of the mirror segment are determined to be $100\mathrm{mm}\times 100\mathrm{mm}\times 0.5\mathrm{mm}$. This size happens to be similar to a 150 mm in diameter wafer that is commonly produced and processed by the semiconductor industry, enabling us to use commercially available equipment and silicon blocks to facilitate mirror segment production and to minimize cost.

3.1.1.

Mirror substrate fabrication

The mirror substrate fabrication process,^19–23 shown in Fig. 2, starts with a commercially procured block of monocrystalline silicon, measuring $150\mathrm{mm}\times 150\mathrm{mm}\times 75\mathrm{mm}$, shown in the upper-left panel. In the next step, upper-middle panel of Fig. 2, a conical approximation contour is cut with a band saw into the block, which is then lapped on a precision conical tool to generate a precision conical surface that is a zeroth- and first-order approximation to an x-ray mirror segment. Then, the block is brought back to the band saw again to slice off a thin silicon shell, as illustrated in upper-right panel of Fig. 2. This silicon shell, because of the cutting and lapping process, has damage to its crystal structure. To remove the damage, it is etched in a standard industrial process with an HNA solution, a mix of hydroflouric acid, nitric acid, and acetic acid. After this etching step, the thin shell is a single crystal where practically every atom is on its lattice location. The entire shell is free of any internal stress. At this point, the shell’s surface is rough and not capable of reflecting x-rays at all, let alone forming images.

Fig. 2

Six major steps of fabricating a mirror substrate. This entire process, using no special equipment other than what is commonly available, takes about 15 h labor time and 1 week of calendar time. The process is highly amenable to automation and mass production methods, leading to high throughput and low cost.

Then, the conical substrate is polished with synthetic silk on a cylindrical tool to achieve required specularity and microroughness. In order for the reciprocation to be random in both the circumferential direction and axial direction to avoid grooving, the conical substrate is elastically bent into a cylindrical shape during polishing. This is equivalent to stress-polishing that was successfully used for making aspheric mirrors for the Keck telescopes. This step results in a mirror substrate whose clear aperture is $\sim 100\mathrm{mm}\times 100\mathrm{mm}$, with roll-off errors near the four edges that are typical of full-aperture polishing processes, shown in the lower-middle panel of Fig. 2. The areas near the edges are removed on a dicing saw, resulting in a mirror substrate of the required size, shown in the lower-right panel of Fig. 2. The monocrystalline nature of the substrate is such that the figure of the remaining mirror does not change at all as a result of the operation.

The final step of the mirror substrate fabrication is a figuring process using an ion beam. The mirror substrate is measured on an interferometer to produce a topographical map that is used to guide the ion beam to preferentially remove material where the surface is high. As of October 2018 many mirror substrates have been fabricated. Figure 3 shows the parameters of one of the best mirror substrates produced. Its overall quality is similar to Chandra’s mirror. Two mirrors like this one, when properly aligned, are predicted to achieve images of 0.5 in. HPD at 1 keV. In the coming years, every step of the entire substrate fabrication process will be examined, refined, and perfected to achieve better substrates, reaching the diffraction limit by sometime in the middle of the 2020s. We expect to be able to make substrates meeting Lynx requirements by the end of 2019.

Fig. 3

Measured properties of a finished mirror substrate. (a) sagittal depth variation as a function of azimuth. This substrate’s average sagittal depth of 166 nm differs from the design value of $174\mathrm{nm}$ by $8\mathrm{nm}$. The RMS variation of the sagittal depth is 4 nm. (b) Surface error topography. After removal of the sagittal depth, this mirror has an RMS height error of only 5 nm. (c) Slope power spectral density (black solid curve) in comparison with Chandra’s mirror (dashed curve). All of the errors combine to make this mirror substrate have an image quality of 0.5 arc sec HPD (two reflection equivalent).

3.1.2.

Mirror coating

Bare silicon surface is a poor x-ray reflector. It needs to be coated with thin films to enhance its reflectivity. There are potentially many different ways of coating the bare silicon surface to achieve high reflectance, but for the purpose of this technology development, we assume the use of the traditional iridium coating. Other coatings, when fully demonstrated, can be implemented with little to no change to the process presented here. The major issue related to coating is the fact that coating introduces stress that can severely distort the figure of a mirror substrate.²⁴ The preservation of the substrate figure requires a way to cancel or otherwise compensate for its effect.

The coating process, shown in Fig. 4, starts with a bare silicon substrate cleaned of particulate and molecular contaminants. Using the standard semiconductor industry’s dry oxide growth process, we coat the backside, i.e., the convex side or the nonreflecting side, with a layer of ${\mathrm{SiO}}_2$. The ${\mathrm{SiO}}_2$ exerts compressive stress on the substrate, causing it to distort as shown in Fig. 4 (step 2). Then, a thin film of iridium, with an undercoat of chrome serving as a binding layer, is sputtered on the front side. The compressive stress of the iridium film counteracts the ${\mathrm{SiO}}_2$ stress, canceling some of the distortion, shown in Fig. 4 (step 3), but still, significant distortion remains. The final step is to trim the thickness of the ${\mathrm{SiO}}_2$ layer thickness to achieve precise cancellation of stresses and restore the figure of the substrate. The trimming is guided by precise figure measurement and finite element analysis.

Fig. 4

Illustration of mirror coating process to enhance x-ray reflectance while preserving the figure quality of silicon substrate. The distortion caused by the stress of the iridium thin film is precisely balanced or compensated for by the stress of the silicon oxide on the other side of the mirror substrate.

One way of trimming the thickness of the ${\mathrm{SiO}}_2$ layer is using chemical etching. This has been recently demonstrated.²⁵ Another way of trimming is using an ion beam, the same as figuring the silicon substrate. Since this is a dry process, as opposed to the wet chemical etching process, it has the advantage of being cleaner. We expect this to be experimented with in 2019.

3.2.

Mirror Alignment

A mirror segment needs to be aligned and bonded to form part of a mirror module. We have chosen to support a mirror segment at four optimized locations,²⁶ as shown in Fig. 5. Four supports, as in the case of three supports for a flat mirror, necessarily and sufficiently determine the location and orientation of a curved mirror, such as an x-ray mirror. Using gravity, or the weight of the mirror segment, as the nesting force, the alignment of the mirror segment is determined by the heights of the four supports, which are interchangeably called posts or spacers. The alignment task is reduced to the precision grinding of the heights of these spacers.

Fig. 5

Illustration of the four-point kinematic support of an x-ray mirror. The four supports are approximately located one quarter way inboard from each corner. See text for a discussion of the advantages of aligning and bonding a mirror segment using these four supports, which are also called spacers or posts.

The alignment process is an iteration of Hartmann measurement²⁷ using a beam of visible light monitored by a CCD camera, shown in Fig. 6, and precision grinding of the heights of the spacers. The precision of the spacer heights required depends on the radius of curvature of the mirror segment. In the worst case for Lynx for the largest radius of curvature of 1500 mm, the 0.1 arc sec alignment error budgeted in Table 2 translates into a spacer height error of 25 nm. With a deterministic grinding or material removal process, this precision is easily achievable. In the course of the last 2 years, we have repeatedly aligned many mirror segments, both primary and secondary ones individually, and primary and secondary segments combined. We have been able to achieve alignment accuracy of $\sim 1$ arc sec. HPD, which is dominated by the diffraction effect of the visible light, limiting the precision of alignment determination. Our plan is to refine this process by using visible light of a shorter wavelength to minimize the diffraction effect to achieve 0.1 arc sec alignment precision.

Fig. 6

Illustration of the Hartmann setup using a beam of visible light to measure the location and orientation of the mirror segment being aligned.

3.3.

Mirror Bonding

Bonding the mirror segment is a direct and easy extension of the alignment process. Once the four spacers have the correct heights as determined by the Hartmann measurement, the mirror segment is removed, a small amount of epoxy is applied to the top of each of the four spacers, and then the mirror segment is placed on them again. Finally, vibrations are applied to help the mirror segment settle in its optimal configuration, the same way as during the iterative alignment process. During the settling process, because of the weight of the mirror and the vibrations, the epoxy on each spacer is spread and compressed. The mirror segment is permanently bonded when the epoxy completes curing.²⁵

This way of supporting and bonding the mirror segment has many advantages. First, the gravity-induced distortion is not frozen in permanently. Because of the optimization of the locations of the four spacers, the gravity distortion disappears once the gravity is released. Second, the epoxy bonds do not affect the alignment of the mirror segment. Third, any local distortion caused by epoxy cure is minimal as the diameter of the spacer is only a few times larger than the thickness of the mirror segment. The mirror segment, being 0.5 mm in thickness, is very stiff over the length scale of several millimeters similar to the diameter of the spacers.

The validity of the entire process, from mirror substrate fabrication to alignment and bonding, has been demonstrated by successfully building and testing mirror modules repeatedly as shown in Fig. 7. It was placed in the 600-m x-ray beam line at the Goddard Space Flight Center and produced images with 2.2 in. HPD, as shown in Fig. 7(b). The same module was also tested at the Panter 100-m x-ray beam line and measured for its effective areas at several different energies, agreeing within 2% with calculations based on atomic form factors independently measured.

Fig. 7

(a) A pair of mirrors aligned and bonded on a silicon plate. Each mirror is bonded at four locations with silicon spacers (not visible in this view). The four spacers on the back of each of the two mirrors are therefore the next pair of mirrors. (b) An x-ray image obtained with a beam of 4.5 keV (Ti K) x-rays, with a half-power diameter of 2.2 in.. The effective areas at several energies are measured at MPE’s Panter x-ray beam line, thanks to Dr. Vadim Burwitz and his team, to agree with theoretical expectations.

3.4.

Building and Testing Mirror Modules

Building a mirror module is just many repetitions of the process described in Secs. 3.1, 3.2, and 3.3: fabrication, coating, aligning, and bonding of one mirror after another, as shown in Fig. 8. In the middle of the stack of mirror pairs is a thick silicon plate, annotated as flight plate, in Fig. 8, that will be a permanent part of the module and will be used as the load-bearing structure to align and bond the module to the metashell. The interim plate in Fig. 8, on the other hand, is a piece of ground support equipment and will be removed once the module construction is complete. It should be noted that this way of aligning and bonding one mirror segment is free of any stack-up errors as each mirror segment is aligned without referencing to any other mirror segment that has already been bonded. The mirror segments previously bonded underneath the current one only serve as a structural support. This prevention of any stack-up errors allows each mirror segment to realize its own full potential. It also allows a pair of mirrors to be optimized. Another feature of every module is that, as part of its construction process, it carries a reference from which to measure its focal length, as shown in Fig. 8, step 1.

Fig. 8

Building-up of a mirror module. It is a repetition of fabrication, alignment, and bonding of one mirror segment after another. The interim plate is for the construction process only. It will be removed before the module is integrated into a metashell with the flight plate as its load-bearing structure and focal length reference.

Each module is individually tested in an x-ray beam for science performance, such as angular resolution and effective area, both before and after a battery of environmental tests, including vibration, thermal-vacuum, acoustic, and shock tests. One significant advantage of our hierarchical approach is that each module is small in size and weight and therefore can be handled and tested easily, without the need for any special and expensive equipment or test facility. In particular, since each module has many identical copies, managing spares is easily done by making one or two additional modules of each prescription.

3.5.

Progression Toward Fully Meeting Lynx Requirements

The process of building and testing mirror modules described in the Sec. 2 will be continually refined and perfected in the next few years to meet all requirements: science performance, spaceflight environments, production schedule, and production cost. Table 2 shows the three-pronged strategy to mature this technology. The three prongs are building and testing modules of progressively more mirror segments and meeting progressively more stringent requirements. Many process parameters will be investigated and optimized. Among them are: