Our current three main projects in this area are stress-based x-ray mirror figure correction using ion implantation, thermal oxide patterning, and ultrafast laser micro-stressing. They all follow the same paradigm:
1. Measure mirror figure.
2. Calculate stress distribution that will bend the mirror into its desired shape.
3. Apply calculated stress distribution in deterministic fashion and measure resulting figure.
Due to the desired shape of the mirrors (usually paraboloids and hyperboloids of revolution), precision figure metrology is a non-trivial problem. We are undertaking a major effort in this area. In addition, since these mirrors are very thin and easily bent, holding them without distortion during figure measurement is a challenge we have also been working on.
Imaging of celestial x-ray sources is of great scientific interest, but typical refractive telescope designs do not work in the x-ray band. There are two main reasons why it is very difficult to make refractive lenses (such as typical glass lenses in optical telescopes) for x rays, leading to contradictory requirements:
1. The index of refraction n for x rays is very close to n = 1 for all practical materials. Designing with refractive lenses would therefore require very thick lenses or impractically long telescope focal lengths (thousands of kilometers).
2. X rays are very easily absorbed by matter. That means refractive lenses would have to be extremely thin in order to avoid excessive loss of x-ray light.
Reflective optical designs using mirrors also do not work, except for designs that only use mirror reflections at small angles of grazing incidence, less than the critical angle for total external reflection. The most popular design for x-ray telescopes so far has been the Wolter-I optic, where nested shells of parabolic grazing incidence mirrors are followed by nested shells of hyperbolic grazing incidence mirrors.
Due to the small graze angles x-ray mirrors have to be very long along the optical axis, and their effective collecting area is only a few percent or even permil of their reflecting area. To catch as many x rays as possible with a given telescope diameter it is necessary to nest and align many shells around a common optical axis, and to make the shells as thin as possible. Thin shells are also preferred for launch into space due to their lower mass. These requirements of course conflict with the desire for the best possible telescope angular resolution, because thin shells are less stiff and difficult to shape into the correct figure, to polish, to coat (for better reflectivity), to mount and to align without distortions.
Wolter-I telescope mirrors deployed in space have been manufactured following three main approaches:
1. Make a single parabola-hyperbola (PH) shell from a massive cylinder by drilling out a hole from the middle and then figuring and polishing the inside walls. Advantages: Excellent angular resolution. Disadvantages: Cost, mass. Example: Chandra mirrors.
2. Replicate a complete PH shell from a figured and polished mandrel using electroplating. Advantages: Thin, relatively light shells. Disadvantages: Relatively poor figure compared to first approach. Optic diameter limited by size of mandrels. Example: XMM-Newton
3. Replicate a segment (azimuthal sector) of a shell from a figured and polished mandrel using thermal shaping (slumping) of glass. Advantages: Lowest mass mirrors, mandrels are smaller, low cost. Disadvantages: Lowest stiffness, hardest to obtain good figure, need release layer, dust problems, most work to assemble and align. Example: NuSTAR mirrors.
The mirrors for the Suzaku mission are a combination of approaches 2. and 3.
4. Slicing and precision-polishing thin mirror segments from monocrystalline silicon. Advantages: Better mechanical and thermal properties than glass, utilize semiconductor industry experience with silicon.
5. Adjust slumped-glass segments using piezo actuators. Advantage: Active control of figure errors.
6. Dicing, ribbing, and stacking of silicon wafers (silicon pore optics). Advantage: Highly automated production of mirror stacks, ruggedness.
Figure correction with ion implantation
Implanting high-energy ions into glass or silicon substrates results in a stable stressed layer near the implanted surface, the magnitude of which can be controlled by the ion dose. Controlling the stress distribution on the surface of a substrate allows us to deform the substrate on the order of microns, to correct low-spatial frequency height errors. Ion implantation can also be used to compensate for deformation caused by non-uniform film stress, such as that from an iridium coating applied to X-ray mirrors. We have demonstrated ~20x reduction of stress-induced deformation of 30 nm-thick chromium films on flat Si substrates using ion implantation.
For ions implanted normal to the substrate surface, or for some materials (e.g., silicon), the stress state that develops due to ion implantation is equibiaxial, where the stress is equal in all in-plane directions. Typically, stress from thin coatings is equibiaxial as well, so ion implantation is well-suited to compensating for that type of stress. However, for general correction of substrate figure, we must be able to apply non-equibiaxial stress states as well. We have shown that in some types of glass substrates (e.g., Corning Eagle XG and Schott D-263), ions implanted at an angle can generate non-equibiaxial stress states. We have demonstrated general figure correction of D-263 glass wafers using ion implantation, resulting in a ~4x reduction in figure error. However, we found that the stress generated in this type of glass is not sufficiently stable over time for use in X-ray mirrors.
Ion implantation can be applied from both sides of a thin mirror, and we expect that ions can be implanted even after coating of mirrors with high-reflectivity layers to compensate for thin-film stress.
Compensating coating stress using thermal oxide patterning
Approach 4 has demonstrated high precision silicon mirrors with high angular resolution (~1’’). However, the required metal optical coatings on mirror front surfaces are difficult to deposit without significant compressive thin film stress, which threatens to distort mirrors and negate the benefits of the high quality substrates. Coating stress reduction methods have been investigated by several groups, but none to date have reported success on real mirrors to the required tolerances. We invented a thermal oxide patterning method for correcting mirrors with stress-induced distortion which utilizes a micro-patterned silicon oxide layer on the mirror’s back side. Due to the excellent lithographic precision of the patterning process, we have successfully demonstrated stress compensation control to a precision of ~0.3%. The process is simple and inexpensive due to the relatively large pattern features on the photomask. The correction process has been tested on flat silicon wafers with 30 nm-thick chrome coatings under compressive stress and achieved surface slope improvements of a factor of ~80. We have also successfully compensated several iridium-coated Wolter-I silicon mirrors. The RMS slope errors on coated mirrors after compensation were only degraded by ~0.06 arc-seconds RMS axial slope compared to the initial uncoated state. Further improvements of the method are under development.
Ultrafast laser micro-stressing
Contact-free thermal air bearing slumping
In slumping of glass sheets there needs to be a separation layer between glass and mandrel to keep them from fusing together. Inhomogeneities in that layer and dust trapped between glass and mandrel lead to mid-spatial frequency ripples in the shape of the glass. In this project we are avoiding this problem by using a porous air bearing as the mandrel and floating the glass sheet without any hard contact during the slumping process.