Shaping & Assembly of X-Ray Mirrors

Our current two main projects in this area are contact-free thermal air bearing slumping and figure correction with ion implantation.

Motivation

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:

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, and to coat (for better reflectivity) and 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.

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.

Figure correction with ion implantation

Ion implantation offers a promising method of modifying the shape of thin mirrors by imparting internal stresses in a substrate, which are a function of the ion species and dose. This technique has the potential for highly deterministic mirror shape correction using a rapid, low cost process. We have implanted wafers of silicon and glass (D-263 and BK-7) with Si+ ions at 150 keV, and the changes in shape have been measured using our Shack-Hartmann metrology system. A uniform dose over the surface repeatably changes the spherical curvature of the substrates, and we have demonstrated correction of spherical curvature in wafers. Modeling based on experiments with spherical curvature correction shows that ion implantation could be used to eliminate higher-order shape errors, such as astigmatism and coma, by using a spatially-varying implant dose. This technique 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.

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