Kirkpatrick-Baez optics for the Generation-X mission

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1 Kirkpatrick-Baez optics for the Generation-X mission Nishanth Rajan and Webster Cash Center for Astrophysics and Space Astronomy University of Colorado at Boulder ABSTRACT Generation-X is a Vision Mission for a future x-ray observatory. It is to have an effective area of 150 m 2 at 1 kev, a resolution of ~0.1 arc seconds and the goal of probing the universe from redshifts of 5 to 10. Fabrication of the telescope is quite challenging and the best approach is unclear. We report our study of the use of Kirkpatrick-Baez telescopes applied to Gen-X. Such systems can be manufactured relatively inexpensively using simple flat mirrors. Huge effective areas can be obtained without the need for complicated deployable optics. In this study we found that Kirkpatrick-Baez optics provide an attractive and feasible approach to fabrication. The trade off is a 5km focal length. Keyword list: Generation-X, Kirkpatrick-Baez 1. Introduction Structure formation in the universe is one of the primary frontiers of modern cosmology. The primary diagnostics of this frontier are the very first stars, galaxies and black holes. In particular, the black holes are expected to be powerful x-ray sources that penetrate the dust and gas of their surrounding environments. To properly study the development of these objects to the present day, we require a new generation of x-ray telescopes, with thousand times greater sensitivity than those that exist today. This is the challenge that faces the Generation-X Observatory. Gen-X mission parameters are primarily driven by early cosmological structures. To detect the x-ray luminosity of a high redshift (z ~10) galaxy, Gen-X would require a collecting area of 150 m 2 at 1 kev 1. A Vision Mission that follows the resounding success of Chandra and XMM-Newton x-ray observatories and the yet to be launched Constellation-X mission will necessarily have to address a lofty range of science objectives. Gen-X is expected to be able to probe stellar flares in the solar neighborhood, resolve protoplanetary disks and planet formation in fluorescent x- rays, study compact binary populations, probe matter in extreme environments such as black hole event horizons and help determine the chemical evolution of the universe with spectra of the hot interstellar medium in nearby galaxies. Gen-X should also make the x-ray equivalent of the Sloan Digital Sky Survey, yielding accurate positions of millions of sources for follow up study Kirkpatrick-Baez Telescope Concept Building a telescope with 150 m 2 of collecting area is no small task. Such a telescope implies a deployable optic of at least 15 meters in aperture. When one accounts for the reflectivity losses in the waveband of 1-10 kev, the actual diameter may double. A successful Gen-X design must emphasize a pragmatic approach to deploying and aligning a large number of optical components in space. We propose a Kirkpatrick-Baez system of flat mirrors, which should be relatively easy to construct and deploy, and yet achieve Gen-X s requirements for high performance. Kirkpatrick Baez (KB) grazing incidence systems were first proposed by Kirkpatrick and Baez in This system forms real x-ray images and consisted originally of two orthogonal spheres.

2 Figure 1: Kirkpatrick-Baez setup. The single mirror geometry is shown in figure A. The nested mirror geometry is shown in figure B. The surface area may be easily increased by nesting the plates, using many parallel mirrors. More recently, the KB design has lost favor in the x-ray community to the ubiquitous Wolter telescopes consisting of nested hyperboloidparaboloid combinations. However, KB telescopes may be well suited to Gen-X design goals as they are inexpensive to fabricate, allowing vast surface areas relatively inexpensively. Within the Gen-X frameworks, flat mirror surfaces can be used to drive down the cost of many square meters of expensive optics. 3. Telescope Design and Performance The Kirkpatrick-Baez Gen-X design consists of two spacecraft. The large effective area is achieved by flying two layers of nested flat mirrors which are orthogonal to each other. The alignment of these mirror layers sets the distances between the mirrors and their angles. The nested mirrors form miniature apertures within the telescope where each mirror in a layer crosses each mirror in the other layer forming a pixilated plane. The detector craft is flown some distance away at the focal plane. Figure 2: Face-on view of the proposed Generation-X telescope setup and the appropriate focal lines of each nested layer.

3 Figure 3: Illustration of telescope array and focal plane. Note that the actual KB array is two layers of nested Kirkpatrick-Baez flat mirrors. 3.1 Resolution and projected lengths Gen-X goals require an angular resolution of 0.1 arc seconds, a resolution 10 times better than the Chandra X- ray Observatory. This implies that the size of each miniature aperture cannot be so small as to violate the diffraction limit. The resolution of each aperture is the ratio of the wavelength (λ) to the projected length (s). R = l / s. (1) Figure 4: A diagram of the projected length, mirror length and graze angle Choosing the lower extreme of our bandpass at 1 kev, we have a minimum wavelength of 1.2 nm. For a diffraction limited aperture at a resolution of 0.1 arc seconds, we require a minimum projection length of 2.5 mm. Practical considerations require that the mirrors have some thickness. To account for mirror thickness and support, we allot an extra 0.5 mm to each cell. We use a 3 mm width for each cell in the grid (shown in Figure 2).

4 3.2 Distance to the Focal Plane While the diffraction limit determines the size of the aperture, we can use the resolution requirement at the focal plane to determine the distance to the detector spacecraft. Resolution is determined by the ratio of projected length (s) to the distance to the focal plane F. R = s / F. (2) Given the resolution figure of 0.1 and a projected length of 2.5 mm, we find that the focal plane is 5.3 km away. 3.3 Array Size and Mirror Angles The size of the mirror array (the nested KB mirror layers) is determined by the effective area of the aperture. For 150 m 2 of collecting area, the mirror array has to have a length of at least 12.5 m. Adding the extra allotment for mirror thickness raises this figure to 15 meters in length to maintain the effective area requirement. KB systems work for graze incidences of x-ray photons off the flat mirrors. Assuming a gold coating on the flat mirrors, we determine that in the 1-10 kev band we can expect at least 50% reflectivity losses. Confirmation of the loss figure after the graze angles are established reveals that this assumption is robust up to 8.5 kev (see figure 5). Figure 5: Change in effective area across the wavelength of observation. The maximum area at 100% reflectivity is 150 m 2. The area doubling leads to a length scale of 21.3 meters. For the predetermined individual array length scale of 3 mm, this gives us 6770 nested mirrors in each layer. The length scale of the mirror array helps determine the individual mirror angles. Geometrical considerations show that the radius of the array is simply the distance to the focal plane multiplied by the angle of projection of the array to the focal plane.

5 Figure 6: Relationship between array diameter, projection angle and distance to focal plane The projection angle can be translated into the individual (i th ) mirror angle θ i by noting that the two orthogonal reflections of flat mirrors equate the projection angle to 2* 2*θ i. Thus we are left with the following equation to determine the mirror angles. Radius = F 2 2q. (3) Good coverage characteristics at 6 kev suggest a minimum angle of 0.4 degrees. Since the focal axis of the mirror is away from the primary axis of the mirror, a minimum angle of 0.4 degrees places the closest mirror array vertex meters off the focal plane axis. Figure 7: Off axis placement of KB array A length scale of 21.3 meters translates to a diagonal length of 30 meters placing the furthest vertex meters away. This translates to a maximum angle of 0.51 degrees over the entire mirror array. Over the 6770 mirrors, each mirror is incremented 1.66*10-5 degrees with respect to the previous mirror. 4. Spatial Resolution To establish the optical performance of the optic we performed some simple ray tracing. The optic consists of two layers of 6770 flat mirrors spaced 3mm apart across 21m. Each mirror in the ray trace was approximately 400mm by

6 21m and 5mm thick. In practice, these would likely be mounted in smaller squares, but that was not included in this preliminary assessment. The two layers were essentially identical, but rotated by 90 degrees about the optic axis. The graze angle of the i th mirror (in degrees) was given by: -5 q = i *1.66x10. (4) The raytracing was purely geometric, to assess the aberrations in the system. With such a small range of angles included, the two reflections did not cause any cross effects between layers. Figure 8: Spot diagram five points separated by 0.2 arcseconds from the adjacent points Figure 8, which shows five points separated by 0.2 arcseconds, demonstrates resolution of approximately 0.1 arcseconds on axis. Exploration of the field of view shows it to be both flat and wide. There is no degradation of image even 0.2 degrees off axis. Thus the field of view will be limited by vignetting of the optics and constraints on graze angle. 5. Discussion Our proposed Kirkpatrick-Baez optic could be made from 568,680 mirrors, each 500mm square and half a millimeter thick. Such a vast number of mirrors is actually affordable because they could be made from silicon wafers. Such wafers are used by the electronics industry and cost only a few dollars each. Currently, the flatness of silicon wafers is a few microns which represents a resolution limitation of a few arcseconds. Special care will be needed to maintain flatness to the submicron level. It takes a 5km focal length to avoid the use of curved optics and still achieve individual mirror apertures wide enough to suppress diffraction to below 0.1. This distance then becomes the separation between the two craft. Formation flying to millimeter precision over kilometers has yet to be demonstrated. However, a variety of future missions incorporate formation flying and these tolerances are not particularly challenging. It is reasonable to assume that this capability will be available by the time Gen-X launches. Another disadvantage of this design comes from the two spacecraft approach. There can be no tube stretching between the craft to reject stray light. A careful design to reject stray light is needed, including the need to reject both x- rays and longer wavelength radiation that may in some way degrade the detector performance. Since the optic subtends

7 only a quarter of degree as viewed from the detector, a long, extendable tube might be used to reject diffuse x-rays. Alternatively, a grid collimator might be used. The sheer size of the focal plane represents a disadvantage. A point source is 3mm square in the focal plane, so a 300x300 image would require a square meter of detector. For some applications the plate scale is not a problem (e.g. Constellation-X has a 0.75mm focal spot). But for many applications this would be expensive and perhaps noisy due to the increased cross section to cosmic rays. An optic can be designed to concentrate (demagnify) the focal plane at the cost of some throughput. This disadvantage has to be traded against the relative ease of building the optic. But, overall, we feel that further study of this approach would be of interest as it still represents an approach that might actually be feasible and affordable. Acknowledgements We wish to thank Steve Osterman and Randy McEntaffer for assistance and advice. This work was supported by NASA Grant NAG References 1) 2) Brissendon et. al., Generation-X vision mission proposal., White Paper, ) P.Kirkpatrick & A.V. Baez, Formation of optical images by x-rays, Jour. Optical. Soc. America., Vol 38 Issue 9, ) Giaconni et. al., Grazing Incidence Telescopes for X-Ray Astronomy, Space Sciences Review, , ) R.A. Cameron et. al. Generation-X: mission and technology studies for an x-ray observatory vision mission, Proc. Soc. Photo-Opt. Instr. Eng., ) N.E.White et. al., The Science Goals of the Constellation-X mission, Proc. Soc. Photo-Opt. Instr. Eng., ) A.N. Parmer et. al. Science with XEUS: the X-Ray Evolving Universe Spectroscopy Mission, Proc. Soc. Photo-Opt. Instr. Eng., )