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Proposed x-ray telescope offers very high angular resolution

An x-ray telescope consisting of a Fresnel zone plate and refractive lens, in theory, has much better angular resolution than any single telescope at any wavelength.
7 February 2006, SPIE Newsroom. DOI: 10.1117/2.1200601.0011

Objects that are not detectable by visible light or radio telescopes are observable in the x-ray band. They have temperatures above 1,000,000°C, or contain very-high-energy particles that radiate in the presence of very-high magnetic fields or undergo inverse Compton scattering with lower-energy photons. Starting with launches in 1999, NASA's Chandra X-Ray Observatory1 and the European Space Agency's XMM-Newton2 have obtained an impressive collection of x-ray images and spectra of clusters of galaxies, quasars, supernova remnants, and other objects. Figure 1 is an x-ray image of Cassiopeia A, the remnant of a supernova explosion that took place approximately 350 years ago.

Figure 1. A Chandra X-Ray Observatory image of expanding shock waves in the 350-year-old supernova remnant, Cas A.

X-ray exposures are particularly effective at finding extragalactic objects with unusual activity, the most common type being quasars and their closer counterparts where a central supermassive black hole is still active. However, the resolution of x-ray telescopes has not come close to their diffraction limit. The mid-range wavelength of visible light is 500nm. The Hubble Space Telescope, free from the atmospheric distortion that limits ground-based telescopes, has an angular resolution of 0.1 arc seconds, which is roughly equal to its diffraction limit. The wavelength of a cosmic x-ray is typically in the range 0.2–2nm.

The Chandra x-ray telescope (see Figure 2) is composed of four concentric mirror shells whose projected areas in the plane of incidence are annuli. Their average width is approximately 1.5cm, resulting in a diffraction limit of 10-2 arc seconds at 0.6nm (2keV). However, Chandra's resolution is only 0.5 arc seconds. While this is still the best resolution by far of any x-ray telescope—past, present, and approved for future missions—it is cruder than the diffraction limit by a factor of 50. The discrepancy is due to the difficulty of figuring and polishing the optics of a grazing incidence telescope for imaging very short wavelengths. The physical area that must be accurately figured and highly polished is some hundred times larger than the aperture seen by incident photons. The reflection efficiency and scattering cross section of x-rays are affected by figure errors and surface roughness that are too small-scale to affect longer wavelength visible light.

Figure 2. Graphic of Chandra's telescopes. The mirrors are concentric shells, each consisting of a parabola section followed by a hyperbola.

A new technology is capable of achieving significantly better angular resolution than Chandra. Components 2mm in size used in x-ray microscopy or for concentrating x-ray beams at synchrotron radiation facilities are scaled up by a factor of one thousand. They can be combined to produce a telescope with a resolution as good as the diffraction limit.3–5

The components consist of a Fresnel zone plate and a refractive lens. The zone plate is comprised of alternately open and closed concentric rings of approximately equal area. It acts like a converging lens with an efficiency of 10%. The refractive x-ray lens acts like a visible-light lens except that its refraction of x-rays is extremely weak, about 10-5 that of glass for visible light, and of the opposite sign. Its transparency is a key issue. The lens is made of beryllium or another material with a very low atomic number. In contrast to the very high cost of building Chandra's telescope, the zone plate and lens can be made inexpensively in a machine shop.

Both devices operate by transmitting rather than reflecting x-rays. Therefore, their angular resolution is not subject to the degradation by surface and figure irregularities that reflected x-rays suffer. Also, their physical area is equal to their aperture: it is not 100 times larger, so their mass-to-area ratio is very low. Within a mass limit these devices can have larger diameter than grazing-incidence telescopes for an even better diffraction limit.

However, there are two issues. We describe a solution to one: the other is a temporary technological barrier. Both the zone plate and lens are highly chromatic. The zone plate acts like a converging lens whose focal length is directly proportional to photon energy. The lens' focal length increases with the square of the energy. However, when a diverging lens is placed in contact with a zone plate whose focal length at a particular energy is half that of the lens, there exists an energy band with a width of 10%, where the change in focal length is within the tolerance for 10-3 arc second resolution. Current solid-state, position-sensitive x-ray detectors have the energy resolution needed to isolate that band.

The more challenging issue is a consequence of the weak refractive power of the lens and its absorption. For the lens to be sufficiently thin and transparent, its focal length has to be extremely long. Replacing the full body lens with a Fresnel lens (a concentric array of setback ring lenses similar in concept to thin sheet magnifiers and lighthouse lenses) can ease the absorption problem. The annuli of the Fresnel lens can have smaller radii of curvature and consequently shorter focal length. However, the diffraction limit is degraded because it is governed by the smaller widths of the Fresnel rings rather than the diameter of the system. While it is shortened, the focal length remains very large at 104km.

The system requires long-distance, high-precision formation flying between one spacecraft containing the optics and another with the detector. We currently lack the space technology to accommodate 104km focal lengths, however formation flying is the wave of the future. NASA is committed to developing it for the LISA gravitational wave detection system where the separations among spacecraft are even larger. These systems will be in a solar orbit either following or leading the Earth. Maintaining the alignment between optics and detector spacecraft with a solar gravity gradient acting against it is made possible by furnishing one spacecraft with an ion drive engine capable of providing sufficient thrust to counteract the gravity gradient for a very long time.

In conclusion, a diffractive-refractive x-ray telescope has potentially much better angular resolution than Chandra or any other single telescope at any wavelength. This telescope should be lightweight and relatively inexpensive to construct. However, its deployment in space requires a long-distance formation-flying capability that NASA currently lacks. We expect the demand of this and other programs will result in the eventual development of the necessary technology.

Paul Gorenstein 
Harvard-Smithsonian Center for Astrophysics
Cambridge, MA
Paul Gorenstein has been an X-ray astronomer since 1965, three years after the discovery of the first source. He has been a Principal Investigator of several NASA programs including Apollo. He is a recipient of a NASA medal for outstanding scientific achievement. He a continuing member of the organizing committee of the annual symposium on Optics for EUV, X-Ray, and Gamma-Ray astronomy and has chaired many sessions.

2. http://xmm.vilspa.esa.es/external/xmm_science/gallery/public/index.php 
3. P. Gorenstein, Concepts: X-ray telescopes with high angular resolution and high throughput, Proc. SPIE, Vol: 4851, pp. 599-606, 2003.
4. G. K. Sinner, Diffractive-refractive optics for high energy astronomy, ll variations on the theme, A&A, Vol: 383, pp. 352-359, 2002.
5. P. Gorenstein, J. D. Philips, R. D. Reasenberg, Refractive/diffractive telescope with very high angular resolution for x–ray astronomy, Proc. SPIE, Vol: 5900, pp. 369-376, 2005.