X-ray optics

(electromagnetism) A title-by-analogy of those phases of x-ray physics in which x-rays demonstrate properties similar to those of light waves. Also known as roentgen optics.

By analogy with the science of optics, those aspects of x-ray physics in which x-rays exhibit properties similar to those of light waves. X-ray optics may also be defined as the science of manipulating x-rays with instruments analogous to those used in visible-light optics. These instruments employ optical elements such as mirrors to focus and deflect x-rays, zone plates to form images, and diffraction gratings to analyze x-rays into their spectral components. X-ray optics is important in many fields, including x-ray astronomy, biology, medical research, thermonuclear fusion, and x-ray microlithography. It is essential to the construction of instruments that manipulate and analyze x-rays from synchrotrons and particle storage rings for synchrotron radiation research. See also Geometrical optics; Optics; Physical optics; X-rays.

When W. C. Roentgen discovered x-rays in 1895, he unsuccessfully attempted to reflect, refract, and focus them with mirrors, prisms, and lenses of various materials. The reason for his lack of success became evident after it was established that x-rays are electromagnetic waves of very short wavelength for which the refractive index of all materials is smaller than unity by a only a small decrement. In addition, x-rays are absorbed by materials. The refractive index can be written as a complex quantity, as in Eq. (1),
1.
where 1 − δ represents the real part, n, of the refractive index and β is the absorption index. These quantities are strongly dependent on the wavelength of the x-rays and the material. X-rays of wavelength about 0.1 nanometer or less are called hard x-rays and are relatively penetrating, while x-rays of wavelength 1–10 nm are less penetrating and are called soft x-rays. Radiation in the wavelength range 10– 50 nm, called the extreme-ultraviolet (EUV) region, is very strongly absorbed by most materials. Values of δ remain very small throughout the x-ray and extreme-ultraviolet regions with the consequence that radiation is very weakly refracted by any material. Thus lenses for x-rays would have to be very strongly curved and very thick to achieve an appreciable focusing effect. However, because the absorption index, β, is so high in comparison, such thick lenses would absorb most of the incident radiation, making such lenses impractical. See also Absorption of electromagnetic radiation; Refraction of waves; Ultraviolet radiation.

If radiation is incident normally (that is, perpendicular) to a surface between two media of differing refractive index, the fraction of the energy that is reflected is ¼(δ² + β²). This is clearly impractically small for a normal-incidence mirror for x-rays. However, useful mirrors can be constructed by using the principle of total reflection. If electromagnetic waves are incident on the boundary between one material of refractive index n₁ and another of lower refractive index n₂, there exists an angle of incidence I_c, called the critical angle, given by Eq. (2).
2.
If the angle of incidence (the angle of incident radiation with respect to the normal to the surface) is greater than this critical angle, all the wave energy is reflected back into the first medium. This phenomenon can be seen when looking upward into an aquarium tank; objects in the tank are reflected in the surface of the water, which acts as a perfect mirror. An analogous situation occurs for x-rays. Since the refractive index for all materials is slightly less than 1, x-rays incident from vacuum (or air) on a polished surface of, say, a metal encounter a lower refractive index and there exists a critical angle given by sin I_c = 1 − δ. Since δ is very small, I_c is very close to 90°. In this case the angle of incidence is customarily measured from the tangent to the surface rather than from the normal, and the angle θ_c = 90° − I_c is termed the angle of glancing (or grazing) incidence. This angle is typically in the range 0.1–1.0°. See also Reflection of electromagnetic radiation.

Although the reflectivity of surfaces at glancing angles greater than the critical angle is very small, this reflectivity can be enhanced by depositing a stack of ultrathin films having alternately high and low values of δ on the surface. The individual thicknesses of these films is adjusted so that the reflections from each interface add in phase at the top of the stack in exact analogy to the multilayer mirrors used for visible light. However, whereas visible multilayers require film thicknesses of hundreds of nanometers, in the x-ray region the thickness of each film must be between 1 and 100 nm. Such ultrathin films can be made by a variety of vacuum deposition methods, commonly sputtering and evaporation. The response of these artificial multilayers is strongly wavelength-selective. See also X-ray diffraction.

As a coating for glancing-incidence optics, multilayers allow a mirror to be used at a shorter wavelength (higher x-ray energy) for a given glancing angle, increasing the projected area and thus the collection efficiency of the mirror. At wavelengths longer than 3 or 4 nm, multilayer mirrors can be used to make normal-incidence mirrors of relatively high reflecting power. For example, stacks consisting of alternating layers of molybdenum and silicon can have reflectivities as high as 65% at wavelengths of 13 nm and longer. These mirrors have been used to construct optical systems that are exact analogs of mirror optics used for visible light. For example, normal-incidence x-ray telescopes have photographed the Sun's hot outer atmosphere at wavelengths of around 18 nm. Multilayer optics at a wavelength of 13.5 nm can be used to perform x-ray microlithography by the projection method to print features of dimensions less than 100 nm.

Crystals are natural multilayer structures and thus can reflect x-rays. Many crystals can be bent elastically (mica, quartz, silicon) or plastically (lithium fluoride) to make x-ray focusing reflectors. These are used in devices such as x-ray spectrometers, electron-beam microprobes, and diffraction cameras to focus the radiation from a small source or specimen on a film or detector. Until the advent of image-forming optics based on mirrors and zone plates, the subject of x-ray diffraction by crystals was called x-ray optics. See also X-ray crystallography; X-ray spectrometry.

Zone plates are diffraction devices that focus x-rays and form images. They are diffracting masks consisting of concentric circular zones of equal area, and are alternately transparent and opaque to x-rays. Whereas mirrors and lenses focus radiation by adjusting the phase at each point of the wavefront, zone plates act by blocking out those regions of the wavefront whose phase is more than a half-period different from that at the plate center. Thus a zone plate acts as a kind of x-ray lens. Zone-plate microscopy is the most promising candidate method for x-ray microscopy of biological specimens. See also Diffraction.

X-ray optics is the branch of optics which manipulates X-rays instead of visible light. While lenses for visible light are made of a transparent material with an index of refraction substantially different from 1, there is no equivalent material for X-rays ^[1]. The only methods of X-ray manipulation, other than simple image modulation, are through reflection, diffraction and interference effects, or by combining a number of lenses into a compound refractive lens.

Contents 1 Reflection 2 Diffraction 3 Interference 4 Technologies 5 Mirrors for X-ray optics 6 References 7 See also

Reflection

Several designs have been used in X-ray telescopes based on grazing incidence reflection: the Kirkpatrick-Baez design and a couple of designs by Wolter (Wolter I-IV)

The basic idea is to reflect a beam of X-rays from a surface and to measure the intensity of X-rays reflected in the specular direction (reflected angle equal to incident angle). It has been shown that a reflection off a parabolic mirror followed by a reflection off a hyperbolic mirror can lead to the focusing of X-rays.^[2]

The ratio of reflected intensity to incident intensity is the X-ray reflectivity for the surface. If the interface is not perfectly sharp and smooth, the reflected intensity will deviate from that predicted by the law of Fresnel reflectivity. The deviations can then be analyzed to obtain the density profile of the interface normal to the surface. For films with multiple layers, X-ray reflectivity may show oscillations with wavelength, analogous to the Fabry-Pérot effect. These oscillations can be used to infer layer thicknesses and other properties.

Diffraction

Symmetrically spaced atoms cause re-radiated X-rays to reinforce each other in the specific directions where their path-length difference, 2d sin θ, equals an integer multiple of the wavelength λ

In X-ray diffraction a beam strikes a crystal and diffracts into many specific directions. The angles and intensities of the diffracted beams indicate a three-dimensional density of electrons within the crystal. X-rays produce a diffraction pattern because their wavelength is typically the same order of magnitude (0.1-10.0 nm) as the spacing between the atomic planes in the crystal.

Each atom, re-radiates a small portion of an incoming beam's intensity as a spherical wave. If the atoms are arranged symmetrically (as is found in a crystal) with a separation d, these spherical waves will be in synch (add constructively) only in directions where their path-length difference 2d sin θ is equal to an integer multiple of the wavelength λ. The incoming beam therefore appears to have been deflected by an angle 2θ, producing a reflection spot in the diffraction pattern.

X-ray diffraction is a form of elastic scattering; the outgoing X-rays have the same energy, and thus same wavelength, as the incoming X-rays, only with altered direction. By contrast, inelastic scattering occurs when energy is transferred from the incoming X-ray to an inner-shell electron exciting it to a higher energy level. Such inelastic scattering reduces the energy (or increases the wavelength) of the outgoing beam. Inelastic scattering is useful for probing such electron excitation, but not in determining the distribution of atoms within the crystal.

Longer-wavelength photons (such as ultraviolet radiation) would not have sufficient resolution to determine the atomic positions. At the other extreme, shorter-wavelength photons such as gamma rays are difficult to produce in large numbers, difficult to focus, and interact too strongly with matter, producing particle-antiparticle pairs.

Similar diffraction patterns can be produced by scattering electrons or neutrons. X-rays are usually not diffracted from atomic nuclei.

Interference

X-ray interference is the addition (superposition) of two or more X-ray waves that results in a new wave pattern. X-ray interference usually refers to the interaction of waves that are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.

Two non-monochromatic X-ray waves are only fully coherent with each other if they both have exactly the same range of wavelengths and the same phase differences at each of the constituent wavelengths.

The total phase difference is derived from the sum of both the path difference and the initial phase difference (if the X-ray waves are generated from two or more different sources). It can then be concluded whether the X-ray waves reaching a point are in phase (constructive interference) or out of phase (destructive interference).

Technologies

There are a variety of techniques used to funnel X-ray photons to the appropriate location on a X-ray detector:

• Grazing incidence mirrors in a Wolter telescope^[3][4][2] or a Kirkpatrick-Baez X-ray reflection microscope.
• Zone plates
• Bent crystals^[5]
• Normal-incidence mirrors making use of multilayer coatings
• Normal-incidence lens much like an optical lens, such as a compound refractive lens
• Microstructured optical arrays, namely capillary/polycapillary optical systems ^[6][7][8][9]
• Coded aperture imaging
• Modulation collimators

Most X-ray optical elements (with the exception of grazing incidence mirrors) are very small, and must be designed for a particular incident angle and energy, thus limiting their applications in divergent radiation. Although the technology has advanced rapidly, its practical uses are still limited. One of the applications showing greater promise is in enhancing both the contrast and resolution of mammographic images, compared to conventional anti-scatter grids.

Mirrors for X-ray optics

The mirrors can be made of ceramic or metal foil^[10]. The most commonly used glancing or grazing angle incidence materials for X-ray mirrors are gold and iridium. Even with these the critical reflection angle is energy dependent. For gold at 1 keV, the critial reflection angle is 3.72 degrees.

The utilization of X-ray mirrors for simultaneously requires

• the ability to determine the location at the arrival of an X-ray photon in two dimensions and
• a reasonable detection efficiency.

References

1. ^ Spiller, E (2003). "X-Ray Optics". Encyclopedia of Optical Engineering: Taylor & Francis. doi:10.1081/E-EOE-120009497. 
2. ^ ^{a b} Rob Petre. "X-ray Imaging Systems". NASA. http://imagine.gsfc.nasa.gov/docs/science/how_l2/xtelescopes_systems.html. 
3. ^ Wolter, H. (1952). "Glancing Incidence Mirror Systems as Imaging Optics for X-rays". Ann. Physik 10: 94. 
4. ^ Wolter, H. (1952). "A Generalized Schwarschild Mirror Systems For Use at Glancing Incidence for X-ray Imaging". Ann. Physik 10: 286. 
5. ^ Pikuz, T.A.; Faenov, A.Ya.; Fraenkel, M.; Zigler, A.; Flora, F.; Bollanti, S.; Di Lazzaro, P.; Letardi, T.; Grilli, A.; Palladino, L.; Tomassetti, G.; Reale, A.; Reale, L.; Scafati, A.; Limongi, T.; Bonfigli, F.; Alainelli, L.; Sanchez del Rio, M. (2000). "Using spherically bent crystals for obtaining high-resolution, large-field, monochromatic X-ray backlighting imaging for wide range of Bragg angles". Plasma Science. Proceedings of the 27th IEEE International Conference on Plasma Science. pp. 183. 
6. ^ Kumakhov, MA (1990). "Channeling of photons and new X-ray optics". Nuclear Instruments and Methods in Physics Research Section B 48, (1-4): 283--286. doi:10.1016/0168-583X(90)90123-C. 
7. ^ Dabagov, SB (2003). "Channeling of neutral particles in micro- and nanocapillaries". Physics Uspekhi 46, (10): 1053--1075. doi:10.1070/PU2003v046n10ABEH001639. 
8. ^ An introduction to X-Ray Optics
9. ^ Polycapillary Optics
10. ^ "Mirror Laboratory". http://astrophysics.gsfc.nasa.gov/xrays/MirrorLab/xoptics.html. 

See also

• Wolter telescope A type of X-ray telescope built with glancing incidence mirrors
• Chandra X-ray Observatory Orbiting observatory, uses X-ray optics
• XMM-Newton Orbiting X-ray observatory, again using X-ray optics

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