x-ray optics

X-ray 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 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 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 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 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 X-ray crystallography

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 Diffraction

x-ray optics