X-ray optics
Encyclopedia
X-ray optics is the branch of optics
which manipulates X-ray
s instead of visible light. While lenses for visible light are made of transparent materials that can have a refractive index
substantially larger than 1, for X-rays the index of refraction
is slightly smaller than unity. The principal methods to manipulate X-rays are therefore by reflection
, diffraction
and interference. Examples of applications include X-ray microscope
s and X-ray telescope
s. Refraction is the basis for the compound refractive lens
, many small X-ray lenses in series that compensate by their number for the X-rays' minute index of refraction. The imaginary part of the refractive index, corresponding to absorption, can also be used to manipulate X-rays: one example is the pin-hole camera, which also works for visible light.
a beam of X-ray
s 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.
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.
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 electron
s 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 ray
s 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 neutron
s. X-rays are usually not diffracted from atomic nuclei.
) of two or more X-ray wave
s 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 wavelength
s 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).
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 grid
s.
and iridium
. Even with these the critical reflection angle is energy dependent. For gold at 1 keV, the critical reflection angle is 3.72 degrees.
The utilization of X-ray mirrors simultaneously requires
space telescope working up 79 keV, was made using multi-layered coatings, computer aided manufacturing, and other techniques. The mirrors use a Tungsten (W)/Silicon (Si) or Platinum(Pt)/Silicon Carbide(SiC) multi-coating on slumped glass, allowing a Wolter telescope design.
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...
which manipulates X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s instead of visible light. While lenses for visible light are made of transparent materials that can have a refractive index
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
substantially larger than 1, for X-rays the index of refraction
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
is slightly smaller than unity. The principal methods to manipulate X-rays are therefore by reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
, diffraction
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
and interference. Examples of applications include X-ray microscope
X-ray microscope
An X-ray microscope uses electromagnetic radiation in the soft X-ray band to produce images of very small objects.Unlike visible light, X-rays do not reflect or refract easily, and they are invisible to the human eye. Therefore the basic process of an X-ray microscope is to expose film or use a...
s and X-ray telescope
X-ray telescope
An X-ray telescope is a telescope that is designed to observe remote objects in the X-ray spectrum. In order to get above the Earth's atmosphere, which is opaque to X-rays, X-ray telescopes must be mounted on high altitude rockets or artificial satellites.-Optical design:X-ray telescopes can use...
s. Refraction is the basis for the compound refractive lens
Compound refractive lens
A Compound refractive lens is a series of individual lenses arranged in a linear array in order to achieve focusing of X-rays in the energy range of 5-40 keV....
, many small X-ray lenses in series that compensate by their number for the X-rays' minute index of refraction. The imaginary part of the refractive index, corresponding to absorption, can also be used to manipulate X-rays: one example is the pin-hole camera, which also works for visible light.
Reflection
The basic idea is to reflectReflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...
a beam of X-ray
X-ray
X-radiation is a form of electromagnetic radiation. X-rays have a wavelength in the range of 0.01 to 10 nanometers, corresponding to frequencies in the range 30 petahertz to 30 exahertz and energies in the range 120 eV to 120 keV. They are shorter in wavelength than UV rays and longer than gamma...
s 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.
The ratio of reflected intensity to incident intensity is the X-ray reflectivity
X-ray reflectivity
X-ray reflectivity sometimes known as X-ray specular reflectivity, X-ray reflectometry, or XRR, is a surface-sensitive analytical technique used in chemistry, physics, and materials science to characterize surfaces, thin films and multilayers...
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
Diffraction
Diffraction refers to various phenomena which occur when a wave encounters an obstacle. Italian scientist Francesco Maria Grimaldi coined the word "diffraction" and was the first to record accurate observations of the phenomenon in 1665...
into many specific directions. The angles and intensities of the diffracted beams indicate a three-dimensional density of electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s within the crystal. X-rays produce a diffraction pattern because their wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
is typically the same order of magnitude
Order of magnitude
An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount...
(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
Elastic scattering
In scattering theory and in particular in particle physics, elastic scattering is one of the specific forms of scattering. In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified .-Electron elastic scattering:When an alpha particle...
; 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
Inelastic scattering
In particle physics and chemistry, inelastic scattering is a fundamental scattering process in which the kinetic energy of an incident particle is not conserved . In an inelastic scattering process, some of the energy of the incident particle is lost or gained...
occurs when energy is transferred from the incoming X-ray to an inner-shell electron exciting it to a higher energy level
Energy level
A quantum mechanical system or particle that is bound -- that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy. These discrete values are called energy levels...
. Such inelastic scattering reduces the energy (or increases the wavelength) of the outgoing beam. Inelastic scattering is useful for probing such electron excitation
Electron excitation
Electron excitation is the movement of an electron to a higher energy state. This can either be done by photoexcitation , where the original electron absorbs the photon and gains all the photon's energy or by electrical excitation , where the original electron absorbs the energy of another,...
, but not in determining the distribution of atoms within the crystal.
Longer-wavelength photons (such as ultraviolet
Ultraviolet
Ultraviolet light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than X-rays, in the range 10 nm to 400 nm, and energies from 3 eV to 124 eV...
radiation
Electromagnetic radiation
Electromagnetic radiation is a form of energy that exhibits wave-like behavior as it travels through space...
) would not have sufficient resolution to determine the atomic positions. At the other extreme, shorter-wavelength photons such as gamma ray
Gamma ray
Gamma radiation, also known as gamma rays or hyphenated as gamma-rays and denoted as γ, is electromagnetic radiation of high frequency . Gamma rays are usually naturally produced on Earth by decay of high energy states in atomic nuclei...
s are difficult to produce in large numbers, difficult to focus, and interact too strongly with matter, producing particle-antiparticle pairs
Pair production
Pair production refers to the creation of an elementary particle and its antiparticle, usually from a photon . For example an electron and its antiparticle, the positron, may be created...
.
Similar diffraction patterns can be produced by scattering electrons or neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
s. X-rays are usually not diffracted from atomic nuclei.
Interference
X-ray interference is the addition (superpositionSuperposition principle
In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...
) of two or more X-ray wave
Wave
In physics, a wave is a disturbance that travels through space and time, accompanied by the transfer of energy.Waves travel and the wave motion transfers energy from one point to another, often with no permanent displacement of the particles of the medium—that is, with little or no associated mass...
s that results in a new wave pattern. X-ray interference usually refers to the interaction of waves that are correlated or coherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
with each other, either because they come from the same source or because they have the same or nearly the same frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...
.
Two non-monochromatic X-ray waves are only fully coherent
Coherence (physics)
In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....
with each other if they both have exactly the same range of wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
s and the same phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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 telescopeWolter telescopeA Wolter telescope is a telescope for X-rays using only grazing incidence optics. Visible light telescopes are built with lenses or parabolic mirrors at nearly normal incidence. Neither works well for X-rays. Lenses for visible light are made of a transparent material with an index of refraction...
, or a Kirkpatrick-Baez X-ray reflection microscopeX-ray microscopeAn X-ray microscope uses electromagnetic radiation in the soft X-ray band to produce images of very small objects.Unlike visible light, X-rays do not reflect or refract easily, and they are invisible to the human eye. Therefore the basic process of an X-ray microscope is to expose film or use a...
, - Zone plateZone plateA zone plate is a device used to focus light or other things exhibiting wave character. Unlike lenses or curved mirrors however, zone plates use diffraction instead of refraction or reflection. Based on analysis by Augustin-Jean Fresnel, they are sometimes called Fresnel zone plates in his honor...
s, - Bent crystals,
- Normal-incidence mirrors making use of multilayer coatings,
- Normal-incidence lens much like an optical lens, such as a compound refractive lens,
- Microstructured optical arraysMicrostructured optical arraysMicrostructured optical arrays are instruments for focusing x-rays. MOAs utilise total external reflection at grazing incidence from an array of small channels in order to bring x-rays to a common focus. This method of focusing means that MOAs exhibit low absorption...
, namely capillary/polycapillary optical systems, - Coded apertureCoded apertureCoded Apertures or Coded-Aperture Masks are grids, gratings, or other patterns of materials opaque to various wavelengths of light. The wavelengths are usually high-energy radiation such as X-rays and gamma rays. By blocking and unblocking light in a known pattern, a coded "shadow" is cast upon a...
imaging, or - 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
Angle of incidence
Angle of incidence is a measure of deviation of something from "straight on", for example:* in the approach of a ray to a surface, or* the angle at which the wing or horizontal tail of an airplane is installed on the fuselage, measured relative to the axis of the fuselage.-Optics:In geometric...
and energy, thus limiting their applications in divergent radiation
Radiation
In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...
. 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
Contrast (vision)
Contrast is the difference in visual properties that makes an object distinguishable from other objects and the background. In visual perception of the real world, contrast is determined by the difference in the color and brightness of the object and other objects within the same field of view...
and resolution
Image resolution
Image resolution is an umbrella term that describes the detail an image holds. The term applies to raster digital images, film images, and other types of images. Higher resolution means more image detail....
of mammographic images, compared to conventional anti-scatter grid
Anti-scatter grid
An anti-scatter grid is a device for limiting the amount of radiation scatter created in a radiographic exposure reaching the detector.The grid is constructed of a series of alternating parallel strips of lead and a radiolucent substance such as a plastic. The grid is placed between the patient and...
s.
Mirrors for X-ray optics
The mirrors can be made of ceramic or metal foil. The most commonly used glancing or grazing angle incidence materials for X-ray mirrors are goldGold
Gold is a chemical element with the symbol Au and an atomic number of 79. Gold is a dense, soft, shiny, malleable and ductile metal. Pure gold has a bright yellow color and luster traditionally considered attractive, which it maintains without oxidizing in air or water. Chemically, gold is a...
and iridium
Iridium
Iridium is the chemical element with atomic number 77, and is represented by the symbol Ir. A very hard, brittle, silvery-white transition metal of the platinum family, iridium is the second-densest element and is the most corrosion-resistant metal, even at temperatures as high as 2000 °C...
. Even with these the critical reflection angle is energy dependent. For gold at 1 keV, the critical reflection angle is 3.72 degrees.
The utilization of X-ray mirrors simultaneously requires
- the ability to determine the location of the arrival of an X-ray photon in two dimensions and
- a reasonable detection efficiency.
Hard X-ray mirrors
An X-ray mirror optic for NuStarNuclear Spectroscopic Telescope Array
Nuclear Spectroscopic Telescope Array is a planned space-based X-ray telescope that will use grazing incidence mirrors to focus high energy X-rays at 5 to 79 keV from astrophysical sources, especially for nuclear spectroscopy...
space telescope working up 79 keV, was made using multi-layered coatings, computer aided manufacturing, and other techniques. The mirrors use a Tungsten (W)/Silicon (Si) or Platinum(Pt)/Silicon Carbide(SiC) multi-coating on slumped glass, allowing a Wolter telescope design.
See also
- X-ray telescopeX-ray telescopeAn X-ray telescope is a telescope that is designed to observe remote objects in the X-ray spectrum. In order to get above the Earth's atmosphere, which is opaque to X-rays, X-ray telescopes must be mounted on high altitude rockets or artificial satellites.-Optical design:X-ray telescopes can use...
- Wolter telescopeWolter telescopeA Wolter telescope is a telescope for X-rays using only grazing incidence optics. Visible light telescopes are built with lenses or parabolic mirrors at nearly normal incidence. Neither works well for X-rays. Lenses for visible light are made of a transparent material with an index of refraction...
, a type of X-ray telescope built with glancing incidence mirrors - XMM-NewtonXMM-NewtonThe XMM-Newton is an orbiting X-ray observatory launched by ESA in December 1999 on a Ariane 5 rocket...
and Chandra X-ray ObservatoryChandra X-ray ObservatoryThe Chandra X-ray Observatory is a satellite launched on STS-93 by NASA on July 23, 1999. It was named in honor of Indian-American physicist Subrahmanyan Chandrasekhar who is known for determining the maximum mass for white dwarfs. "Chandra" also means "moon" or "luminous" in Sanskrit.Chandra...
, orbiting observatories using X-ray optics - X-ray spectroscopyX-ray spectroscopyX-ray spectroscopy is a gathering name for several spectroscopic techniques for characterization of materials by using x-ray excitation.-Characteristic X-ray Spectroscopy:...
, X-ray photoelectron spectroscopyX-ray photoelectron spectroscopyX-ray photoelectron spectroscopy is a quantitative spectroscopic technique that measures the elemental composition, empirical formula, chemical state and electronic state of the elements that exist within a material...
, X-ray crystallographyX-ray crystallographyX-ray crystallography is a method of determining the arrangement of atoms within a crystal, in which a beam of X-rays strikes a crystal and causes the beam of light to spread into many specific directions. From the angles and intensities of these diffracted beams, a crystallographer can produce a...