In chemistry, a structural isomer (or constitutional isomer in the IUPAC nomenclature) of a compound is a compound that contains the same number and type of atoms, but with a different connectivity (i.e. arrangement of bonds) between them. The term metamer was formerly used for the same concept.
The concept applies also to polyatomic ions with the same total charge. A classical example is the cyanate ion O=C=N− and the fulminate ion C−≡N+−O−. It is also extended to ionic compounds, so that (for example) ammonium cyanate[NH4]+[O=C=N]− and urea(H2N−)2C=O are considered structural isomers, and so are methylammonium formate[H3C−NH3]+[HCO2]− and ammonium acetate[NH4]+[H3C−CO2]−.
Structural isomerism is the most radical type of isomerism. It is opposed to stereoisomerism, in which the atoms and bonding scheme are the same, but only the relative spatial arrangement of the atoms is different.[5][6] Examples of the latter are the enantiomers, whose molecules are mirror images of each other, and the cis and trans versions of 2-butene.
Among the structural isomers, one can distinguish several classes including skeletal isomers, positional isomers (or regioisomers), functional isomers, tautomers, and structural isotopomers.
Skeletal isomerism
A skeletal isomer of a compound is a structural isomer that
differs from it in the atoms and bonds that are considered to comprise
the "skeleton" of the molecule. For organic compounds, such as alkanes, that usually means the carbon atoms and the bonds between them.
For example, there are three skeletal isomers of pentane: n-pentane (often called simply "pentane"), isopentane (2-methylbutane) and neopentane (dimethylpropane).
Position isomers (also positional isomers or regioisomers) are structural isomers that can be viewed as differing only on the position of a functional group, substituent, or some other feature on the same "parent" structure.
For example, replacing one of the 12 hydrogen atoms –H by a hydroxyl group –OH on the n-pentane parent molecule can give any of three different position isomers:
Functional isomers are structural isomers which have different functional groups, resulting in significantly different chemical and physical properties.
An example is the pair propanal H3C–CH2–C(=O)-H and acetone H3C–C(=O)–CH3: the first has a –C(=O)H functional group, which makes it an aldehyde, whereas the second has a C–C(=O)–C group, that makes it a ketone.
Another example is the pair ethanol H3C–CH2–OH (an alcohol) and dimethyl ether H3C–O–CH2H (an ether). In contrast, 1-propanol and 2-propanol are structural isomers, but not functional isomers, since they have the same significant functional group (the hydroxyl –OH) and are both alcohols.
Besides the different chemistry, functional isomers typically have very different infrared spectra.
The infrared spectrum is largely determined by the vibration modes of
the molecule, and functional groups like hydroxyl and esters have very
different vibration modes. Thus 1-propanol and 2-propanol have
relatively similar infrared spectra because of the hydroxyl group, which
are fairly different from that of methyl ethyl ether.
In chemistry, one usually ignores distinctions between isotopes of the same element. However, in some situations (for instance in Raman, NMR, or microwave spectroscopy)
one may treat different isotopes of the same element as different
elements. In the second case, two molecules with the same number of
atoms of each isotope but distinct bonding schemes are said to be structural isotopomers.
Thus, for example, ethene would have no structural isomers under the first interpretation; but replacing two of the hydrogen atoms (1H) by deuterium atoms (2H)
may yield any of two structural isotopomers (1,1-dideuteroethene and
1,2-dideuteroethene), if both carbon atoms are the same isotope. If, in
addition, the two carbons are different isotopes (say, 12C and 13C), there would be three distinct structural isotopomers, since 1-13C-1,1-dideuteroethene would be different from 1-13C-2,2-dideuteroethene. And, in both cases, the 1,2-dideutero structural isotopomer would occur as two stereoisotopomers, cis and trans.
Structural equivalence and symmetry
Structural equivalence
Two molecules (including polyatomic ions) A and B have the same structure
if each atom of A can be paired with an atom of B of the same element,
in a one-to-one way, so that for every bond in A there is a bond in B,
of the same type, between corresponding atoms; and vice versa. This requirement applies also to complex bonds that involve three or more atoms, such as the delocalized bonding in the benzene molecule and other aromatic compounds.
Depending on the context, one may require that each atom be
paired with an atom of the same isotope, not just of the same element.
Two molecules then can be said to be structural isomers (or, if
isotopes matter, structural isotopomers) if they have the same molecular
formula but do not have the same structure.
Structural symmetry and equivalent atoms
Structural symmetry of a molecule can be defined mathematically as a permutation
of the atoms that exchanges at least two atoms but does not change the
molecule's structure. Two atoms then can be said to be structurally equivalent if there is a structural symmetry that takes one to the other.
Thus, for example, all four hydrogen atoms of methane are structurally equivalent, because any permutation of them will preserve all the bonds of the molecule.
Likewise, all six hydrogens of ethane (C 2H 6)
are structurally equivalent to each other, as are the two carbons;
because any hydrogen can be switched with any other, either by a
permutation that swaps just those two atoms, or by a permutation that
swaps the two carbons and each hydrogen in one methyl group with a
different hydrogen on the other methyl. Either operation preserves the
structure of the molecule. That is the case also for the hydrogen atoms
in cyclopentane, allene, 2-butyne, hexamethylenetetramine, prismane, cubane, dodecahedrane, etc.
On the other hand, the hydrogen atoms of propane
are not all structurally equivalent. The six hydrogens attached to the
first and third carbons are equivalent, as in ethane, and the two
attached to the middle carbon are equivalent to each other; but there is
no equivalence between these two equivalence classes.
Symmetry and positional isomerism
Structural equivalences between atoms of a parent molecule reduce the
number of positional isomers that can be obtained by replacing those
atoms for a different element or group. Thus, for example, the
structural equivalence between the six hydrogens of ethaneC 2H 6 means that there is just one structural isomer of ethanolC 2H 5OH, not 6. The eight hydrogens of propaneC 3H 8
are partitioned into two structural equivalence classes (the six on the
methyl groups, and the two on the central carbon); therefore there are
only two positional isomers of propanol (1-propanol and 2-propanol). Likewise there are only two positional isomers of butanol, and three of pentanol or hexanol.
Symmetry breaking by substitutions
Once a substitution is made on a parent molecule, its structural
symmetry is usually reduced, meaning that atoms that were formerly
equivalent may no longer be so. Thus substitution of two or more
equivalent atoms by the same element may generate more than one
positional isomer.
The classical example is the derivatives of benzene.
Its six hydrogens are all structurally equivalent, and so are the six
carbons; because the structure is not changed if the atoms are permuted
in ways that correspond to flipping the molecule over or rotating it by
multiples of 60 degrees. Therefore, replacing any hydrogen by chlorine
yields only one chlorobenzene.
However, with that replacement, the atom permutations that moved that
hydrogen are no longer valid. Only one permutation remains, that
corresponds to flipping the molecule over while keeping the chlorine
fixed. The five remaining hydrogens then fall into three different
equivalence classes: the one opposite to the chlorine is a class by
itself (called the para position), the two closest to the chlorine form another class (ortho), and the remaining two are the third class (meta). Thus a second substitution of hydrogen by chlorine can yield three positional isomers: 1,2- or ortho-, 1,3- or meta-, and 1,4- or para-dichlorobenzene.
ortho-Dichlorobenzene
meta-Dichlorobenzene
para-Dichlorobenzene
1,2-Dichlorobenzene
1,3-Dichlorobenzene
1,4-Dichlorobenzene
For the same reason, there is only one phenol (hydroxybenzene), but three benzenediols; and one toluene (methylbenzene), but three toluols, and three xylenes.
On the other hand, the second replacement (by the same
substituent) may preserve or even increase the symmetry of the molecule,
and thus may preserve or reduce the number of equivalence classes for
the next replacement. Thus, the four remaining hydrogens in meta-dichlorobenzene still fall into three classes, while those of ortho- fall into two, and those of para-
are all equivalent again. Still, some of these 3 + 2 + 1 = 6
substitutions end up yielding the same structure, so there are only
three structurally distinct trichlorobenzenes: 1,2,3-, 1,2,4-, and 1,3,5-.
1,2,3-Trichlorobenzene
1,2,4-Trichlorobenzene
1,3,5-Trichlorobenzene
If the substituents at each step are different, there will usually be more structural isomers. Xylenol, which is benzene with one hydroxyl substituent and two methyl substituents, has a total of 6 isomers:
2,3-Xylenol
2,4-Xylenol
2,5-Xylenol
2,6-Xylenol
3,4-Xylenol
3,5-Xylenol
Isomer enumeration and counting
Enumerating or counting structural isomers in general is a difficult
problem, since one must take into account several bond types (including
delocalized ones), cyclic structures, and structures that cannot
possibly be realized due to valence or geometric constraints, and
non-separable tautomers.
For example, there are nine structural isomers with molecular formula C3H6O having different bond connectivities. Seven of them are air-stable at room temperature, and these are given in the table below.
A miniature USB microscope with inbuilt LED lights next to the lens at left.Sea salt crystals seen with a USB microscope.Table salt crystals seen with a USB microscope.The top side of a sage leaf seen with a USB microscope - trichomes are visible.The USB image of the underside of a sage leaf - more trichomes are visible on this side.
A USB microscope is a low-powered digital microscope which connects to a computer's USB
port. Microscopes essentially the same as USB models are also available
with other interfaces either in addition to or instead of USB, such as
via WiFi.
They are widely available at low cost for use at home or in commerce.
Their cost varies in the range of tens to thousands of dollars. In
essence, a USB microscope is a webcam with a high-powered macro lens,
and generally uses reflected rather than transmitted light, using
built-in LED light sources surrounding the lens. The camera is usually
sensitive enough not to need additional illumination beyond normal
ambient lighting. The camera attaches directly to the USB port of a
computer without the need for an eyepiece, and the images are shown
directly on the computer's display.
They usually provide modest magnifications (about 1× to 200×)
without the need to use eyepieces, at cost very much lower than
conventional stereomicroscopes.[1] The quality of the final image depends on the lens and sensor quality, resolution—which may range from 1.3 megapixels to 5 MP or more—operator skill, and illumination quality. Both still images and videos can be recorded on most systems.
Usage
Images can be recorded and stored on a computer in the same way as
with a webcam. The camera is usually fitted with a light source,
although extra sources (such as a fiber-optic light) can be used to highlight features of interest in the object. They generally offer a large depth of field and a range of magnification
when examining the image on the computer. The camera is usually
sufficiently sensitive to generate an image with normal ambient
lighting, without the need for an extra light source.
USB microscopes are most useful when examining flat objects such as coins, printed circuit boards, or documents such as banknotes, but can be used on surfaces of irregular shape such as fibres owing to the high depth of field. Their use is generally similar to that of a reflection optical microscope or a stereo microscope. USB microscopes are much less bulky than conventional stereo microscopes. They are useful in examining large items in situ where use of a conventional microscope is impractical.
Simple ways in which the microscope can be used is a comparison of salt crystals, such as sea salt and table salt. A common millimeter scale at the tops of the micrographs show the smaller size of the cubic table salt crystals. The good depth of field available is shown by USB micrographs of a sage leaf.
Such devices are useful in forensic engineering where large fracture
surfaces need direct examination, an application where conventional
light microscopes are restricted in use. They are normally handheld for
this application, but can also be mounted in a small stand.
USB microscopes are used in crime scene investigation units. As
they do not come into contact with the object viewed, sensitive crime
scene evidence is not contaminated.
They also find use in medical application such as ENT examinations.[2]
Endoscopy
Related devices include a USB endoscope, where the digital camera
is fitted to a long length of cable and enables the camera to be used
to inspect cavities which are otherwise difficult to examine (such as
car engine interiors, pipe interiors, sewers and so on). As with the
microscope, the cable is fitted with a USB plug to engage with the PC.
Alternatively, a simple USB device can be fitted to a conventional
endoscope. Endoscopes with a small screen are also available, allowing
the user to see the hidden scene directly without the use of a laptop computer.
Since this area of technology is still developing very rapidly,
further design and technical improvements as well as lower prices may be
expected in the near future (in February 2016, there were units costing
less than $10 offered on internet sites). The software used for image manipulation already offers big improvements in capability, allowing the digital images to be cropped and brightness and image contrast changed as needed, for example. Accessories such as polarizers are expensive but allow extra control of unwanted specular reflections from the subject, for example.
Effective magnification
The precise magnification is determined by the working distance between the camera
and the object, and good supports are needed to control the image,
especially at higher magnifications. The magnifying abilities of these
instruments are often overstated; typically offering 200× magnification,
this claim is based usually on 25× to 30× actual magnification which is
then further magnified by the expansion of the image by display on the
screen. High magnifications are available only if the camera has a high
resolution, so the image from a 5-megapixel camera can be enlarged to a
greater extent than that from a 2-megapixel camera, for example.
Figure 1. The light path through a Michelson interferometer.
The two light rays with a common source combine at the half-silvered
mirror to reach the detector. They may either interfere constructively
(strengthening in intensity) if their light waves arrive in phase, or
interfere destructively (weakening in intensity) if they arrive out of
phase, depending on the exact distances between the three mirrors.
Interferometers are devices that extract information from
interference. They are widely used in science and industry for the
measurement of microscopic displacements, refractive index
changes and surface irregularities. In the case with most
interferometers, light from a single source is split into two beams that
travel in different optical paths, which are then combined again to produce interference; two incoherent sources can also be made to interfere under some circumstances. The resulting interference fringes give information about the difference in optical path lengths.
In analytical science, interferometers are used to measure lengths and
the shape of optical components with nanometer precision; they are the
highest-precision length measuring instruments in existence. In Fourier transform spectroscopy they are used to analyze light containing features of absorption or emission associated with a substance or mixture. An astronomical interferometer
consists of two or more separate telescopes that combine their signals,
offering a resolution equivalent to that of a telescope of diameter
equal to the largest separation between its individual elements.
Basic principles
Figure 2. Formation of fringes in a Michelson interferometerFigure
3. Colored and monochromatic fringes in a Michelson interferometer:
(a) White light fringes where the two beams differ in the number of
phase inversions; (b) White light fringes where the two beams have
experienced the same number of phase inversions; (c) Fringe pattern
using monochromatic light (sodium D lines)
Interferometry makes use of the principle of superposition to combine
waves in a way that will cause the result of their combination to have
some meaningful property that is diagnostic of the original state of the
waves. This works because when two waves with the same frequency combine, the resulting intensity pattern is determined by the phase
difference between the two waves—waves that are in phase will undergo
constructive interference while waves that are out of phase will undergo
destructive interference. Waves which are not completely in phase nor
completely out of phase will have an intermediate intensity pattern,
which can be used to determine their relative phase difference. Most
interferometers use light or some other form of electromagnetic wave.
Typically (see Fig. 1, the well-known Michelson configuration) a single incoming beam of coherent light will be split into two identical beams by a beam splitter
(a partially reflecting mirror). Each of these beams travels a
different route, called a path, and they are recombined before arriving
at a detector. The path difference, the difference in the distance
traveled by each beam, creates a phase difference between them. It is
this introduced phase difference that creates the interference pattern
between the initially identical waves.
If a single beam has been split along two paths, then the phase
difference is diagnostic of anything that changes the phase along the
paths. This could be a physical change in the path length itself or a change in the refractive index along the path.
As seen in Fig. 2a and 2b, the observer has a direct view of mirror M1 seen through the beam splitter, and sees a reflected image M′2 of mirror M2. The fringes can be interpreted as the result of interference between light coming from the two virtual images S′1 and S′2 of the original source S.
The characteristics of the interference pattern depend on the nature of
the light source and the precise orientation of the mirrors and beam
splitter. In Fig. 2a, the optical elements are oriented so that S′1 and S′2 are in line with the observer, and the resulting interference pattern consists of circles centered on the normal to M1 and M'2. If, as in Fig. 2b, M1 and M′2
are tilted with respect to each other, the interference fringes will
generally take the shape of conic sections (hyperbolas), but if M′1 and M′2
overlap, the fringes near the axis will be straight, parallel, and
equally spaced. If S is an extended source rather than a point source
as illustrated, the fringes of Fig. 2a must be observed with a telescope
set at infinity, while the fringes of Fig. 2b will be localized on the
mirrors.
Use of white light will result in a pattern of colored fringes (see Fig. 3).
The central fringe representing equal path length may be light or dark
depending on the number of phase inversions experienced by the two beams
as they traverse the optical system. (See Michelson interferometer for a discussion of this.)
History
The law of interference of light was described by Thomas Young in his 1803 Bakerian Lecture to the Royal Society of London. In preparation for the lecture, Young performed a double-aperture
experiment in a water ripple tank. His interpretation in terms of the
interference of waves was rejected by most scientists at the time
because of the dominance of Isaac Newton's corpuscular theory of light proposed a century before.
The French engineer Augustin-Jean Fresnel, unaware of Young's results, began working on a wave theory of light and interference and was introduced to François Arago.
Between 1816 and 1818, Fresnel and Arago performed interference
experiments at the Paris Observatory. During this time, Arago designed
and built the first interferometer, using it to measure the refractive
index of moist air relative to dry air, which posed a potential problem
for astronomical observations of star positions. The success of Fresnel's wave theory of light was established in his
prize-winning memoire of 1819 that predicted and measured diffraction
patterns. The Arago interferometer was later employed in 1850 by Leon Foucault to measure the speed of light in air relative to water, and it was used again in 1851 by Hippolyte Fizeau to measure the effect of Fresnel drag on the speed of light in moving water.
Jules Jamin
developed the first single-beam interferometer (not requiring a
splitting aperture as the Arago interferometer did) in 1856. In 1881,
the American physicist Albert A. Michelson, while visiting Hermann von Helmholtz in Berlin, invented the interferometer that is named after him, the Michelson Interferometer,
to search for effects of the motion of the Earth on the speed of light.
Michelson's null results performed in the basement of the Potsdam
Observatory outside of Berlin (the horse traffic in the center of Berlin
created too many vibrations), and his later more-accurate null results
observed with Edward W. Morley at Case College
in Cleveland, Ohio, contributed to the growing crisis of the
luminiferous ether. Einstein stated that it was Fizeau's measurement of
the speed of light in moving water using the Arago interferometer that
inspired his theory of the relativistic addition of velocities.
Categories
Interferometers and interferometric techniques may be categorized by a variety of criteria:
Homodyne versus heterodyne detection
In homodyne detection, the interference occurs between two beams at the same wavelength (or carrier frequency).
The phase difference between the two beams results in a change in the
intensity of the light on the detector. The resulting intensity of the
light after mixing of these two beams is measured, or the pattern of
interference fringes is viewed or recorded. Most of the interferometers discussed in this article fall into this category.
The heterodyne
technique is used for (1) shifting an input signal into a new frequency
range as well as (2) amplifying a weak input signal (assuming use of an
active mixer). A weak input signal of frequency f1 is mixed with a strong reference frequency f2 from a local oscillator (LO). The nonlinear combination of the input signals creates two new signals, one at the sum f1 + f2 of the two frequencies, and the other at the difference f1 − f2. These new frequencies are called heterodynes.
Typically only one of the new frequencies is desired, and the other
signal is filtered out of the output of the mixer. The output signal
will have an intensity proportional to the product of the amplitudes of
the input signals.
The most important and widely used application of the heterodyne technique is in the superheterodyne receiver (superhet), invented in 1917-18 by U.S. engineer Edwin Howard Armstrong and French engineer Lucien Lévy. In this circuit, the incoming radio frequency
signal from the antenna is mixed with a signal from a local oscillator
(LO) and converted by the heterodyne technique to a lower fixed
frequency signal called the intermediate frequency (IF). This IF is amplified and filtered, before being applied to a detector which extracts the audio signal, which is sent to the loudspeaker.
Optical heterodyne detection is an extension of the heterodyne technique to higher (visible) frequencies. While optical heterodyne interferometry is usually done at a single point it is also possible to perform this widefield.
Figure 4. Four examples of common-path interferometers
A double-path interferometer is one in which the reference beam and sample beam travel along divergent paths. Examples include the Michelson interferometer, the Twyman–Green interferometer, and the Mach–Zehnder interferometer.
After being perturbed by interaction with the sample under test, the
sample beam is recombined with the reference beam to create an
interference pattern which can then be interpreted.
A wavefront splitting interferometer divides a light wavefront emerging from a point or a narrow slit (i.e.
spatially coherent light) and, after allowing the two parts of the
wavefront to travel through different paths, allows them to recombine. Fig. 5 illustrates Young's interference experiment and Lloyd's mirror.
Other examples of wavefront splitting interferometer include the
Fresnel biprism, the Billet Bi-Lens, diffraction-grating Michelson
interferometer, and the Rayleigh interferometer.
Figure 5. Two wavefront splitting interferometers
In 1803, Young's interference experiment
played a major role in the general acceptance of the wave theory of
light. If white light is used in Young's experiment, the result is a
white central band of constructive interference
corresponding to equal path length from the two slits, surrounded by a
symmetrical pattern of colored fringes of diminishing intensity. In
addition to continuous electromagnetic radiation, Young's experiment has
been performed with individual photons, with electrons, and with buckyball molecules large enough to be seen under an electron microscope.
Lloyd's mirror
generates interference fringes by combining direct light from a source
(blue lines) and light from the source's reflected image (red lines)
from a mirror held at grazing incidence. The result is an asymmetrical
pattern of fringes. The band of equal path length, nearest the mirror,
is dark rather than bright. In 1834, Humphrey Lloyd interpreted this
effect as proof that the phase of a front-surface reflected beam is
inverted.
An amplitude splitting interferometer uses a partial reflector to
divide the amplitude of the incident wave into separate beams which are
separated and recombined.
The Fizeau interferometer is shown as it might be set up to test an optical flat.
A precisely figured reference flat is placed on top of the flat being
tested, separated by narrow spacers. The reference flat is slightly
beveled (only a fraction of a degree of beveling is necessary) to
prevent the rear surface of the flat from producing interference
fringes. Separating the test and reference flats allows the two flats to
be tilted with respect to each other. By adjusting the tilt, which adds
a controlled phase gradient to the fringe pattern, one can control the
spacing and direction of the fringes, so that one may obtain an easily
interpreted series of nearly parallel fringes rather than a complex
swirl of contour lines. Separating the plates, however, necessitates
that the illuminating light be collimated. Fig 6 shows a collimated beam of monochromatic light illuminating the two flats and a beam splitter allowing the fringes to be viewed on-axis.
The Mach–Zehnder interferometer
is a more versatile instrument than the Michelson interferometer. Each
of the well separated light paths is traversed only once, and the
fringes can be adjusted so that they are localized in any desired plane. Typically, the fringes would be adjusted to lie in the same plane as
the test object, so that fringes and test object can be photographed
together. If it is decided to produce fringes in white light, then,
since white light has a limited coherence length, on the order of micrometers,
great care must be taken to equalize the optical paths or no fringes
will be visible. As illustrated in Fig. 6, a compensating cell would be
placed in the path of the reference beam to match the test cell. Note
also the precise orientation of the beam splitters. The reflecting
surfaces of the beam splitters would be oriented so that the test and
reference beams pass through an equal amount of glass. In this
orientation, the test and reference beams each experience two
front-surface reflections, resulting in the same number of phase
inversions. The result is that light traveling an equal optical path
length in the test and reference beams produces a white light fringe of
constructive interference.
The heart of the Fabry–Pérot interferometer
is a pair of partially silvered glass optical flats spaced several
millimeters to centimeters apart with the silvered surfaces facing each
other. (Alternatively, a Fabry–Pérot etalon uses a transparent plate with two parallel reflecting surfaces.)
As with the Fizeau interferometer, the flats are slightly beveled. In a
typical system, illumination is provided by a diffuse source set at the
focal plane
of a collimating lens. A focusing lens produces what would be an
inverted image of the source if the paired flats were not present, i.e.,
in the absence of the paired flats, all light emitted from point A
passing through the optical system would be focused at point A'. In
Fig. 6, only one ray emitted from point A on the source is traced. As
the ray passes through the paired flats, it is multiply reflected to
produce multiple transmitted rays which are collected by the focusing
lens and brought to point A' on the screen. The complete interference
pattern takes the appearance of a set of concentric rings. The sharpness
of the rings depends on the reflectivity of the flats. If the
reflectivity is high, resulting in a high Q factor (i.e., high finesse), monochromatic light produces a set of narrow bright rings against a dark background.[26] In Fig. 6, the low-finesse image corresponds to a reflectivity of 0.04 (i.e., unsilvered surfaces) versus a reflectivity of 0.95 for the high-finesse image.
Fig. 6 illustrates the Fizeau, Mach–Zehnder, and Fabry–Pérot
interferometers. Other examples of amplitude splitting interferometer
include the Michelson, Twyman–Green, Laser Unequal Path, and Linnik interferometer.
Michelson-Morley
Michelson and Morley (1887) and other early experimentalists using interferometric techniques in an attempt to measure the properties of the luminiferous aether,
used monochromatic light only for initially setting up their equipment,
always switching to white light for the actual measurements. The reason
is that measurements were recorded visually. Monochromatic light would
result in a uniform fringe pattern. Lacking modern means of environmental temperature control,
experimentalists struggled with continual fringe drift even though the
interferometer might be set up in a basement. Since the fringes would
occasionally disappear due to vibrations by passing horse traffic,
distant thunderstorms and the like, it would be easy for an observer to
"get lost" when the fringes returned to visibility. The advantages of
white light, which produced a distinctive colored fringe pattern, far
outweighed the difficulties of aligning the apparatus due to its low coherence length. This was an early example of the use of white light to resolve the "2 pi ambiguity".
Applications
Physics and astronomy
Interferometry is used in radio astronomy, with timing offsets of: Dsinθ
In physics, one of the most important experiments of the late 19th century was the famous "failed experiment" of Michelson and Morley which provided evidence for special relativity.
Recent repetitions of the Michelson–Morley experiment perform
heterodyne measurements of beat frequencies of crossed cryogenic optical resonators. Fig 7 illustrates a resonator experiment performed by Müller et al. in 2003. Two optical resonators constructed from crystalline sapphire,
controlling the frequencies of two lasers, were set at right angles
within a helium cryostat. A frequency comparator measured the beat
frequency of the combined outputs of the two resonators. As of 2009, the precision by which anisotropy of the speed of light can be excluded in resonator experiments is at the 10−17 level.
Figure 7. Michelson–Morley experiment with cryogenic optical resonators
Figure 8. Fourier transform spectroscopy
Figure 9. A picture of the solar corona taken with the LASCO C1 coronagraph
Michelson interferometers are used in tunable narrow band optical filters and as the core hardware component of Fourier transform spectrometers.
When used as a tunable narrow band filter, Michelson
interferometers exhibit a number of advantages and disadvantages when
compared with competing technologies such as Fabry–Pérot interferometers or Lyot filters.
Michelson interferometers have the largest field of view for a
specified wavelength, and are relatively simple in operation, since
tuning is via mechanical rotation of waveplates rather than via high
voltage control of piezoelectric crystals or lithium niobate optical
modulators as used in a Fabry–Pérot system. Compared with Lyot filters,
which use birefringent elements, Michelson interferometers have a
relatively low temperature sensitivity. On the negative side, Michelson
interferometers have a relatively restricted wavelength range and
require use of prefilters which restrict transmittance.
Fig. 8 illustrates the operation of a Fourier transform
spectrometer, which is essentially a Michelson interferometer with one
mirror movable. (A practical Fourier transform spectrometer would
substitute corner cube reflectors for the flat mirrors of the
conventional Michelson interferometer, but for simplicity, the
illustration does not show this.) An interferogram is generated by
making measurements of the signal at many discrete positions of the
moving mirror. A Fourier transform converts the interferogram into an
actual spectrum.
Fig. 9 shows a doppler image of the solar corona made using a
tunable Fabry-Pérot interferometer to recover scans of the solar corona
at a number of wavelengths near the FeXIV green line. The picture is a
color-coded image of the doppler shift of the line, which may be
associated with the coronal plasma velocity towards or away from the
satellite camera.
Fabry–Pérot thin-film etalons are used in narrow bandpass filters
capable of selecting a single spectral line for imaging; for example,
the H-alpha line or the Ca-K line of the Sun or stars. Fig. 10 shows an Extreme ultraviolet Imaging Telescope (EIT) image of the Sun at 195 Ångströms (19.5 nm), corresponding to a spectral line of multiply-ionized iron atoms. EIT used multilayer coated reflective mirrors that were coated with
alternate layers of a light "spacer" element (such as silicon), and a
heavy "scatterer" element (such as molybdenum). Approximately 100 layers
of each type were placed on each mirror, with a thickness of around
10 nm each. The layer thicknesses were tightly controlled so that at the
desired wavelength, reflected photons from each layer interfered
constructively.
The Laser Interferometer Gravitational-Wave Observatory (LIGO) uses two 4-km Michelson–Fabry–Pérot interferometers for the detection of gravitational waves. In this application, the Fabry–Pérot cavity is used to store photons
for almost a millisecond while they bounce up and down between the
mirrors. This increases the time a gravitational wave can interact with
the light, which results in a better sensitivity at low frequencies.
Smaller cavities, usually called mode cleaners, are used for spatial
filtering and frequency stabilization of the main laser. The first observation of gravitational waves occurred on September 14, 2015.
The Mach–Zehnder interferometer's relatively large and freely
accessible working space, and its flexibility in locating the fringes
has made it the interferometer of choice for visualizing flow in wind tunnels, and for flow visualization studies in general. It is frequently used in
the fields of aerodynamics, plasma physics and heat transfer to measure
pressure, density, and temperature changes in gases.
Mach–Zehnder interferometers are also used to study one of the
most counterintuitive predictions of quantum mechanics, the phenomenon
known as quantum entanglement.
An astronomical interferometer achieves high-resolution observations using the technique of aperture synthesis, mixing signals from a cluster of comparatively small telescopes rather than a single very expensive monolithic telescope.
Early radio telescope interferometers used a single baseline for measurement. Later astronomical interferometers, such as the Very Large Array
illustrated in Fig 11, used arrays of telescopes arranged in a pattern
on the ground. A limited number of baselines will result in insufficient
coverage. This was alleviated by using the rotation of the Earth to
rotate the array relative to the sky. Thus, a single baseline could
measure information in multiple orientations by taking repeated
measurements, a technique called Earth-rotation synthesis. Baselines thousands of kilometers long were achieved using very long baseline interferometry.
Astronomical optical interferometry
has had to overcome a number of technical issues not shared by radio
telescope interferometry. The short wavelengths of light necessitate
extreme precision and stability of construction. For example, spatial
resolution of 1 milliarcsecond requires 0.5 μm stability in a 100 m
baseline. Optical interferometric measurements require high sensitivity,
low noise detectors that did not become available until the late 1990s.
Astronomical "seeing",
the turbulence that causes stars to twinkle, introduces rapid, random
phase changes in the incoming light, requiring data collection rates to
be faster than the rate of turbulence. Despite these technical difficulties, three major facilities are now in operation offering resolutions down to the fractional milliarcsecond range.
Electron holography
is an imaging technique that photographically records the electron
interference pattern of an object, which is then reconstructed to yield a
greatly magnified image of the original object. This technique was developed to enable greater resolution in electron
microscopy than is possible using conventional imaging techniques. The
resolution of conventional electron microscopy is not limited by
electron wavelength, but by the large aberrations of electron lenses.
Neutron interferometry has been used to investigate the Aharonov–Bohm effect, to examine the effects of gravity acting on an elementary particle, and to demonstrate a strange behavior of fermions that is at the basis of the Pauli exclusion principle:
Unlike macroscopic objects, when fermions are rotated by 360° about any
axis, they do not return to their original state, but develop a minus
sign in their wave function. In other words, a fermion needs to be
rotated 720° before returning to its original state.
Atom interferometry techniques are reaching sufficient precision to allow laboratory-scale tests of general relativity.
Interferometers are used in atmospheric physics for
high-precision measurements of trace gases via remote sounding of the
atmosphere. There are several examples of interferometers that utilize
either absorption or emission features of trace gases. A typical use
would be in continual monitoring of the column concentration of trace
gases such as ozone and carbon monoxide above the instrument.
Engineering and applied science
Figure 13. Optical flat interference fringes. (left) flat surface, (right) curved surface.How interference fringes are formed by an optical flat resting on a reflective surface. The gap between the surfaces and the wavelength of the light waves are greatly exaggerated.
Newton (test plate) interferometry is frequently used in the optical
industry for testing the quality of surfaces as they are being shaped
and figured. Fig. 13 shows photos of reference flats being used to check
two test flats at different stages of completion, showing the different
patterns of interference fringes. The reference flats are resting with
their bottom surfaces in contact with the test flats, and they are
illuminated by a monochromatic light source. The light waves reflected
from both surfaces interfere, resulting in a pattern of bright and dark
bands. The surface in the left photo is nearly flat, indicated by a
pattern of straight parallel interference fringes at equal intervals.
The surface in the right photo is uneven, resulting in a pattern of
curved fringes. Each pair of adjacent fringes represents a difference in
surface elevation of half a wavelength of the light used, so
differences in elevation can be measured by counting the fringes. The
flatness of the surfaces can be measured to millionths of an inch by
this method. To determine whether the surface being tested is concave or
convex with respect to the reference optical flat, any of several
procedures may be adopted. One can observe how the fringes are displaced
when one presses gently on the top flat. If one observes the fringes in
white light, the sequence of colors becomes familiar with experience
and aids in interpretation. Finally one may compare the appearance of
the fringes as one moves ones head from a normal to an oblique viewing
position. These sorts of maneuvers, while common in the optical shop, are not
suitable in a formal testing environment. When the flats are ready for
sale, they will typically be mounted in a Fizeau interferometer for
formal testing and certification.
Fabry-Pérot etalons are widely used in telecommunications, lasers and spectroscopy to control and measure the wavelengths of light. Dichroic filters are multiple layer thin-film etalons. In telecommunications, wavelength-division multiplexing,
the technology that enables the use of multiple wavelengths of light
through a single optical fiber, depends on filtering devices that are
thin-film etalons. Single-mode lasers employ etalons to suppress all optical cavity modes except the single one of interest.
Figure 14. Twyman–Green Interferometer
The Twyman–Green interferometer, invented by Twyman and Green in
1916, is a variant of the Michelson interferometer widely used to test
optical components. The basic characteristics distinguishing it from the Michelson
configuration are the use of a monochromatic point light source and a
collimator. Michelson (1918) criticized the Twyman–Green configuration
as being unsuitable for the testing of large optical components, since
the light sources available at the time had limited coherence length.
Michelson pointed out that constraints on geometry forced by limited
coherence length required the use of a reference mirror of equal size to
the test mirror, making the Twyman–Green impractical for many purposes. Decades later, the advent of laser light sources answered Michelson's
objections. (A Twyman–Green interferometer using a laser light source
and unequal path length is known as a Laser Unequal Path Interferometer,
or LUPI.)
Fig. 14 illustrates a Twyman–Green interferometer set up to test a
lens. Light from a monochromatic point source is expanded by a diverging
lens (not shown), then is collimated into a parallel beam. A convex
spherical mirror is positioned so that its center of curvature coincides
with the focus of the lens being tested. The emergent beam is recorded
by an imaging system for analysis.
Mach–Zehnder interferometers are being used in integrated optical circuits, in which light interferes between two branches of a waveguide that are externally modulated
to vary their relative phase. A slight tilt of one of the beam
splitters will result in a path difference and a change in the
interference pattern. Mach–Zehnder interferometers are the basis of a
wide variety of devices, from RF modulators to sensors to optical switches.
Some proposed and future extremely large astronomical telescopes, such as the Thirty Meter Telescope and the Extremely Large Telescope,
will be of segmented design. Their primary mirrors will comprise
hundreds of hexagonal mirror-segments. Polishing and figuring these
highly aspheric and non-rotationally symmetric mirror segments presents a
major challenge. Traditional means of optical testing compare a surface
against a spherical reference with the aid of a null corrector. Computer-generated holograms
supplement null correctors in test setups for complex aspheric
surfaces. Fig. 15 illustrates how this is done. (Unlike the figure,
actual CGHs have line spacing on the order of 1 to 10 μm.) When laser
light is passed through the hologram, the zero-order diffracted beam
experiences no wavefront modification. The wavefront of the first-order
diffracted beam, however, is modified to match the desired shape of the
test surface. In the illustrated Fizeau interferometer test setup, the
zero-order diffracted beam is directed towards the spherical reference
surface, and the first-order diffracted beam is directed towards the
test surface in such a way that the two reflected beams combine to form
interference fringes.
Figure 15. Optical testing with a Fizeau interferometer and a computer generated hologram
Ring laser gyroscopes (RLGs) and fibre optic gyroscopes (FOGs) are interferometers used in navigation systems. They operate on the principle of the Sagnac effect.
The distinction between RLGs and FOGs is that in a RLG, the entire ring
is part of the laser while in a FOG, an external laser injects
counter-propagating beams into an optical fiber
ring, and rotation of the system then causes a relative phase shift
between those beams. In a RLG, the observed phase shift is proportional
to the accumulated rotation, while in a FOG, the observed phase shift is
proportional to the angular velocity.
In telecommunication networks, heterodyning is used to move
frequencies of individual signals to different channels which may share a
single physical transmission line. This is called frequency division multiplexing (FDM). For example, a coaxial cable used by a cable television
system can carry 500 television channels at the same time because each
one is given a different frequency, so they don't interfere with one
another. Continuous wave (CW) doppler radar detectors are basically heterodyne detection devices that compare transmitted and reflected beams.
Optical heterodyne detection is used for coherent Doppler lidar
measurements capable of detecting very weak light scattered in the
atmosphere and monitoring wind speeds with high accuracy. It has
application in optical fiber communications,
in various high resolution spectroscopic techniques, and the
self-heterodyne method can be used to measure the linewidth of a laser.
Figure
16. Frequency comb of a mode-locked laser. The dashed lines represent
an extrapolation of the mode frequencies towards the frequency of the
carrier–envelope offset (CEO). The vertical grey line represents an
unknown optical frequency. The horizontal black lines indicate the two
lowest beat frequency measurements.
Optical heterodyne detection is an essential technique used in
high-accuracy measurements of the frequencies of optical sources, as
well as in the stabilization of their frequencies. Until relatively few
years ago, lengthy frequency chains were needed to connect the microwave
frequency of a cesium or other atomic time source to optical frequencies. At each step of the chain, a frequency multiplier
would be used to produce a harmonic of the frequency of that step,
which would be compared by heterodyne detection with the next step (the
output of a microwave source, far infrared laser, infrared laser, or
visible laser). Each measurement of a single spectral line required
several years of effort in the construction of a custom frequency chain.
Currently, optical frequency combs
have provided a much simpler method of measuring optical frequencies.
If a mode-locked laser is modulated to form a train of pulses, its
spectrum is seen to consist of the carrier frequency surrounded by a
closely spaced comb of optical sideband
frequencies with a spacing equal to the pulse repetition frequency
(Fig. 16). The pulse repetition frequency is locked to that of the frequency standard,
and the frequencies of the comb elements at the red end of the spectrum
are doubled and heterodyned with the frequencies of the comb elements
at the blue end of the spectrum, thus allowing the comb to serve as its
own reference. In this manner, locking of the frequency comb output to
an atomic standard can be performed in a single step. To measure an
unknown frequency, the frequency comb output is dispersed into a
spectrum. The unknown frequency is overlapped with the appropriate
spectral segment of the comb and the frequency of the resultant
heterodyne beats is measured.
One of the most common industrial applications of optical
interferometry is as a versatile measurement tool for the high precision
examination of surface topography. Popular interferometric measurement
techniques include phase shifting interferometry (PSI), and vertical scanning interferometry (VSI), also known as scanning white light interferometry (SWLI) or by the ISO term coherence scanning interferometry (CSI), CSI exploits coherence to extend the range of capabilities for interference microscopy. These techniques are widely used in micro-electronic and micro-optic
fabrication. PSI uses monochromatic light and provides very precise
measurements; however it is only usable for surfaces that are very
smooth. CSI often uses white light and high numerical apertures, and
rather than looking at the phase of the fringes, as does PSI, looks for
best position of maximum fringe contrast or some other feature of the
overall fringe pattern. In its simplest form, CSI provides less precise
measurements than PSI but can be used on rough surfaces. Some
configurations of CSI, variously known as Enhanced VSI (EVSI),
high-resolution SWLI or Frequency Domain Analysis (FDA), use coherence
effects in combination with interference phase to enhance precision.
Figure 17. Phase shifting and Coherence scanning interferometers
Phase Shifting Interferometry addresses several issues associated
with the classical analysis of static interferograms. Classically, one
measures the positions of the fringe centers. As seen in Fig. 13, fringe
deviations from straightness and equal spacing provide a measure of the
aberration. Errors in determining the location of the fringe centers
provide the inherent limit to precision of the classical analysis, and
any intensity variations across the interferogram will also introduce
error. There is a trade-off between precision and number of data points:
closely spaced fringes provide many data points of low precision, while
widely spaced fringes provide a low number of high precision data
points. Since fringe center data is all that one uses in the classical
analysis, all of the other information that might theoretically be
obtained by detailed analysis of the intensity variations in an
interferogram is thrown away. Finally, with static interferograms, additional information is needed
to determine the polarity of the wavefront: In Fig. 13, one can see that
the tested surface on the right deviates from flatness, but one cannot
tell from this single image whether this deviation from flatness is
concave or convex. Traditionally, this information would be obtained
using non-automated means, such as by observing the direction that the
fringes move when the reference surface is pushed.
Phase shifting interferometry overcomes these limitations by not
relying on finding fringe centers, but rather by collecting intensity
data from every point of the CCD
image sensor. As seen in Fig. 17, multiple interferograms (at least
three) are analyzed with the reference optical surface shifted by a
precise fraction of a wavelength between each exposure using a piezoelectric transducer (PZT). Alternatively, precise phase shifts can be introduced by modulating the laser frequency. The captured images are processed by a computer to calculate the
optical wavefront errors. The precision and reproducibility of PSI is
far greater than possible in static interferogram analysis, with
measurement repeatabilities of a hundredth of a wavelength being
routine. Phase shifting technology has been adapted to a variety of
interferometer types such as Twyman–Green, Mach–Zehnder, laser Fizeau,
and even common path configurations such as point diffraction and
lateral shearing interferometers. More generally, phase shifting techniques can be adapted to almost any
system that uses fringes for measurement, such as holographic and
speckle interferometry.
Figure 18. Lunate cells of Nepenthes khasiana visualized by Scanning White Light Interferometry (SWLI)Figure 19. Twyman–Green interferometer set up as a white light scanner
In coherence scanning interferometry, interference is only achieved when the path length delays of the
interferometer are matched within the coherence time of the light
source. CSI monitors the fringe contrast rather than the phase of the
fringes. Fig. 17 illustrates a CSI microscope using a Mirau interferometer
in the objective; other forms of interferometer used with white light
include the Michelson interferometer (for low magnification objectives,
where the reference mirror in a Mirau objective would interrupt too much
of the aperture) and the Linnik interferometer (for high magnification objectives with limited working distance). The sample (or alternatively, the objective) is moved vertically over
the full height range of the sample, and the position of maximum fringe
contrast is found for each pixel. The chief benefit of coherence scanning interferometry is that systems
can be designed that do not suffer from the 2 pi ambiguity of coherent
interferometry, and as seen in Fig. 18, which scans a 180μm x 140μm x 10μm volume, it
is well suited to profiling steps and rough surfaces. The axial
resolution of the system is determined in part by the coherence length
of the light source. Industrial applications include in-process surface metrology,
roughness measurement, 3D surface metrology in hard-to-reach spaces and
in hostile environments, profilometry of surfaces with high aspect
ratio features (grooves, channels, holes), and film thickness
measurement (semi-conductor and optical industries, etc.).
Holographic interferometry is a technique which uses holography
to monitor small deformations in single wavelength implementations. In
multi-wavelength implementations, it is used to perform dimensional
metrology of large parts and assemblies and to detect larger surface
defects.
Holographic interferometry was discovered by accident as a result
of mistakes committed during the making of holograms. Early lasers were
relatively weak and photographic plates were insensitive, necessitating
long exposures during which vibrations or minute shifts might occur in
the optical system. The resultant holograms, which showed the
holographic subject covered with fringes, were considered ruined.
Eventually, several independent groups of experimenters in the
mid-60s realized that the fringes encoded important information about
dimensional changes occurring in the subject, and began intentionally
producing holographic double exposures. The main Holographic interferometry article covers the disputes over priority of discovery that occurred during the issuance of the patent for this method.
Double- and multi- exposure holography is one of three methods
used to create holographic interferograms. A first exposure records the
object in an unstressed state. Subsequent exposures on the same
photographic plate are made while the object is subjected to some
stress. The composite image depicts the difference between the stressed
and unstressed states.
Real-time holography is a second method of creating holographic
interferograms. A holograph of the unstressed object is created. This
holograph is illuminated with a reference beam to generate a hologram
image of the object directly superimposed over the original object
itself while the object is being subjected to some stress. The object
waves from this hologram image will interfere with new waves coming from
the object. This technique allows real time monitoring of shape
changes.
The third method, time-average holography, involves creating a
holograph while the object is subjected to a periodic stress or
vibration. This yields a visual image of the vibration pattern.
Figure 20. InSAR Image of Kilauea, Hawaii showing fringes caused by deformation of the terrain over a six-month period.
Figure 21. ESPI fringes showing a vibration mode of a clamped square plate
Interferometric synthetic aperture radar (InSAR) is a radar technique used in geodesy and remote sensing. Satellite synthetic aperture radar
images of a geographic feature are taken on separate days, and changes
that have taken place between radar images taken on the separate days
are recorded as fringes similar to those obtained in holographic
interferometry. The technique can monitor centimeter- to
millimeter-scale deformation resulting from earthquakes, volcanoes and
landslides, and also has uses in structural engineering, in particular
for the monitoring of subsidence and structural stability. Fig 20 shows
Kilauea, an active volcano in Hawaii. Data acquired using the space
shuttle Endeavour's X-band Synthetic Aperture Radar on April 13, 1994
and October 4, 1994 were used to generate interferometric fringes, which
were overlaid on the X-SAR image of Kilauea.
Electronic speckle pattern interferometry
(ESPI), also known as TV holography, uses video detection and recording
to produce an image of the object upon which is superimposed a fringe
pattern which represents the displacement of the object between
recordings. (see Fig. 21) The fringes are similar to those obtained in
holographic interferometry.
When lasers were first invented, laser speckle
was considered to be a severe drawback in using lasers to illuminate
objects, particularly in holographic imaging because of the grainy image
produced. It was later realized that speckle patterns could carry
information about the object's surface deformations. Butters and
Leendertz developed the technique of speckle pattern interferometry in
1970, and since then, speckle has been exploited in a variety of other
applications. A photograph is made of the speckle pattern before
deformation, and a second photograph is made of the speckle pattern
after deformation. Digital subtraction of the two images results in a
correlation fringe pattern, where the fringes represent lines of equal
deformation. Short laser pulses in the nanosecond range can be used to
capture very fast transient events. A phase problem exists: In the
absence of other information, one cannot tell the difference between
contour lines indicating a peak versus contour lines indicating a trough. To resolve the issue of phase ambiguity, ESPI may be combined with phase shifting methods.
A method of establishing precise geodetic baselines, invented by Yrjö Väisälä,
exploited the low coherence length of white light. Initially, white
light was split in two, with the reference beam "folded", bouncing
back-and-forth six times between a mirror pair spaced precisely 1 m
apart. Only if the test path was precisely 6 times the reference path
would fringes be seen. Repeated applications of this procedure allowed
precise measurement of distances up to 864 meters. Baselines thus
established were used to calibrate geodetic distance measurement
equipment, leading to a metrologically traceable scale for geodetic networks measured by these instruments. (This method has been superseded by GPS.)
Other uses of interferometers have been to study dispersion of
materials, measurement of complex indices of refraction, and thermal
properties. They are also used for three-dimensional motion mapping
including mapping vibrational patterns of structures.
Potential military applications of laser interferometry,
documented as of 1964, included "precision positioning in research,
manufacture, and in field use of equipment, such as missile alignment or
turret aiming equipment; in geodesy and mapping, where one does not
need a map accurate to microinches, but where the accurate establishment
of base lines is essential; and in the remote measuring of variations
of temperature in the atmosphere [...] which affect optical seeing
ability."
Biology and medicine
Optical interferometry, applied to biology and medicine, provides
sensitive metrology capabilities for the measurement of biomolecules,
subcellular components, cells and tissues. Many forms of label-free biosensors rely on interferometry because the
direct interaction of electromagnetic fields with local molecular
polarizability eliminates the need for fluorescent tags or nanoparticle
markers. At a larger scale, cellular interferometry shares aspects
with phase-contrast microscopy, but comprises a much larger class of
phase-sensitive optical configurations that rely on optical interference
among cellular constituents through refraction and diffraction. At the
tissue scale, partially-coherent forward-scattered light propagation
through the micro aberrations and heterogeneity of tissue structure
provides opportunities to use phase-sensitive gating (optical coherence
tomography) as well as phase-sensitive fluctuation spectroscopy to image
subtle structural and dynamical properties.
Figure 22. Typical optical setup of single point OCT
Optical coherence tomography
(OCT) is a medical imaging technique using low-coherence interferometry
to provide tomographic visualization of internal tissue
microstructures. As seen in Fig. 22, the core of a typical OCT system is
a Michelson interferometer. One interferometer arm is focused onto the
tissue sample and scans the sample in an X-Y longitudinal raster
pattern. The other interferometer arm is bounced off a reference mirror.
Reflected light from the tissue sample is combined with reflected light
from the reference. Because of the low coherence of the light source,
interferometric signal is observed only over a limited depth of sample.
X-Y scanning therefore records one thin optical slice of the sample at a
time. By performing multiple scans, moving the reference mirror between
each scan, an entire three-dimensional image of the tissue can be
reconstructed. Recent advances have striven to combine the nanometer phase retrieval
of coherent interferometry with the ranging capability of low-coherence
interferometry.
Figure 24. Spyrogira cell (detached from algal filament) under phase contrast
Figure 26. High resolution phase-contrast x-ray image of a spider
Phase contrast and differential interference contrast
(DIC) microscopy are important tools in biology and medicine. Most
animal cells and single-celled organisms have very little color, and
their intracellular organelles are almost totally invisible under simple
bright field illumination. These structures can be made visible by staining
the specimens, but staining procedures are time-consuming and kill the
cells. As seen in Figs. 24 and 25, phase contrast and DIC microscopes
allow unstained, living cells to be studied. DIC also has non-biological applications, for example in the analysis of planar silicon semiconductor processing.
Angle-resolved low-coherence interferometry (a/LCI) uses scattered light to measure the sizes of subcellular objects, including cell
nuclei. This allows interferometry depth measurements to be combined
with density measurements. Various correlations have been found between
the state of tissue health and the measurements of subcellular objects.
For example, it has been found that as tissue changes from normal to
cancerous, the average cell nuclei size increases.
Phase-contrast X-ray imaging (Fig. 26) refers to a variety of
techniques that use phase information of a coherent x-ray beam to image
soft tissues. (For an elementary discussion, see Phase-contrast x-ray imaging (introduction). For a more in-depth review, see Phase-contrast X-ray imaging.)
It has become an important method for visualizing cellular and
histological structures in a wide range of biological and medical
studies. There are several technologies being used for x-ray
phase-contrast imaging, all utilizing different principles to convert
phase variations in the x-rays emerging from an object into intensity
variations. These include propagation-based phase contrast, Talbot interferometry, Moiré-based far-field interferometry, refraction-enhanced imaging, and x-ray interferometry. These methods provide higher contrast compared to normal
absorption-contrast x-ray imaging, making it possible to see smaller
details. A disadvantage is that these methods require more sophisticated
equipment, such as synchrotron or microfocus x-ray sources, x-ray optics, or high resolution x-ray detectors.
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