Structure and Function

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OCD

▶Oriented Circular Dichroism Spectroscopy

ODC Mitochondrial Oxodicarboxylate Carrier

▶Mitochondrial Transport Protein Family

OGC Mitochondrial Oxoglutarate Carrier

▶Mitochondrial Transport Protein Family

OLID-FRET

▶Photochromic F€orster Energy Transfer

Oligomeric Proteins

Richard C. Garratt, Napolea˜o Fonseca Valadares and Jose´ Fernando Ruggiero Bachega

Institute of Physics of Sao Carlos, University of Sao Paulo, Sa˜o Carlos-SP, Brazil

Synonyms

Protein oligomers;Protein–Protein interactions

Definition

Oligomeric proteins are those composed of more than one subunit (polypeptide chain).

Introduction

Oligomeric proteins, by definition, are composed of more than one subunit (polypeptide chain). As such, they possess a quaternary structure, generally consid- ered to be the highest level of organization within the protein structural hierarchy. This describes the way in which the various subunits are arranged one with respect to another. Oligomeric proteins may be composed either exclusively of several copies of identical polypeptide chains, in which case they are termed homo-oligomers, or alternatively by at least one copy of different polypeptide chains (hetero-oligomers).

Oligomerization is the norm rather than the excep- tion and one estimate for proteins from Escherichia coliputs the percentage of monomeric proteins as low as 20% (Goodsell and Olsen2000). Of the remaining 80% of proteins which possess two or more subunits, homo-oligomers outnumber hetero-oligomers by approximately 4 to 1. However, historically this has not been reflected by depositions in the PDB where monomeric proteins are overrepresented. This may be merely a distortion introduced by differences in the ease of crystallization in which case it is to be expected that it will be overcome with time (Jones and Thornton1996).

Caution should also be exercised in the interpretation of the PDB atomic coordinate files themselves since there is no direct correlation between the biologically active oligomeric state and the contents of the asymmetric unit as G.C.K. Roberts (ed.),Encyclopedia of Biophysics, DOI 10.1007/978-3-642-16712-6,

#European Biophysical Societies’ Association (EBSA) 2013

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deposited in the databank (Berman et al.2000). The latter may contain less than the full oligomeric particle in which case the use of crystallographic symmetry will be necessary in order to generate the biologically active unit of interest. Alternatively, there may be more than one copy of the biologically relevant unit present and it is important to be able to distinguish between, for example, an asymmetric unit which contains two copies of a monomeric protein from one that contains a genuine dimer. The PISA server (Krissinel and Henrick2007) is a generally reliable tool for predicting the correct oligomeric state of a protein from its atomic coordinates.

More than one study has highlighted the prevalence of oligomers containing an even number of subunits (particularly dimers and tetramers) over those that contain an odd number (Klotz et al. 1975; Goodsell and Olsen2000). This is a subtle point. It may be that since small odd numbers are alsoprimenumbers these oligomers cannot be built up from others containing fewer subunits during evolution. Given that dimers and tetramers are particularly prevalent it may also be that isologous interfaces are favored over heterologous (see below).

There is no generally accepted classification or nomenclature for oligomers. However, proteins in general have been divided into two broad classes, globular and fibrous. This classification is well suited to the description of oligomers, as the vast majority is based on some form of symmetrical arrangement of subunits.

If the symmetry is that of a closed point group then the oligomer will tend to be globular. If, on the other hand, it is based on helical (or screw axis) symmetry, then the result will be a filamentous structure which can extend, in principle, infinitely in both directions. Other types of filamentous oligomers are also possible, such as colla- gen which is based on three intertwining extended chains supercoiling around one another and septins which are based on nonpolar filaments possessing twofold and pseudo-twofold axes (see below) perpendicular to the filament axis.

Types of Interfaces

In globular homo-oligomers the subunits may interact with one another via two fundamentally different types of interface, isologous interfaces and heterologous interfaces (Monod et al.1965). An isologous interface is the result of a twofold axis (a rotation of 180) relating two identical subunits. Such a relationship implies that if a region A on subunit 1 interacts with

region B on subunit 2, thennecessarilyregion A on subunit 2 will interact with region B on subunit 1 (Fig. 1). Only two possible arrangements based exclusively on twofold symmetry are possible. These correspond to homodimers which possess one twofold axis and homo-tetramers possessing three mutually perpendicular twofold axes.

Heterologous interfaces arise from higher-order symmetry: threefold (120rotation), fourfold (90rotation), fivefold (72 rotation), etc. In this case, while region A on subunit 1 interacts with region B on subunit 2, the opposite is not so (Fig. 1). The result may be either a linear polymer or a closed circular structure based on cyclic point-group symmetry. If the subunits are approximately spherical then there is a tendency for the cavity at the center of the structure to increase in size with the number of subunits (Fig. 1d). This may be used to form pores in membranes such as the protein secretory appa- ratus and the potassium channel which have six- and fourfold symmetry, respectively.

Types of Point-Group Symmetry

The vast majority of homo-oligomers can be described by one of three types of point-group symmetry: cyclic groups, dihedral groups, and higher-order symmetry groups (cubic or icosahedral). These can be described by use of either the International or Schoenflies point- group nomenclature (Hahn 1996). Cyclic groups, as described above, are characterized by a single rotation axis, which can be of any order, although very high orders tend to be rare. They form cyclic structures which present the same side of each subunit on the surfaces perpendicular to the rotation axis. They tend to form channels or pores and are suited to interacting with planar surfaces such as membranes as is the case of the fivefold related B subunits of heat-labile enterotoxin.

Dihedral groups, besides having ann-fold principal rotation axis, also possessntwofold axes perpendicular to it. This type of symmetry generates a greater variety of interfaces between subunits and these can be exploited for generating allosterism (see below). For example, it is far more common to encounter tetrameric enzymes displaying 222 dihedral symmetry (also known as D2 in the Schoenflies nomenclature) than it is to belong to the cyclic point group 4 (or C4).

The difference between the two is made apparent in Fig. 2. In the case of cyclic symmetry it is more difficult for diametrically opposite subunits to make

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direct contact with one another whereas it is common in the case of dihedral symmetry for each subunit to share interfaces with all others. Dihedral symmetry is often used to form hollow cylindrical cavities with entrances at both ends as observed in the proteasome and GroEL, both of which are based on 72 symmetry.

In both cases layers of heptameric rings related by the perpendicular twofold axes are stacked on top of one another in a face-to-face fashion thus increasing the

length of the internal cavity and even generating sub-cavities within (Voet and Voet2010).

Cubic symmetry is based on four threefold axes running in the direction of the body diagonals of a cube and icosahedral symmetry includes both threefold and fivefold axes. Both are ideal for the formation of approximately spherical shell-like structures harboring an internal hollow cavity sheltered from the external milieu.

Based on point-group symmetry Garratt and Orengo (2008) have produced a chart which, while not exhaustive, captures the diversity of arrangements adopted by globular oligomers (Fig. 3). Their classification is primarily based on the highest-order rotation axis of the oligomer, which increases on moving from left to right across the table. The background to each cell is used to distinguish between cyclic, dihedral, and higher-order point groups. One attractive feature of this table is that besides organizing structures in a rational manner, functional attributes of each of the selected proteins are also present. The octagon around each structure provides functional information which can be readily extracted by reference to the legend on the left.

A B

Isologous interface

Heterologous interfaces leading to a cyclic oligomer

Heterologous interface leading to a filamentous polymer

a

b

c

d Oligomeric Proteins,

Fig. 1 Subunit interfaces.

(a) Isologous interfaces are the result of twofold symmetry.

Heterologous interfaces can lead to filaments (b) or to cyclic structures (c). The latter tend to form progressively larger central pores as the number of subunits increases (d)

Oligomeric Proteins, Fig. 2 Two alternative ways of being tetrameric.On theleft4 (or C4) cyclic symmetry and on theright 222 (D2) dihedral symmetry

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Functional Attributes of Oligomers

What are the advantages of oligomeric proteins from a functional point of view? Many have been identified and reviewed previously (Goodsell and Olsen 2000;

Ali and Imperiali 2005). The Protein Chart uses a classification based on eight major functional classes.

Size and Stability

By accumulating a greater number of weakly stabiliz- ing interactions large proteins, and particularly oligomeric assemblies, gain stability. Furthermore, one of the major advantages of increased mass is the associated relative reduction in exposed surface area which diminishes the risk of degradation, including proteolytic attack. Large size also permits for building voluminous cavities such as those required by GroEL for engulfing unstructured polypeptide chains and accelerating their folding. On the other hand, for

functions which require rapid diffusion and/or degradation such as extracellular hormones, small monomeric proteins are ideal.

Cooperativity and Allosterism

By possessing more than one equivalent binding site, oligomeric enzymes have the potential to permit the communication between these, leading to a phenomenon known as cooperativity. Furthermore, the complexity of oligomers and their varied intersubunit interfaces allows for effector molecules to bind at sites distant from the active site and thereby induce conformational changes which affect activity. Homotropic allosteric effectors influence the binding of the same molecule to a different subunit while heterotropic effectors affect the binding of a second ligand. The model proposed by Monod et al.

(1965) suggests that the enzyme cycles between two extreme states (R and T, for relaxed and tense) both of Oligomeric Proteins, Fig. 3 A summary of oligomeric structures.The oligomeric table from the Protein Chart, reproduced with permission from Wiley-VCH

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which preserve the same symmetry but with different intersubunit interactions. The R and T forms of the cooperative enzyme glucosamine 6-phosphate deaminase are shown in Fig. 4. In this case, as with most allosteric enzymes, there are alteration to both the tertiary and quaternary structure on cycling between the R and T-states. The principal advantage of cooperativity and allosterism is that they allow for fine control of enzyme activity as a function of the concentration of relevant intercellular components and thus the control of flux through metabolic pathways.

Cavities, Channels, and Pores

Cyclic point groups are particularly well suited to generate structures which have central pores or channels. Closed hollow cavities can be formed by higher-order point groups. Ferritin, for example, which is built from 24 subunits with cubic 432 symmetry, is capable of sequestering over 4,000 iron ions within its internal cavity, thus protecting the intracellular environment from redox damage.

Icosahedral viral capsids, based on multiples of 60 copies, form an effective way to protect the viral genetic material for transport and infection.

Multiple Sites, Cross-Linking, and Membrane Association

Immunoglobulins and many plant lectins are able to cross-link target molecules simply because they possess more than one binding site, a result of being oligomeric. For example, IgG type immunoglobulins possess two identical light chains and two identical heavy chains. One of each is necessary for the formation of a single antigen-binding site and IgG molecules therefore possess two. If each site binds to a separate target molecule, such as membrane receptors located on different cells, this can lead to cross-linking and the formation of large aggregates. Alternatively, a series of binding sites present on different subunits of a cyclic oligomer could simultaneously bind to a series of receptors on the surface of the same cell leading to an increase in affinity. This is observed for cholera toxin and the heat-labile enterotoxin, which bind to specific glycolipids in the target cell membrane.

Functional (Active) Site Formation

Oligomerization provides the possibility of generating novel active site cavities at subunit interfaces and it has been commented that one sixth of oligomeric enzymes Oligomeric Proteins, Fig. 4 Aspects of oligomeric structures.

(a) The conformational change from the R (red) to T (blue) state in glucosamine 6-phosphate deaminase involves alterations to the tertiary and quaternary structures including relative domain motions. (b) Aspartate transcarbamoylase is an example of a hetero-oligomer composed of six catalytic subunits (blueand

green) and six regulatory subunits (cyanandred). (c) The trp repressor is a highly intertwined dimer and (d) cystatins are domain swapped. (e) Peanut lectin has one twofold axis (solid line), which applies to the tetramer, and two local twofold axes (dotted lines) relating theredsubunit to thegreenand theblue subunit to theyellow, respectively

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present such features (Ali and Imperiali 2005).

The HIV protease is dimeric with each monomer providing one essential aspartic acid to the catalytic appa- ratus. In the case of allosteric enzymes, effector binding sites are often found to be similarly located at interfaces, as is the case in glucosamine 6-phosphate deaminase (Fig. 4). Sometimes effector binding can lead to a change in the oligomeric state itself, as is observed in phosphofructokinase 2 fromE. coli.

Rulers

Goodsell and Olsen (2000) have pointed out that an ingenious application of oligomers is the ability to act as rulers by establishing a fixed distance between two active sites, something that would be impossible with independent monomers. A classic example is that observed in dimeric DNA-binding proteins (such as the regulators, repressor, and Cro, from the bacteriophage lambda), which recognize palindromic nucleotide sequences. This region of the double helix, therefore, possesses a local pseudo-twofold axis perpendicular to the main helical axis. This aligns with the twofold axis of the regulator protein on binding such that each monomer interacts with one half of the palindrome. For this to happen, the two halves of the palindrome must lie on the same side of the double helix and thus the separation between them corresponds to one turn of B-DNA (10 base pairs or 34 A˚ ). Furthermore, the separation between the two binding sites on the dimeric regulator must also correspond to this distance, as is observed.

Thus the dimeric nature of the regulator serves to accu- rately establish an appropriate distance between equivalent binding sites. The trp repressor is a further example and appears inFig. 4.

The proteasome is responsible for cleaving substrate proteins into octapeptides for binding to the central groove of HLA type 1 molecules. Therefore, unlike most proteolytic enzymes, its specificity is not so much based on the recognition of a particular type of amino acid but rather on the size of its product. This is controlled by the spatial separation between active sites within the proteasome central cavity, which is a function of its oligomeric assembly (Fig. 3). It is an example of a proteolytic ruler.

Multiple Functions

It is common for the different types of subunit within a hetero-oligomer to play different roles. The enzyme aspartate transcarbamoylase possesses both catalytic

and regulatory subunits (Fig. 4), the heat-labile enterotoxin fromE. colihas both toxic- and receptor- binding subunits, and IgG molecules have both antigen-binding sites (formed at the interface between the heavy and light chains) and an Fc receptor-binding site (exclusive to the heavy chains).

Economy of Genetic Material

One of the principal advantages of oligomeric proteins is that large structures can be built from a limited amount of genetic material. Furthermore, it becomes easier to per- form quality control since subunits containing errors can be excluded from incorporation into the final oligomer.

The extreme example of coding efficiency is seen in spherical viruses. Their reduced dimensions mean that there would be insufficient internal volume for housing enough genetic material to encode the capsid if this were made of a single polypeptide chain. A large number of copies of identical subunits (multiples of 60) provide the solution (Branden and Tooze1999).

The Nature of Intersubunit Interfaces and Structural Motifs

Oligomeric proteins employ a wide range of interactions at their interfaces in order to guarantee their stability and many have dissociation constants within the nanomolar range. A classical intersubunit interface is formed by a central contiguous hydrophobic patch surrounded by hydrophilic residues and water molecules at the periph- ery. However, approximately two thirds of intersubunit interfaces show a large number of hydrophilic interactions and water-filled cavities spread over the entire surface. It has been suggested that these may be remnants of an ancestral monomer which have survived as evolution drove the protein in the direction of oligomerization.

Many interfaces are relatively planar with approximately circular interacting surfaces which tend to bury

>1,400 A˚², at least in the case of obligate homodimers.

They tend to show greater shape complementarity than transient complexes such as those of antibodies with their cognate antigens. Some dimers, such as the trp repressor (Fig. 4) are built from heavily intertwined monomers which are probably unstable in isolation.

Others, such as the cystatin dimer (Fig. 4) are best described as domain swapped.

Coiled coil motifs, such as leucine zippers, and helix-loop-helix motifs are both structural assemblies ofa-helices used for dimerization (Fig. 5). Coiled coils, however, may also be used to form oligomers of

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higher order. The unsatisfied hydrogen-bonding potential of edge strands ofb-sheets is also often used for stabiliz- ing oligomers. Transthyretin, the heat-labile enterotoxin, the archeal SmAP protein, and a-hemolysin (Fig. 5) are examples. However, this hydrogen-bonding potential is potentially dangerous (Richardson and Richardson 2002). If not used to close a cyclic structure, the result will be polymerization leading to the formation of amyloid. For this reason proteins have inbuilt negative design (such as edge strand distortion and coverage) in order to minimize the risk of forming these undesirable aggregates.

Filamentous Oligomers

Most filamentous oligomers are based on helical symmetry. Actin filaments, microtubules, and the tobacco mosaic virus are examples.Figure 6 shows the RecA filament which has 61helical symmetry and wraps binds to both single- and double-stranded DNA. However, some nonpolar filaments do not present helical symmetry, rather they are the result of a series of twofold axes perpendicular to the filament axis. Septins (Fig. 6) form hetero-oligomeric complexes which include both true and pseudo-symmetric twofolds.

Oligomeric Proteins, Fig. 5 Oligomerization motifs. The leucine zipper (a) and the helix-loop-helix (b) are dimerization motifs.b-sheet strands are often used to stabilize oligomers, particularly those with cyclic symmetry such as the SmAP protein involved in the formation of small nuclear ribonucleoprotein particles (c) and the staphylococcala-hemolysin (d)

Oligomeric Proteins, Fig. 6 Filamentous oligomers. (a) A RecA polar filament which presents 6₁helical symmetry and (b) an apolar septin hetero-filament with twofold (solid lines)

and pseudo-twofold axes (dotted lines) indicated perpendicular to the filament axis

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Pseudosymmetry, Quasi-Symmetry, and Asymmetric Oligomers

Pseudosymmetry may arise when an oligomer is composed of similar, but not identical, subunits. The familiar tetrameric hemoglobin molecule is composed of twoaand twobchains which share approximately 45% sequence identity. The tetramer has point group symmetry 2, but approximate 222 symmetry due to the similarity between theaandbsubunits (Fig. 7). A different variant on the theme is shown by the bacterial DNA polymerase III (Fig. 3) which is formally only twofold symmetric but has a pseudo sixfold axis due to the presence of three homologous domains within each subunit.

Quasi-symmetry is observed in spherical viruses.

These take advantage of inter-domain flexibility of the capsid proteins in order that these may occupy approximately identical local environments (Branden and Tooze1999).

Asymmetric oligomers are rare. However, occa- sionally oligomeric proteins will present a lower

symmetry than is theoretically possible. For example, peanut lectin is composed of four identical polypeptide chains and would be expected to belong to one of two possible point groups in order to exploit its full potential in terms of symmetry (point groups 4 or 222).

In fact the tetramer has only one twofold axis (point group 2). However, it also possesses two local twofold axes which apply separately to the two dimers which comprise the tetramer (Fig. 4). These do not lie perpendicular to the true twofold and the three axes therefore do not form a point group. The advantages of this arrangement in this particular case are unclear.

Homologous Families of Oligomers

The number of subunits and their arrangement are not always well conserved among members of a protein family.7a–cshows three different arrangements of the four subunits of different tetrameric hemoglobins.

Radically different interfaces are used in all three cases. A more dramatic example is the giant hemoglobin found in annelids (Fig. 7). The 144 globin chains Oligomeric Proteins, Fig. 7 Different oligomeric arrange-

ments of hemoglobins. (a) Hemoglobin from the innkeeper worm has four identical subunits with 222 symmetry while human hemoglobin (b) has only one true twofold axis (solid line) and two pseudo-twofolds (dotted lines) relating the a-chains to the b-chains. Tetrameric clam hemoglobin is

shown in (c) and a tetrameric unit from the giant hemoglobin from the earthworm (e) is shown in (d). In this case all four chains are different. Three such tetramers are related by a local threefold axis (g). However, due to differences between the additional linker chains (green, purple, andorange) in fact this is really only a pseudo-threefold (f)

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are based on 36 tetrameric units, which themselves are different from the three described above. Three tetramers are arranged around a local threefold axis and sit upon a trimer of homologous but nonidentical linker chains reducing this axis to a pseudo-threefold. Twelve such mushroom-shaped units arranged into two six- membered rings present 622 symmetry. This 3.6 MDa complex is an extracellular protein whose size is important for avoiding loss from the hemolymph of the worm.

Its arrangement allows for significant allosteric communication between its subunits and represents a spectacu- lar example of many of the concepts described in this entry.

Summary

Oligomeric proteins are common and possess a series of advantages in terms of functional attributes.

The vast majority are based on symmetric arrangements which may be described by either closed point groups, leading to globular oligomers with a finite number of subunits, or by helical symmetry involving a translational component which generates filaments.

Oligomeric proteins have evolved under selective pressure which, in many cases, favors larger structures due to their intrinsic stability. Other advantages include cooperativity and allosterism, the formation of interfacial active sites, multiple functionality, and the formation of cavities, pores, and rulers as well as an overall economy in terms of genetic material.

Cross-References

▶3D Domain Swapping

▶Amyloid Formation

▶Macromolecular Crystallography: Overview

References

Ali MH, Imperiali B. Protein oligomerization: how and why.

Bioorg Med Chem. 2005;13:5013–20.

Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE. The protein data bank. Nucl Acid Res. 2000;28:235–42. http://www.rcsb.

org/pdb.

Branden C, Tooze J. Introduction to protein structure.

New York: Garland; 1999.

Garratt RC, Orengo CA. The protein chart. Weinheim: Wiley- VCH; 2008.

Goodsell DS, Olsen AJ. Structural symmetry and protein function. Annu Rev Biophys Biomol Struct. 2000;29:105–53.

Hahn T, editor. International tables for crystallography, Vol. A, 4th edn (rev). Dordrecht: Kluwer, 1996.

Jones S, Thornton JM. Principles of protein-protein interactions.

Proc Natl Acad Sci USA. 1996;93:13–20.

Klotz IM, Darnell DW, Langerman NR. Quarternary structure of proteins. New York: Academic; 1975.

Krissinel E, Henrick K. Inference of macromolecular assemblies from crystalline state. J Mol Biol. 2007;372:774–97.

Monod J, Wyman J, Changeux J-P. On the nature of allosteric transitions: a plausible model. J Mol Biol. 1965;12:88–118.

Richardson JS, Richardson DC. Naturalb-sheet proteins use negative design to avoid edge-to-edge aggregation. Proc Natl Acad Sci USA. 2002;99:2754–9.

Voet D, Voet JG. Biochemistry. New York: Wiley; 2010.

Oligosaccharide Analysis and Conformation

▶Techniques Applied to Glycan Structure and Conformation

Oligosaccharide Stereochemistry

▶Anomeric Effect in Sugars

Oligosaccharide-Protein Interactions

▶Lectins

Oligosaccharides

▶Glycoproteins

One-Dimensional Protein Structure Prediction

▶Protein Secondary Structure Prediction in 2012

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ONIOM

Marc Willem van der Kamp

Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, UK

Definition

ONIOM stands for “Our own N-layered Integrated molecular Orbital and molecular Mechanics method.”

This method can treat a molecular system in several layers, e.g., ab initio QM, semiempirical QM, and MM. The higher the level (typically related to higher computational expense and accuracy), the smaller the subsystem that is treated with it. The total energy of a system is then calculated by the total energy at the lowest level plus the energy of the subsystems at the higher levels and minus the equivalent energy of these subsystems at the lower levels. It is therefore referred to as a “subtractive approach.”

For enzyme reaction modeling, the ONIOM approach is often used as a QM/MM method, which involves a straightforward “mechanical” embedding of the QM region in the MM environment. Initially, the method treated interactions between the QM and MM regions purely classically, with point charges representing the QM system for its interaction with the MM environment. This means that polarization of the QM region is not included. Further development has meant that polarization of the QM region by the MM atomic charges is now possible, through “electro- static embedding.”

Cross-References

▶QM/MM Methods

▶Semiempirical Quantum Mechanical Methods

Open-Probability

▶Potassium Channel Selectivity and Gating at the Selectivity Filter: Structural Basis

Optical Activity

▶Carbohydrate Circular Dichroism

▶Circular Dichroism Signals: Qualitative Description of Origins

▶Protein Circular Dichroism: Theoretical Aspects

Optical Analysis of Surfaces, Interfaces, and Thin Films Under Microscopic Observation

▶Brewster Angle Microscopy and Imaging Ellipsometry

Optical Fluorescence Microscopy

Alberto Diaspro^1,2, Paolo Bianchini^1,2, Francesca Cella Zanacchi^1,2and Cesare Usai³

1Department of Nanophysics, Italian Institute of Technology (IIT), Genoa, Italy

2Department of Physics, University of Genoa, Genoa, Italy

3Institute of Biophysics, National Research Council, Genoa, Italy

Synonyms

Wide-field optical fluorescence microscopy

Definition

It is a wide-field optical microscopy method utilizing fluorescence as contrast mechanism.

Basic Characteristics

The wide-field fluorescence microscope is a modifica- tion of the compound optical microscope, arranged to admit light of a selected wavelength to fluorescently labeled specimens and to image them through the emitted radiation. Since fluorescence emission has a lifetime in the nanosecond scale, continuous excitation is needed to collect an image having fluorescence as contrast mechanism. In a classical wide-field optical fluorescence microscope, the light source of a fluorescent microscope

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is a gas-vapor arc lamp, using either a discrete (Mercury) or a continuous (Xenon) light-emission spectrum. Con- tinuous- or pulsed-light-emitting lasers are now used in modern fluorescence microscopy beam-scanning techniques, as confocal laser-scanning microscopy and multi-photon excitation microscopy. In the most common configuration, i.e., epifluorescence microscope, the excitation wavelength, selected by an excitation filter, is reflected by a suitable dichroic mirror (dichromatic beam splitter), reaching the specimen through a focalizing objective. A careful regulation of excitation intensity is required to minimize the extinction of the fluorophore emission (photobleaching). The fluorescence radiation emitted by the fluorescent dyes is usually collected back by the very same objective used for excitation, transmitted through a dichroic mirror, spectrally selected from undesired wavelengths by an emission filter (stop filter), and finally focalized at the eyepiece image plane or sent to the sensitive target of a camera. In most epifluorescence microscopes, different combinations of excitation filters, dichroic mirrors, and emission filters are preassembled in an epifluorescence box. Resolution in a fluorescence optical microscope is limited by dif- fraction and can be estimated approximately 250 nm in the image plane (x,y) and 500 nm along the z-axis.

Thanks to the very fast growth of the number and type of fluorescent molecules, fluorescence microscopy is currently the most popular microscopic technique for biomedical and biophysical applications. Fluorescent dyes can be divided into two main families: morpholog- ical dyes, mainly addressed to evidence structural details of biological structures, and functional dyes, mainly addressed to reveal or measure physiological processes in tissues and cells in vivo. Modern fluorescence microscopes allow one to label cells with different types of fluorescent dyes simultaneously. In recent decades, some advanced techniques in optical fluorescence microscopy have been demonstrated. These techniques have been further improved with the advent of confocal laser-scanning microscopy and two-photon excitation microscopy.

Among the advanced variations on the fluorescence microscopy methods the most utilized for probing molecular interactions are Fluorescence Resonance Energy Transfer (FRET) microscopy, Fluorescence Lifetime Imaging microscopy (FLIM), and Fluorescence Recov- ery After Photobleaching (FRAP). For several decades, detection of microscopic images has been committed to ordinary photographic cameras using emulsion-based films as storage medium. Thanks to the rapid

improvement of photographic technology, in the last 20 years electronic imaging has gradually replaced conventional photomicrography. Initially, cameras were video rate cameras. This kind of camera makes use of light detectors based on vacuum-tube technology and generates an analog output signal that conforms to the industry standards RS-170, PAL, RGB, NTSC, etc. The electrical signal is usually recorded into analog signal storage devices as video recorders; however, to be sent to a computer for image analysis, it must be digitized by a frame grabber device. Actually, vacuum-tube-based detectors (photomultipliers) are used only in beam-scanning microscopy techniques. In recent years, video rate cameras have been replaced by cameras using a solid- state detector whose output is already a digital signal.

Solid-state detectors are two-dimensional arrays of pho- todiodes mainly manufactured according to CCD (charge-coupled device) or CMOS (complementary metal-oxide semiconductor) technology. High-level per- formance is expected from scientific grade digital cameras. According to the application of interest, some main features have to be taken into account like the following:

resolution, which mainly depends on the cross-sectional illuminated area of every photodiode (pixel); sensitivity mainly affected by the exposure time, the pixel area, and the quantum efficiency of the CCD; signal-to-noise ratio influenced by the readout noise, dependent on the CCD manufacturing, the electronics of the device, the readout speed, and thermal noise that can be reduced by cooling the sensitive chip of the camera; dynamic range being the ratio between the maximum light intensity observable without saturation of the CCD and the noise level.

Cross-References

▶Confocal Laser Scanning Fluorescence Microscopy

▶Fluorescence and FRET in Membranes

▶Fluorescence Three-Dimensional Optical Imaging

▶Fluorescence: General Aspects

▶FRAP

▶Two-Photon Excitation Fluorescence Microscopy

References

Bradbury S, Bracegirdle B. Introduction to light microscopy.

In: Royal microscopical society microscopy handbooks, vol 42. Oxford, United Kingdom: BIOS Scientific; 1998.

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Diaspro A. Confocal and two-photon microscopy: foundations, applications, and advances. New York: Wiley-Liss; 2002.

Diaspro A, editor. Optical fluorescence microscopy: from the spectral to the nano dimension. Heidelberg: Springer; 2010a. p. 1–244.

Diaspro A, editor. Nanoscopy and multidimensional optical fluorescence microscopy. Baco Raton: Taylor &Francis Group/A Chapman & Hall Book/CRC Press; 2010b. p. 1–448.

Haugland P. Handbook of fluorescence probes and research products. Eugene: Molecular Probes; 2002.

Herman B. Fluorescence microscopy. In: Royal microscopical society microscopy handbooks, vol 40. New York: BIOS Scientific/Springer-Verlag; 1998.

Mertz J. Introduction to optical microscopy. Greenwood Village: Roberts; 2009.

Pawley JB, editor. Handbook of biological confocal microscopy.

3rd ed. New York: Springer Science; 2006.

Periasamy A, editor. Methods in cellular imaging. Oxford, UK:

Oxford University Press; 2001.

Wolfbeis OS (ed). Fluorescence methods and applications: spectroscopy, imaging, and probes. Annals of the New York Academy of Sciences, Vol. 1130, Blackwell Pub. on behalf of the New York Academy of Sciences; 2008.

Optical Rotation

▶Carbohydrate Circular Dichroism

Optical Spectroscopy: Future Fourier Transform Spectroscopy

Theodor W. H€ansch^1,2and Nathalie Picque´^1,2,3

1Max Planck Institute for Quantum Optics, Garching, Germany

2Ludwig–Maximilians–University of Munich, Munich, Germany

3Institut des Sciences Mole´culaires d’Orsay, CNRS, Orsay, France

Synonyms

Infrared Spectroscopy;Femtosecond laser

Definition

Fourier transform spectroscopy with laser frequency combs is an emerging spectrometric technique without moving parts that allows to record broad spectral bandwidth spectra within very short acquisition times.

Introduction

Molecular spectroscopy proves an efficient tool for the determination of the structure of molecules, the quantitative analysis of complex mixtures, the investi- gation of dynamic systems, biomedical spectroscopy, micro-spectroscopy and hyperspectral imaging, and the study of many types of interfacial phenomena. To date, the overriding broad-spectral-bandwidth analytic spectroscopic instrument in the optical region of the electromagnetic spectrum with applications throughout the physical, chemical, and biological sciences has been the Michelson-based Fourier transform spectrometer (Griffiths and De Haseth 2007). Starting in the early seventies, Fourier transform spectroscopy has dramatically improved the quality of optical spectra and minimized the time required to obtain data. In addition, with constant improvements to computers, molecular spectroscopy has made further great strides.

An optical spectrometer can be deployed in a large number of roles, such as minimally invasive medical diagnostics, environmental and workplace monitoring, industrial real-time process control, and even security applications. However, the design of scanning Michel- son-based Fourier transform interferometers has hardly evolved since and the instrument no longer meets some of the demanding capabilities of modern physics and sensing. In particular, the use of incoherent light sources limits the sensitivity, the resolution is set by the excursion of a mechanical moving mirror, and the moving-mirror displacement speed determines the recording time, which ranges between seconds and hours depending on the desired resolution. In recent years, a new approach to Fourier transform spectroscopy has been proposed and implemented. The resulting interferometers without moving parts take advantage of laser frequency combs and do not involve anymore the scanning Michelson interferometer. They have recently demonstrated an intriguing potential for dramatic advances in molecular spectroscopy.

Laser Frequency Combs

An optical frequency comb (H€ansch 2006; Udem et al. 2002; Cundiff and Ye 2003; H€ansch and Picque 2012) produces an optical spectrum, which consists of several millions of perfectly evenly spaced spectral lines. Most of the time, the periodic pulse train

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generated by femtosecond mode-locked lasers is used for producing very broadband frequency combs. In the time domain (Fig. 1), the output of such lasers is a sequence of pulses that are essentially copies of the same pulse separated by the laser cavity round-trip time. In the frequency domain (Fig. 1), the separation between two modes or comb lines is just equal to the repetition frequency f_r. This remains true even if the pulses are not identical replicas but if a reproducible slip of the phase of the electromagnetic carrier wave relative to the pulse envelope from pulse to pulse is allowed for. Such phase slips occur in a laser because of dispersion in the cavity. The entire comb will then be shifted relative to the integer harmonics of the repetition frequency f_r by a carrier-envelope offset frequency f0, that equals the net phase slip modulo 2p per pulse interval. The frequency of a comb line with integer mode number n is then given by f_n¼n f_r+ f₀. The frequency of any comb line can be calculated from the two radio frequencies f_rand f₀together with the integer mode number n. Such a comb acts like a ruler in frequency space that can, for instance, be used to

measure a large separation between two different optical frequencies in terms of the pulse repetition frequency f_r.

The coherent nature of short pulses emitted by mode- locked lasers has hence led to a remarkable union of the two previously distinct fields of ultrafast optics and precision spectroscopy. Frequency combs can conveniently link optical and microwave frequencies, and they provide the long missing clockwork for optical atomic clocks. So far no fundamental limit of the accuracy of frequency combs has been discovered. By extending the limits of time and frequency metrology, they enable new tests of fundamental physics laws. Precise comparisons of optical resonance frequencies of atoms, ions, and molecules with the microwave frequency of a cesium atomic clock are establishing sensitive limits for possible slow variations of fundamental constants. Extensions of frequency comb techniques to new spectral regions from THz frequencies to the extreme ultraviolet are now under exploration and might open new spectral territories for precision spectroscopy. Emerging novel techniques for frequency comb generation include four wave mixing of

0 f_n = n f_r+ f_o

= f_r (n + ΔΠ/2π) I(f)

f

f_o f_r

Frequency domain E(t)

ΔΠ

τr.t = 1/f_r Time domain

t

Optical Spectroscopy: Future Fourier Transform Spectros- copy, Fig. 1 Time- and frequency-domain representation of the output of a laser frequency comb.Upper trace In the time domain, the output of a laser frequency comb consists of a periodic train of pulses. As the carrier wave moves with the phase velocity while the envelope moves with a different group velocity, the carrier wave shifts byDjafter each round trip with respect to the pulse envelope.Lower trace In the frequency domain, the spectrum (blue lines) of a frequency comb is

broad, as the spectral span is inversely proportional to the pulse duration. The spectrum is centered at the carrier frequency of the ultrashort pulses and consists of several hundred thousand perfectly evenly spaced spectral lines. The comb lines in the radio- frequency region (red lines) show that the continuous shift of the carrier wave results in a frequency offset f₀¼Dj/trt, which prevents the comb from being comprised of exact harmonics of the pulse repetition frequency f_r

Optical Spectroscopy: Future Fourier Transform Spectroscopy 1793

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whispering gallery modes in microscopic toroidal optical resonators (Kippenberg et al. 2011). It has also been quickly realized that important applications in many areas of science and technology could benefit from these exquisite laser sources. In particular, frequency comb techniques are providing a key to attosecond science by permitting control of the phase of the electric field of ultrashort laser pulses. The calibration of astro- nomical spectrographs with laser frequency combs will permit sensitive searches for earth-like planets, and precise interferometric distance measurements will allow new space missions with highly controlled formations of space vehicles. Here, we discuss the growing impor- tance of laser frequency combs in broadband molecular spectroscopy. Several approaches to molecular spectroscopy with frequency combs are being explored (Thorpe et al.2006; Adler et al.2010; Foltynowicz et al.2011;

Diddams et al.2007; Mandon et al. 2009); this entry focuses on the technique of dual-comb spectroscopy.

Dual-Comb Fourier Transform Spectroscopy The broad spectral bandwidth and the high-resolution structure of the frequency comb make it an attractive tool for broadband direct absorption molecular spectroscopy and fingerprinting. Dramatic advances in molecular science are foreseen for new spectroscopic methods based on frequency combs. Recent experiments of multi-heterodyne frequency comb Fourier transform spectroscopy (also called dual-comb spectroscopy)

have demonstrated that the precisely spaced spectral lines of a laser frequency comb can be harnessed for the rapid and sensitive acquisition of highly multiplexed spectra of molecules and have therefore the potential to vastly enhance the range and capabilities of molecular laser spectroscopy.

In an implementation of dual-comb spectroscopy (Fig. 2), an absorbing sample is interrogated by a frequency comb laser source. The information encoded by this interrogating comb then needs to be retrieved by a spectrometer. This is achieved by heterodyning the interrogating comb with a second comb, which serves as a reference: The two lasers beat against each other and the resulting interference signal is monitored as a function of time. It provides simultaneous and accurate access to a broad spectral bandwidth within a short measurement time and can physically be equally understood in terms of time-domain interferences, multi-heterodyne detection, optical free induction decay, linear optical sampling, or cross-correlation between two electric fields. In practice, the light transmitted by the sample is superimposed on a second frequency comb with slightly different repetition frequency. A single fast photodetec- tor then produces an output signal with a comb of radio frequencies due to interference between pairs of optical comb lines. In the frequency domain (Fig. 3a), the optical spectrum is thus effectively mapped into the radio- frequency regime, where it becomes accessible to fast digital signal processing. In the time domain (Fig. 3b), the pulse train of the interrogating comb excites the absorbing sample at regular time intervals. A second cell

D.

1/δ

1/frep,1 1/frep, 2

Optical Spectroscopy: Future Fourier Transform Spectros- copy, Fig. 2 Two nearly identical frequency combs, 1 and 2, are used: They have the same spectral and temporal properties, except that their line spacings (i.e., pulse repetition frequency) slightly differ. One of these combs, 1, is transmitted through the

cell and heterodyned against the second comb, yielding a down- converted radio-frequency comb containing information on the absorption and dispersion experienced by each line of the comb 1. Other implementations allow the two combs to interrogate the sample

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pulse train of different repetition frequency interferomet- rically samples the transient response or “free induction decay” of the medium, akin to an optical sampling oscil- loscope. The detector time-domain signal therefore carries, in addition to the signal from each laser at the pulse repetition frequency (which can easily be fil- tered out), the cross-correlation signal resulting from

interference between pulse pairs from the two lasers.

Here the phase correlations between successive laser pulses are crucial for reproducible sampling, even if the free induction decay happens on a time scale that is short compared to the time interval between two laser pulses.

The first low-resolution proof-of-principle experiment has been performed in 2004 with unstabilized f_r2

f_2,n f_1,n

f_{r1 =}f_r2(1+a)

Df_rep=a f_r2

optical frequencies TeraHertz

Down-converted frequencies

a

b

Radiofrequencies Downconversion

factor a = (f_r1-f_r2)/f_r2

FC2

FC2 time

time FC1

FC1 I(t)

I(t) Optical Spectroscopy:

Future Fourier Transform Spectroscopy,

Fig. 3 Physical principle of frequency comb Fourier transform spectroscopy. The repetition frequency of the two lasers is respectively f_r1and f_r2 and they differ byDfr<< f_r1.

The technique requires to keep constant the differences f_r1f_r2and f₀₁f₀₂during the measurement or to monitor their variations to synchronize the data acquisition or to make a posteriori corrections. (a) In the frequency domain, the reference comb 2 with f_r2 line spacing acts as a highly multiplexed heterodyne receiver to generate a radio-frequency comb. The radio-frequency comb can be straightforwardly digitally processed, whereas in the optical domain, there are no means to directly count frequencies. As the comb parameters f_r1,f_r2,f₀₁,f₀₂may be also directly counted, measuring the radio-frequency comb makes it possible to a posteriori calibrate the optical frequency scale. (b) In the time domain, the reference comb FC2 pulse train slowly walks through the

interrogating pulses from FC1 to generate a measurement I(t) of the interrogating electric field. Each point of I(t) results from the interference between a pair of pulses. Only a few pairs of such pulses are represented for clarity

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mode-locked lasers (Keilmann et al.2004), and a few groups have been contributing since in the THz (Yasui et al.2005) or infrared region (Schliesser et al.2005;

Bernhardt et al.2010a,2010b; Coddington et al.2008, 2010; Ideguchi 2012; Giaccari et al.2008; Baumann et al.2011; Jacquet et al.2009).

These first implementations have demonstrated a very exciting potential of dual-comb spectroscopy without moving parts for ultrarapid and ultrasensitive recording of complex molecular spectra. Compared to conventional Michelson-based Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds, with intriguing prospects for spectroscopy of short-lived transient species or for hyperspectral imaging. The resolution improves proportionally to the measurement time. Therefore, longer recordings allow high-resolution spectroscopy of molecules with extreme precision, since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock. Selected experimental examples illustrate these features in the next paragraph.

Experimental Illustrations of Dual-Comb Fourier Transform Spectroscopy

An experiment (Jacquet et al.2009) carried out in the telecommunication region may first be used to high- light an important benefit of dual-comb spectroscopy.

Two 1,550-nm Er-doped fiber lasers emit 90 fs pulses at a repetition frequency of the order of 100 MHz and 20 mW average output power. The difference between the repetition rates of the two combs is set to a value ranging between 10 Hz and 20 kHz. For Doppler-limited resolution, the combs can be let free running, while higher resolutions could only be reached with an active stabilization. The available spectral domain is limited by the Er-doped fiber oscil- lators to500 cm¹. A single comb interrogates the cell, which is filled with acetylene. The two comb beams are recombined with a 50–50 beam-mixer.

They beat on a fast InGaAs photodiode and the electric signal is amplified and digitized.

The upper part of Fig. 4 shows an experimental interferogram. Due to the slight mismatch between the constant repetition frequencies of the pulses of the two combs, the interferogram repeats itself at a period which is the inverse of the difference in the

repetition frequencies of the two lasers. Strong bursts occur when pulses from the two lasers overlap. On one side of these bursts, the modulation of the interferogram, zoomed on in the second row ofFig. 4, is due to the molecular signatures. When a single comb interrogates the sample, the resulting interferometer can indeed be viewed as the equivalent of a dispersive Fourier transform Michelson interferometer, in which the sample is placed in one arm of the spectrometer.

The Fourier transform of a small part of the interferogram time sequence reveals the spectrum.

A spectrum of acetylene in the region of then1+ n3

overtone band spanning 470 cm¹is measured within a single recording of 42ms, which brings a unapodized resolution of 0.18 cm¹. For comparison, recording such a spectrum with a conventional Fourier transform spectrometer requires more than 10 s. The method indeed demonstrates, when compared to Michelson- based FT spectroscopy, a million-fold improvement in recording times at identical signal-to-noise ratio.

Furthermore, due to the periodic structure of the interferogram, one can analyze spectral information at rates above 200 Hz for spectral resolutions at best equal to the comb line spacing. Techniques to increase the refresh rate by changing the difference in repetition frequencies of the two lasers have been proposed, resulting in an intriguing potential for time-resolved spectroscopy of single events.

The sensitivity of molecular fingerprinting with dual-comb spectroscopy is dramatically improved when the absorbing sample is placed in a high-finesse optical cavity, because the effective path length is increased. When the equidistant lines from a laser frequency comb are simultaneously injected over a large spectral range into the cavity holding the gas sample, multiple trace gases may be identified within a few tens of microseconds. The cavity finesse determines the enhancement factor for the intracavity absorption signal. Using femtosecond Yb-doped femtosecond fiber lasers that emit around 1.0mm, weak overtone molecular transitions could be probed with high sensitivity.

As an experimental demonstration, the rovibrational spectrum of ammonia, a molecule of astrophysical and environmental interests, is recorded in the region of the 3n1band. The cavity finesse F> 1,200 enhances the effective absorption length to 880 m. InFig. 5, the cavity transmission spans about 20 nm and the spectrum consisting of 1,500 spectral elements, with 4.5 GHz

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resolution and a signal-to-noise ratio of 380, is measured within 18ms. The weak overtone transitions of the 3n₁ band are rotationally resolved for the first time, to our knowledge. The minimum-detectable-absorption coeffi- cienta_min and the noise-equivalent absorption coeffi- cient at 1 s time averaging are 3 10⁸ cm¹ and 1 10¹⁰ cm¹ Hz^1/2, respectively. This proof-of- principle experiment (Bernhardt et al.2010a) already demonstrates, with a 100-fold shorter measurement

time, aa_mincoefficient, which is 20-fold better than the one reported in (Thorpe et al.2006). The spectral bandwidth is presently limited by the Ytterbium amplifier.

However, special mirror design managing dispersion has demonstrated to overlap the cavity modes and the comb components across 100 nm simultaneously and the multiplex spectrometer principle allows for the measurement of multi-octave spanning spectra. Therefore, a bandwidth of 100 nm should easily be achievable by NH₃

9670 cm⁻¹ Wavenumber 9470 cm⁻¹

Optical Spectroscopy: Future Fourier Transform Spectros- copy, Fig. 5 Cavity-enhanced spectrum of the crowded region of the 3n1overtone band of ammonia. These weak transitions are

observed at high resolution for the first time to our knowledge and are of interest for the modeling of radiative transfer in the atmospheres of the giant Jovian planets

Time domain

Frequency domain Fourier transformation 4.5 ms

86 ms

1 μs 42 μs

0 ms

6250

6493 6610

C₂H₂

(cm⁻¹) 6720

Optical Spectroscopy: Future Fourier Transform Spectros- copy, Fig. 4 The upper part of the figure displays a typical interferogram. It reproduces periodically, with a period equal to 1/Dfr. Depending on the desired optical resolution, the Fourier transform (FT) of only a portion of this sequence is calculated.

For instance, the FT of an interferogram of 42ms duration is

enough to resolve the Doppler-broadened profiles of the molecular sample, as shown on the lower part of the figure. The entire emission domain of the Erbium-fiber lasers is represented. The last row of the figure shows a zoom on then1 +n3 band of acetylene, at 3 GHz unapodized resolution, resulting from a 42ms measurement without averaging

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the spectral broadening of the combs with highly nonlinear optical fibers.

Frequency combs proved a revolutionary tool for frequency metrology. In dual-comb spectroscopy, increasing the measurement time and including in the Fourier transform calculation a sequence which com- prises more than two bursts (upper part of Fig. 4) enables to resolve the individual comb lines (Fig. 6).

The resulting spectra (Jacquet et al.2009) are sampled by combs of 100-MHz line spacing that may cover domains of tens of nm with comb lines exhibiting kHz optical linewidth. A dense grid of accurate frequency markers therefore allows precise self-calibration of the wavenumber scale. However, the molecular spectra are sampled by the comb line spacing, with a step equal to the repetition frequency. As f_rmost often lies between 50 MHz and 200 MHz, most of molecular profiles at room temperature in the gas phase are appropriately sampled by the line spacing of the comb. In case better resolutions would be needed, interleaving techniques may sample the spectra down to the ultimate optical resolution imposed by the width of the comb lines.

The demanding conditions on the stability of the pulse repetition frequency and carrier-envelope pulse- to-pulse phase slip presently impede the realization of the full capabilities of dual-comb spectroscopy for real-time applications. To record a distortion-free real-time interferogram, the timing jitter between subsequent pulses must indeed be kept lower than 10 as. As a consequence, the interferograms may have to be averaged (Coddington et al.2008; Baumann et al.2011) over several seconds with combs stabilized

against state-of-the-art cavity-stabilized continuous- wave lasers with a hertz-level line-width or a posteriori corrections (Giaccari et al.2008) requiring multiple data acquisition channels and additional computational time may be performed, thus preventing fast acquisition rates.

A new concept of real-time dual-comb spectroscopy that enables to record high quality spectra with free- running femtosecond lasers has been recently introduced (Ideguchi2012). It does not require phase-lock electronics or a posteriori computer processing. The quality of the results far exceeds that of frequency comb systems stabilized against radio-frequency references and this new scheme, called adaptive dual-comb spectroscopy, might represent an important step toward the dissemina- tion of dual-comb spectroscopy to communities unfamiliar with the sophisticated tools of frequency metrology.

Conclusion and Outlook

Dual-comb spectroscopy holds much promise for establishing the basis of a revolutionary spectroscopic tool: As with any Fourier transform spectrometer, the spectral span is only limited by the source and single detector spectral bandwidth. Overall consistency of the simultaneously measured spectral elements that may prove crucial when, e.g., investigating unstable molecular species is granted by the multiplex advantage. Much improved signal-to-noise ratios and reduced measurement times are provided by the high spectral radiance of frequency comb sources. The absence of moving parts overcomes the speed and resolution limitations of the C₂H₂ν1+ν3 band

6485 cm⁻¹

2 cm⁻¹ Optical Spectroscopy:

Future Fourier Transform Spectroscopy,

Fig. 6 Portion of a spectrum of acetylene in the region of the Pe(27) line of then1 +n3 band with two different resolutions. In the upper trace, the resolution of 100 MHz is suitable for the Doppler- broadened profiles. In the lower trace, the comb lines are resolved (2.3 kHz linewidth, 100 MHz spacing) and their intensities are shaped by the acetylene profiles

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Michelson-based approach. The comb structure of the spectrum dramatically improves the detection sensitivity via optimal use of cavity-enhanced techniques. Self- calibration of the frequency scale of the spectra is achieved when the comb lines are resolved. Furthermore, compact high-resolution instruments may be designed and one may even envision a chip-size dual-comb spectrometer based on microresonators (Wang2011) for real-time spectroscopy in the liquid phase. Dual-comb Fourier transform spectroscopy may be combined with, e.g., hyperspectral imaging, microscopy, or temporal resolution, while keep- ing their already demonstrated capabilities. Since laser frequency combs involve intense ultrashort laser pulses, nonlinear interactions can additionally be harnessed and the combination of coherent control and high-sensitivity broadband frequency comb spectroscopy might be envisioned. Frequency comb Fourier transform spectroscopy might therefore open up new insights in the under- standing of the structure of matter as well as new horizons in advanced nonintrusive instruments, for instance, in chemistry or biomedicine. However, dual-comb spectroscopy is still in its infancy and requires considerable efforts to express its full potential. Several technically challeng- ing issues, like the development of suitable comb sources in the “molecular fingerprint” mid-infrared and ultraviolet regions, have to be overcome. Significant insights and improvements are also needed before the technique can spread throughout scientific communities unfamiliar with advanced ultrashort laser and frequency metrology instruments.

Summary

The advent of laser frequency combs a decade ago has already revolutionized optical frequency metrology and precision spectroscopy. Extensions of laser combs from the THz region to the extreme ultraviolet and soft x-ray frequencies are now under exploration. Such laser combs have become enabling tools for a growing tree of applications, from optical atomic clocks to attosecond science. Recently, the millions of precisely controlled laser comb lines that can be produced with a train of ultrashort laser pulses have been harnessed for highly multiplexed molecular spectroscopy. Fourier spectroscopy, multi-heterodyne spectroscopy, and asynchro- nous optical sampling spectroscopy with frequency combs are emerging as powerful new spectroscopic tools. The first proof-of-principle experiments have

demonstrated a very exciting potential of dual-comb spectroscopy for ultrarapid and ultrasensitive recording of complex molecular spectra. Compared to conventional Fourier transform spectroscopy, recording times could be shortened from seconds to microseconds, with intriguing prospects for spectroscopy of short-lived transient species or for hyperspectral imaging. Longer recording times allow high-resolution spectroscopy of molecules with extreme precision, since the absolute frequency of each laser comb line can be known with the accuracy of an atomic clock.

Cross-References

▶Fourier Transform Infrared Spectroscopy for Biophysical Applications: Technical Aspects

▶Molecular Vibrations and Their Interaction with Electromagnetic Radiation

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