Dustin W. Shipp, Faris Sinjab, and Ioan Notingher, "Raman spectroscopy: techniques and applications in the life sciences," Adv. Opt. Photon. 9, 315-428 (2017)

Raman spectroscopy is an increasingly popular technique in many areas, including biology and medicine. It is based on Raman scattering, a phenomenon in which incident photons lose or gain energy via interactions with vibrating molecules in a sample. These energy shifts can be used to obtain information regarding molecular composition of the sample with very high accuracy. Applications of Raman spectroscopy in the life sciences have included quantification of biomolecules, hyperspectral molecular imaging of cells and tissue, medical diagnosis, and others. This review briefly presents the physical origin of Raman scattering, explaining the key classical and quantum mechanical concepts. Variations of the Raman effect will also be considered, including resonance, coherent, and enhanced Raman scattering. We discuss the molecular origins of prominent bands often found in the Raman spectra of biological samples. Finally, we examine several variations of Raman spectroscopy techniques in practice, looking at their applications, strengths, and challenges. This review is intended to be a starting resource for scientists new to Raman spectroscopy, providing theoretical background and practical examples as the foundation for further study and exploration.

Duo Lin, Hao Huang, Sufang Qiu, Shangyuan Feng, Guannan Chen, and Rong Chen Opt. Express 24(3) 2222-2234 (2016)

References

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Character Table for Point Group ${\mathsf{D}}_{\infty \mathsf{h}}$ Showing Behavior of Irreducible Representations under Symmetry Operations^{a}

${D}_{\infty h}$

$E$

$2{C}_{\infty}$

$\infty {\sigma}_{v}$

$i$

$2{S}_{\infty}$

$\infty {C}_{2}$

${A}_{1g}$

1

1

1

1

1

1

${A}_{2g}$

1

1

−1

1

1

−1

${E}_{1g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

2

$-2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

${E}_{2g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

${E}_{3g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

2

$-2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

${A}_{1u}$

1

1

1

−1

−1

−1

${A}_{2u}$

1

1

−1

−1

−1

1

${E}_{1u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

−2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

${E}_{2u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

−2

$-2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

${E}_{3u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

−2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

${\mathrm{CO}}_{2}$ is a member of this point group, so the irreducible representations describe vibrational modes of this linear molecule.

Table 2.

Character Table for Point Group ${\mathsf{D}}_{\infty \mathsf{h}}$ Showing Linear, Rotational, and Quadratic Transformations of Irreducible Representations

${\mathsf{D}}_{\infty \mathsf{h}}$

Linear

Rotation

Quadratic

${A}_{1g}$

—

—

${x}^{2}+{y}^{2}$, ${z}^{2}$

${A}_{2g}$

—

${R}_{z}$

—

${E}_{1g}$

—

${R}_{x}$, ${R}_{y}$

${x}^{2}$, ${y}^{2}$

${E}_{2g}$

—

—

${x}^{2}-{y}^{2}$, $xy$

${E}_{3g}$

—

—

—

${A}_{1u}$

$z$

—

—

${A}_{2u}$

—

—

—

${E}_{1u}$

$x$, $y$

—

—

${E}_{2u}$

—

—

—

${E}_{3u}$

—

—

—

Table 3.

Assignments for Major Raman Bands Associated with Nucleic Acids

Finds variables responsible for variance between spectra

no

none

high

Cluster analysis

Identifies groups of similar spectra

no

none

medium

Linear discriminant analysis (LDA)

Separates classes using linear boundary

yes

binary classes

low

Logistic regression

Separates classes using logarithmic boundary

yes

classes

medium

Support vector machines (SVM)

Maximizes separation between classes using higher-order boundary

yes

classes

high

Decision tree (incl. random forest)

Classifies spectra based on series of binary decisions

yes

classes

high

Partial least squares (PLS)

Identifies spectral features correlated to training values

yes

numerical value (e.g., concentration)

medium

Artificial neural network (ANN)

Calculations through a series of “neurons”

yes

classes or numerical value

high

Ant colony optimization

Paths to successful models attract subsequent paths

yes

fitness parameter

high

Genetic algorithm

Model parameters “evolve” to succeeding generations

yes

fitness parameter

high

High sensitivity indicates that the method is capable of distinguishing smaller differences between spectra but also has a higher tendency for over-training.

Tables (8)

Table 1.

Character Table for Point Group ${\mathsf{D}}_{\infty \mathsf{h}}$ Showing Behavior of Irreducible Representations under Symmetry Operations^{a}

${D}_{\infty h}$

$E$

$2{C}_{\infty}$

$\infty {\sigma}_{v}$

$i$

$2{S}_{\infty}$

$\infty {C}_{2}$

${A}_{1g}$

1

1

1

1

1

1

${A}_{2g}$

1

1

−1

1

1

−1

${E}_{1g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

2

$-2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

${E}_{2g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

${E}_{3g}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

2

$-2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

${A}_{1u}$

1

1

1

−1

−1

−1

${A}_{2u}$

1

1

−1

−1

−1

1

${E}_{1u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

−2

$2\text{\hspace{0.17em}}\mathrm{cos}(\varphi )$

0

${E}_{2u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

−2

$-2\text{\hspace{0.17em}}\mathrm{cos}(2\varphi )$

0

${E}_{3u}$

2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

−2

$2\text{\hspace{0.17em}}\mathrm{cos}(3\varphi )$

0

${\mathrm{CO}}_{2}$ is a member of this point group, so the irreducible representations describe vibrational modes of this linear molecule.

Table 2.

Character Table for Point Group ${\mathsf{D}}_{\infty \mathsf{h}}$ Showing Linear, Rotational, and Quadratic Transformations of Irreducible Representations

${\mathsf{D}}_{\infty \mathsf{h}}$

Linear

Rotation

Quadratic

${A}_{1g}$

—

—

${x}^{2}+{y}^{2}$, ${z}^{2}$

${A}_{2g}$

—

${R}_{z}$

—

${E}_{1g}$

—

${R}_{x}$, ${R}_{y}$

${x}^{2}$, ${y}^{2}$

${E}_{2g}$

—

—

${x}^{2}-{y}^{2}$, $xy$

${E}_{3g}$

—

—

—

${A}_{1u}$

$z$

—

—

${A}_{2u}$

—

—

—

${E}_{1u}$

$x$, $y$

—

—

${E}_{2u}$

—

—

—

${E}_{3u}$

—

—

—

Table 3.

Assignments for Major Raman Bands Associated with Nucleic Acids

Finds variables responsible for variance between spectra

no

none

high

Cluster analysis

Identifies groups of similar spectra

no

none

medium

Linear discriminant analysis (LDA)

Separates classes using linear boundary

yes

binary classes

low

Logistic regression

Separates classes using logarithmic boundary

yes

classes

medium

Support vector machines (SVM)

Maximizes separation between classes using higher-order boundary

yes

classes

high

Decision tree (incl. random forest)

Classifies spectra based on series of binary decisions

yes

classes

high

Partial least squares (PLS)

Identifies spectral features correlated to training values

yes

numerical value (e.g., concentration)

medium

Artificial neural network (ANN)

Calculations through a series of “neurons”

yes

classes or numerical value

high

Ant colony optimization

Paths to successful models attract subsequent paths

yes

fitness parameter

high

Genetic algorithm

Model parameters “evolve” to succeeding generations

yes

fitness parameter

high

High sensitivity indicates that the method is capable of distinguishing smaller differences between spectra but also has a higher tendency for over-training.