The many faces of Raman: confocal, FT, resonance, SERS, TERS, CARS, SRS and SORS

This is the third article in the series. It assumes the ideas of the second, Vibrational spectroscopy, plasmonics and SERS, from first principles — in particular how Raman scattering arises from a vibration that modulates the polarisability, and how a metal nanoparticle concentrates light. Where those are needed, the link points there rather than repeating them. Numbers in square brackets refer to the references.

01The starting point: spontaneous Raman and its five limits

When light of frequency \(\omega_L\) meets a molecule, its electric field \(\mathbf E\) induces a dipole \(\mathbf p = \alpha\mathbf E\), where \(\alpha\) is the polarisability. If a vibration of frequency \(\omega_v\) changes \(\alpha\), the dipole oscillates also at \(\omega_L \pm \omega_v\) and radiates there: the Stokes and anti-Stokes Raman lines [1, 2] (derived step by step in the first article). The power scattered by \(N\) molecules into the detector is

$$P_\text{Raman} = N\,\sigma\,I_L\,\eta, \qquad \sigma \propto \omega_s^4\,\Big|\frac{\partial\alpha}{\partial Q}\Big|^2 ,$$

where \(\sigma\) is the Raman cross-section of the band, \(I_L\) the laser intensity (power per area), \(\eta\) the collection and detection efficiency, \(\omega_s\) the scattered frequency and \(Q\) the vibrational coordinate. Because each molecule acts alone and with a random phase, the signal is incoherent: it grows in proportion to \(N\) and goes out in all directions.

That simple picture already contains five limits:

1. Weak signal. Typical cross-sections are about 10⁻³⁰–10⁻²⁹ cm² per molecule, some 10¹⁴ times smaller than the absorption cross-section of a good dye. Roughly one photon in 10⁷–10⁹ is Raman-scattered.
2. Fluorescence. If the laser is absorbed by anything in the sample, its fluorescence — far stronger — can bury the Raman bands completely.
3. Diffraction. A lens cannot focus light below about half a wavelength, so ordinary Raman cannot resolve structures smaller than a few hundred nanometres.
4. Surface only. In turbid samples (tissue, powders, plastics) light is scattered within a fraction of a millimetre, and a conventional instrument mostly sees the surface.
5. Speed. With weak, incoherent signals, a good spectrum takes 0.1–10 s, so a 500 × 500 pixel image takes hours.

Each variant below attacks one or two of these limits — and usually pays for it with another.

02A map of the variants

The sections follow the order in which the problems usually appear in practice: first find where to measure, then get rid of fluorescence, then make the signal stronger, then make it fast, and finally reach below the surface.

03Confocal Raman microscopy — where in the sample?

Why it is needed

A macro Raman probe collects light from a volume of perhaps a cubic millimetre. For a single cell, a multilayer film or an inclusion in a crystal, that averages the interesting part with everything around it. Confocal Raman microscopy (CRM) makes each spectrum come from a volume of about a cubic micrometre, and so turns spectroscopy into chemical imaging in three dimensions — the method behind single-cell Raman since the work on living cells and chromosomes in 1990 [3].

How it works

A high-numerical-aperture objective focuses the laser to a diffraction-limited spot. The scattered light is imaged back onto a small pinhole (or the core of a fibre, or a slit and a few CCD rows) placed in a plane conjugate to the focus. Light from the focal spot passes; light from above or below the focus arrives defocused and is mostly blocked. Scanning the sample or the beam then builds an image, and moving the focus builds depth profiles. For an ideal confocal system with a small pinhole the resolutions (full width at half maximum) are approximately

$$\delta_\text{lat} \approx 0.37\,\frac{\lambda}{\mathrm{NA}}, \qquad \delta_\text{ax} \approx \frac{0.64\,\lambda}{n - \sqrt{n^2 - \mathrm{NA}^2}} ,$$

where \(\lambda\) is the wavelength (of the Raman light), NA the numerical aperture of the objective (\(\mathrm{NA} = n\sin\theta\), with \(\theta\) the half-angle of the cone of light it accepts) and \(n\) the refractive index of the immersion medium. With 532 nm excitation and NA 0.9 in air, \(\delta_\text{lat}\) is about 230 nm and \(\delta_\text{ax}\) about 0.6 µm — in practice 1.5–2 times worse with a realistic pinhole.

Figure 1 · Interactive

Advantage over plain Raman, and the catches

The gain is localisation: maps of lipid droplets, nuclei and mitochondria in a living cell, layers in a polymer laminate, phases in a mineral. The catches are worth knowing. Mapping is slow (one spectrum per voxel), which coherent Raman will address below. And when a dry objective focuses into a sample of higher refractive index, refraction stretches and shifts the focal volume: apparent depths and thicknesses of buried layers can be wrong by a factor of about two, and the depth resolution much worse than the formula suggests — oil or water immersion matched to the sample helps a great deal [4].

04Why fluorescence buries Raman

Fluorescence is absorption followed by emission. Its strength is the absorption cross-section times the fluorescence quantum yield \(\Phi_F\): for a dye about \(10^{-16}\ \text{cm}^2 \times \Phi_F\). Raman is a scattering process with \(\sigma \approx 10^{-30}\) cm². Even an impurity with \(\Phi_F = 10^{-4}\) at a concentration 10⁶ times lower than the analyte gives a fluorescence background comparable to, or larger than, the Raman signal — and its shot noise remains even after the smooth background is subtracted. The noise on a background of \(B\) counts is \(\sqrt B\), so the signal-to-noise ratio of a Raman band with \(S\) counts is

$$\mathrm{SNR} = \frac{S}{\sqrt{S + B + D}},$$

with \(D\) the detector noise contribution. A background a hundred times stronger than the band reduces the SNR about tenfold, however long you measure. Biological samples, polymers, pharmaceuticals and many minerals fluoresce under visible excitation. There are three ways out: excite where nothing absorbs (the near-infrared — next section), excite so far in the ultraviolet that fluorescence is emitted well away from the Raman lines (deep-UV Raman), or use the timing or the shape of the signal (pulsed gating, shifted-excitation subtraction). The figure shows the trade-offs as a function of the laser wavelength.

Figure 2 · Interactive

05FT-Raman — escaping fluorescence at 1064 nm

Why it is needed

Very few molecules absorb at 1064 nm, the line of the Nd:YAG laser: electronic transitions of organic molecules and most impurities lie at shorter wavelengths. Exciting there removes most fluorescence at its source, which made Raman routine for dyes, polymers, natural products and pharmaceuticals in the 1980s and 1990s.

The price, and why Fourier transform

Two penalties come with 1064 nm. The ν⁴ factor: compared with 785 nm, a band at 1000 cm⁻¹ is about 4 times weaker, compared with 532 nm about 20 times (the ratio of the fourth powers of the scattered frequencies). And the Raman light, at 1100–1500 nm, lies beyond the sensitivity of silicon detectors; InGaAs or cooled germanium detectors are noisier. A dispersive spectrometer with a single noisy detector would have to scan the spectrum point by point and would collect most of the time only one wavelength. A Michelson interferometer instead sends all wavelengths to the detector at once, with a large circular aperture rather than a slit — the multiplex (Fellgett) and throughput (Jacquinot) advantages described for FTIR in the spectroscopy article. When the detector noise dominates, measuring everything at once wins, which is exactly the near-infrared Raman situation [5]. The spectrum is recovered as the cosine transform of the interferogram, and the wavenumber axis is calibrated by a reference laser.

Advantage over visible dispersive Raman

Fluorescence-free spectra of strongly fluorescent samples, excellent wavenumber accuracy, and a large sampling volume (useful for heterogeneous solids). The disadvantages: weaker signal, larger laser powers (heating of dark samples), lower spatial resolution, and water absorption overtones near 1.4 µm. Today 785 nm dispersive Raman with deep-depletion silicon CCDs is the usual compromise; 1064 nm is chosen when 785 nm still fluoresces, increasingly with dispersive InGaAs arrays as well as FT instruments.

06Resonance Raman — borrowing an electronic transition

Why it is needed

FT-Raman removes the background but leaves the signal weak. The opposite strategy is to make the signal stronger by moving the laser towards an electronic absorption of the molecule of interest.

From first principles

Quantum mechanically, the Raman polarisability for a transition from the initial vibrational state \(|i\rangle\) to the final state \(|f\rangle\) is a sum over all excited states \(|r\rangle\) — the Kramers–Heisenberg–Dirac expression [6]:

$$\alpha_{\rho\sigma} = \frac{1}{\hbar}\sum_r\left[\frac{\langle f|\mu_\rho|r\rangle\langle r|\mu_\sigma|i\rangle}{\omega_{ri} - \omega_L - i\Gamma_r} + \frac{\langle f|\mu_\sigma|r\rangle\langle r|\mu_\rho|i\rangle}{\omega_{rf} + \omega_L + i\Gamma_r}\right] ,$$

where \(\mu_\rho, \mu_\sigma\) are components of the dipole-moment operator, \(\omega_{ri}\) the frequency of the transition from \(|i\rangle\) to \(|r\rangle\), \(\Gamma_r\) the damping (line width) of state \(r\), and \(\hbar\) the reduced Planck constant. Far from any absorption all terms are small and comparable — ordinary Raman. When \(\omega_L\) approaches an electronic transition, the first denominator nearly vanishes and that state dominates. In the Albrecht “A-term” approximation [6] the enhanced amplitude is

$$\alpha_A \propto \frac{|\mu_{eg}|^2}{\hbar}\sum_v \frac{\langle f|v\rangle\langle v|i\rangle}{\omega_{vi} - \omega_L - i\Gamma} ,$$

with \(\mu_{eg}\) the electronic transition dipole and \(\langle f|v\rangle\) Franck–Condon overlaps between ground- and excited-state vibrational levels \(v\). Only vibrations whose equilibrium geometry changes in the excited state (displaced oscillators) have large overlaps — so resonance Raman is enhanced by 10³–10⁶ and, just as importantly, selective: it shows the vibrations of the chromophore and hides the rest of the sample.

Advantage over plain Raman, and the costs

The heme of haemoglobin or cytochromes, carotenoids, retinal in rhodopsin and many dyes give strong, selective spectra at micromolar concentrations; deep-UV excitation (around 200–260 nm) puts aromatic amino acids, the peptide backbone and nucleobases in resonance, while fluorescence is emitted far to the red of the Raman lines [7]. The costs: the sample absorbs the laser (photodegradation, heating), fluorescence is usually close by in the visible, the spectrum can be self-absorbed, and a tunable or UV laser is often needed. Resonance and SERS combine in SERRS, used for the brightest SERS tags (Raman reporters).

07SERS — borrowing a plasmon

Resonance requires a chromophore. Surface-enhanced Raman scattering enhances any molecule close enough to a gold or silver nanostructure: the localised surface plasmon concentrates the field, and the enhancement of the Raman intensity scales roughly as the fourth power of the local field,

$$G_\text{SERS} \approx \left|\frac{E_\text{loc}(\omega_L)}{E_0}\right|^2\left|\frac{E_\text{loc}(\omega_s)}{E_0}\right|^2 \approx \left|\frac{E_\text{loc}}{E_0}\right|^4 ,$$

where \(E_0\) is the incident field and \(E_\text{loc}\) the local field at the molecule [8, 9]. Average enhancements are 10⁴–10⁸; in the narrow gaps between particles (“hot spots”) they reach 10¹⁰, enough for single molecules [10, 11]. Metals also quench fluorescence. The physics is derived in the spectroscopy article; the chemistry — how molecules reach the surface, Raman reporters, quantification — is the subject of the next one, Label-free and labelled SERS.

Advantage over resonance Raman: no chromophore needed, larger enhancement, fluorescence quenched. Costs: the molecule must be within a few nanometres of the metal, the enhancement varies strongly from spot to spot, and the spectrum reports only what adsorbs — and it tells you nothing about where on the surface the signal came from.

08TERS — a hot spot you can move

Why it is needed

A SERS substrate has millions of hot spots at unknown places, and the far-field optics that collect the light are still limited by diffraction. Tip-enhanced Raman scattering puts a single hot spot at the apex of a sharp gold or silver tip — an atomic-force or scanning-tunnelling microscope probe — and scans it over the sample [12]. The Raman signal is now enhanced only under the tip, so the spatial resolution is set by the size of the apex and the tip–sample gap, not by the wavelength.

How it works

The laser illuminates the tip with its field along the tip axis; the tip apex acts as an optical antenna, and in the gap between the tip and a metal substrate (“gap mode”) the field is strongest. The enhancement follows the same \(|E_\text{loc}/E_0|^4\) law as SERS, with typical values of 10³–10⁷. Because the laser spot also produces ordinary Raman from the surrounding area, two quantities are used: the measured contrast and the enhancement factor it implies,

$$C = \frac{I_\text{tip in}}{I_\text{tip out}} - 1, \qquad \mathrm{EF}_\text{TERS} = C\,\frac{A_\text{focus}}{A_\text{tip}} ,$$

where \(I_\text{tip in}\) and \(I_\text{tip out}\) are the signals with the tip engaged and retracted, and \(A_\text{focus}/A_\text{tip}\) the ratio of the laser focus area to the area under the tip. A contrast of only 1 from a 10 nm tip in a 500 nm focus already means an enhancement of about 2500: the near-field signal must beat the far-field signal from a far larger area.

Advantage over SERS, and the costs

Chemical imaging at 10–20 nm under ambient conditions, and in ultra-high vacuum at low temperature down to sub-nanometre resolution, resolving the inside of a single molecule [13]. TERS images carbon nanotubes, graphene defects, DNA, membranes and catalytic surfaces molecule by molecule. The costs are practical ones: tips are hard to make reproducibly and degrade, scans are slow, topography and optical signals can mix, and the near-field signal from a monolayer is weak in absolute terms.

09Coherent Raman — driving the molecules in step

All the methods so far keep Raman scattering spontaneous: each molecule scatters independently, so the signal is weak and imaging is slow. Coherent Raman scattering takes a different route. Two lasers, a pump at \(\omega_p\) and a Stokes beam at \(\omega_s\), are tuned so that their difference matches a vibration, \(\omega_p - \omega_s = \Omega_R\). The beat between the two fields drives that vibration like a pushed swing — all molecules in the focus oscillate in phase. Their scattered fields then add coherently: the signal grows as \(N^2\) instead of \(N\), goes into a well-defined direction, and needs no spectrometer for imaging at one band.

The response is described by the third-order nonlinear susceptibility \(\chi^{(3)}\), the material property that relates the induced polarisation to the product of three fields. Near a Raman band it has a resonant part with a Lorentzian shape and a non-resonant part \(\chi_\text{NR}\) from the electrons of every molecule, resonant or not:

$$\chi^{(3)}(\omega_p - \omega_s) = \chi_\text{NR} + \frac{A}{\Omega_R - (\omega_p - \omega_s) - i\Gamma} ,$$

where \(A\) is proportional to the number density of the molecules and their Raman cross-section, and \(\Gamma\) the half-width of the band. Two kinds of experiment measure two different parts of it: CARS and SRS.

10CARS — fast, directional, but with a background

In coherent anti-Stokes Raman scattering the driven vibration scatters a second pump photon to the anti-Stokes frequency

$$\omega_\text{as} = 2\omega_p - \omega_s, \qquad I_\text{CARS} \propto \big|\chi^{(3)}\big|^2\, I_p^2\, I_s ,$$

which is emitted only along the phase-matched direction, \(\Delta\mathbf k = 2\mathbf k_p - \mathbf k_s - \mathbf k_\text{as} \approx 0\) (\(\mathbf k\) being the wave vectors); with tightly focused collinear beams the condition is fulfilled automatically in the small focal volume [14]. Its advantages over spontaneous Raman are large: signals many orders of magnitude stronger, blue-shifted from the lasers so that one-photon fluorescence does not overlap them, and intrinsic 3D sectioning because the signal only arises where both beams are focused. CARS microscopy reached video rate in living tissue, imaging lipids through their strong CH₂ stretch near 2850 cm⁻¹ [15].

The weakness is visible in the formula: the signal is \(|\chi_R + \chi_\text{NR}|^2\). The non-resonant part produces a background everywhere — also from water — and interferes with the resonant part, so the band appears distorted (a peak shifted to lower wavenumber followed by a dip) and its height is not proportional to concentration (\(|\chi|^2\) grows as \(N^2\) and contains a cross term).

Figure 3 · Interactive

11SRS — the background-free answer

How it works

In stimulated Raman scattering nothing new is generated at a new frequency. Instead, when \(\omega_p - \omega_s\) matches a vibration, energy flows from the pump beam to the Stokes beam through the molecules: the pump loses a little intensity (stimulated Raman loss, SRL) and the Stokes beam gains the same number of photons (stimulated Raman gain, SRG):

$$\Delta I_s \propto \mathrm{Im}\,\chi^{(3)}\, I_p\, I_s, \qquad \Delta I_p \propto -\,\mathrm{Im}\,\chi^{(3)}\, I_p\, I_s .$$

Only the imaginary part of \(\chi^{(3)}\) appears, and \(\chi_\text{NR}\) is real — so the non-resonant background vanishes. \(\mathrm{Im}\,\chi^{(3)}\) is exactly the spontaneous Raman line shape, so SRS spectra can be compared directly with Raman libraries, and the signal is linear in concentration. The change is tiny, \(\Delta I/I \approx 10^{-4}\)–\(10^{-8}\), so one beam is modulated at megahertz frequencies and the change is picked out of the other beam with a lock-in amplifier, beyond the low-frequency laser noise [16].

Advantage over CARS, and what it enabled

Background-free, quantitative contrast at the same speed. SRS microscopy reached video rate in vivo [17], and a fibre-laser SRS microscope taken into the operating room produced virtual haematoxylin-and-eosin images of unprocessed brain-tumour specimens in minutes, with diagnoses in near-perfect agreement with conventional histology [18]. Combined with alkyne, nitrile or deuterium labels in the cell-silent region (why it is silent), SRS images drugs and metabolites with minimal perturbation [19, 20]. The costs of both coherent methods are two synchronised pulsed lasers, more complex optics, and — at a single frequency pair — only one band at a time unless broadband or hyperspectral schemes are used.

12SORS — reading beneath the surface

Why it is needed

Confocal Raman reaches perhaps a hundred micrometres into a clear sample and much less into a turbid one. In tissue, powders and plastics, photons are scattered every 0.1 mm or so and quickly forget their direction. Most Raman light collected at the laser spot was generated near the surface — the container wall, the tablet coating, the skin — and drowns the signal from what lies beneath.

How it works

Diffusing photons that travel further sideways have, on average, also travelled deeper. Spatially offset Raman spectroscopy collects the Raman light at a distance \(\Delta s\) from the laser spot [21]. As the offset grows, the contribution of deeper layers rises relative to the surface. Two spectra, at zero and at a large offset, can then be combined by scaled subtraction,

$$S_\text{deep} \approx S(\Delta s) - k\,S(0) ,$$

with \(k\) chosen to remove the bands of the surface layer, leaving the spectrum of the layer below. A related geometry, transmission Raman, collects on the opposite side of the sample and averages over its whole thickness.

Figure 4 · Interactive

Advantage over conventional and confocal Raman, and the costs

Depths of millimetres to centimetres, through barriers: liquids in coloured plastic bottles at airport security [22], counterfeit drugs through packaging, bone through skin, and the prospect of non-invasive diagnosis of tissue [23]. Combined with SERS nanoparticles (SESORS), signals have been recovered through about 2 cm of tissue [24]. The costs are lower total signal at large offsets, depth information that is statistical rather than a sharp section, and the need for careful processing to separate the layers.

13Comparison and how to choose

The variants combine: confocal SERS maps, resonance-enhanced SERS (SERRS), SRS with Raman tags, SESORS. The next article, Label-free and labelled SERS, looks closely at the variant most used for sensing — and at the chemistry that decides what it sees.

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The figures use the simple models stated in their captions — an illustrative fluorescence model, the \(\chi^{(3)}\) line shape, a photon random walk and ideal confocal formulas — for teaching, not instrument design. Corrections and questions are welcome at rakesh_n@cpqct.iitr.ac.in.