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Raman spectroscopy shares many of the principles that apply to other spectroscopic measurements discussed in Spectrophotometry and Light-Scattering 851. Raman is a vibrational spectroscopic technique and is therefore related to IR (IR) and near-IR (NIR) spectroscopy. The Raman effect itself arises as a result of a change in the polarizability of a molecular bond and is measured as inelastically scattered radiation.
A Raman spectrum is generated by exciting the sample of interest to a virtual state with a monochromatic source, typically a laser. Light elastically scattered (no change in wavelength) is known as Rayleigh scatter and is not of analytical interest. However, if the sample relaxes to a vibrational energy level differing from the initial state, the scattered radiation is shifted in energy. The shift is commensurate with the energy difference between the initial and final vibrational states. This “inelastically scattered” light is referred to as Raman scatter. Only about one in 108 photons incident to the sample undergoes Raman scattering. If the Raman scattered photon is of lower energy, it is referred to as Stokes scattering. If it is of higher energy, it is referred to as anti-Stokes scattering. In practice, nearly all analytically useful Raman measurements make use of Stokes-shifted Raman scatter.
The appearance of a Raman spectrum is much like an absorption Fourier transform–IR (FT–IR) spectrum. The intensities, or the number of Raman photons counted, are plotted against the shifted energies. The x-axis is generally labeled “Raman Shift/cm–1” or “Wavenumber/cm–1”. The shift position is usually expressed in frequency and represents the frequency of the peak relative to the laser frequency. The spectrum is interpreted in the same manner as the commensurate absorption FT–IR spectrum. The positions of the shift frequencies for a given bond in an analyte are similar to their respective absorption frequencies in an IR spectrum. However, the peaks emphasized in a Raman spectrum are often de-emphasized in an IR spectrum and vice versa. This is why the two spectroscopic techniques are often said to be complementary.
Raman spectroscopy is advantageous because quick and accurate measurements can often be made without destroying the sample (solid, semi-solid, liquid, or gas) and with minimal or no sample preparation. The signal is typically in the visible or NIR range, allowing efficient coupling to fiber optics. This also means that a signal can be obtained from any medium transparent to the laser, such as glass, plastics, or samples in aqueous media. From an instrumental point of view, modern systems are easy to use, provide fast analysis times (seconds to several minutes), and are reliable. The Raman spectrum contains information on fundamental vibrational modes of the sample that can yield both sample and process understanding. Finally, the analysis modeling may be simpler than that associated with other spectroscopic techniques. (Both univariate and multivariate methods and calibrations can be used.)
In addition to normal Raman spectroscopy, there are a number of more specialized Raman techniques. These include resonance Raman (RR), surface-enhanced Raman spectroscopy (SERS), Raman optical activity (ROA), coherent anti-Stokes Raman spectroscopy (CARS), Raman gain or loss spectroscopy, and hyper-Raman spectroscopy. These techniques are not widely implemented currently, and are not addressed in this general information chapter.

There are two general classes of commonly performed Raman measurements: qualitative and quantitative.

Qualitative Raman Measurements
Qualitative Raman measurements yield accurate spectral information about the vibrational bands present in the sample. Because the Raman spectrum is specific for a given compound, qualitative Raman measurements may be used as a compendial ID test, as well as for structural elucidation.
Quantitative Raman Measurements
Quantitative Raman measurements follow a relationship comparable to Beer's law:
in which IV is the peak intensity at a given wavelength, K represents instrument and sample constants, L is the path length, C is the molar concentration of a particular component in the sample, and I0 is the laser intensity. In practice, path length is more accurately described as sampling volume, which is an instrumental variable described by the focus of the laser and the collection optics. From the equation, it is apparent that peak intensity is directly correlated to concentration. It is this relationship that is the basis for the majority of quantitative Raman applications.

Sample-Based Factors
The most important sample-based factors are fluorescence, sample heating, and matrix absorption. Fluorescence is typically observed as a broad sloping background underlying the Raman spectrum. The effect on quantitation is therefore that of an unstable baseline and decreased signal-to-noise ratio. The exact wavelength and intensity are dependent on the identity and concentration of the fluorescing material. Because fluorescence is generally a much more efficient process, even very minor amounts of fluorescent impurities can lead to significant Raman signal degradation. Fluorescence can be minimized by using longer wavelength excitation sources such as 785 nm or 1064 nm. However, the intensity of the Raman signal is proportional to –4, where is the excitation wavelength. The optimum signal-to-noise ratio will be obtained by balancing fluorescence rejection, signal strength, and detector response.
Fluorescence in solids can also be mitigated by exposing the sample to the laser source for a period of time before measurement. This process is called photobleaching, and operates by degrading the highly absorbing species. Photobleaching is less effective in liquids, where the sample is mobile, or if the amount of fluorescent material is more than a trace.
Sample heating can cause a variety of issues, such as physical form change (melting), polymorph conversion, or sample burning. This is usually an issue for colored, highly absorbing species, or very small particles that have low heat transfer. The effects of sample heating are usually observable either as changes in the Raman spectrum over time or by visual inspection of the sample. Besides decreasing the laser flux, a variety of methods can be employed to diminish heating, such as moving the sample or laser during the measurement or improving the heat transfer of the sample with thermal contact or liquid immersion.
Absorption of the Raman signal by the matrix can also occur. This problem is more prevalent with long wavelength FT–Raman systems where the Raman signal can overlap with a NIR overtone absorption. This effect will be dependent on the optics of the system as well as on the sample presentation. Associated with this effect is variability from scattering in solids as a result of packing and particle size differences. The magnitude of all of these effects, however, is typically less severe than in NIR because of the limited depth of penetration and the relatively narrower wavelength region sampled in Raman spectroscopy.
Sampling Factors
Quantitative Raman spectroscopy differs from many other spectroscopic techniques in that it is a single beam measurement with no background. Careful instrument design and sampling can minimize this variation but not entirely remove it. Thus the absolute Raman signal intensity is very difficult to use for direct quantitation of an analyte. Among the potential sources of variation are changes in sample opacity, sample heterogeneity, changes in laser power at the sample, and changes in optical collection geometry or sample position. These effects can be minimized by sampling in a reproducible, representative manner.
Use of an internal reference is the most common and robust method of eliminating variations due to absolute intensity fluctuations. There are several choices for this approach. An internal standard can be deliberately added, and isolated peaks from this standard can be employed. In a solution, an isolated solvent band can be employed because the solvent will remain relatively unchanged from sample to sample. Also, in a formulation, an excipient peak can be used if it is in substantial excess compared to the analyte. The entire spectrum can also be used as a reference, with the assumption that laser and sample orientation changes will affect the entire spectrum equally.
A second important sampling-based factor to consider is spectral contamination. Raman is a weak effect that can be masked by a number of external sources. Common contamination sources include sample holder artifacts (container or substrate) and ambient light. Typically, these issues can be identified and resolved by careful experimentation.

All modern Raman measurements involve irradiating a sample with a laser, collecting the scattered radiation, rejecting the Rayleigh scattered light, differentiating the Raman photons by wavelength, and detecting the resulting Raman spectrum. All commercial Raman instruments therefore share the following common features to perform these functions:
  1. Excitation source (laser)
  2. Sampling device
  3. Device to filter/reject light scattered at the laser wavelength
  4. Wavelength processing unit
  5. Detector and electronics
Table 1 identifies several common lasers used for pharmaceutical applications. UV lasers have also been used for specialized applications but have various drawbacks that severely limit their utility for general analytical measurements.
Table 1. Typical Lasers Used in Pharmaceutical Applications
Laser , nm (nearest whole number) Type Typical Power
at Laser
Wavelength Range, nm (Stokes Region, 100 cm–1 to 3000 cm–1 shift) Comments
NIR Lasers
1064 Solid state
Up to 3W 1075–1563 Commonly used in
Fourier transform
785 Diode Up to 500 mW 791–1027 Most ubiquitous
dispersive Raman
Visible Lasers
488–632.8 Ion gas and solid
state frequency
doubled lasers
Up to 1W 488–781 Fluorescence risks
A wide variety of sampling arrangements are possible, including direct optical interfaces, microscopes, fiber optic-based probes (either noncontact or immersion optics), and sample chambers (including specialty sample holders and automated sample changers). The sampling optics may also be designed to obtain the polarization-dependent Raman spectrum, which often contains additional information. Selection of the sampling device will often be dictated by the analyte. However, considerations such as sampling volume, speed of the measurement, laser safety, and reproducibility of sample presentation should be evaluated to optimize the sampling device for any given application.
Scattered light at the laser wavelength (Rayleigh) is many orders of magnitude greater than the Raman signal and must be rejected prior to the detector. Notch filters are almost universally used for this purpose and provide excellent rejection and stability combined with small size. The traditional use of multistage monochromators for this purpose, although still viable, is now rare. In addition, various filters or physical barriers to shield the sample from external radiation sources (e.g., room lights, laser plasma lines) may be required depending on the collection geometry of the instrument.
The wavelength may be processed by either dispersion or interferometry (Fourier transform). The specific benefits and drawbacks of each of the dispersive designs compared to the FT instrument are beyond the scope of this chapter. Any properly qualified instruments should be suitable for qualitative measurements. However, care must be taken when selecting an instrument for quantitative measurements, as dispersion and response linearity may not be uniform across the full spectral range (for example, when using an echelle spectrograph).
The silicon-based charge-coupled device (CCD) is the most common detector for dispersive instruments. The cooled array detector allows fast, full-spectrum measurements with low noise. It also has peak wavelength responsivity when matched to the commonly used 785-nm diode laser. Fourier transform instruments typically use single-channel germanium or indium–gallium–arsenide (InGaAs) detectors responsive in the NIR to match neodymium:yttrium–aluminum–garnet (Nd:YAG) 1064-nm excitation.
Raman instrument calibration consists of three components: primary wavelength (x-axis), laser wavelength, and intensity (y-axis).
In the case of FT–Raman instruments, primary wavelength-axis calibration is maintained with an internal He–Ne laser. Most dispersive instruments utilize atomic emission lamps for primary wavelength-axis calibration. In all Raman systems suitable for analytical Raman measurements, the vendor will offer a procedure of x-axis calibration that can be performed by the user. For dispersive Raman instruments, a calibration based on multiple atomic emission lines is preferred. The validity of this calibration approach can be verified subsequent to laser wavelength calibration using a suitable Raman shift standard. For scanning dispersive instruments, calibration may need to be performed more frequently, and precision in both a scanning and static operation mode may need to be verified.1
Laser wavelength variation can impact both the wavelength precision and the photometric (intensity) precision of a given instrument. Even the most stable current lasers can vary slightly in their measured wavelength output. The laser wavelength must therefore be confirmed to ensure that the Raman shift positions are accurate for both FT–Raman or dispersive Raman instruments. A reference Raman shift standard material such as those outlined in ASTM E1840-96(2002)1 or other suitably verified materials can be utilized for this purpose. [NOTE—Reliable Raman shift standard values for frequently used liquid and solid reagents, required for wavenumber calibration of Raman spectrometers, are provided in the ASTM Standard Guide cited. These values can be used in addition to the highly accurate and precise low-pressure arc lamp emission lines that are also available for use in Raman instrument calibration.] Spectrophotometric grade material can be purchased from appropriate suppliers for this use. Certain instruments may use an internal Raman standard separate from the primary optical path. External calibration devices exactly reproduce the optical path taken by the scattered radiation. [Note—When chemical standards are used, care must be taken to avoid standard contamination and to confirm standard stability.]
Unless the instrument is of a continuous calibration type, the primary wavelength axis calibration should be performed, as per vendor procedures, just prior to measuring the laser wavelength. For external calibration, the Raman shift standard should be placed at the sample location and measured using appropriate acquisition parameters. The peak center of a strong, well-resolved band in the spectral region of interest should be evaluated. The position can be assessed manually or with a suitable, valid peak-picking algorithm. The software provided by the vendor may measure the laser wavelength and adjust the laser wavelength appropriately so that this peak is at the proper position. If the vendor does not provide this functionality, the laser wavelength should be adjusted manually.
Calibration of the photometric axis can be critical for successful quantitation using certain analytical methods (chemometrics) and method transfer between instruments. Both FT–Raman units and dispersive Raman units should undergo similar calibration procedures. The tolerance of photometric precision acceptable for a given measurement should be assessed during the method development stage.
To calibrate the photometric response of a Raman instrument, a broad-band emission source should be used. There are two accepted methods: Method A, which utilizes an NIST-traceable tungsten white light source2 (and is applicable to all common laser excitation wavelengths listed in Table 1) and Method B, which utilizes NIST SRM 2241,3 a doped-glass fluorescence source that is currently available only for systems with 785-nm nominal excitation.
Method A— The NIST-traceable source should be placed at the sample location with the laser off and the response of the detector measured (using parameters appropriate for the instrument). The output for the source used for calibration should be known. The ratio of the measured response to the true response should be determined and a correction file generated. This correction should be applied to all spectra acquired with the instrument. Most manufacturers will provide both appropriate calibration sources and software for this approach. If the manufacturer does not provide a procedure or method, the user may accomplish the task using a source obtained from NIST and appropriate software. If using a manufacturer's method, attention must be paid to the calibration procedure and source validity. The user should obtain appropriate documentation from the manufacturer to ensure a qualified approach.
Method B— The NIST SRM 2241 should be placed at the sample location. With the laser on, a spectrum of the SRM should be obtained (using parameters appropriate for the instrument). The output for the source used for calibration should be known. The ratio of the measured response to the true response should be determined and a correction file generated. This correction should be applied to all spectra acquired with the instrument. Most manufacturers will provide both appropriate calibration sources and software for this approach. If the manufacturer does not provide a procedure or method, the user may accomplish the task using a source obtained from NIST and appropriate software. If using a manufacturer's method, attention must be paid to the calibration procedure and source validity. The user should obtain appropriate documentation from the manufacturer to ensure a qualified approach. [NOTE—Method B is currently appropriate only for a system with 785-nm laser excitation. NIST is currently producing other SRM materials that will be wavelength-specific for 1064-, 632.8-, 532-, and 514-nm excitation (and available in the 2004–2006 timeframe).]
External calibration
Detailed functional validation employing external reference standards is recommended to demonstrate instrumental suitability for laboratory instruments, even for instruments possessing an internal calibration approach. The use of external reference standards does not negate the need for internal quality control procedures; rather, it provides independent documentation of the fitness of the instrument to perform the specific analysis/purpose. For instruments installed in a process location or in a reactor where positioning of an external standard routinely is not possible, including those instruments possessing an internal calibration approach, periodic checking of the relative performance of an internal vs. external calibration approach should be made. The purpose of this test is to check for change in components that may not be included in the internal calibration method (process lens, fiber-optic probe, etc.), e.g., photometric calibration of the optical system.

The suitability of a specific instrument for use in a given method is ensured by a thorough technology-suitability evaluation for the application; a routine, periodic instrument operational qualification; and the more frequent performance verification (see Definition of Terms and Symbols). The purpose of the technology-suitability evaluation is to ensure that the technology proposed is suitable for the intended application. The purpose of the instrument qualification is to ensure that the instrument to be used is suitable for its intended application and, when requalified periodically, continues to function properly over extended time periods. When the device is used for a specific qualitative or quantitative analysis, regular performance verifications are made. Because there are many different approaches to measuring Raman spectra, instrument operational qualification and performance verification often employ external standards that can be used on any instrument. As with any spectrophotometric device, a Raman instrument needs to be qualified for both wavelength (x-axis and shift from the excitation source) and photometric (intensity axis) precision.
In performance verification, a quality of fit to an initial scan or group of scans (often referred to in nonscanning instruments as an accumulation) included in the instrumental qualification can be employed. In such analysis, it is assumed that reference standard spectra collected on a new or a newly repaired, properly operating instrument represent the best available spectra. Comparison of spectra taken over time on identical reference standards [either the original standard or identical new standards (if stability of the reference standards is a concern)] form the basis for evaluating the long-term stability of a Raman measurement system.
Frequency of Testing
Instrumental qualification is performed at designated intervals or following a repair or significant optical reconfiguration, such as a laser replacement or changing excitation wavelengths. Full instrument requalification may not be necessary when changing between sampling accessories such as a microprobe, a sample compartment, or a fixed fiber-optic probe. Performance verification tests may be sufficient in these cases; instrument-specific guidance from the vendor on qualification requirements should be followed. Tests include wavelength (x-axis and shift from the excitation source) and photometric (intensity axis) precision. Instrument qualification tests require that specific application-dependent tolerances be met.
Performance verification is carried out on the instrument configured for the analytical measurements and is done more frequently than instrument qualification. Performance verification includes wavelength uncertainty and intensity-scale precision. Wavelength precision and intensity-scale precision tests may be needed prior to any data collection on a given day. Performance is verified by matching the current spectra to those collected during the previous instrument qualification.
Instrument Operational Qualification
It is important to note that the acceptance specifications given in both the Instrument Operational Qualification and Performance Qualification sections are applicable for general use; specifications for particular instruments and applications may vary depending on the analysis method used and the desired accuracy of the final result. ASTM standard reference materials are also specified, with the understanding that under some circumstances (specifically remote on-line applications) calibration using one of these materials may be impractical, and other suitably verified materials may be employed. At this juncture it is important to note that specific parameters such as spectrometer noise, limits of detection (LOD), limits of quantification (LOQ), and acceptable spectral bandwidth for any given application should be developed as part of the analytical method development. Specific values for tests such as spectrometer noise and bandwidth will be dependent on the instrument chosen and the purpose required. In view of this, specific instrument tests for these parameters are not dictated in this information chapter.
Wavelength (x-axis) Precision
It is important to ensure the precision of the wavelength axis via calibration to maintain the integrity of Raman peak positions. Wavelength calibration of a Raman spectrometer consists of two parts: primary wavelength axis and laser wavelength calibration. After calibrating both the primary wavelength axis and the laser wavelength, instrument wavelength uncertainty can be determined. This can be accomplished using a Raman shift standard such as the ASTM shift standards or other suitably verified material. Selection of a standard with bands present across the full Raman spectral range is recommended so that instrument wavelength uncertainty can be evaluated at multiple locations within the spectrum. The tolerance of wavelength precision that is required for a given measurement should be assessed during the method-development stage. [NOTE—For scanning dispersive instruments, calibration may need to be performed more frequently, and precision in both a scanning and static operation mode may need to be verified.]
Photometric Precision
Laser variation in terms of the total emitted photons occurring between two measurements can give rise to changes in the photometric precision of the instrument. Unfortunately, it is very difficult to deconvolute changes in the photometric response associated with variations in the total emitted laser photons from the sample and sampling-induced perturbations. This is one of the reasons why absolute Raman measurements are strongly discouraged and why the photometric precision specification is set relatively loosely. The tolerance of photometric precision required for a given measurement should be assessed during the method-development stage.
Performance Qualification
The objective of performance qualification is to ensure that the instrument is performing within specified limits with respect to wavelength precision, intensity axis precision, and sensitivity. In certain cases when the instrument has been set up for a specific measurement (for example, installed in a process reactor), it may no longer be possible or desirable to measure the wavelength and photometric (intensity) qualification reference standards identified above. Provided instrument operational qualification has shown that the equipment is fit for use, a single external performance verification standard can be used to reverify function on a continuing basis (for example, a routinely used process solvent signal, for both wavelength and photometric precision, following reactor cleaning). The performance verification standard should match the format of the samples in the current analysis as closely as possible and use similar spectral acquisition parameters. Quantitative measurements of an external performance verification standard spectrum checks both the wavelength (x-axis and laser wavelength) and the photometric (intensity) precision. Favorable comparison of a series of performance verification spectra demonstrates proper continued operation of the instrument.
Wavelength Precision
The wavelength precision should be measured by collecting data for a single spectrum of the selected Raman shift standard for a period equal to that used in the photometric consistency test. Peak positions across the spectral range of interest are used to calculate precision. Performance is verified by matching the current peak position to those collected during the previous instrument qualification and should not vary by more than ±0.3 cm–1, although this specification may be adjusted according to the required accuracy of the measurement.
Photometric Consistency
The photometric consistency should be measured by collecting data for a single spectrum of a suitably verified reference standard material for a specified time. The areas of a number of bands across the spectral range of interest should be calculated using an appropriate algorithm. The most intense band area is set to an intensity of 1, and all other envelopes are normalized to this band. Performance is verified by matching the current band areas to their respective areas collected during the previous instrument qualification. The areas should vary by no more than 10%, although this specification may be adjusted according to the required accuracy of the measurement.
This test is applicable only to Raman instruments with automatic, internal laser power meters. Instruments without laser power measurement should utilize a calibrated laser power meter from a reputable supplier. The laser output should be set on a representative output, dictated by the requirements of the analytical measurement and the laser power measured. The output should be measured and checked against the output measured at instrument qualification. The power (in milliwatts or watts) should vary by no more than 25% compared to the qualified level. If the power varies by more than this amount, the instrument should be serviced (as this variation may indicate, among other things, a gross misalignment of the system or the onset of failure of the laser).
For instruments with an automatic, internal laser power meter, the accuracy of the values generated from the internal power meter should be compared to a calibrated external laser power meter at an interval of not more than 12 months. The internally calculated value should be compared to that generated by the external power meter. Performance is verified by matching the current value to that generated during the previous instrument qualification. The manufacturer may provide software to facilitate this analysis. If the instrument design prevents the use of an external power meter, then the supplier should produce documentation to ensure the quality of the instrument and provide a recommended procedure for the above analysis to be accomplished during a scheduled service visit.

Validation of Raman methods will follow the same protocols described in Validation of Compendial Methods 1225 in terms of accuracy, precision, etc. However, several of these criteria are affected by variables specific to Raman.
Fluorescence is the primary variable that can affect the suitability of a method. The presence of fluorescent impurities in samples can be quite variable and have little effect on the acceptability of a material. The method must be flexible enough to accommodate different sampling regimes that may be necessary to minimize the effects of these impurities.
Detector linearity must be confirmed over the range of possible signal levels. Fluorescence may drive the signal baseline higher than that used in the validation, in which case the fluorescence must be decreased, or the method validated to accommodate the higher fluorescence levels. This is also true for the precision, LOD, and LOQ of the method, as increased baseline noise will negatively impact all of these values. Because fluorescence may also affect quantitation due to baseline shifts, confirmation of acceptable quantitation at different levels of photobleaching, when used, should also be obtained.
The impact of the laser on the sample must be determined. Visual inspection of the sample and qualitative inspection of the Raman spectrum for measurements with differing laser powers and exposure times will confirm that the sample is not being altered (other than by photobleaching). Specific variables to confirm in the spectrum are shifts in peak position, changes in peak intensity and band width, and unexpected changes in background intensity.
Method precision must also encompass sample position. The sample presentation is a critical factor for both solids and liquids, and must be either tightly controlled or accounted for in the calibration model. Sample position sensitivity can often be minimized by appropriate sample preparation or sample holder geometry, but will vary from instrument to instrument based on excitation and collection optical configuration.

Calibration model is a mathematical expression that relates the response from an analytical instrument to the properties of samples.
Instrument bandwidth is a measure of the ability of a spectrometer to separate radiation of similar wavelengths.
Multiple linear regression is a calibration algorithm used to relate the response from an analytical instrument to the properties of samples. The distinguishing feature of this algorithm is the use of a limited number of independent variables. Linear-least-squares calculations are performed to establish a relationship between these independent variables and the properties of the samples.
Multivariate curve resolution (MCR) is a curve deconvolution technique that separates spectral components on the basis of their linear contributions to the overall spectrum.
Operational qualification is the process by which it is demonstrated and documented that the instrument performs according to specifications, and that it can perform the intended task. This process is required following any significant change such as instrument installation, relocation, major repair, etc.
Partial least squares (PLS) is a calibration algorithm used to relate instrument responses to the properties of samples. The distinguishing feature of this algorithm is that, although similar to PCR, this algorithm includes data concerning the properties of the samples used for calibration in the calculation of the factors used to describe the instrument responses.
Performance qualification is the process of using one or more well-characterized and stable reference materials to verify consistent instrument performance. Qualification may employ the same or different standards for different performance characteristics.
Principal component analysis and regression (PCA and PCR) is a calibration algorithm used to relate the response from an analytical instrument to the properties of samples. This algorithm, which expresses a set of independent variables as a linear combination of factors, is a method of relating those factors to the properties of the samples for which the independent variables were obtained.
Raman spectrum4 is a graph of the radiant energy, or number of photons, scattered by the sample through the indirect interaction between the molecular vibrations in the sample and monochromatic radiation of frequency much higher than that of the vibrations. The abscissa is usually the difference in wavenumber between the incident and scattered radiation.
(Normal) Raman scattering4 is Raman scattering that occurs through the polarizability, not the hyper-polarizabilities, and is excited by radiation that is not in resonance with electronic transitions in the sample. The scattering, in fact, occurs through the derived polarizability tensors, i.e., through changes in the polarizability during the vibrations.
Raman wavenumber shift4,
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is the wavenumber of the exciting line minus the wavenumber of the scattered radiation. SI unit: m–1. Common unit: cm–1 = 100 m–1.
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is positive for Stokes scattering and negative for anti-Stokes scattering.

Chemometrics can legitimately be used with Raman data to create models that can be used for qualitative and/or quantitative analysis.
Data Pretreatments
Pretreatments are mathematical manipulations of the spectra performed prior to the primary modeling step. The goal of pretreatments is to reduce the amount of irrelevant information, eliminating it from the model prior to the application of the primary technique. There are several data pretreatments that are typically used for removal of baseline anomalies. These include multiplicative scatter correction (MSC), standard normal variate (SNV), and derivatives. Pearson's method, an iterative approach to baseline decurvature, works well for the correction of some sets of data.
Library Construction and Use
Raman libraries are often used for compound identification. The test material can be tentatively known to the user or not. Libraries used for the purpose of raw material, intermediate, or formulation identity confirmation are best constructed from real production materials. This is particularly prudent in light of the fact that materials differing in crystallinity or polymorphic constitution will yield varying Raman spectra. Raman libraries purchased from a third party should be used judiciously.
Qualitative algorithms vary, and the appropriate choice is application dependent. For simple identifications, correlation algorithms often work well. These algorithms can be based on a variety of mathematical manipulations. Principal component-based methods such as discriminant analysis can also be used for qualitative analysis.
Quantitative Calibration Approach
Raman spectroscopy can be used for quantitative analysis both for in-line and off-line work. There are some unique aspects concerning the use of quantitative Raman spectra that should be noted.
Algorithms for Quantitation
As in the case of NIR spectroscopy (see Near-Infrared Spectrophotometry 1119), multivariate methods may be used to model Raman data. However, univariate analyses are often appropriate because of the resolution of information that Raman affords.
Both peak areas and peak heights can appropriately be used for Raman quantitation when univariate models are employed. Peaks should be reasonably well resolved when this approach is employed. As described above, peak ratios, as a rule, should be employed to account for peak intensity changes not related to the analyte. The judicious choice for a reference band is critical in such cases. Multivariate methods are also viable for Raman quantitation.
Multivariate curve resolution (MCR), which attempts to deconvolute the spectral data as a linear sum of its contributions, is a particularly effective means of dealing with Raman data that exhibit substantial change. This algorithm can potentially isolate the contribution from the analyte of interest and quantify the level of this contribution from sample to sample. The method is often employed in a non-negative mode, making the resulting factors potentially interpretable.
Principal components analysis (PCA) can be used similarly to MCR. The contribution of each component generated can be used to semiquantitatively estimate the level of the analyte. Related to PCA, principal component regression (PCR) can also be used. This provides an opportunity for reference data to be employed and is thus truly quantitative.
In many circumstances, multiple linear regression (MLR) can be very effective for Raman quantitation. MLR gives the user the capability of using denominator data points, which can be very useful for Raman data. As with other types of data, the ability to choose multiple numerators can also work synergistically in a quantitative analysis.
Partial least squares (PLS) regression remains one of the more popular choices for Raman quantitation. PLS uses the reference data to orient the factor generation. This can be very effective, especially for the quantitation of low-level analytes.
The choice of appropriate quantitation tools varies from project to project. Both pretreatment methods and quantitative algorithms should be chosen wisely according to the goals. If isolated analyte and reference bands are available, univariate models are often a good choice. If quantitative estimates are all that are necessary or the sample set is a closed set (no future predictions will be made), then MCR or PCA is a good choice. For reasonably extensive data sets with available reference data, MLR, PCR, or PLS can be used.

1  ASTM E1840-96(2002) Standard Guide for Raman Shift Standards for Spectrometer Calibration, ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA, USA 19428-2959.
2  NIST-traceable tungsten white light source statement: While the calibration of the Raman frequency (or Raman shift, cm–1) axis using pure materials and an existing ASTM standard is well accepted, techniques for calibration of the Raman intensity axis are not. Intensity calibrations of Raman spectra can be accomplished with certified white light sources.
3   NIST SRM 2241: Ray, K. G.; McCreery, R L. Raman intensity correction standard for systems operating with 785-nm excitation. Appl. Spectrosc. 1997, 51, 108–116.
4  Chalmers, J., Griffiths, P., Eds. Handbook of Vibrational Spectroscopy; John Wiley & Sons, Ltd: New York, 2002.

Auxiliary Information—
Staff Liaison : Gary E. Ritchie, M.Sc., Scientific Fellow
Expert Committee : (GC05) General Chapters 05
USP29–NF24 Page 2983
Pharmacopeial Forum : Volume No. 30(6) Page 2139
Phone Number : 1-301-816-8353