Jürgen Popp

Raman spectroscopy is based on Raman scattering, an inelastic scattering process that is only observed in a tiny proportion (~1 in 10

) of the photons scattered by a molecule. As Raman spectroscopy typically measures the vibrational states, it can be used to characterize the molecular components of the sample, and hence, it provides a unique fingerprint of the sample. The technology is being applied in many scenarios in biology, forensics, diagnostics, pharmaceutics, and food science. Its power is further enhanced by spectral analysis methods, which can extract subtle changes from Raman spectra and translate the fingerprint information to high-level knowledge efficiently. The Raman spectral analysis is composed of three main parts: the experimental design; the preprocessing; and the data modeling (1). In this article, we would like to highlight the 11 key steps to analyze Raman data, which is depicted in Figure 1.

FIGURE 1: The 11 key steps of Raman spectral analysis, which are linked to the main steps: DoE, pre-processing, and modelling.

Sample size planning (SSP) is the most important step of experimental design (DoE) in the field of Raman spectral analysis. It aims to estimate the minimal number of samples to reach a statistically meaningful conclusion or to build a model with acceptable performance. The term sample refers to the highest level of the sampling hierarchy; for example, it could be a patient, a (biological) batch, or a (biological/technical) replicate. SSP can be achieved based on the learning curve that characterizes a predefined metric over the increasing sample size; look for the minimal sample size where the metric does not improve further (2).

Measured Raman spectra are not perfect, but are corrupted by different (side) effects originating from the instrument, the environment, and the sample itself. These corrupting effects are removed via a series of preprocessing steps, including quality control, spikes removal, (spectrometer) calibration, baseline correction, smoothing, and normalization. These steps are not independent, but they do impact each other. We recommend putting them into a closed loop and adjusting one step according to the feedback of the other steps.

Cosmic spikes occur when high-energy cosmic particles hit the charge coupled device (CCD) or complementary metal oxide semiconductor (CMOS) detector. They manifest themselves as narrow but extremely intense bands, and they can appear randomly at any wavenumber positions. In practice, spikes are normally detected as abnormal intensity changes when comparing two successively measured spectra or screening along the wavenumber axis within one spectrum. Methods are also reported to jointly inspect such intensity changes along the wavenumber axis and between the successive measurements simultaneously (3). The detected spikes are replaced with either an interpolation-based value using the boundary points of the spike position or the intensities of its successive measurement at the same wavenumber positions. In the latter way, the fluorescence and the intensity variations between the two measurements have to be handled well.

The spectrometer calibration is to remove spectral variations caused by the changes in devices and environment so that the spectra become comparable among different measurements. Typically, it involves a wavenumber and intensity calibration (4). Spectra of standard materials are measured in both cases. For wavenumber calibration, the calibration function is estimated by aligning the measured band positions of the wavenumber standard to their theoretical values—for instance, through a polynomial fitting. For the intensity calibration, the intensity response function can be calculated as the ratio between the measured and theoretical emission of an intensity standard. This response function is then used to divide the measured Raman intensities for the calibration.

Baseline correction normally refers to the correction of fluorescence of the sample. Fluorescence shows as a slowly changing baseline under Raman bands; this property can be used to correct it. Many mathematical approaches exist for this correction, including derivative spectra, the sensitive nonlinear iterative peak (SNIP) clipping, asymmetric least squares smoothing, polynomial fitting, standard normal variate (SNV), multiplicative scattering correction (MSC), and extended multiplicative signal correction (EMSC).

Smoothing is usually achieved via a moving-window low-pass filtering (for example, mean, median, or Gaussian) in the spectral or spatial domain. The spectral filtering works along the wavenumber axis; hence, it can be applied for a single spectrum. The spatial filtering, in contrast, is calculated over multiple spectra collected from a spatial neighborhood, and thus, it is only applicable in hyperspectral data cubes. In either manner, smoothing may degrade the subsequent analysis and is recommended only for highly noisy data.

Normalization is performed to suppress the fluctuation of the excitation intensity or changes in the focusing conditions of the setup. Here, the spectral intensities are divided by the area, maximum, or l

 norm of a selected spectral region (R), respectively; R, dependent on the task, can be the whole spectrum, a single wavenumber position, or a Raman band with supposedly constant intensities.

After the data is preprocessed, the spectral signals are translated into high-level information (such as response variables), for instance, the disease status or the concentration of a component. This requires a certain number of samples with known response variables. A statistical or machine learning model is constructed with part of the data set (training data) and evaluated with the rest (testing data). The model with optimal performance is afterward used for unknown samples to obtain their response variables directly. The major steps of statistical or data modeling are explained in the next section.

Dimension reduction helps to extract useful features from the data and reduce redundant information. Depending on whether the response information is needed or not, existent approaches can be categorized as supervised or unsupervised procedures. Typical examples are principal component analysis (PCA) and the partial least squares (PLS), respectively. Dimension reduction can also be grouped into feature selection or feature extraction. Methods for feature selection pick the variables that are the most significant according to a predefined benchmark, whereas feature extraction transforms the spectral data into a new space of lower dimension and represent the original spectra with new coordinates. Typical approaches in such case are PCA, vertex component analysis (VCA), N-Finder, independent component analysis (ICA), and multivariate curve resolution alternative least squares (MCR-ALS) (1).

The output of the dimension reduction is supplied to a machine learning model to translate the spectral signal into high-level information. Existent models can be categorized as unmixing, clustering, classification, or regression. The unmixing and clustering are applicable for image generation and rough data inspection—for example, to see the spatial pattern of a hyperspectral data cube. The classification relates the spectral signals to a categorical variable such as disease status. Regression models derive a quantitative value, such as the concentration of given substances, from the spectral signal. No clear separation exists between classification and regression models; as a matter of fact, classification is often achieved via a regression model.

After being constructed, the prediction performance of the model is evaluated with testing data. All supervised procedures contributing to the model prediction should be involved in such an evaluation, be it dimension reduction or the machine learning model itself. The prediction performance is characterized via the deviation of the prediction from the known true values. Examples of performance markers of the models are the root-mean squared-error of prediction (RMSEP) for regression models and accuracy, sensitivity, specificity, selectivity, and Cohen’s kappa for classification models (1). To make better use of the known samples, it is recommended to perform model evaluation in the framework of cross-validation, where the known data is split into training and testing data for multiple times. The predictions over all data splits are averaged to evaluate the performance of the model. In all splits, the testing data must be independent to the training data to avoid model overestimation. That means, the two data sets must be from different patients or batches (5).

Model interpretation is another important step in data modeling, which could be performed based on the variable significance indicated by the established model. Variables of the spectroscopic data that are shown to be important to the model should link to chemical or biological explanations. This can help further feature selection to build a more parsimonious model. In the long run, such a model interpretation can help to discover the biomarkers that play a role in the given investigation.

As sensitive as Raman spectroscopy, it is common to see significant shifts of Raman bands or changes in Raman intensities between spectra measured from different replicates or on different devices. Hence, an established model can perform badly when predicting new data—for instance, Raman spectra measured from a patient to be diagnosed. Model transfer is utilized in this case, which helps to improve the prediction of an existent model on new data. This can be achieved either by either removing the spectral variations between the different measurements or adjusting the model parameters by taking the features of the new data into account (6).

To summarize, we walked through the key steps of the Raman spectral analysis workflow and briefly discussed their aims and available approaches. Possible errors upon misconducting of the steps are summarized in (7). With such a condensed article, we hope to unveil the mystery of Raman spectral analysis so that the results of the analysis are more easily understood and interpreted. For more detailed and comprehensive conceptions of each step, the readers are kindly referred elsewhere (1,8).

This work is supported by the BMBF, funding program Photonics Research Germany (FKZ:13N15466 (BT1), FKZ:13N15706 (BT2) FKZ:13N15715 (BT4)) and is integrated into the Leibniz Center for Photonics in Infection Research (LPI). The LPI initiated by Leibniz-IPHT, Leibniz-HKI, UKJ and FSU Jena is part of the BMBF national road map for research infrastructures.

(1) Guo, S.; Popp, J.; Bocklitz, T. Chemometric Analysis in Raman Spectroscopy from Experimental Design to Machine Learning–based Modeling. 

 5426–5459. DOI: 10.1038/s41596-021-00620-3

(2) Ali, N.; Girnus, S.; Roesch, P.; Popp, J.; Bocklitz, T. W. Sample-Size Planning for Multivariate Data: A Raman-Spectroscopy-Based Example. 

 12485–12492. DOI: 10.1021/acs.analchem.8b02167

(3) Ryabchykov, O.; Bocklitz, T.; Ramoji, A.; Neugebauer, U.; Foerster, M.; Kroegel, C.; Bauer, M.; Kiehntopf, M.; Popp, Automatization of Spike Correction in Raman Spectra of Biological Samples. J. 

 1–6. DOI: 10.1016/j.chemolab.2016.03.024

(4) Bocklitz, T. W.; Dörfer, T.; Heinke, R.; Schmitt, M.; Popp, J. Spectrometer Calibration Protocol for Raman Spectra Recorded with Different Excitation Wavelengths. 

Spectrochim. Acta. A. Mol. Biomol. Spectrosc.

 544–549. DOI: 10.1016/j.saa.2015.04.079

(5) Guo, S.; Bocklitz, T.; Neugebauer, U.; Popp, J. Common Mistakes in Cross-validating Classification Models. 

 (30), 4410–4417. DOI: 10.1039/C7AY01363A

(6) Guo, S.; Kohler, A.; Zimmermann, B.; Heinke, R.; Stöckel, S.; Rösch, P.; Popp, J.: Bocklitz, T. Extended Multiplicative Signal Correction Based Model Transfer for Raman Spectroscopy in Biological Applications. 

 (16), 9787–9795. DOI: 10.1021/acs.analchem.8b01536

(7) Ryabchykov, O.; Schie, I.; Popp, J.; Bocklitz, T. Errors and Mistakes to Avoid when Analyzing Raman Spectra. 

(4), 48–50. DOI: 10.56530/spectroscopy.zz8373x6

(8) Guo, S.; Ryabchykov, O.; Ali, N.; Houhou, R.; T. Bocklitz, T, in 

Reference Module in Chemistry, Molecular Sciences, and Chemical Engineering; 

 are with the Leibniz Institute of Photonic Technology in Jena, Germany. 

 are also with the Friedrich Schiller University in Jena, Germany. 

 is also with the Institute of Computer Science, Faculty of Mathematics, Physics & Computer Science, at the University Bayreuth (UBT), in Bayreuth, Germany. Direct correspondence to: 

Articles

A more successful blueprint for analyzing Raman spectral data is outlined by following the 11 important steps, which are outlined here.

Key Steps in the Workflow to Analyze Raman Spectra

	Raman spectroscopy has become a highly popular and powerful approach to conduct label-free assessment of molecular information of biological and clinical samples (1,2). The Raman method is based on an inelastic scattering between a photon and a molecule, exciting molecular vibrations, and providing in this way the molecular information of a sample in a label-free and nondestructive manner (3). Although the quality of informational is exceptional, the application of this method for the characterization of eukaryotic cells requires significant know-how, starting with the right choice of instrumentation, as well as the method of data preprocessing and analysis. Here, we provide a brief outline of what to consider for the application of Raman spectroscopy for the characterization of eukaryotic cells.

Select the Right Instruments for Your Task to Get the Best Outcome

	The requirements for biomedical Raman instrumentation for the label-free characterization of eukaryotic cells are significantly more demanding in comparison to typical applications found in industrial processing, such as pharmaceutical authentication. Besides the small volume of a eukaryotic cell, most intracellular macromolecules, such as proteins, carbohydrates, and nucleic acids are present at low molecular concentrations. Furthermore, cells or the molecules they contain can exhibit additional fluorescence signals, whose Raman signal can also become resonantly enhanced, obscuring important intracellular differences. Thus, the choice of the correct excitation wavelength is an important one. The most common excitation laser wavelengths for Raman spectroscopy of eukaryotic cells are 532 nm and 785 nm. While the 532 nm excitation wavelength has a 4.74-times higher signal intensity, when compared with the 785 nm excitation wavelength, it also is more prone to excite autofluorescence, and also to resonantly excite molecules. Moreover, this wavelength is also more likely to cause intracellular damage in living cells. For dried cells, the 532 nm excitation wavelength can also result in burning of the sample, even at moderate excitation power. Despite the reduced scattering efficiency, 785 nm is frequently a better choice. The choice of the spectrometer, and especially the charge-coupled device (CCD), is intrinsically constrained by the choice of the excitation wavelength. The CCD detector is the most crucial component in any Raman setup, because it most-heavily taxes the signal-to-noise ratio (S/N), and, as such, the performance. Besides the obvious property of quantum efficiency, which defines the ratio of photon conversion, factors such as signal gain, dark current, and readout noise have to be considered to enable satisfactory results in the analysis of cells. For a 785 nm excitation, the etaloning suppression is of significant importance, and deep-depletion CCDs, which come at a higher cost, are required.

	The proper data calibration strategy has always been of highest importance, specifically when data have to be matched between different devices and different data acquisition conditions; for example, for different excitation wavelengths, and for different spectral resolution. Usually, calibration refers to a calibration of the wavenumber axis, and the correction for the optical system transfer function. For the wavelength calibration, two common methods are used, based on the measurement of a reference standard; for example, polystyrene or 4-acetaminophenol, or based on the measurement of an atomic reference emission source (neon lamp). In either case, the measured peak positions, which are detected on different pixels of the CCD camera, are matched to the wavenumber positions of a reference spectrum of this substance. Points in between are interpolated, using an 

-order polynomial function. The intensity calibration is typically performed using a National Institute of Standards and Technology (NIST) reference material, or a referenced white light emission lamp, both with known emission profiles (4). Here, a reference spectrum is acquired, and a transfer function calculated, based on the known emission profile of the emitter. Each measured spectrum is then corrected, using the calculated system response function.

	The experimental design is key to extract the necessary information for a given problem. Most frequently, Raman experiments of eukaryotic cells are performed in imaging mode, which enables the visualization of the distribution of the macromolecular content, and also helps to capture all of the intracellular variation of a cell. This, however, is very time consuming. Typical acquisition times for individual spectra are on the order of 1 to 2 s, which results in an acquisition time of 26 to 52 min for an entire cell at diffraction limited resolution, resulting in a very limited number of sampled cells per day. While the information on the distribution of cells can be alluring, most frequently researchers tend to take the average spectra of the cells for further analysis, ending up with a limited number of cells, which can reduce the statistical meaning of the results. When imaging information is not required, it is highly advisable to sample a large number of cells with only one or a few spectra per cell. One always has the option to acquire individual spectra of cells, which capture the required information of the cells. One has to keep in mind that intracellular changes are often larger than the cell type or cell stage differences. Hence, it is important to acquire either multiple Raman spectra of a cell and use the average of these measurements, or as we have shown previously, to acquire integrated Raman spectra of the cells (5). There are two options to do that-either by expanding the beam diameter, or by rapidly scanning a diffraction limited spot over the cell. The advantage of the latter approach is that the sampling size can be chosen for each cell individually, and can be selected from a few micrometers up to nearly 100 µm, which is not dynamically possible with an extended beam approach. Another linked question, which has to go into the experimental design, is the required sample size. There are several publications that deal with this very crucial aspect. As mentioned in the previous point, proper experimental planning includes data-size planning, which specifically depends on the problem at hand and the effect that is to be measured (6).

	There are multiple steps that have to be performed to remove artifacts, such as cosmic spikes, unwanted background contributions from auto-fluorescence, and laser scattering. Furthermore, as outlined in the paragraph "Data Calibration," the 

-axis has to be calibrated, and the data have to be corrected, for the system response function. Furthermore, depending on the S/N of the signal, a denoising of the data can be advisable. The order of these processes is highly important, because it can not only affect the performance of the algorithms, but can also result in the generation of artifacts. The common preprocessing order is:

	4) calibration for system transfer function

	Of course, this outline is only a guide, and variations or additional steps may be required to improve the specific preprocessing needs, especially when dealing with very complex background contributions. To perform the different steps, particularly steps 3, 5, and 6, a variety of algorithms are available and required. For example, for the background correction step, methods such as iterative polynomial background correction, asymmetric least squares fitting, and extended multiplicative scattering correction (EMSC) are frequently used (7). EMSC has proven especially powerful, because it considers prior knowledge of background components and pure components, and additionally uses polynomial fitting to remove the background contributions. To perform the denoising frequently Savitzky-Golay filtering, the Whittaker Smoother, or a single value decomposition (SVD) can be performed. An example for raw spectra and background corrected spectra are shown in Figure 1.


	Figure 1: The raw Raman spectra of eukaryotic cells contain a significant number of background contributions and artifacts. Before any analysis of the spectra can be completed, a significant number of steps have to be performed to extract the molecular information of the cells. (a) Uncorrected cell spectra during acquisition; (b) typical cell spectra after quartz correction and intensity calibration; (c) typical cell final spectra following quartz correction, intensity calibration, background correction, cosmic ray removal, de-noising, cropping, and normalization.

	Once the data have been sufficiently corrected, as outlined in the previous paragraph, data analysis can take place. Depending on the task at hand and the specific experimental question, a variety of suitable approaches are available. The most obvious one is a simple visual inspection of the data and visual comparison between the spectra of the different groups. The assessment can be done by simply calculating a difference spectrum between the relevant groups. Comparison of band positions and band intensities offers a simple method to understand the spectral differences. Since the Raman signal is linearly dependent on the concentration, which is the number of molecules in the focal volume, one may perform binary concentration series experiments with nonoverlapping bands; then relevant band intensities can be plotted against the concentration for a semiquantitative analysis. Nowadays, those simple approaches are rarely used, and researchers heavily relay on multivariate statistical analysis and machine learning approaches. One has to keep in mind that a Raman spectrum provides information on the vibration of molecular bonds in a sample, and the same molecular bonds can exhibit different molecular vibration, providing correlated information. This is also true for most intracellular macromolecules, such as nucleic acids, proteins, and lipids. Here, changes in a specific band will also frequently be indicative of changes in other bands of the macromolecule. In essence, this means that Raman spectra contain a lot of redundant information, that is, different spectral bands that describe the same type of information. As such, dimension reduction techniques are heavily used in Raman spectroscopy. Depending on the specific application, which could be, for example, of class differentiation or concentration series, different methods can be used. For dimensionality reduction in a class-differentiation problem, one of the most commonly used methods is principal component analysis (PCA), which decomposes data in new and ordered orthogonal components, where the first component explains the highest variance of the data set, the second component explains the second highest variance, and so on (Figure 2). Once the dimensionality is reduced, then greater than 95% of the variance in the data set can readily be explained by the first 15 principal components-the calculated score values are used for further analysis. The dimensionality of the initial spectrum, which usually contains more than 1000 variables, is now reduced to the defined number of components; for example, 15. This is still challenging for a visual inspection; hence, the additional methods are required. Here, well known approaches from machine-learning, such as support vectors machines (SVM), linear discriminant analysis (LDA), or random-forest classification (RFC) are used.


	Figure 2: The analysis of the Raman data is a highly complex process and requires a good amount of knowledge in multivariate statistical analysis and machine-learning approaches. PCA is a frequent choice for the dimensionality reduction and allows the user to assess the relevant information of the data in a comprehensible way. (a) The scatter plot matrix of the score values shows that Raman spectra of different cell types create distinct clusters. (b) The PCA-loadings allow the assessment of the spectral information responsible for the differences. (c) The image of the score information enables the visualization of the distribution of the molecular information.

	Financial support of the EU, the Thüringer Ministerium für Wirtschaft, Wissenschaft und Digitale Gesellschaft, the Thüringer Aufbaubank, the Federal Ministry of Education and Research, Germany (BMBF), the German Science Foundation, the Fonds der Chemischen Industrie and the Carl-Zeiss Foundation are greatly acknowledged.

	(1) C. Krafft, I.W. Schie, T. Meyer, and J. Popp, 

(7), 1819–1849. (2016). doi: 10.1039/C5CS00564G.

	(2) C. Krafft, M. Schmitt, I.W. Schie, D. Cialla-May, C. Matthäus, T. Bocklitz, and J. Popp, 

	(4) S.J. Choquette, E.S. Etz, W.S. Hurst, D.H. Blackburn, and S. Leigh, 

	(5) I.W. Schie, R. Kiselev, C. Krafft, and J. Popp, 

	(6) C. Beleites, U. Neugebauer, T. Bocklitz, C. Krafft, and J.Popp, 

	(7) E. Cordero, F. Korinth, C. Stiebing, C. Krafft, I.W. Schie, and J. Popp, 

 are with the Leibniz Institute of Photonic Technology, in Jena, Germany. 

 is also with the Institute of Physical Chemistry and Abbe Center of Photonics at Friedrich Schiller University, in Jena, Germany. Direct correspondence to: 

Jürgen Popp

Articles

Key Steps in the Workflow to Analyze Raman Spectra

A Short Guide for Raman Spectroscopy of Eukaryotic Cells