\\n\\n
More than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\\n\\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\\n\\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\\n\\nAdditionally, each book published by IntechOpen contains original content and research findings.
\\n\\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\\n\\n\\n\\n
\\n"}]',published:!0,mainMedia:null},components:[{type:"htmlEditorComponent",content:'
Simba Information has released its Open Access Book Publishing 2020 - 2024 report and has again identified IntechOpen as the world’s largest Open Access book publisher by title count.
\n\nSimba Information is a leading provider for market intelligence and forecasts in the media and publishing industry. The report, published every year, provides an overview and financial outlook for the global professional e-book publishing market.
\n\nIntechOpen, De Gruyter, and Frontiers are the largest OA book publishers by title count, with IntechOpen coming in at first place with 5,101 OA books published, a good 1,782 titles ahead of the nearest competitor.
\n\nSince the first Open Access Book Publishing report published in 2016, IntechOpen has held the top stop each year.
\n\n\n\nMore than half of the publishers listed alongside IntechOpen (18 out of 30) are Social Science and Humanities publishers. IntechOpen is an exception to this as a leader in not only Open Access content but Open Access content across all scientific disciplines, including Physical Sciences, Engineering and Technology, Health Sciences, Life Science, and Social Sciences and Humanities.
\n\nOur breakdown of titles published demonstrates this with 47% PET, 31% HS, 18% LS, and 4% SSH books published.
\n\n“Even though ItechOpen has shown the potential of sci-tech books using an OA approach,” other publishers “have shown little interest in OA books.”
\n\nAdditionally, each book published by IntechOpen contains original content and research findings.
\n\nWe are honored to be among such prestigious publishers and we hope to continue to spearhead that growth in our quest to promote Open Access as a true pioneer in OA book publishing.
\n\n\n\n
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Fourier transform infrared (FTIR) spectroscopy is a label-free and non invasive technique that exerts an enormous attraction in biology and medicine, since it allows to obtain in a rapid way a biochemical fingerprint of the sample under investigation, giving information on its main biomolecule content. This spectroscopic tool is successfully applied not only to the study of the structural properties of isolated biomolecules, such as proteins, nucleic acids, lipids, and carbohydrates, but also to the characterization of complex biological systems, for instance intact cells, tissues, and whole model organisms.
In particular, FTIR microspectroscopy, obtained by the coupling of an infrared microscope to a FTIR spectrometer, makes it possible to collect the IR spectrum from a selected sample area down to ~ 20 microns x 20 microns when conventional IR source and detector are employed, and down to of a few micrometers when more specialized and sensitive detectors and the highly brilliant synchrotron light source are used. In this way, FTIR microspectroscopy provides detailed information on several biological processes in situ, among which stem cell differentiation [1-5], somatic cell reprogramming [6], cell maturation [7, 8], amyloid aggregation [9-12] and cancer onset and progression [13-15], making it possible to disclose the infrared response not only from single cells, but also from subcellular compartments [8, 16, 17].
The FTIR spectra of biological systems are very complex since they consist of the overlapping absorption of the main biomolecules; for this reason, to pull out the significant and non-redundant information contained in the spectra it is necessary to apply an appropriate multivariate analysis, able to process very high-dimensional data. This is even more crucial when time-dependent biological processes, such as cell maturation or differentiation, are studied. Indeed, in this case it is fundamental to be able to extract from the spectral data the relevant information of the process you are investigating [18-21].
In Figure 1 we schematized the procedure that should be followed to successfully tackle the FTIR characterization of complex biological systems.
Scheme of the FTIR approach to study complex biological systems. The IR absorption spectra are analysed by resolution enhancement approaches (e.g. second derivatives) to resolve the overlapped absorption components and to monitor their variations during the process under investigation. The spectroscopic results are validated by an appropriate multivariate analysis approach, to identify firstly specific marker bands of the studied process. The interpretation of the spectroscopic data should be then confirmed by standard biochemical assays.
Several multivariate analysis approaches exist and for the scope of this book they can be divided into two main categories: regression and classification techniques. In the first category fall all methods that allow to derive a model describing the relationship between two sets of variables. The second category includes techniques to split observations into groups or classes.
In this chapter, we will firstly introduce the most widely used multivariate analysis approaches in the field of spectroscopy.
We will then illustrate the basic principles and experimental details for the application of principal component - linear discriminant analysis (PCA-LDA) to the analysis of FTIR spectral data of complex biological systems. The potential of these combined tools will be described on illustrative examples of cell biological process studies. In particular, we will discuss in details its application on our FTIR study of murine oocytes characterized by two different types of chromatin organisation around the nucleolus, strongly affecting their development after fertilization. In this case, PCA-LDA analysis made it possible to identify not only the maturation stage in which the fate separation between the two kinds of oocytes occurred, but also to disclose the most significant cellular processes responsible for the different oocyte destiny, thus validating the visual inspection of the infrared spectra [7].
Fourier transform infrared (FTIR) microspectroscopy is a powerful technique that allows to obtain a molecular fingerprint of the sample under investigation in a rapid and non-invasive way. In the case of complex biological systems it provides simultaneously, in a single measurement, information on the main biomolecules, such as lipids, proteins, nucleic acids, and carbohydrates, requiring also a very limited amount of sample. For these reasons, it became recently a very attracting tool for biomedical research [20, 22-24], being successfully employed for the study of several biological systems, from intact cells [6, 7, 25] to tissues [11, 26, 27] and whole model organisms (i.e. the nematode Caenorhabditis elegans) [9, 28].
As an example, in Figure 2 it is reported the FTIR absorption spectrum of a single intact murine oocyte. As shown, its IR response is very complex, being due to the absorption of the main biomolecules. In particular, between 3050 - 2800 cm-1 and 1500 - 1350 cm-1 the absorption of the lipid acyl chains occurs, while around 1740 cm-1 the ester carbonyl absorbs [29]. Moreover, the amide I and amide II bands - mainly due to the C=O stretching and the NH bending of the peptide bond respectively - give information on the protein secondary structure [30], while the spectral range between 1000 and 800 cm-1 is very informative on nucleic acid absorption, since it is due in particular to sugar vibrations sensitive to their conformation and to backbone vibrational modes [31, 32]. Finally, we should also mention the very complex spectral range between 1250 - 1000 cm-1, mainly due to phosphodiester groups of nucleic acids and phospholipids and to the C-O absorption of glycogen and other carbohydrates [31, 33, 34].
Making it possible to obtain a sample biochemical fingerprint in a rapid and non destructive way, FTIR microspectroscopy is widely applied to the in situ characterization of cellular processes, such as cell maturation, differentiation, and reprogramming [3, 5-7, 25, 35], and to the detection of several diseases, as, for instance, cancer [13-15] and neurodegenerative disorders [10, 11], whose onset is accompanied by changes in the composition and structure of several biomolecules.
Since water has a strong absorption in the mid-infrared spectral range, samples have to be dried rapidly before IR measurements, in particular when working in transmission mode (see for details the following paragraph). The suitability of such “dry-fixing” has been proved by Raman spectroscopy, a vibrational tool complementary to FTIR, whose response is not affected by water. In particular, Raman measurements performed on differentiating human embryonic stem cells, hydrated and dry-fixed, demonstrated that the rapid desiccation didn’t affect the spectroscopic response of the main biomolecules. Indeed, in both cases the same temporal pattern of the differentiation marker bands - due to tryptophan, nucleic acid backbone and base vibrations - was observed during the biological process under investigation [36].
FTIR absorption spectrum of a single intact murine oocyte. The measured absorption spectrum of a single intact murine oocyte (surrounded nucleolus, MI 10 H) is reported without any corrections. The oocyte - deposited on a BaF2 window - was measured in transmission by the IR microscope UMA 500, coupled to the FTIR spectrometer FTS 40A (both from Digilab), at a resolution of 2 cm-1. The absorption regions of the main biomolecules are indicated.
We should add that to obtain reliable results on the studied process it is crucial to standardize firstly the sample preparation, since - for instance - metabolic changes due to cell aging could result in significant spectral changes that could, in turn, hide the IR response specifically due to the process of interest, as it has been recently reported in the literature [37]. For these reasons, it is fundamental to check accurately the stage of cell growth in culture before performing spectroscopic measurements.
We should also briefly mention that, before spectral analyses, the measured IR spectra could require some corrections due to artifacts that can interfere with the spectroscopic response. For instance, single cells, or subcellular compartments, or particles of the size of the same order of that of the incident infrared light (∼3-10 microns) could give rise to Mie scattering, that significantly distorts the measured spectrum, causing misinterpretation of the results. For this reason, before further analyses, it is strongly recommended to correct the measured spectra with opportune algorithms specifically developed to this aim [38].
Since the IR spectra of complex biological systems are due to the overlapping spectral features of multiple components, their analysis requires often the employment of resolution enhancement procedures to better resolve their absorption bands, an essential prerequisite for the identification of peak positions and their assignment to the vibrational modes of the different molecules. Among these, second derivative analysis is widely applied, as described in [39]. Since second derivative band intensity is inversely proportional to the square of the original band half-width, this procedure introduces an enhancement of sharp lines, as those due to vapour and noise. For this reason, this analysis requires spectral data free of vapour absorption and with excellent signal to noise ratio.
Furthermore, due to the intrinsic complexity of biological systems, their spectral analysis requires the support of appropriate multivariate analysis approaches able to tackle the study of high-dimensional data, to verify firstly the reproducibility of the results and then to extract the most significant spectral information [18-21] (see for details paragraph 4).
FTIR microspectroscopy is realized coupling to a FTIR spectrometer an infrared microscope characterized by an all reflecting optics, since typical lenses and condensers of visible microscopy - being made of glass, not transparent to the IR radiation - cannot be employed.
The main advantage of FTIR microspectroscopy is that it offers the possibility to study selected areas of the sample under investigation, resulting particularly useful in the case of systems characterized by an intrinsic heterogeneity, such as biological systems.
Two main types of IR microscopy exist, depending on the detector employed, and both equipped with an IR thermal source (globar), whose spatial resolution is diffraction-limited.
The first, conventional, generally equipped with a nitrogen cooled mercury cadmium telluride (MCT) detector, makes it possible to measure IR absorption spectra from a microvolume within the sample, selected by a variable aperture of the microscope, whose side can be adjusted down to a few tens of microns.
The second type of IR microscope, more advanced, is equipped with a focal plane array (FPA), consisting of an array of infrared detector elements, that enables not only to collect the IR absorption spectrum of the sample, but also an IR chemical imaging, where the image contrast is given by the response of selected sample regions to particular IR wavenumbers. Depending mainly on the detection array, the spatial resolution in this kind of microscopy is approximately between 20 and 5 microns, making it possible to reach, therefore, a resolution near to the diffraction limit.
We should, however, add that the use of a synchrotron IR light source, with a brightness of at least two orders of magnitude higher than that of a conventional thermal source, makes it possible to achieve diffraction-limited spatial resolution with enhanced signal-to-noise ratio. In this way, synchrotron light could allow to explore the IR spectra at the subcellular level.
A final remark should be done concerning the spectral acquisition mode. Indeed, infrared measurements can be mainly performed in transmission, reflectance or attenuated total reflection (ATR) mode. Typically, measurements on complex biological systems are performed in transmission mode, using appropriate IR transparent supports for the deposition of the sample, such as BaF2, CaF2, ZnSe. In this case, the IR beam goes through the sample, that - depending mainly on its molar extinction coefficient - should have a uniform thickness, not exceeding 15-20 microns.
Moreover, in reflectance mode - where the sample is placed onto proper reflective slides - the IR beam passes the sample, is reflected by the slide, and passes the sample again. In particular, the sample slides reflect mid-infrared radiation almost completely and usually are also transparent to visible light, allowing sample inspection by a conventional light microscope. This approach is, for instance, useful for tissue characterizations.
Finally, in the ATR approach, where the sample is placed into contact with a higher refractive index and an IR transparent element (mainly germanium and diamond), samples with higher thickness than in transmission can be processed. In particular, the IR beam reaches the interface between the ATR support and the sample at an angle larger than that corresponding to the total reflection. In this way the beam is totally reflected by the interface and penetrates into the sample as an evanescent wave, where it can be absorbed. The beam penetration depth is of the order of the IR wavelength (a few micrometers) and depends on the wavelength, the incident angle, as well as on the refractive indices of the sample and of the ATR element. Furthermore, it should be noted that this kind of approach makes it possible to measure also samples not necessarily deposited onto an IR transparent support, as in ATR measurements it is only required that the sample be in close contact with the ATR element.
For a review of the technical aspects of FTIR microspectroscopy, see [40-42].
Several phenomena can only be described or explained by taking into account several variables at the same time. These cases represent the realm of the Multivariate statistical analysis (MVA).
We now define the structure of our data that will be kept throughout the text for all described techniques. For a given phenomenon we perform a certain measurement and store the value in a uni- or multivariate variable called
Each instance associated to the variable y is stored in a matrix Y composed of n rows (the observations) and m columns (the independent variables).
Each element of matrix Y can be indicated as
The matrix Y (composed of the independent variables y) represents the only input for several multivariate techniques described here; in some other cases the matrices Y and Z (composed of the dependent variables z) are both required.
In the following part, we will make a distinction between regression and classification techniques. However, it should be clear that the separation between these two domains is not always sharp and the same technique can be either used for regression or for classification purposes.
LMVR (or MLR) can be used to model linear relationships between one or more z (dependent variable) and one or more y (independent variable). In the most general case, we have n independent multivariate variables y represented by the matrix Y and the corresponding response multivariate variable z, stored in the matrix Z.
The LMVR is based, as many other statistical techniques, on the generalized linear model:
In some cases linear models cannot be used and one could try to apply non-linear models.
Common models which frequently apply to natural phenomena are the exponentials (which, indeed, is a transformed linear model. A linear model can be applied upon on the logarithm of the data), logistic models or power law models.The regressed model has the general form of
The optimal values for the coefficients
When the number of observations is smaller than the number of variables (as it often happens for spectral data), the matrix
Increasing the number of observations (above the number of variables) will not always solve the problem. This is due to the so-called near-multicollinearity which means that some variables can be written approximately as linear functions of other variables. This problem is often found among spectral measurements. Even if the solution will be mathematically unique, it may be unstable and lead to poor prediction performances.
Linearly correlated or quasi-linearly correlated variables have to be removed prior to apply a regression method. In the following sections, we will describe two methods that are frequently used to remove correlations among variables, namely principal component analysis (PCA) and partial least squares (PLS).
4.2.3.1. Principal Component Analysis (PCA)
We should first recall the structure of the data. Suppose that we have n observations, each one defined by a vector
By using PCA, our intent is to develop a smaller number of uncorrelated artificial variables, called principal components (PC), that will account for most of the variance in the observed variables. The new uncorrelated variables are obtained as linear combination of the original data as
Given the sample mean of the m-dimensional vector
For uncorrelated variables, the off-diagonal values of the sample covariance matrix are zero, that is, S is diagonal. The covariance of linearly transformed variables
Thus, we want to find the matrix A such that the covariance matrix of the transformed data,
The eigenvalues, which coincide with the matrix
The number of eigenvalues is equal to the number of original variables; however, since the eigenvalues are equal to the variance of the principal components and they are sorted in a decreasing order, the first k eigenvalues can account for a large portion of the variance of the data.
Hence, to describe our original dataset we can use only the first k uncorrelated principal components, instead of the complete set of redundant m variables. In matrix notation this can be written as
Choosing which and the number of principal components that should be retained in order to summarize our data is a task that can be solved using several strategies [43, 49]. For example, one way commonly used is to retain the first k principal components that explain a given total percentage of the variance, e.g. 90% [43, 44]. Another rule is to plot the eigenvalues in decreasing order. Moving from left to right, the eigenvalues usually have an initial steep drop followed by a slow decrease. All the components after the elbow between the steep and the flat part of the curve should be discarded. This test is called screen plot.
Alternatively, one can select the principal components that can be associated to a physical meaning related to the studied system. For example, following the differentiations of a cell line growing in different experimental conditions, one principal component may represents the different conditions, while another PC may describe the maturation stage of the cells. None of the above methods are better than the other; usually more than one test should be done and the results compared.
The principal component analysis allows to obtain uncorrelated variables and then to remove the multicollinearity problem.
4.2.3.2. Principal Component Regression (PCR): multivariate regression following PCA
Once a set of k principal components has been obtained using the PCA method, they can be used as input variables for a multivariate regression analysis instead of the original data. The regression equation
4.2.3.3. Partial Least Squares (PLS)
Another way to face the multicollinearity problem is to use PLS. The goal of PLS regression is to predict Z from Y and to describe their common structure [50].
In the PCR method described above, the principal components are selected based on their ability of explaining the variance of the Y matrix (the dependent variable matrix). By contrast, PLS regression finds components from Y that are also relevant for Z. Specifically, PLS regression searches for a set of components that performs a simultaneous decomposition of Y and Z, with the constraint that these components explain as much as possible the covariance between Y and Z. In this way, compared to the PCR, the principal components contain more information about the relationship between predictors and dependent variables [50]. For categorical dependent variables, the PLS method takes the name of partial least square discriminant analysis (PLS-DA) [43].
Classification methods can be divided into two main categories, supervised and unsupervised. Supervised techniques require the knowledge of the group membership of the observations and can be used to understand the structure of the data, e.g. why certain observations belong to a given group. Moreover, once the classification model is calibrated on a “training” dataset, it can be used in a predictive way to group observations whose group membership is unknown.
On the other hand, unsupervised methods try to group the observations without any knowledge of the group membership.
In the following paragraph, we will describe the main multivariate classification approaches.
Discriminant analysis is mainly a supervised technique which was originally developed by Ronald Fisher as a way to subdivide a set of taxonomic observations into two groups based on some measured features [51]. Later, DA was extended to treat cases where there are more than two groups, the so-called “multiclass discriminant analysis” [49, 52, 53].
DA can have mainly two objectives. First, it can be used in a supervised way to describe and explain the differences among the groups. As we will see later, mathematically DA finds the optimal hyperplane that separates the groups among each other. Or, in other words, it finds the optimal linear combination of the original variables that maximizes the distance among the groups. The transformed observations are called discriminant functions.
The use of a linear combination implies that each original variable is weighted by a coefficient which can be used to study the relative importance of the variable in the separation among the groups. A second possible role of DA is to classify observations into groups. An observation, which has to be assigned to a group, is evaluated by a discriminant function (already calibrated on another dataset) and it is assigned to one of the groups at which most likely it belongs [43, 44, 49]; in this view DA is used as an unsupervised method.
When only linear transformations are applied to the variables used as DA input, the discriminant analysis is called linear discriminant analysis (LDA).
In some cases, LDA alone is not suitable and the original variables can be mapped to a new space via any non-linear function. Then, the LDA is applied in this non-linear space (which is equivalent to non-linear classification in the original space). This procedure can be seen under several names such as “non-linear DA” (NLDA) or “kernel Fisher discriminant analysis” (KFD) or “generalized discriminant analysis”.
In the following sections we will focus on LDA, first describing the descriptive approach and subsequently the classification approach.
4.3.1.1. Linear DA (LDA) as a descriptive method
The initial dataset is an ensemble of multivariate observations partitioned into G distinct groups (e.g. different experimental treatments, times or conditions). Each of the G groups contains
Our goal in LDA is to search for the linear combination that optimally separates our multivariate observation into G groups.
The linear transformation of
Since
where
We now introduce the between groups sum of squares B in equation 5 (measure of the dispersion among the groups) and the within-group sum of squares E in equation 6 (measure of the dispersion within one group). First, we define them for the uni-dimensional case relatively to the untransformed data:
and
where
Analogously, in the multivariate case (where each observation is constituted by m variables) we have the two matrices:
and
Finding the optimal linear combination that separates our multivariate observations into k groups means to find the vector w which maximizes the rate between the between-groups sum of squares over the within-groups sum of squares. Using the equations for the transformed data (equations 3 and 4) into the equations 7 and 8, we can write:
We want to find w such that λ is maximized.
Equation 9 can be rewritten in the form
where
\n\t\t\t\t\tThe solutions of equation 10 are the eigenvalues
The discriminant functions are then obtained considering only the first s positive eigenvalues and multiplying the original data by the eigenvectors
Discriminant functions are uncorrelated but not orthogonal since the matrix
In many cases the first two or three discriminant functions account for most of
The weighting vectors
If the variables are on very different scales and with different variance, to assess the importance of each variable in the group separation the standardized discriminant functions can be used. The standardization is done by multiplying the unstandardized coefficients by the square root of the diagonal element of the within-group covariance matrix.
Another way to assess the variable importance is to look at the correlation between each variable and the discriminant function. These correlations are called structure or loading coefficients. However, it has been shown that these parameters are intrinsically univariate and they only show how a single variable contributes to the separation among groups, without taking into account the presence of the other variables [49].
4.3.1.2. Linear as a classification method
After a set of discriminant functions are calibrated as described in the previous section, the discriminant analysis can be applied to classify new observations into the most probable groups. From this point of view, the linear discriminant analysis becomes a predictive tool, since it is able to classify observations whose group membership is unknown [43, 49]. The discrimination ability of our LDA model can be tested by a procedure called “re-substitution” [49]. This method consists of producing an LDA model using our dataset (i.e. finding the optimal w). Then, each observation vector is re-submitted to the classification function (
The fitting accuracy is the ability to reproduce the data, namely how the model is able to reproduce the data that were used to build the model (the training set). This corresponds to the apparent classification rate and it is obtained using the re-substitution procedure.
The prediction accuracy is the ability to predict the value or the class of an observation, that was not included in the construction of the model. This kind of accuracy is often referred to as the ability of the model to generalize. The data used to measure this accuracy are called “test set”. The prediction accuracy can be called “actual classification rate”. This is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. To have an estimation of the actual classification rate, two main procedures can be applied: the hold-out and cross-validation [43].
In the hold-out, the dataset is divided into two partitions: one partition is used to develop the model (e.g. the discriminant functions) and the second partition is given as input to the model. The first partition is usually called “training set” or “calibration set”, while the second partition is the validation set [54].
When the number of observations is small, the cross-validation is usually preferred over the hold-out. The basic idea of the cross-validation procedure is to divide the entire dataset into L disjoint sets. L-1 sets are used to develop the model (i.e. the calibration set on which the discriminant functions are computed) and the omitted portion is used to test the model (i.e. the validation set given as input to the model). This is repeated for all the L sets and an average result is obtained.
Apparent or actual classification accuracies can be summarized in a confusion matrix. As an example, total N observations,
The confusion matrix becomes then:
Actual group | Predicted group | |
1 | 2 | |
1 | ||
2 |
A powerful analysis tool is the combination of the principal component analysis with the linear discriminant analysis [52]. This is particularly helpful when the number of variables is large. In particular, if the number of observations (N) is less than the number of variables (m) - specifically N-1<m - the covariance matrix is singular and cannot be inverted (see section 4.2.3.). We then need to find a way to reduce the number of variables, for example using the PCA [49, 55]. This procedure has been widely used for several problems in different fields [35, 52, 56-60]. The condition N-1<m almost always appears in spectroscopy, where the number of observations (N) is usually 102 and the number of variables (m) is typically within 102 to 103.
Let\'s take into account the same situation described for the many group linear discriminant analysis. The original dataset is an ensemble of multivariate observations which is partitioned into k distinct groups. Again, we want to find the discriminant functions which optimally separate our multivariate observation into the k groups. Then, the discriminant functions can be used to identify the most important variables in terms of ability of distinguishing among the groups. Thus, first the original dataset is submitted to the PCA to reduce the number of variables; subsequently, the reduced dataset is analyzed using the LDA.
Another way that can be used instead of PCA is to perform the PLS.
In a way analogous to the PCA-LDA procedure, here we first apply the PLS algorithm to the original data and then the LDA on the selected principal components [61].
Given that the PLS searches for a set of components that performs a simultaneous decomposition of the dependent and independent datasets, the main difference with PCA-LDA is that the principal components resulting as output of PLS better describe the relationship between independent and dependent variables. This does not necessarily mean that this method is better in general. Indeed, applying PCA or PLS on the same dataset often leads to similar results [62, 63] and the classification accuracy or the descriptive ability is mostly determined by the underlying structure of the data which can make one of the two methods more suitable than the other.
The goal of cluster analysis is to find the best grouping of the multivariate observations such that the clusters are dissimilar to each other but the observations within a cluster are similar [44].
CA is an unsupervised technique, that is, the group membership of the observations (and often the number of groups) is not known in advance.
At first we have to define a measure of similarity or dissimilarity also called distance functions. The most common distance functions are: i) the Euclidean distance; ii) the Manatthan distance; iii) the Mahalanobis distance; iv) the maximum norm.
Based on the procedure they use, clustering algorithms can be divided into three main groups: hierarchical, partitional and density-based clustering. None of the following algorithms is better than the other. The choice of the clustering method strongly depends on the structure of the data and on which kind of results one would expect.
Hierarchical clustering algorithms can be again subdivided into agglomerative or divisive. The agglomerative clustering starts with all observations placed in different clusters and in each step an observation or a cluster of observations is merged into another cluster. The most commonly employed agglomerative clustering strategies are complete-linkage, average-linkage, single-linkage, centroid-linkage. The drawback of the agglomerative clustering algorithms is that observations cannot be moved among the clusters once a cluster is made.
The divisive method starts with one single cluster containing all observations and then it divides the cluster into two sub-clusters at each step. Divisive methods have the same drawback of the agglomerative clustering, that is, once a cluster is made, an observation cannot be moved to another cluster. Divisive methods are suited when large clusters are searched for.
The partitional algorithm assigns the observations to a set of clusters without using hierarchical approaches. One of the most used non-hierarchical approach is the k-means clustering.
The density-based clustering seeks to search for regions of high density without any assumption about the shape of the cluster.
The artificial neural networks are mathematical models that were developed in analogy to a network of biological neurons [64]. Mathematically, a neuron can be modeled as a switch that receives, as input, a series of values and produces an output consisting of a weighted sum of the input eventually transformed by a function f. Many neurons can be combined to create more complex networks. Depending on the type of neurons and on how the neurons are connected to each others, different kinds of neural networks can be created. The most common type of neural network is the feed-forward neural network, in which neurons are grouped into layers, each neuron of a layer is connected to all the neurons of the next layer and the information flows from the input to the output without loops. For a comprehensive description of neural networks and their applications see [54, 65].
In the following, we will provide a few selected examples of the application of FTIR microspectroscopy coupled with multivariate analysis for biomedical relevant studies, with the aim to highlight the importance of linking the two approaches to extract the most significant spectral information from highly informative systems.
In some cases, PCA alone represents a powerful method for the analysis of multidimensional FTIR spectra. Indeed, several interesting works are reported in the literature, in which this approach is employed to support the spectroscopic investigation of complex biological systems and processes. For instance, synchrotron based FTIR microspectroscopy coupled with PCA has been applied to the characterization of human corneal stem cells [27, 66], in cancer research for the screening of cervical cancer [14], as well as to disclose the effects induced by a surface glycoprotein in colon carcinoma cells [67].
For instance, Matthew German and colleagues [68] coupled high-resolution synchrotron radiation-based FTIR (SR-FTIR) microspectroscopy with PCA to investigate the characteristics of putative adult stem cell (SC), transiently amplified (TA) cell, and terminally differentiated (TD) cell populations of the corneal epithelium. Using PCA, each spectrum, composed by many variables (the wavenumbers), is reduced to a point in a low dimensional space. Then, each observation can be visualized in a two or three dimensional score plot. Choosing the appropriate principal components, the authors were able to clearly distinguish the three cell populations confirming the ability of SR-FTIR microspectroscopy to identify SC, TA cell, and TD cell populations.
PCA alone is extremely powerful to reduce the number of variables; however, it is not a clustering algorithm and the group into clusters must be done with other techniques.
For example, Tanthanuch and colleagues applied FTIR microspectroscopy-supported by PCA and unsupervised hierarchical cluster analysis (UHCA) to identify specific spectral markers of the differentiation of murine embryonic stem cell (mESCs) and to distinguish them into different neural cell types [25]. In particular, focal plane array (FPA) - FTIR and SR-FTIR microspectroscopy measurements - performed on cell clumps and single cells respectively - allowed to obtain a biochemical fingerprint of different mESC developmental stages, namely embryoid bodies (EBs), neural progenitor cells (NPCs) and embryonic stem-derived neural cells (ESNCs). Interestingly, it should be noted that the results obtained on cell clumps and on single cells were found to be comparable, corroborating the FPA-FTIR results on cell clumps. The analysis of second derivative spectra enabled to highlight important spectral changes occurring during ES cell differentiation, mainly in the lipid CH2 and CH3 stretching region and in the protein amide I band. Noteworthy, these results overall indicated that during neural differentiation the cell lipid content increased significantly, likely reflecting modifications in cell membranes, whose lipid content is known to have a key role in neural cell differentiation and signal transduction. Moreover, changes in the profile of amide I band, mainly involving the alpha-helix component around 1650-1652 cm-1, indicated an increased expression of alpha-helix reach protein in ESNCs compared with their progenitor cells, a result that could reflect the expression of cytoskeleton protein, crucial for the establishment of neural structure and function. These results were then strongly supported by PCA, that made it possible to disclose regions of the IR spectrum which most contributed to the spectral variance, namely amide I band and C-H stretching region. Furthermore, the application of UHCA allowed to successfully discriminate and classify each stage of ESNCs differentiation, again considering the spectra in the spectral range mainly due to acyl chain vibrations and the extended region between 1750 and 900 cm-1.
As discussed previously, PCA is frequently used for preliminary dimensionality reduction before further analyses, as LDA [21]. Indeed, a limit of using PCA alone is that it does not allow to obtain an unambiguous grouping of the data into clusters, requiring therefore the application of another analysis step able to reduce the intra-category variation while maximizing that inter-category [69]. The coupling, for instance, of PCA with LDA is a well established procedure which enables not only to classify the observations into groups but to quantify the importance of the single variables for this group separation. In this view, the advantage of LDA is that it makes it possible to reveal clusters, identifying objectively also the most contributory wavenumbers responsible for spectra discrimination [21, 58]. In particular, the application of PCA-LDA to spectroscopic investigation of complex biological systems proved to be a useful tool for the identification of spectral biomarkers of the process under investigation [7, 35, 69, 70, 71].
One outstanding work, worth to mention here, was done by Kelly and colleagues [70], where the authors showed how infrared spectroscopy and multivariate techniques can be used as a novel diagnostic approach for endometrial cancer screening. They first demonstrated how SR-FTIR microspectroscopy with subsequent PCA-LDA allows the clear segregation of different subtypes of endometrial carcinoma. However, the requirement of a particle accelerator impairs the use of endometrial spectroscopy as practical diagnostic application.
Recently, Taylor and colleagues applied ATR-FTIR spectroscopy supported by PCA-LDA analysis to interrogate endometrial tissues, employing in particular a conventional IR radiation source [72], showing that this approach, that can be applied directly to liquid or solid samples without further preparation, could provide a useful and simple objective test for endometrial cancer diagnosis.
Furthermore, in the work of Walsh and colleagues [69], ATR microspectroscopy has been successfully applied to the characterization of samples of exfoliative cervical cytology of different categories, with increasing severity of atypia. The spectral analysis was supported by PCA, with or without subsequent LDA, to verify if it was possible to discriminate among normal, low grade and high grade of exfoliative cytology. Indeed, important differences were found in the spectral range between 1500 and 1000 cm-1, mainly due to proteins, glycoproteins, phosphates and carbohydrates. Noteworthy, the authors stressed that only the employment of the combined PCA-LDA allowed to maximize the inter-category variance, whilst reducing that intra-category. In particular, they found that the glycogen content strongly influenced the intra-category variance, while that inter-category resulted to be mainly due to protein and DNA conformational changes. In this view, FTIR microspectroscopy coupled with PCA-LDA could allow for an objective classification approach to class cervical cytology.
We should note that a delicate point of PCA-LDA is the choice of the principal components to be used as LDA input and, as described in the previous section about PCA, several ways have been developed to perform this task. Alternatively, the PLS method can be used instead of PCA [6, 73, 74]. For instance, Sandt and colleagues, using synchrotron infrared microspectroscopy coupled with PLS-DA, were able to characterize the metabolic fingerprint of induced pluripotent stem cells (iPSCs). In particular, they found that iPSCs are characterized by a chemical composition that leads to a spectral signature indistinguishable from that of embryonic stem cells (ESCs), but entirely different from that of the original somatic cells [6].
Recently, we applied FTIR microspectroscopy supported by PCA-LDA to the study of murine oocytes characterized by two different types of chromatin organization, namely surrounded nucleolus (SN) oocytes in which the chromatin is highly condensed and forms a ring around the nucleolus, and the not surrounded nucleolus (NSN) type where chromatin is dispersed and less condensed around the nucleolus [7, 75]. Interestingly, only SN oocytes are capable to complete the embryonic development after fertilization, while the NSN type, if fertilized, arrests at the two cell stage. To try to get new insights on the mechanisms that drive the different chromatin organization in the two kinds of oocytes, crucial for their embryonic development after fertilization, we studied the infrared absorption of single intact cells at different maturation stages, namely antral germinal vesicle (GV), metaphase I (MI, matured for 10 hours in vitro), and metaphase II (MII, matured for 20 hours in vitro).
Indeed, as we will show in the following, the FTIR spectra of the oocytes taken at the different maturation stages are very complex, since they provide information on different processes that were taking place simultaneously within the cells. For this reason, beside a fundamental visual inspection of the data, enabling the identification and assignment of the different spectral bands, it was crucial the application of PCA-LDA that made it possible to draw out the most significant spectral information responsible for the different cell behavior. Moreover, PCA-LDA allowed to identify the stage at which the separation between the SN and NSN oocytes took place, leading to their well distinct cell destinies.
As we discussed in paragraph 2, since the FTIR spectrum of cells is due to the overlapping contributes of the main biomolecules (see Figure 2), we analysed the second derivative spectra to identify the band peak positions and to assign them to the different biomolecule vibrational modes. The spectral analysis, strongly supported by PCA-LDA, allowed us to disclose the most important spectral differences between the two types of oocytes, at each maturation stage, that were found to occur mainly in the lipid and nucleic acid absorption regions, as we will discuss below. For a full discussion of the results see [7].
5.1.1.1. NSN oocytes
The analysis between 3050 and 2800 cm-1, mainly due to the lipid carbon-hydrogen stretching vibrations [29], disclosed significant variations in the lipid content of NSN oocytes during their maturation up to MII. Indeed, besides an increase of the CH2 band intensity up to MII, respectively at 2922 cm-1 and 2852 cm-1, important changes concerned mainly the unsaturated fatty acid composition, as indicated by variations of the band between 3020 and 3000 cm-1 due to the olefinic group absorption. Indeed, as shown in Figure 3A, a single peak around 3013 cm-1 was present at GV and MI stages, while a splitting in two components at ~ 3016 cm-1 and at ~ 3010 cm-1 characterized the MII stage (see the inset of Figure 3A). These results could reflect important changes in membrane fluidity, which in turn could confer to the oocyte a different division ability after fertilization [8].
5.1.1.2. SN oocytes
SN oocytes were found to be characterized - during maturation up to MII - by a significant increase of the 2937 cm-1 component that could be likely due to cholesterol and/or phospholipids (Figure 3B) [76, 77]. As discussed for NSN oocytes, the observed changes could reflect variations in the membrane properties, again highlighting the crucial role of lipids as markers of oocyte developmental competence [8, 78].
Second derivative absorption spectra of NSN (A) and SN (B) oocytes in the lipid absorption region. The second derivatives of the FTIR absorption spectra of single oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the acyl chain absorption region, after normalization at the tyrosine peak (~1516 cm-1). In the inset a magnification of the olefinic group band is shown.
5.1.1.3. PCA-LDA analysis
The results obtained by the direct inspection of second derivative spectra were confirmed by PCA-LDA analysis performed on raw spectra. Firstly, the analysis was made on each type of oocyte taken at the different maturation stages. For the SN oocytes, the component carrying the highest discrimination weight resulted that at 2938 cm-1, likely due to cholesterol and / or phospholipids [76, 77], in agreement with what found by the direct inspection of the spectra.
Concerning the NSN oocytes, on the other hand, the wavenumbers with the highest discrimination weight were the 2922 cm-1, due to the CH2 stretching vibration, which increases up to MII, and the 3018 cm-1, assigned to the olefinic group =CH of polyunsaturated fatty acids, whose absorption was observed to vary during the oocyte maturation.
We, then, compared the two types of oocyte at each maturation stage - as illustrated in Figure 4 - and we found that at the antral and MII stages the spectral components with the highest discrimination weight were those due to cholesterol and /or phospholipids, while at MI was that due to the olefinic group. Furthermore, to support the crucial role played by lipids in determining at some extent the oocyte developmental capacity, we should add that when we compared by PCA-LDA the spectra of the two oocyte types at the same maturation stage in the 1800-1500 cm-1 spectral range, dominated by the amide I and amide II absorption, the wavenumber with the highest discrimination weight was the 1739 cm-1, due to the carbonyl stretching vibration of esters [7, 29].
PCA-LDA analysis of SN and NSN oocytes in the lipid acyl chain absorption region (3050 – 2800 cm-1). The separation between the two types of oocytes at each maturation stage is reported as average of PCA-LDA scores. The height of the boxes and the whiskers corresponds to 1 and 1.5 standard deviations from the mean values, respectively. The analysis has been performed on the measured spectra.
5.1.2.1. NSN oocytes
We then analyzed the nucleic acid IR response of NSN and SN oocytes during their maturation, exploring the spectral region between 1000 and 800 cm-1, where RNA and DNA vibrational modes mainly occur [31, 32].
We found that NSN oocytes maintain, in all the studied stages, an appreciable transcriptional activity as indicated mainly by the simultaneous presence of the RNA ribose component around 921 cm-1 and of the DNA deoxyribose between 895-898 cm-1 - indicative of a DNA/RNA hybrid - whose relative intensities were seen to vary during maturation (see Figure 5A). In particular, the intensity of these two components is higher at the antral stage, while it decreases at MI, to increase again up to MII. These results were also supported by the response of the complex band between 980-950 cm-1, mainly due to the CC stretching vibration of DNA backbone. Indeed, the profile of this band varies depending on the DNA structure that, in turn, could reflect a different nucleic acid activity. In particular, for the NSN oocytes we found that at the antral stage DNA is mainly in A-form - with a triplet at 975 cm-1, 966 cm-1 and 951 cm-1 - typical of the DNA/RNA hybrid during transcription. At MI, the reduction of the 975 cm-1 and 966 cm-1 bands and the appearance of that at 969 cm-1 indicate that DNA is mainly in the B-form, suggesting a sort of transcriptional “stand by state”, further supported by the reduction extent of the DNA/RNA hybrid, as discussed above. From this “stand by state” NSN oocytes seem to resume their transcriptional activity at MII, where a coexistence of DNA A and B forms was observed, as indicated by the increase of the ~ 975 cm-1 band and again in agreement with the simultaneous increase of the ribose (921 cm-1) and deoxyribose (898 cm-1) components.
Second derivative absorption spectra of NSN (A) and SN (B) oocytes in the nucleic acid absorption region. The second derivatives of the FTIR absorption spectra of single oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the 1000-800 cm-1 absorption region, after normalization at the tyrosine peak (~1516 cm-1).
Furthermore, the analysis of the low frequency range, between 840-820 cm-1, allowed us to obtain information on DNA methylation. In particular, in this spectral range, bands due to DNA S-type sugar puckering modes occur, which are sensitive to changes in the DNA sugar conformation induced by cytosine methylation [32]. The possibility to monitor changes in the profile of this spectral region in whole intact cells makes it possible, therefore, to obtain information on the variation of global DNA methylation in the CpG islands. In this way, we found that in the NSN oocytes DNA methylation was high at the antral stage, while it became very low, almost negligible at MII, in agreement with what found for the transcriptional activity pattern at the different maturation stages.
Finally, significant spectral differences were found between 890 and 850 cm-1, where four different bands due to adenine and uracil vibrational modes occur (see Figure 5) [79]. Interestingly, the relative variation of these bands enables to monitor the mRNA polyadenylation extent, a crucial mechanism that regulates transcription. We found, in particular, that NSN oocytes were characterized during maturation by a low level of mRNA polyadenylation, being the polyadenylic acid band at 884 cm-1 absent at MII, while a new band at 854 cm-1 - likely due to adenine possibly not involved in polyA tail [80] – appeared. These results seem to suggest that an inadequate level of mRNA polyadenylation could preclude the possibility to resume meiosis, leaving the NSN oocytes in an unsuccessful transcriptional state.
5.1.2.2. SN oocytes
The analysis of SN oocytes (Figure 5B) in the spectral range between 1000 and 800 cm-1 led to very different results compared to NSN oocytes (see Figure 5A). Briefly, during all the studied maturation stages, the SN oocyte transcriptional activity was found to be maintained at lower levels than NSN oocytes, as revealed by the analysis of the CC stretching of the DNA backbone (980-950 cm-1) and the monitoring of the ribose (~ 922 cm-1) and deoxyribose (895-898 cm-1) vibrations. These results were supported by the temporal evolution of the DNA methylation bands that suggested a partial CpG methylation at the antral and MI stages, which dramatically increased at MII, contrary to what observed for NSN oocytes.
Noteworthy, while no evidence of mRNA polyadenylation was observed for SN oocytes at the antral stage - as indicated by the absence of the two polyadenylic acid bands around 884 cm-1 and 860 cm-1 - starting from MI the adenine and uracile bands at 870 cm-1 and 850 cm-1 appeared, to then dramatically increase up to MII. These findings likely indicate that SN MII oocytes are characterized by an adequate level of maternal polyadenylated mRNAs, making them ready to sustain a proper embryo development, contrary to NSN oocytes.
5.1.2.3. PCA-LDA analysis
The above results overall indicate that the IR spectra of oocytes at different maturation stages are very informative in the nucleic acid absorption region, allowing to obtain information on several cell processes simultaneously, including transcriptional activity, DNA methylation, and RNA polyadenylation. For this reason, PCA-LDA analysis was crucial to disclose the most significant spectral response, enabling to identify the marker bands able to discriminate between the two kinds of oocytes.
Firstly, we analyzed the different maturation stages of each kind of oocyte. In particular, NSN oocytes displayed a segregation into three separated clusters, each corresponding to a maturation stage, with a classification accuracy of about 80%. Noteworthy, the wavenumber with the highest weight (1.0) was that around 880 cm-1, due to polyadenylic acid, that, as revealed by second derivative analysis, was present only at the antral stage and disappeared upon maturation up to MII.
On the other hand, PCA-LDA analysis of SN oocytes led to an excellent discrimination accuracy (97%), with the wavenumbers with the highest discrimination weight at 817 cm-1 (1.0) and 859 cm-1 (0.83). While this last component is due to polyadenylic acid, the assignment of the 817 cm-1 band is not unequivocal, being due to overlapping contributions of DNA and polyadenylic acid.
The above results were then confirmed by the PCA-LDA analysis performed between 1400-1000 cm-1, where contributions due to nucleic acids, such as sugar-phosphate vibrations, also occur [31]. In particular, for the NSN oocytes the wavenumber with the highest discrimination weight (1.0) was the 1305 cm-1, which is due to free adenine, possibly not involved in polyadenylation [79]. In agreement with the temporal pattern of the adenine band at 870 cm-1, discussed previously, the 1305 cm-1 component displayed a higher intensity at MII, confirming that an inadequate mRNA polyadenylation could preclude NSN oocytes from a successful embryonic development (see Figure 6).
Second derivative absorption spectra of NSN oocytes in the absorption region of “free” adenine. The second derivatives of the FTIR absorption spectra of single NSN oocytes, measured at the antral (continuous line), MI 10 H (dotted line), and MII 20 H (dashed line) stages, are reported in the 1330-1270 cm-1 spectral range, where “free” adenine absorbs, after normalization at the tyrosine peak (~1516 cm-1).
We then compared by PCA-LDA the two types of oocytes taken at the same maturation stage. As reported in Figure 7, we found the largest spectral distance at MI (92% classification accuracy), with the components carrying the highest discrimination weight due to A-DNA, likely reflecting differences in the transcriptional activity. In this view, MI stage could be considered a sort of crucial checkpoint, when some molecular rearrangements occur, deciding the oocyte fate.
PCA-LDA analysis of SN and NSN oocytes in the nucleic acid absorption region (1000 - 800 cm-1). The separation between the two types of oocytes at each maturation stage is reported as average of PCA-LDA scores. The height of the boxes and the whiskers corresponds to 1 and 1.5 standard deviations from the mean values, respectively. The analysis has been performed on the measured spectra.
These findings have been strongly supported by the comparison of the SN and NSN oocytes at each maturation stage, altogether. A very good discrimination accuracy (89%) was again found analyzing the nucleic acid absorption region, between 1000 and 800 cm-1, that led to a clear cut separation into two groups (see Figure 8): one containing only the MII SN oocytes, and the other containing all the other SN and NSN stages. In particular, the wavenumbers carrying the highest discrimination weight were found at 926 cm-1 (1.00), due to ribose vibration, and at 855 cm-1 (0.97), assigned to adenine vibration, indicating again that differences in the temporal evolution and extent of transcription and polyadenylation play a crucial role in determining the different oocyte fate: the MII SN oocytes, with their proper content of maternal mRNAs polyadenylated, ready to support successfully the embryonic development; on the other hand, the MII NSN oocytes, with their mRNA lacking the appropriate polyadenylation, are kept in an unsuccessful transcriptional state.
PCA–LDA analysis of SN and NSN oocytes in the nucleic acid absorption region. The PCA–LDA analysis has been carried out on measured FTIR absorption spectra obtained from SN and NSN oocytes at each maturation stage, between 1000 and 800 cm−1. The semi-axes of ellipsoids in the 3D score plot correspond to two standard deviations of the data along each direction.
FTIR microspectroscopy has recently emerged as a powerful tool in biomedical research, thanks to the possibility of providing, in a non-invasive and rapid way, a chemical fingerprint of biological samples. In particular, being successfully applied to the study of complex biological systems, it makes it possible not only to characterize in situ biological processes, but also to provide a rapid diagnosis of several diseases, such as cancer and amyloid-based disorders.
We should, however, note that the intrinsic complexity of the IR response of biological systems - due to the overlapping absorption of the main biomolecules - requires the support of an appropriate multivariate analysis approach able to draw out the significant and non-redundant information contained in these highly dimensional data. Indeed, only a suitable combination of biospectroscopy and of multivariate analysis would provide robust and reliable results through the identification of specific biomarkers, an essential prerequisite for unbiased result interpretation [19, 20].
D. A. is indebted to the University of Milano-Bicocca (I) for the supporting postdoctoral fellowship. P. M. acknowledges a postdoctoral fellowship from Italian Institute of Technology. S.M. D. acknowledges the financial support of the FAR (Fondo di Ateneo per la Ricerca) of the University of Milano-Bicocca (I).
The authors wish to thank Carlo Alberto Redi and his collaborators at the University of Pavia (I) for the collaboration on murine oocyte maturation, and Antonino Natalello of the University of Milano-Bicocca (I) for helpful discussions.
An optical fiber is an extended cylindrical optical waveguide. In its simplest form, it consists of a core having a certain refractive index nc and is surrounded by a clad (sometimes called skin) of refractive index ncl (or ns). An optical fiber is used to guide light through its core, from one end to another, based on the principle of total internal reflection which mandates that nc must be always higher than ncl. Basically, optical fibers are made of highly pure silica glass doped with some impurities in order to increase nc or decrease ncl [1, 2, 3]. Recently, polymeric optical fibers got more attention as alternatives of some glass based optical fibers [1, 4].
Optical fibers are involved in many technological applications such as telecommunications, sensing [4, 5]; fiber lasers and fiber amplifiers [6]; fiber gratings which can act as mirrors [7, 8]; mode converters [9]; modulators; and couplers and switches [10, 11]. Optical fibers are considered ideal optical transmission media since communication cables hundreds of kilometers in length can be obtained with low absorption and low loss due to the purity and cross-sectional uniformity of the manufactured optical fibers. Moreover, accurate tuning of the refractive indices of both core and clad guarantee extremely low scattering loss at the interfaces [1].
The commonly known optical fibers are step index and graded index (GR-IN) optical fibers. The former means that the core’s refractive index is homogeneous while it suffers an abrupt change at the boundary with the clad. For a GR-IN optical fiber, the core does not have a constant value of refractive index but it rather has a radial distribution of refractive index. These two types of optical fibers can be classified into either single-mode or multi-mode optical fibers. Single-mode optical fiber only sustains one mode of propagation while the multi-mode optical fiber can sustain up to hundreds of propagation modes [1, 3]. The number of the propagation modes is related to the numerical aperture of the fiber, which, in turn, depends on the refractive indices of both core and clad.
Accurate characterization of optical fibers is required in order to know about their functions and performances. There are many methods of optical fibers characterization such as optical microscopy, electron microscopy, X-ray spectrometry, infrared spectroscopy, light diffraction, light scattering, optical interferometry, and digital holography [1, 3, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29]. Optical interferometry is an effective accurate tool for studying and characterizing optical fibers. It depends on the determination of the phase difference between a ray of light transmitting the fiber’s cross-section and a reference ray reaching the interference plane directly without crossing the fiber. This phase shift can be transformed into a refractive index map representing the radial distribution of the refractive index across the fiber or, in other words, the refractive index profile (RIP). Interferometry can detect tiny changes in refractive index if an external effect is applied on the fiber. The change of refractive index can be in situ detected if the interferometer is developed to achieve this task. Interference patterns can be digitally processed and analyzed in order to increase the accuracy of the obtained results [1, 17, 22, 26, 27, 30, 31, 32, 33, 34, 35].
Interference techniques can be classified into either two-beam interferometers such as Michelson, Mach-Zehnder, Pluta polarizing microscope, Lioyd’s mirror, etc., or multiple-beam interferometers such as Fabry-Pérot and Fizeau interferometers [1, 3, 25, 36, 37, 38, 39]. A two-beam interferometer produces a pattern of alternate bright and dark fringes of equal thicknesses when two beams, usually, of equal intensities Io suffering a relative phase difference δ are superposed. The resultant intensity distribution I of the interference pattern is given as:
Multiple-beam interference takes place when light rays fall on two parallel optical plates enclosing a small distance between each other while their inner surfaces are highly reflecting and partially transparent. The intensities of both reflected, I(r), and transmitted, I(t), light distributions that are redistributed due to the multiple-beam interference are given as [40]
where, I(i) is the intensity of the incident light, T and R are the products of the transmission and reflection coefficients of the two surfaces, respectively, while δ is the phase difference between any two consecutive interfered rays.
On the other hand, holography was firstly presented by Gabor in 1947 as a lens-less process for image formation by reconstruction of wave-fronts [41, 42, 43]. It offers 3D characterization such as the depth of field from recording and reconstructing the whole optical wave field, intensity, and phase [41, 42]. Holographic interferometry is a non-destructive, contactless tool that can be used for measuring shapes, deformations and refractive index distributions [44, 45]. The modern digital holography was introduced in 1994 [46, 47, 48]. Moreover, the phase shifting interferometric (PSI) technique was introduced by Hariharan et al. as an accurate method for measuring interference fringes in the real time [49]. Recently, digital holographic phase shifting interferometry (DHPSI) was used to investigate some optical parameters of fibrous materials [17, 18, 21, 26, 27, 28, 29].
In DHPSI, frequently a set of four [20] or five [23, 33] phase shifted holograms with known mutual phase shifts starting with 00 and having 900 separations have to be recorded [21]. These recorded holograms can be represented by:
where a(ζ, η) and b(ζ, η) are the additive and the multiplicative distortions and
or,
In digital holography, the recorded wavefield is reconstructed, based on Fresnel diffraction integral, by multiplying the stored hologram by the complex conjugate of the reference wave r*(ζ, η) to calculate the diffraction field b’(x’, y’) in the image plane, see Figure 1. This can be calculated using the finite discrete form of the Fresnel approximation to the diffraction integral as:
Geometry of digital holographic axes and the planes systems.
The parameters used in this formula depend on the used CCD array of N × M pixels and the pixel pitches Δζ and Δη. The distance between the hologram and the image plane is denoted by d’. The pixel spacings in the reconstructed field of image are:
The convolution of h(ζ, η)r*(ζ, η) can be used as alternative of Fresnel approximation [37]. The resulting pixel spacing for this convolution approach is
In addition, the phase shifted holograms are used to overcome the problems of the d.c. term and twin image, in which the calculated complex wavefield is used instead of a real hologram in the convolution approach.
The intensity and phase distributions in the reconstruction plane are given by
So, the optical phase differences due to phase objects can be extracted.
Mach-Zehnder interference-like system is used as a digital holographic setup as shown in Figure 2 [20, 23, 29, 33]. The optical waveguide sample, such as optical fiber, is immersed in a liquid of refractive index nL near or matching the cladding refractive index nclad of the sample. The interference patterns are recorded using a charge-coupled device, that is, CCD camera.
Mach-Zehnder digital holographic interferometric set-up, S F: spatial filter, L: collimating lens, BS: beam splitter, M: mirror, and MO: microscopic objective.
In this chapter, we illustrate some featured work on interferometric characterization (sometimes, implying digital holographic interferometry) of different optical fibers done by our research group during the last three decades. In Section 2, interferometric characterization of conventional step-index and GR-IN optical fibers is presented. Section 3 illustrates characterization of the conventional optical fibers when they are suffering mechanical bending. In Section 4, interferometric characterization of a special type of optical fibers called polarization maintaining (PM) optical fibers is presented. In the last section, we elucidate thick optical fibers and their interferometric characterization with a special interferometric system, developed in our laboratory, called lens-fiber interferometry (LFI).
In 1994, Hamza et al. derived a mathematical expression to calculate the RIP of an optical fiber by considering the refraction of optical rays at the liquid-clad and clad-core interfaces, see Figure 3 [12]. It was the first time to consider the refraction of the transmitted rays to reconstruct the RIP of a fiber. The derived expressions for calculating the RIP in case of two-beam and multiple-beam interferences, based on Figure 3, are given by Eqs. (12) and (13), respectively.
An incident ray (object ray) is refracted due to a clad-core fiber causing a fringe shift Z when interferes with a reference ray.
where, R is the fiber’s radius and e is the skin’s thickness. nL, ns, and nc are the refractive indices of the immersion liquid, skin, and core, respectively. λ is the wavelength of the used illuminating source. Ls and Lc are the geometrical path lengths inside the skin and the core, respectively. Z is the fringe shift due to the presence of the fiber while h is the interfringe spacing and d is the distance measured from the center of the fiber to the position of the incident ray.
In that work, they used Fizeau interferometer to determine the refractive index profile of FOS Ge-doped step-index multi-mode optical fiber with a core radius 19.5 μm. The fiber was immersed in a liquid of refractive index nL = 1.4665, which was a little bit greater than ns while the wavelength of the used illuminating source was λ = 546.1 nm. The Fizeau interferogram of this fiber is shown in Figure 4a. The obtained RIP was compared with the profile calculated for the same fiber when the refraction of light through the fiber was neglected as was usually done by other authors before this work. There was a significant difference between the two profiles, see Figure 4b. Therefore, the refraction through the fiber was recommended to be considered for calculating RIPs particularly when the refractive index of the immersion liquid is not close to the fiber’s refractive index.
(a) An interference pattern of Fizeau fringes, in transmission, for a FOS step-index optical fiber. (b) RIPs of this fiber in case of considering and neglecting the retraction of the crossing rays inside the fiber.
In 2008, another mathematical model was derived in order to determine RIPs of fibers having regular and/or irregular cross-sections [38]. This method was based on immersing the investigated fiber in two liquids with different, but so closed, refractive indices. They applied this method on a single-mode optical fiber, having a small core of radius <5 μm while the fiber’s radius was 60.6 μm, as shown by Fizeau interferograms in Figure 5 when the fiber was immersed in two liquids with refractive indices (a) 1.4589 and (b) 1.4574. The obtained RIP of this fiber is illustrated in Figure 5c showing that this fiber has nc = 1.4630 and ncl = 1.4596. This method was simple and accurate enough to detect such a small core of a step-index optical fiber.
Fizeau interferograms, in transmission, for a single-mode optical fiber when it was immersed in two liquids of refractive indices (a) 1.4589, (b) 1.4574. (c) RIP of the single-mode optical fiber having the interferograms shown in (a) and (b).
A GR-IN optical fiber with a radial refractive index distribution was suggested to be divided into a finite number (M) of concentric layers where each layer has its own value of refractive index, see Figure 6a. The thickness (a) of each layer equals R/M, where R is the radius of the graded-index part. When the ray falls on the fiber at a distance dQ apart from the fiber’s center, the ray refracts through Q layers. The nearest layer to the fiber’s center has a refractive index nQ. The fiber’s RIP can be calculated using Eq. (14) in case of two-beam interference and Eq. (15) in case of multiple-beam interference [13]. Another model was presented in order to get RIP of a GR-IN optical fiber by considering the real path of the optical ray due to the refraction in the core region as well as adding a correction for the ray passing through the immersion liquid [50], see Figure 6b. In this case, the fringe shift was obtained by assuming values for both the profile shape parameter (α) and the difference between refractive indices of core and clad (Δn). A prepared software was programmed to iterate and get the best values of α and Δn and comapre the calculated fringe shift with the experimentally obtained one.
(a) A schematic diagram shows the path of an optical ray crossing Q layers in the core region. (b) A schematic diagram shows the path of an optical ray crossing a GR-IN core optical fiber.
According to Figure 6b, the optical pathlengths of the ray crossing the core
where, R is the core’s radius, k is the minimum distance between the fiber’s center and the bent ray, ε is the half of the angle determined by the two radii that are enclosing the bent ray inside the graded-index region, and γ is the half of the angle between the incident and the emerged rays. Figure 7 shows the interferograms of LDF GR-IN optical fiber when it was investigated by (a) Pluta and (b) Fizeau interferometers. Figure 8 shows the RIPs calculated by these last models for the LDF optical fiber. The last model, presented in 2001 [50], provided more accurate values of the RIP of a GR-IN optical fiber compared with its previous presented model in Ref. [13].
(a) Pluta duplicated image of LDF GR-IN optical fiber and (b) Fizeau interferogram of the same sample. Reference [50] with permission.
A comparison between RIPs of LDF GR-IN optical fiber using the model in Ref. [27] (dots) and model in Ref. [28] (solid curve) in case of (a) multiple-beam Fizeau interference and (b) two-beam Pluta interference. Ref. [50] with permission.
However, the former requires knowing the function describing the index profile while the aim is to find the parameters of this function.
Optical fibers, which are isotropic materials, can suffer a birefringence under external mechanical bending effects [1, 22, 33, 51]. The induced birefringence can be used in sensing applications [52, 53, 54]. However, bending has an unfavorable effect on the optical fibers used in telecommunications where it, sometimes, causes a mode disturbance and consequently a signal attenuation [55, 56]. An approach to calculate the refractive index profile of a bent optical fiber was proposed where the fiber was divided into layers and slabs simultaneously [22]. The refraction of the optical rays at the liquid-clad and clad-core interfaces was considered. Unfortunately, this approach did not consider the change of refractive index inside each slab. Also, the expected change of refractive index due to the release of stresses near the fiber’s free surface has not been considered. However, this approach succeeded to present good information about the variation of mode propagation due to bending.
In 2014, Ramadan et al. calculated the refractive index and the induced birefringence profiles of bent step-index optical fibers using digital holographic Mach-Zehnder interferometer [33]. In that work, they considered two different processes controlling the variations of the refractive index of the bent fiber: (1) the linear refractive index variation due to the applied stress along the bent radius and (2) the release of this stress on the fiber’s surface. The first one is dominant when approaching the center of the fiber while the second one is dominant near the fiber’s free surface and decays on moving toward the fiber’s center. Figure 9 shows the difference between the paths of optical rays through the bent fiber in the compressed and expanded parts. The stress release was supposed to have a radial dependence on the fiber’s radius, which enabled the construction of 2D RIP of the investigated bent homogeneous optical fiber. Based on the expected stress values due to the bending effect, a function describing the RIP was proposed and used to integrate the optical path of the ray traversing the fiber [50]. By adapting the appropriate parameters of this function, the optical phase differences were estimated and matched those phase differences that were experimentally obtained. By this assumption, a realistic induced stress profile due to bending was obtained [33]. DHPSI was used in that study where the recorded phase shifted holograms were combined and processed to extract the phase map of the fiber [18]. By considering both of the mentioned effects, the following function was chosen to describe the RIP of the bent optical fiber [33].
A schematic diagram shows the path of an optical ray crossing a bent homogeneous optical fiber.
where ρ is the strain-optic coefficient, nbf is the refractive index of the bent-free fiber, R is the radius of bending, ro is the radius of the fiber, ncl is the clad’s refractive index, rs is the proposed parameter to control the distance suffering stress release from the surface of the fiber, and x is the distance between the center of the fiber and the position of the incident ray.
The first term of Eq. (18) gives the bent-induced birefringence,
which is correlated to the generated stress S (r,x) inside the fiber
Eq. (20) evaluates the distribution of stress over the fiber’s cross-section for different bending radii where E is the Young’s modulus of the bent fiber. The signs of Δn are opposite to the signs of tensile and compressive stresses. The tensile stress was chosen to be positive.
Since bending such a step-index optical fiber converts it into a weekly graded-index fiber, Bouguer’s formula [40] was used to correlate the radius, incidence angles, and refractive index of the bent fiber as follows:
where n(x,r) is the refractive index at radius r. By applying this formula at the incidence point, one obtains
This equation was numerically solved to get K satisfying the lower integration limit of the optical path difference for a certain value of x. Based on the model described in Ref. [50], the infinitesimal change in the geometrical distance along the path of the optical ray with respect to the radius variation was given as:
By integration with respect to r, the total path length inside the fiber is:
The optical path length difference between this ray, passed through the fiber, and the reference ray passed through the liquid is:
The phase difference is given as:
Figure 10 shows a set of five shifted holograms of a bent step-index optical fiber with a bending radius R = 8 mm when the incident light was vibrating parallel to the fiber’s axis. They were recorded in order to apply the DHPSI technique and reconstruct the RIP of the bent fiber. The 2π shifted interferogram was analyzed and its reconstructed interference phase map, enhanced phase map, and interference phase distribution are shown in Figures 11a–c, respectively. The refractive index cross-section distribution of the bent optical fiber is shown in Figure 12 while the strain-optic coefficients in compression and expansion were 0.208 and 0.224, respectively.
A set of five shifted interferograms of a bent step-index optical fiber.
(a) The reconstructed interference phase map modulo 2π, (b) its enhanced phase map, and (c) the interference phase distribution.
The refractive index cross-section distribution of the bent optical fiber, R = 8.
In 2017, Ramadan et al. presented a theory to recover the RIP of a bent GR-IN optical fiber inside the core region using DHPSI [35]. They assumed the two different processes controlling the shape of the RIP: (1) the linear variation due to stresses in the direction of the bent radius and (2) the release of the stresses near the fiber’s surface.
The total optical path length of the optical ray crossing the bent GR-IN optical fiber is given by Eq. (27), see Figure 13. The calculated optical path length differences of the interfered rays can be transformed, afterward, into a phase difference map using Eq. (26).
schematic diagram shows the ray tracing in case of traversing bent GR-IN fiber.
with,
Figure 14a shows a set of five phase shifted interferograms for the bent GR-IN optical fiber with bending radius R = 8 mm when the incident light was vibrating parallel to the fier’s axis. The enhanced reconstructed phase modulo 2π and the interference phase distribution of the bent fiber are shown in Figure 14b. Due to the bending process, the GR-IN optical fiber exhibited a birefringence where the RIPs when the incident light vibrated parallel and perpendicular to the fiber’s axis were different, see Figure 15.
(a) A set of five phase shifted interferograms of a bent GR-IN optical fiber. (b) The enhanced reconstructed phase modulo 2π and the interference phase distribution. Ref. [35] with permission.
Refractive index cross-section distribution of the bent GR-IN optical fiber when the incident light vibrates (a) parallel and (b) perpendicular to the fiber’s axis. (c) The birefringence cross-section distribution, R = 8 mm. Ref. [35] with permission.
A PM fiber is any fiber that preserves and transmits the polarization state of the light launched into the fiber even if this fiber is subjected to environmental perturbations [57]. This advantage cannot be verified by conventional single-mode optical fibers outside the laboratory conditions. A PM fiber is tailored to oblige the two orthogonally polarized modes traveling with different velocities (i.e., different propagation constants). This difference in velocities prevents the optical energy from suffering a “cross-coupling” and preserves the polarization state of the transmitted light. Therefore, a PM fiber used in any application requires delivering a polarized light such as in telecommunications, medical applications, and sensing. In interferometric applications, it is used to affirm that the interfered rays have the same polarization states. To maintain such a difference of velocities, the core of the fiber has to be anisotropic either geometrically by making the core cross-section as an ellipse or by applying a uniaxial stress. The most known PM fibers used today are, PANDA, bow tie, and elliptical-jacket fibers. These types are designed by the same way where the cores are flanked by areas of high-expansion glass and shrunk-back more than the surrounding silica then the core is frozen under tension. The birefringence is induced due to this tension, which means creation of two different indices of refraction: a higher index in the direction parallel to the applied stress and a lower index perpendicular to the direction of the applied stress. In the next two subsections, we briefly illustrate both the manufacturing process and interferometric characterization of PANDA and bow tie PM optical fibers.
PANDA PM optical fiber is preferable in telecommunications [57, 58]. It is modified by insertion of stress rods to provide PM properties according to the procedure described in Figure 16. In this process, two holes are ultrasonically drilled along a single-mode optical fiber; then, the stress rods are inserted in these two holes and the fiber is finally drawn [57]. In 2014, Wahba used the off-axis DHPSI to reconstruct the 3D RIP of a PM PANDA optical fiber [23]. The multilayer model was used to calculate the RIP of this fiber in the directions of fast and slow axes. By rotating the PANDA fiber, different interferograms were recorded and analyzed in order to reconstrut the 3D RIP of this fiber, see Figure 17. The reconstructed 3D RIPs of PANDA fiber are shown in Figure 18 when the incident light was vibrating in the direction of (a) fast axis and (b) slow axis.
Manufacturing steps of a PANDA PM optical fiber.
The left column shows three orientations of PANDA PM optical fiber as it was rotated during the characterization process where the slow axis makes an angle (a-i) 0°, (b-i) 45° and (c-i) 90° with the horizontal axis. The middle column shows their reconstructed interference phase modulo 2π while the right column shows their phase difference maps. Ref. [23] with permission.
The 3D RIPs of PANDA PM optical fiber in the directions of (a) fast axis and (b) slow axes. Ref. [23] with permission.
A bow tie optical fiber is fabricated on a lathe using the inside vapor-phase oxidation (IVPO) via the process called gas-phase etching to create the required stress [57]. This process is summarized in Figure 19 where a ring of boron-doped silica is purely deposited of boron tribromide in combination with silicon tetrachloride. The rotation of the lathe stopped when a sufficiently thick layer was formed to allow two diametrically opposed sections to be etched away. The final shape of the bow tie and stress levels are controlled by varying the arc through which the etching burner is rotated. Recently, Ramadan et al. estimated the optical phase variations of optical rays traversing a PM optical fiber from its cross-section images [59]. They proposed an algorithm to recognize the different areas of the fiber’s cross-section, which was immersed in a matching liquid and investigated by Mach-Zehnder interferometer.
Manufacturing steps of a bow tie PM optical fiber.
These areas were scanned to calculate the optical paths for certain values of refractive indices and the optical phases across the PM optical fiber were recovered. The experimental interferograms of the bow tie PM optical fiber, shown in Figure 20, were analyzed to extract their optical phase distributions and compare them with the optimized estimated optical phase maps, see Figure 21. This was a direct and accurate method to get information about refractive index, birefringence, and the beat length of a PM optical fiber.
(a and c) Cross-sections of the bow tie optical fiber. (b and d) Experimentally obtained phase shifted interferograms when the incident light vibrates parallel and perpendicular to fiber’s axis, respectively. Ref. [59] with permission.
The calculated and the experimental phase differences of the bow tie optical fiber when the incident light vibrates (a) parallel and (b) perpendicular to the fiber’s axis. Ref. [59] with permission.
Optical fibers having diameters in the order of 100 μm, or less, are convenient to be investigated using interferometric methods when the samples are put in immersion liquids of refractive indices close to the refractive indices of the fibers as described in the previous sections [12, 13]. Optical fibers of diameters bigger than 150 μm cannot be investigated by normal interferometry where the planes of fringes in both liquid and fiber cannot be focused simultaneously. In 2000, Ramadan presented a novel interferometric method to recover such a problem for homogeneous thick optical fibers, commonly used in short-distance data transmission, without using immersion liquids [16]. This type of interference was called lens-fiber interferometry (LFI) since the interference fringes were produced by a combination of an aberrated cylindrical lens and a thick optical fiber. The aberrated cylindrical lens was used to focus a parallel beam on this fiber, which was located in the focal plane of the cylindrical lens [60], see Figure 22.
The ray tracing diagram of an optical ray crossing a homogeneous thick optical fiber.
Two-beam interference produced by the superposition of two optical rays emerging from the fiber was recorded and explained. Due to the aberration of the cylindrical lens, one of these two rays crossed the thick fiber before its center while the other ray crossed after the fiber?s center. Therefore, for each point in the image plane, two rays having two different initial incidence angles on the thick fiber are superposed, see Figure 23. The optical path length of each ray can be obtained by tracing this ray geometrically, as given by Eq. (30), which can be transformed into phase differences for the interfered rays using Eq. (31). The difference in the optical path lengths of each pair of interfered rays can be transformed into an intensity distribution describing the interference fringes using Eq. (32). On the other hand, the scattered rays from the outer surface of the fiber do not contribute in the interference because of the limited range of the incident rays on the fiber. This is in contrast with previous works done by Watkins [14, 15, 61]. By comparing the experimentally obtained interferograms with those reconstructed theoretically as shown in Figure 24, Ramadan was able to determine the refractive index of the investigated thick optical fiber. The advantage is that the used system requires no matching liquid where the experiment is performed when the thick fiber is just held in air. This enables monitoring the probable variation in radius or refractive index of the fiber particularly during the manufacturing process or under external effects.
The relation between the position of each two interfered rays on the screen and their incidence angles on the thick fiber.
(a) A selected and extended part of the obtained interferogram of a thick optical fiber, (b) the enhanced fringes of (a) and (c) the simulated fringes.
where Δ(z1) and Δ(z2) are the optical path lengths of the two interfered rays. In 2004, Hamza et al. developed LFI technique in order to determine the refractive index of the core of a skin-core thick optical fiber [60]. They derived a mathematical expression for the optical paths through the fiber in order to reconstruct the interfernce pattern due to the used fiber when it is used as a thick fiber in the LFI system. By comparing the experimentally obtained patterns with the theoretically reconstructed ones, they were able to estimate the core’s refractive index with an accuracy of 8 × 10−4. Due to its simplicity and applicability, LFI was used, afterward, to measure the refractive index of a liquid [62] and to monitor the thickness variations of a transparent sheet inserted between the cylindrical lens and the thick fiber [63].
This chapter is an attempt to highlight the interferometric techniques used for characterization of optical fibers. Application of two- and multiple-beam interference on different types of fibers is illustrated. Section 2 dealt with conventional optical fibers where we illustrated the theoretical models used to reconstruct the refractive index profiles of these fibers. In these models, the refraction of the light ray traversing the fiber has been considered. Digital holography was explained as an important candidate used for accurate retrieving of phase maps and consequently refractive index profiles of the fibers. In Section 3, we mentioned the problem of fiber bending. Recovering the refractive index profile and mode propagation of a bent fiber considering the refraction of the light rays traversing the fiber is a quite difficult task since bending-induced stresses are responsible for refractive index variations. Also, these stresses are released at the outer surface of the bent fiber. Therefore, we illustrated a successful model that was recently presented to recover the index profile in this case with experimental illustrative data. Another important type of optical fibers is the polarization maintaining optical fibers, which prevent cross-coupling by conserving the state of beam polarization during propagation. In Section 4, we presented interferometric techniques applied on two different polarization maintaining optical fibers, panda and bow tie, to reconstruct their refractive index profiles. Most interference techniques require immersing the fiber in a suitable liquid in order to minimize the phase difference between the fiber and its surrounding medium. In Section 5, an interference technique is presented and applied on a thick optical fiber to recover its refractive index without using an immersion liquid (i.e., in air), which makes the technique suitable for in-situ studying of thick fibers.
The authors would like to acknowledge Prof. A. Hamza, the leader of optics research groups in Mansoura and Damietta Universities, and Prof. T. Sokkar for their continuous support and useful discussions. Also, many thanks to the Optics Research Group members in Damietta University for their useful suggestions and comments.
The authors declare no conflict of interest.
General requirements for Open Access to Horizon 2020 research project outputs are found within Guidelines on Open Access to Scientific Publication and Research Data in Horizon 2020. The guidelines, in their simplest form, state that if you are a Horizon 2020 recipient, you must ensure open access to your scientific publications by enabling them to be downloaded, printed and read online. Additionally, said publications must be peer reviewed.
',metaTitle:"Horizon 2020 Compliance",metaDescription:"General requirements for Open Access to Horizon 2020 research project outputs are found within Guidelines on Open Access to Scientific Publication and Research Data in Horizon 2020. The guidelines, in their simplest form, state that if you are a Horizon 2020 recipient, you must ensure open access to your scientific publications by enabling them to be downloaded, printed and read online. Additionally, said publications must be peer reviewed. ",metaKeywords:null,canonicalURL:null,contentRaw:'[{"type":"htmlEditorComponent","content":"Publishing with IntechOpen means that your scientific publications already meet these basic requirements. It also means that through our utilization of open licensing, our publications are also able to be copied, shared, searched, linked, crawled, and mined for text and data, optimizing our authors' compliance as suggested by the European Commission.
\\n\\nMetadata for all publications is also automatically deposited in IntechOpen's OAI repository, making them available through the Open Access Infrastructure for Research in Europe's (OpenAIRE) search interface further establishing our compliance.
\\n\\nIn other words, publishing with IntechOpen guarantees compliance.
\\n\\nRead more about Open Access in Horizon 2020 here.
\\n\\nWhich scientific publication to choose?
\\n\\nWhen choosing a publication, Horizon 2020 grant recipients are encouraged to provide open access to various types of scientific publications including monographs, edited books and conference proceedings.
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\\n\\nAuthors requiring additional information are welcome to send their inquiries to funders@intechopen.com
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\n\nRead more about Open Access in Horizon 2020 here.
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\n\nIntechOpen publishes all of the aforementioned formats in compliance with the requirements and criteria established by the European Commission for the Horizon 2020 Program.
\n\nAuthors requiring additional information are welcome to send their inquiries to funders@intechopen.com
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