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W idefield Raman Imaging of Cells and T issues 171

within that pixel. The number of pixels within an image depends on
the microchip size of the Raman camera. For example, a typical high
resolution EMCCD camera may have 512 × 512 pixels; therefore, it is
possible to have more than 200,000 spectra in an image. However, the
number of pixels in an image will decrease when the binning param-
eters are increased. Nonetheless, there are copious spectra that make
up an image and require the use of chemometric techniques to ana-
lyze the data. Chemometrics is defined as the use of mathematics and
statistics on chemical data in order to extract useful information that
can be used for decision making. The following section will describe
some of the chemometric techniques used in the analysis of a wide-
field Raman image. Each analytical technique will be briefly described,
but for a more rigorous examination of the techniques, several books
on chemometrics are referenced herein. 64–66

6.5.1 Principal Component Analysis
In the case of a widefield Raman image of a biological tissue, there are
abundant associated Raman spectra. Because they consist of the same
biomaterials (proteins, lipids, nucleic acids, carbohydrates), they are
all very similar; however, within these similar spectra, there should
be some finite number of independent variations occurring in the
spectral data. Hopefully, the largest variations in the spectral data
would be the changes in the spectrum due to different concentrations
of biological molecules that comprise the cells or tissue. Other possi-
ble variations are due to instrument variation (unless removed by
preprocessing steps), environmental conditions, differences in sam-
ple preparation, and so on. It is possible to calculate a set of “variation
spectra” that represent the changes in the Raman scatter at all wave-
lengths in the spectra; these variation spectra could be used instead of
the spectral data for comparison. There should be fewer common
variations amongst the data than the number of spectra; although,
since they come from the original data, the variation spectra retain
the interrelationship of the original spectra.
The variation spectra are called eigenvectors or principal compo-
nents (PCs). The method of breaking down a set of spectroscopic data
into its most basic variations is called principal component analysis or
PCA. It is mathematically defined as an orthogonal linear transforma-
tion that transforms the data to a new coordinate system such that the
greatest variance by any projection of the data comes to lie on the first
coordinate (called the first principal component or first PC), the second
greatest variance on the second coordinate, and so on.
For example, imagine all the spectra from a widefield Raman
image plotted in multi-dimensional space. The first PC would be a
vector plotted through the data to find a single axis to capture or span
as much of the variance of the data as possible. This is accomplished
by a least-squares fit of the data to the new axis. Once the first PC is