= Raman captured-area fraction
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The <Raman captured-area fraction> is the part of a specified complete spectral band's area that lies inside a chosen integration interval. For a nonnegative isolated background-corrected band $S(\widetilde\nu)$ with finite positive complete area,
$$
f(a,b)=\frac{\int_a^b S(\widetilde\nu)\,d\widetilde\nu}{\int_{-\infty}^{\infty}S(\widetilde\nu)\,d\widetilde\nu}.
$$
It lies between zero and one. It quantifies one mechanism of <Raman integration-window bias>: changing the center or width changes the fraction even when the complete area stays fixed. Background errors or overlapping bands can prevent measured intensity from representing the assumed isolated band.
For a <Gaussian function> centered at $\widetilde\nu_0$ with width parameter $s$, substitution of $z=(\widetilde\nu-\widetilde\nu_0)/s$ gives
$$
f(a,b)=\Phi\!\left(\frac{b-\widetilde\nu_0}{s}\right)-\Phi\!\left(\frac{a-\widetilde\nu_0}{s}\right),
$$
where $\Phi$ is the <cumulative distribution function> of the standard <normal distribution>. A centered window with half-width $ks$ captures $2\Phi(k)-1$. Half-widths of one, two and three $s$ capture approximately68.27%,95.45% and99.73% of the complete Gaussian area. These percentages refer to this line shape, not every <Raman spectrum>.
For an original example, a window extending4cm⁻¹ either side of the fitted center captures about0.95450 when $s=2\,\mathrm{cm^{-1}}$, but about0.81758 when $s=3\,\mathrm{cm^{-1}}$. Even if the height decreases so the complete area is unchanged, the finite-window area falls. If one incorrectly uses the first fraction to correct the broader band, the estimated complete area is only $0.81758/0.95450\approx0.85655$ of the true value.
<Raman band-area extrapolation> uses a justified fraction to estimate complete area as $A_{\rm full}=A_{[a,b]}/f$. For example, measured area10 in a centered two-width Gaussian window implies about10.477 in the same area units. The correction depends on the model and its parameters; it is not extra measured signal. At fixed $f$, an absolute area error is multiplied by $1/f$, while uncertainty in $f$ supplies another contribution. Large extrapolations from a narrow interval therefore need especially convincing evidence about the unobserved tails.
Collecting and retaining the full local spectra supports checks of center, width, background and neighboring bands instead of interpreting a single intensity summary alone. Primary manufacturer guidance makes this distinction between simple spectral-intensity images and fitted band parameters explicit.<What Raman images can reveal by Renishaw>[“How do we collect Raman images?”; “How can I analyse Raman images?”, background and fitted spectral parameters]{ref}
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