{c}

A <Raman baseline-induced center shift> is a displacement of an estimated band center caused by the spectral background used or omitted in the analysis. It is one mechanism of <Raman peak-model bias>. A background slope can move the local maximum of a band-plus-background signal even if the underlying band has not shifted. A fitted center can also move when an incomplete background model transfers part of that slope into the fitted band position.

For an original local model, write $x$ for <Raman shift> relative to the true center, and consider a <Gaussian function> band plus a small residual slope:
$$
S(x)=H e^{-x^2/(2s^2)}+bx.
$$
Its stationary-point equation near the band center is $-(Hx/s^2)e^{-x^2/(2s^2)}+b=0$. When the displacement is small compared with $s$, the local maximum is displaced by
$$
\delta x\approx\frac{bs^2}{H}.
$$
For $H=10$ intensity units, $s=2\,\mathrm{cm^{-1}}$ and $b=0.05$ intensity units per $\mathrm{cm^{-1}}$, this is approximately $0.020\,\mathrm{cm^{-1}}$. A positive residual slope moves this local maximum toward increasing <Raman shift>. This local spectral-window model does not assert a physically unbounded linear background.

A <least squares> fitted center answers another question. If $j_i$ is the derivative of a chosen band model with respect to its center, omitted residual background $r_i$ produces the first-order fitted displacement
$$
\delta\mu\approx\frac{\sum_i w_i j_i r_i}{\sum_i w_i j_i^2}
$$
for fixed other parameters and positive weights $w_i$. An omitted background component matters when it projects onto the center-shift response. For symmetric samples and weights, a constant residual is orthogonal to the odd derivative of a symmetric band, whereas a residual slope is not. Asymmetric sampling or weights can remove even that constant-background cancellation.

The three-channel fit in <Raman peak-model bias> gives approximately $0.0330\,\mathrm{cm^{-1}}$ for the same slope and band parameters, because estimating a center from those samples is not the same operation as finding the continuous local maximum. At sample positions $-s,0,s$, the center derivative is proportional to $x$; allowing both a center change and an unknown linear background therefore introduces a first-order <identifiability> problem in that restricted model. Additional spectral samples or independent background information can help separate their responses.

Examining residuals and changing physically justified background models are useful tests before interpreting a <Raman peak-position map> as a map of material changes. Manufacturer guidance distinguishes spectral intensity, background contamination and fitted curve parameters.<What Raman images can reveal by Renishaw>[“How can I analyse Raman images?”, intensity/background ambiguity and curve-fit parameters]{ref} A small conditional <Raman peak-fit uncertainty> alone does not establish that the assumed background is adequate.<Guide to the expression of uncertainty in measurement by JCGM>[§4.1.2, measurement-model completeness; §4.2.5, fitted parameters]{ref}


 Raman baseline-induced center shift (source code)