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Raman spectral rebinning with conserved integrated counts redistributes finite-bin measurements onto a new spectral grid while preserving their summed quantity over the same covered range. It is different from relabeling bin centres or interpolating peak heights. The parent spectral-density conversion between wavelength and Raman shift derives the continuous Jacobian; finite bins require a stated assumption about unresolved variation inside each bin.

For an original piecewise-constant wavelength-density model, let old bin $I_i$ have width $\Delta {\lambda }_i$ and count $N_i$. Invert the new Raman-shift edges to wavelength intervals $J_j$. Define the overlap matrixWhen the new bins partition the old covered range, ${\sum }_j{A}_{ji}=1$, hence ${\sum }_j{N}_j^{\prime }={\sum }_i{N}_i$. Clipping the new range instead excludes the corresponding counts and must be reported.

For original old wavelength bins $[600,602]$ and $[602,604]\mathrm{nm}$ with counts $100$ and $300$, choose new edges corresponding to wavelengths $600$, $601$, $603$ and $604\mathrm{nm}$. ThenThe total remains $400$. A different within-bin model can distribute that total differently; the original measurements do not resolve every sub-bin feature.

Covariance of count-conserving rebinned Raman channels transforms as $C^{\prime }=AC{A}^T$ for this fixed linear operation. Fractional rebinned estimates are therefore not automatically independent Poisson photon counts. Splitting one measured bin among neighbours creates shared uncertainty; finer output pixels do not create additional spectral resolution.

The primary FSRS instrument records a dispersed spectrum on an array and calibrates its Raman-shift axis.^[ref] The overlap algorithm above is an original illustrative reconstruction, not a claim about that instrument's published processing. Apply radiometric response and background corrections consistently with the quantity whose integral is being conserved.

A Raman spectrum records the strength of Raman scattering as a function of scattered optical frequency or, usually, Raman shift relative to the excitation. For vacuum wavelengths in nanometres, a common wavenumber convention isHere the numerical wavelengths are in nanometres. Stokes Raman scattering has positive shift under this convention; Anti-Stokes Raman scattering has negative shift. The strong unshifted Rayleigh scattering line is not a vibrational Raman band.

For an original chosen excitation ${\lambda }_0=500\mathrm{nm}$ and a $1500\mathrm{c}{\mathrm{m}}^{-1}$ vibration, the Stokes wavenumber is $20000-1500=18500\mathrm{c}{\mathrm{m}}^{-1}$, giving ${\lambda }_s\approx 540.54\mathrm{nm}$. The corresponding anti-Stokes wavelength is $10^7/21500\approx 465.12\mathrm{nm}$. Changing the excitation changes these optical wavelengths while the same assumed transition retains its Raman shift. The One-mode Raman spectrum example gives an existing level diagram and a separate numerical spectrum.

The vertical quantity must be stated too: detector counts per spectral bin, calibrated scattered power density and a stimulated gain ratio are different observables. Femtosecond stimulated Raman spectroscopy can plot the Raman pump-on pump-off gain ratio rather than spontaneous photon counts. Its primary apparatus disperses probe and reference beams onto an array and calibrates shifts with known solvent lines.^[ref]

Spectral-density conversion between wavelength and Raman shift also changes the density's units: rebadging the horizontal axis alone need not preserve a spectral integral. Background, excitation rejection, instrument response and spectral resolution affect observed band heights and widths. An integrated band area is not determined by peak height alone. A chemical inference should compare calibrated positions and responses under specified conditions, rather than identify a material from one unqualified peak.