= Stokes shift
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{title2=$\Delta\lambda=\lambda_{\rm em,max}-\lambda_{\rm abs,max}$}
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The <Stokes shift> compares the lowest absorption-band maximum with the <fluorescence emission spectrum> maximum. Relaxation often makes $\Delta\lambda>0$. This comparison differs from using an arbitrary excitation <wavelength>. A spectral-density maximum can move when changing from per unit <wavelength> to per unit <spectroscopic wavenumber>; specify the spectral convention.<What is the Stokes Shift? by Edinburgh Instruments>[Stokes Shift in Fluorescence Spectroscopy, definition, spectral-coordinate caveat, Figures 2 and 4]{ref}
An original illustrative <energy> budget makes the distinction concrete. Excitation at $450\,\mathrm{nm}$ and emission at $520\,\mathrm{nm}$ correspond to about $2.76$ and $2.38\,\mathrm{eV}$ per <photon>, using $E=h c/\lambda$ with <Planck constant> $h$ and <speed of light> $c$ in <vacuum>. The difference, about $0.37\,\mathrm{eV}$, must go elsewhere in the complete <energy> balance. These chosen <wavelengths> are not measured band maxima for a particular <fluorophore>.
Anti-Stokes emission has shorter <wavelength> than excitation. Additional <energy>, for example from a thermally populated level of <molecular vibration> or multiple excitation <photons>, makes it possible. The one-photon, initially relaxed drawing does not cover these cases.<Advanced Fluorescence Microscopy Techniques—FRAP, FLIP, FLAP, FRET and FLIM by Hellen C. Ishikawa-Ankerhold and others>[§1.1.1, final paragraphs: anti-Stokes emission and multiphoton excitation]{ref}
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