Fractional bandwidth normalization for optical spectra with application to the solar blackbody spectrum

Optical spectra are typically normalized per unit wavelength or per unit photon energy, yielding two different expressions or curves. It is advantageous instead to normalize a spectrum to a constant fractional bandwidth, providing a unique expression independent of whether the bandwidth is in dimensions of wavelength or of photon energy. For the Sun, whereas a per-unit-wavelength spectrum peaks in the green and a per-unit-photon-energy spectrum peaks in the IR, when the proposed normalization is used, the output peaks in the red. This approach applies to any spectral source and provides curves of constant spectral resolving power, as produced by many spectrometers.