a Typical spectrometer. Collimated light is spectrally dispersed by the diffraction grating and focused onto a linear sensor. b The narrow linewidth source method requires a narrowband light source for each wavelength to be assessed (top). The measured spectrum output, Sout(λ), is the superposition integral of the true spectrum input, Sin(λ), and the spectrometer impulse response, h(λ, Δλ): Sout(λ)=∫Sin(Λ)h(Λ,λ−Λ)dΛ. If the input approximates a delta function, then the output, Sout(λ), resembles h(λ, Δλ) (bottom). c The broadband interferometry method requires an auxiliary interferometer to create an oscillating interferometric input, Sin(λ) (top). The spectrometer reduces the oscillations in the output, Sout(λ), depending on the impulse response (bottom). See Supplementary Note 6 for a complete description. d In the proposed excess noise method for characterization, an appropriate broadband light source is required (top). The output, Nout(λ), is the superposition integral of the excess noise input, Nin(λ), and h(λ, Δλ). For white noise input, the input autocorrelation matrix, Rin(λ1, λ2), is diagonal. The output autocorrelation matrix, Rout(λ1, λ2), is quasi-diagonal, with broadening depending on the local impulse response (bottom). e In the related method for cross-calibration, an appropriate broadband light source and a coupler are required (top). The excess noise outputs from spectrometers A and B, NA,out(xA) and NB,out(xB), respectively, are cross-correlated to yield RAB,out(xA, xB), where the highest correlation values occur for pixels that measure similar wavelengths (bottom)
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