A cartoon representation of the excalibur method, as described in Section 2. We exaggerate variations in measured line positions, changes in calibration space, and interpolation deviations for clarity. In step one, dimensionality reduction and denoising (Section 2.1), the complete set of line positions for all exposures is analyzed to return a set of K basis vectors g_n, which represent different ways the spectrograph calibration changes. These basis vectors span the K-dimensional calibration space of the spectrograph, which includes all possible wavelength solutions. In step two (Section 2.2), the amplitude of each basis vector, ﹩{a}_{n,k}﹩, is interpolated to return the calibration state for a specific science exposure, returned as a set of denoised calibration lines. The assigned wavelengths of these denoised line positions are then interpolated onto other pixels in step three (Section 2.3) to construct a full wavelength model that returns the wavelength as a function of detector position x and echelle order m.