It was a great research day today. I worked with Lily Zhao (Yale) on the wavelength calibration of the EXPRES spectrograph, which my loyal reader knows is a project of Debra Fischer (Yale). Lily and I cleaned up and sped up (by a lot) the polynomial fitting that the EXPRES team is doing, and showed (with a kind of cross-validation) that the best polynomial order for the fit is in the range 8 to 9. This is for a high-resolution, laser-frequency-comb-calibrated, temperature-controlled, bench-mounted, dual-fiber spectrograph.
But then we threw out that polynomial fit and just worked on interpolating the laser frequency-comb line positions. These are fixed in true wavelength and dense on the detector (for many orders, anyway). Oh my goodness did it work! When we switched from polynomial fitting to interpolation, the cross-validation tests got much better, and the residuals went from being very structured and repeatable to looking like white noise. When we averaged solutions, we got very good results, and when we did a PCA of the differences away from the mean solution, it looks like the variations are dominated by a single variability dimension! So it looks like we are going to end up with a very very low-dimensional, data-driven, non-parametric calibration system that hierarchically pools information from all the calibration data to calibrate every single exposure. I couldn't be more stoked!
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