For TNP determination, NP emission from the trap center is collected and separated by a dichroic beam-splitter into "visible" (λ < 980 nm) and "near-IR" (λ > 980 nm) beams that are dispersed by a pair of spectrographs, with spectral detection observed by deep-cooled Si CCD and InGaAs photodiode cameras. This approach allows the spectrum from 600 -1580 nm to be acquired with adequate signal/noise during each mass measurement. The approach to calibrating the detector sensitivity vs. λ, S(λ), was discussed in detail previously. To extract TNP, the intensity-corrected spectra are fit by a thermal emission model function, consisting of Planck's law for ideal black bodies, corrected by an NP emissivity function, λ -n , that accounts for the effects of the NP being smaller than λ and for any effects of the NP material. The fitting function is given by Eqn. 2.