title: Determination of uncertainty in parameters extracted from single spectroscopic measurements.
abstract: The ability to quantify uncertainty in information extracted from spectroscopic measurements is important in numerous fields. The traditional approach of repetitive measurements may be impractical or impossible in some measurements scenarios, while chi-squared analysis does not provide insight into the sources of uncertainty. As such, a need exists for analytical expressions for estimating uncertainty and, by extension, minimum detectable concentrations or diagnostic parameters, that can be applied to a single noisy measurement. This work builds on established concepts from estimation theory, such as the Cramer-Rao lower bound on estimator covariance, to present an analytical formula for estimating uncertainty expressed as a simple function of measurement noise, signal strength, and spectral overlap. This formalism can be used to evaluate and improve instrument performance, particularly important for rapid-acquisition biomedical spectroscopy systems. We demonstrate the experimental utility of this expression in assessing concentration uncertainties from spectral measurements of aqueous solutions and diagnostic parameter uncertainties extracted from spectral measurements of human artery tissue. The measured uncertainty, calculated from many independent measurements, is found to be in good agreement with the analytical formula applied to a single spectrum. These results are intended to encourage the widespread use of uncertainty analysis in the biomedical optics community.
authors.affiliation: Massachusetts Institute of Technology, G. R. Harrison Spectroscopy Laboratory, Cambridge, Massachusetts 02139, USA. obrad@mit.edu
authors.forename: Obrad R
authors.initials: OR
authors.lastname: Sćepanović
authors.forename: Kate L
authors.initials: KL
authors.lastname: Bechtel
authors.forename: Abigail S
authors.initials: AS
authors.lastname: Haka
authors.forename: Wei-Chuan
authors.initials: WC
authors.lastname: Shih
authors.forename: Tae-Woong
authors.initials: TW
authors.lastname: Koo
authors.forename: Andrew J
authors.initials: AJ
authors.lastname: Berger
authors.forename: Michael S
authors.initials: MS
authors.lastname: Feld
mesh_terms: D002114:Calcinosis / Q000473:pathology; D016893:Carotid Stenosis / Q000175:diagnosis; D003404:Creatinine / Q000032:analysis; D003627:Data Interpretation, Statistical; D005947:Glucose / Q000032:analysis; D006801:Humans; D016014:Linear Models; D019265:Spectroscopy, Near-Infrared / Q000706:statistics & numerical data; D013057:Spectrum Analysis / Q000706:statistics & numerical data*; D013059:Spectrum Analysis, Raman; D014508:Urea / Q000032:analysis
chemical_list: D014508:Urea; D003404:Creatinine; D005947:Glucose