Signal processing
SpO2 Ratio of Ratios: Pulse Oximeter Calibration
The ratio of ratios (R) method is the fundamental calibration technique for pulse oximetry, computing R = (AC_red/DC_red) / (AC_IR/DC_IR) and mapping it to SpO2 via an empirical calibration curve derived from controlled desaturation studies in human volunteers.
How it works
Schematic summary of this guide. Waveforms are illustrative, not measured data.
The theoretical basis derives from the Beer-Lambert law applied to two wavelengths. At the red wavelength (660 nm), deoxyhemoglobin (Hb) absorbs more strongly than oxyhemoglobin (HbO2), while at infrared (940 nm), HbO2 absorbs more. The ratio of ratios is
The ratio normalizes for tissue optical path length and non-hemoglobin absorption, isolating the relative oxyhemoglobin concentration. Theoretically,
but in practice, tissue scattering and multi-path photon propagation invalidate pure Beer-Lambert assumptions.
Empirical calibration is therefore required: healthy volunteers breathe hypoxic gas mixtures under controlled conditions while simultaneous arterial blood gas sampling provides true SaO2 reference values. The resulting R-vs-SpO2 curve is approximately linear for R values of 0.4–1.0 (SpO2 85–100%): is a common linear approximation. Below SpO2 85%, the relationship becomes nonlinear and device-specific calibration tables are essential.
Skin pigmentation affects the R value through melanin absorption, which is wavelength-dependent (higher at 660 nm than 940 nm). Sjoding et al. (2020, NEJM, doi:10.1056/NEJMc2029240) found occult hypoxemia (arterial SaO2 below 88% despite SpO2 of 92–96%) in 11.7% of paired readings from Black patients versus 3.6% from White patients in the University of Michigan cohort.
Frequently Asked Questions
Why can't SpO2 be calculated purely from theory?
Beer-Lambert assumes single-path transmission through a homogeneous medium. In tissue, photons undergo multiple scattering events, taking variable paths through skin, fat, bone, and blood layers. This invalidates theoretical extinction coefficient-based SpO2 calculation.
How often must a pulse oximeter be recalibrated?
Pulse oximeter calibration is fixed at manufacture based on population-level desaturation studies. Individual recalibration is not performed. The calibration curve is stored in firmware and applies identically to all users.
What is the R value at SpO2 = 100%?
At SpO2 = 100% (all hemoglobin oxygenated), R ≈ 0.4. At SpO2 = 85%, R ≈ 1.0. At SpO2 ≈ 83%, R = 1.0 (equal red/IR pulsatile absorption). Below 83%, R > 1.0 and red pulsations exceed infrared.