A Low-Cost Pulse Oximeter with an Honest Accuracy Budget: Design, Error Propagation, and the Accuracy Floor for Triage

Design study (simulated, not measured) of a transmissive finger-clip pulse oximeter built from discrete low-cost parts (bill of materials US $17.50). The ratio-of-ratios response is derived from published haemoglobin extinction coefficients at 660 nm and 940 nm, and detector noise, residual baseline disturbance, motion artefact, calibration scatter, and a melanin-dependent bias term are propagated into a total root-mean-square accuracy (A_rms) over 70-100% saturation as a function of perfusion index, averaging time, motion, and skin pigmentation. Computed A_rms is 1.52 percentage points at perfusion index 3% at rest in light/medium pigmentation, 3.37 points in dark pigmentation with a broad emitter and single calibration, and 2.41 points at the dark low-perfusion corner after narrowband emitters, melanin-stratified calibration, and a 16 s window; raising LED drive current does not improve accuracy. Below perfusion index 1%, or where A_rms exceeds 3.0 points in the conditions of use, the device must blank its readings and must not be trusted for triage.