Light Through a Finger
A fingertip clip shines red (660 nm) and infrared (940 nm) light through skin, fat, bone, venous blood, nail polish, and arterial blood, all at once. It wants one thing out of that pile: what fraction of the hemoglobin in your arteries is carrying oxygen. Oxygenated blood is bright red and deoxygenated blood is dark, and at 940 nm the difference reverses.
Aoyagi's insight was to ignore everything that doesn't pulse. Only arterial blood swells with each heartbeat. Divide each color's pulsing part (AC) by its steady part (DC), then divide red by infrared. Skin, bone, and venous blood cancel out of that ratio of ratios, and what's left depends only on oxygen saturation.
Try this
- Drop the true O₂ to 85 and watch the red trace grow relative to infrared. That growing red swing is the measurement.
- Turn on hand motion. Motion changes the light path for both colors by the same fraction, which pushes R toward 1, and here that reads as about 74%. Real oximeters show the same thing (their R = 1 sits near 82–85%), which is why a patient scratching their nose can set off a desaturation alarm.
- Make the finger cold (low perfusion). The pulsing signal shrinks toward the noise floor and the reading starts wandering, even though nothing about the blood changed.
- Press use my camera. A phone can get your heart rate, but not SpO₂: its camera sees broad color bands with no known wavelengths, and it has no calibration against real blood.
The deep cut
The ratio-of-ratios argument says skin pigment should cancel out, like everything else that doesn't pulse. In practice it doesn't fully cancel. In 2020, Sjoding and colleagues in the NEJM compared pulse-ox readings to arterial blood gases drawn at the same time. Among patients whose oximeter read a reassuring 92–96%, the blood was actually below 88% for 11.7% of Black patients versus 3.6% of White patients.
The calibration curve on the right isn't pure physics. Real light scatters instead of passing straight through, so every device maps R to SpO₂ with an empirical curve fitted on volunteers, and historically those volunteers were mostly light-skinned. You can't reproduce that bias with this simulator, and that's the lesson: the simple model assumes the effect away, just as the calibration did. It's the same dataset-shift problem as a model trained at one hospital and deployed at another. Carbon monoxide works similarly: CO-bound hemoglobin looks nearly the same as oxyhemoglobin at 660 nm, so a two-wavelength oximeter reports a poisoned patient as fine.