where $`I`$ is the intensity of light transmitted through the sample; $`I_{in}`$ is the intensity of the light prior to absorption by the sample; $`D`$ is the optical path length; $`C`$ is the solute concentration; and $`\epsilon`$ is the extinction coefficient, the sample's absorption at a given wavelength of light. Typical commercial pulse oximeters use a red LED (660 nm) and an IR LED (940 nm) to quantify the relative concentration of reduced and oxygen-rich hemoglobin in a person's bloodstream based on the following absorbance curves:
_Figure source: Bülbül, Ali & Küçük, Serdar. (2016). Pulse Oximeter Manufacturing & Wireless Telemetry for Ventilation Oxygen Support. International Journal of Applied Mathematics, Electronics and Computers. 211-211. 10.18100/ijamec.270309._
In order to differentiate the slight intensity change caused by varying oxygen concentration from errors related to skin absorbance, the signal processing algorithm only looks at the AC portion of the signal, since within a reasonable range (~0.5 - 3 Hz) this corresponds to blood rushing through arteries with each heartbeat. As the photodiode sensor does not differentiate by wavelength, the device rapidly cycles between red, IR, and no LED, thus compensating for ambient light as well. Using two wavelengths to quantify two species results in a system of two equations. Note that, as mentioned above, methemoglobin (MetHb) and carboxyhemoglobin (CoHb) are not factored in with this method and can thus cause systematic errors; additional wavelengths are needed to quantify all four hemoglobin species.
In order to differentiate the slight intensity change caused by varying oxygen concentration from errors related to skin absorbance, the signal processing algorithm only looks at the AC portion of the signal, since within a reasonable range (~0.5 - 3 Hz) this corresponds to blood rushing through arteries with each heartbeat, increasing the optical path length and causing periodic oscillations in the absorption signal. As the photodiode sensor does not differentiate by wavelength, the device rapidly cycles between red, IR, and no LED, allowing the system to compensate for ambient light as well. Using two wavelengths to quantify two species results in a system of two equations that can be continuously evaluated. Note that, as mentioned above, methemoglobin (MetHb) and carboxyhemoglobin (CoHb) are not factored in with this method and can thus cause systematic errors; additional wavelengths are needed to quantify all four hemoglobin species.
