A simple model can show how pulse oximetry is able to measure the oxygen saturation of blood. The key idea is that the intensity of light decreases exponentially as it travels through an absorbing medium. This can be written I$=$I$0$e$$x $,$ where I$0$ is the incident intensity, x is the distance traveled through the medium, and is called the absorption coefficient. A larger absorption coefficient causes the intensity to decrease more rapidly. At a wavelength of $660$ nm $,$ the absorption coefficients of oxygenated hemoglobin HbO$2$ and deoxygenated hemoglobin Hb are $2\mathrm{.}5$ cm$1$ and $10$ cm$1$ respectively. Absorption coefficients are customarily given in units of cm$1,$ so the distance x must be in cm $.$ At a wavelength of $940$ nm $,$ the absorption coefficients of HbO$2$ and Hb are $7\mathrm{.}0$ cm$1$ and $3\mathrm{.}0$ cm$1.$ In pulse oximetry, light travels approximately $1\mathrm{.}0$ cm from the LEDs to the detectors. Assume that absorption by hemoglobin is the only factor that affects the light intensity. Pulse oximetry measures the ratio I$660/$I$940$ of the detected intensities at the two wavelengths. Assume that both wavelengths enter the finger with the same intensity. What is the ratio if the hemoglobin is completely deoxygenated, corresponding to an oxygen saturation of $0\%?$ What is the ratio if the hemoglobin is completely oxygenated, corresponding to an oxygen saturation of $100\%?$ You can see that the ratio is very sensitive to the oxygen saturation level. The calculation is more complex, but a measured ratio between these two extremes can be used to deduce the fraction of hemoglobin that is oxygenated.