Oxygenation of a subject's blood is determined by sensing an absorption spectrum of light directed either invasively or non-invasively into the blood, and then calculating an oxygenation value by evaluating a cost function of the remitted spectrum relative to at least two pre-determined reference absorption spectra representing different, known levels of blood oxygenation. The source of light preferably uses stable, long-life, white LEDs, in which case white-balancing of the remitted spectrum can be accomplished by pre-determining and storing the spectrum of the LEDs, one time for all, and then adjusting the remitted spectrum accordingly to compensate for deviations of the LED spectrum from the constant ideal.