the present invention utilizes at least three wavelengths of electromagnetic radiation for determining a blood constituent , such as arterial oxygen saturation , in a patient . the detected radiation scattered by the tissue of the patient is analyzed in a manner that compensates for variations in the detected radiation caused by differences in the scattering of the radiation at different wavelengths . in particular , a result is determined which is equivalent to the sum of a first blood constituent estimate using a first pair of the detected signals , and the difference between the first blood constituent estimate and a second blood constituent estimate , using a different pair of wavelengths , with the difference being multiplied by a multiplicative factor .