An apparatus for non-invasively determining the blood oxygen saturation within a subject's tissue, comprising light sources for transmitting a light signal into the subject's tissue; light detectors for detecting the light signal from the one or more light sources after it has passed through the subject's tissue, wherein the light sources and the light detectors are configured to measure the attenuation of the light signal at two or more light source to detector distances; and a processor connected to the light sources and the light detectors, wherein the light sources and the light detectors are configured to measure the attenuation of the light signal at three or more distinct wavelengths in the range of 650 nm to 3 μm, and the processor includes an algorithm for determining the attenuation of the light signal as a function of the wavelength and the light source to detector distance; calculating the slope of the attenuation of the light signal versus the light source to detector distance as a function of the wavelength; and calculating the blood oxygen saturation within the subject's tissue on the basis of said slope of the attenuation of the light signal and empirically determined data that account for attenuation of the light signal due to light absorbers other than hemoglobin and deoxyhemoglobin in the subject's tissue and due to light scattering in the subject's tissue, characterized in that the data accounting for attenuation of the light signal due to light absorbers includes the wavelength-dependent extinction coefficients of one or more of meconium samples taken from new-born infants, transitional stool samples taken from new-born infants, and biliverdin, that the light sources and the detectors are configured to measure the attenuation of the light signal at three or more distinct wavelengths selected from 695 ± 5 nm, 712 ± 5 nm, 733 ± 5 nm, 743 ± 5 nm, 762 ± 5 nm, 783 ± 5 nm, 790 ± 5 nm, 805 ± 5 nm, 880 ± 5 nm, 895 ± 5 nm, and 910 ± 5 nm, and that the light sources include a collection of light emitting diodes each emitting light at a different wavelength. light sources for transmitting a light signal into the subject's tissue; light detectors for detecting the light signal from the one or more light sources after it has passed through the subject's tissue, wherein the light sources and the light detectors are configured to measure the attenuation of the light signal at two or more light source to detector distances; and a processor connected to the light sources and the light detectors, wherein the light sources and the light detectors are configured to measure the attenuation of the light signal at three or more distinct wavelengths in the range of 650 nm to 3 μm, and the processor includes an algorithm for determining the attenuation of the light signal as a function of the wavelength and the light source to detector distance; calculating the slope of the attenuation of the light signal versus the light source to detector distance as a function of the wavelength; and calculating the blood oxygen saturation within the subject's tissue on the basis of said slope of the attenuation of the light signal and empirically determined data that account for attenuation of the light signal due to light absorbers other than hemoglobin and deoxyhemoglobin in the subject's tissue and due to light scattering in the subject's tissue, characterized in that the data accounting for attenuation of the light signal due to light absorbers includes the wavelength-dependent extinction coefficients of one or more of meconium samples taken from new-born infants, transitional stool samples taken from new-born infants, and biliverdin, that the light sources and the detectors are configured to measure the attenuation of the light signal at three or more distinct wavelengths selected from 695 ± 5 nm, 712 ± 5 nm, 733 ± 5 nm, 743 ± 5 nm, 762 ± 5 nm, 783 ± 5 nm, 790 ± 5 nm, 805 ± 5 nm, 880 ± 5 nm, 895 ± 5 nm, and 910 ± 5 nm, and that the light sources include a collection of light emitting diodes each emitting light at a different wavelength.