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Extinction coefficients of hemoglobin have been studied for five decades by clinical chemists and biochemists, particularly for laboratory spectrophotometric measurements. In the last ten to 15 years, near infrared spectroscopy (NIRS) and imaging for tissue vascular oxygenation, breast tumor detection, and functional brain imaging have been intensively developed for in vivo measurements by groups of physicists, biomedical engineers, and mathematicians. In the approach of NIRS, NIR light in the wavelength range of 650-900 nm is utilized to illuminate tissue in vivo, and the transmitted or reflected light through tissue is recorded for the quantification of hemoglobin concentrations of the measured tissue vasculature. In order to achieve mathematical conversion from the detected light intensity at different wavelengths to hemoglobin concentration, extinction coefficients of hemoglobin, ε, must be used. While the engineers and physicists working in the NIR field have found the correct ε values to use, there has been controversy on what ε values should be used for in vivo NIRS in comparison with the conventional eε that most biochemists have used in the laboratories for in vitro measurements. The purpose of this article is to address this issue and help biomedical engineers and physicists gain a better understanding of e to be used for NIRS and NIR imaging.