Direct measurement of the scattering coefficient

Abstract

In general, the measurement of the main three optical properties (<i>µ</i> _<i>a</i> , <i>µ</i> _<i>s</i> and <i>g</i>) in turbid media requires a very precise measurement of the total transmission (TT), the total reflection (TR) and the collimated transmission (CT). Furthermore, an inverse algorithm such as inverse adding doubling or inverse Monte-Carlo-simulations is required for the reconstruction of the optical properties. Despite many available methods, the error free measurement of the scattering coefficient or the g-factor still remains challenging. In this study, we present a way to directly calculate the scattering coefficient from the total and collimated transmission. To allow this, it can be shown that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac><mml:mrow><mml:mi>T</mml:mi> <mml:mi>T</mml:mi></mml:mrow> <mml:mrow><mml:mi>C</mml:mi> <mml:mi>T</mml:mi></mml:mrow> </mml:mfrac> </mml:math> is proportional to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>e</mml:mi> <mml:mrow><mml:msub><mml:mi>μ</mml:mi> <mml:mi>s</mml:mi></mml:msub> <mml:mo>⋅</mml:mo> <mml:mi>d</mml:mi></mml:mrow> </mml:msup> </mml:math> for a wide range of optical properties if the sample is thick enough. Moreover, a set-up is developed and validated to measure the collimated transmission precisely.