How to measure the optical thickness of scattering particles from the phase delay of scattered waves: application to turbid samples

We present a method based on the optical theorem that yields absolute, calibration free estimates of the optical thickness of scattering particles. The thickness is determined from the phase delay of the zero angle scattered wave. It uses a heterodyne scattering scheme operating in the Raman-Nath approximation. The phase is determined by the position of Talbot-like modulations in the two dimensional power spectrum S(qx, qy) of the transmitted beam intensity distribution. The method is quite insensitive to multiple scattering. It is successfully tested to provide quantitative verification of the optical theorem. Exploratory tests on soft matter samples are reported to suggest its wide applicability to turbid samples.