Hollow-beam geometry for dynamic light scattering measurements: a theoretical analysis

Hollow-beam geometry, in conjunction with mode-selective detection, is of importance for the development of high-sensitivity devices for the measurement of dynamic light scattering in living tissues. Its application to scattering methods in the eye makes it possible to increase diagnostic ability for some diseases that alter the scattering parameters in the vitreous as well as in other transparent tissues of the eye. We present a thorough theoretical analysis of the hollow-beam geometry proposed recently for dynamic light scattering measurements in the human eye. The aims of the analysis are the determination of the excitation and the observation beam profiles at the focal plane and the evaluation of the volume under test in the measurement, which allow prediction of the intensity of the measured signal. The above is carried out with comparisons with the classical setup. From the theoretical point of view, the most appealing feature of the hollow-beam geometry is high collection efficiency combined with high stability. In the analysis performed, the concept of the characteristic length of a scattering system is introduced. With simple formalism, this parameter allows the calculation of the collection efficiency for general beam shaping and is extremely useful for the comparison of the performance of different systems.