Theory and design of photon correlation and light-scattering experiments

The inversion of photon correlation functions, angular light-scattering intensities, and spectral turbidity measurements to recover particle-size distributions and the inversion of photon-counting distributions to determine underlying intensity fluctuation distributions are all ill-conditioned problems whose solutions depend sensitively on noise in the data. The special techniques and precautions required for obtaining reliable results and the implications for experimental design are discussed. An example is presented that shows the weakness of the positivity constraint on the solution of ill-conditioned problems such as these.