Noise on photon correlation functions and its effect on data reduction algorithms

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Abstract In recent years, many different data reduction algorithms have been used to extract information on distribution functions (radius distribution, diffusion coefficient distribution, etc.) from photon correlation functions. Many substantially different methods have been used in such algorithms, ranging from simple cumulants to constrained regularization methods such as CONTIN or maximum entropy. Most of these algorithms have in common that noise estimates for the correlation function are restricted to photon noise. But in fact, with the use of modern multi-bit correlators at high input count rates, intensity noise dominates over photon noise in many experimental situations. Since intensity noise is strongly correlated, its effect on data reduction is more subtle but generally of much higher importance than that of photon noise. This chapter introduces models for photon noise as well as intensity noise, and experimental verifications of these models. The random nature of photon noise is compared with the highly correlated structure of intensity noise, and the effects of such covariant noise on any data reduction method are discussed. Finally, a simple model for the covariance matrix and a new concept for data reduction algorithms incorporating this covariance matrix is developed.