Overview of Least-Squares Analysis

The data for TCSPC satisfy the assumptions of least-squares analysis, so we can now consider its implementation, In any least-squares analysis one starts with a model which is assumed to describe the data. The goal is then to 

In this expression the sum extends over the number (r) of channels or data points used fm a particidar analy and Ot is the standard deviation of each data point 

In TCSPC it is straightfonmnd Id assign the standard deviations (Ojt). From Poisson statistics the standard dratia-tion is known to be the square root of the number of photon counts, at — [Af(rt)]. Hence, for a channel with 10,000 counts, 100, and for lO coonls, lOOO.Therdalive uncertainty in the data decreases as the number of photons increases. The value of is the stun of the squared deviatioos between the measured values N(tt) and the expected values Af (r,t)- divided Iqr squared deviations 

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