Prior to this reprocessing, the fitting function used to fit the lunar calibration time series has been dual exponentials in time with short-period and long-period time constants. This fitting function has the form:

F(t) =  A0 −  A1(1.0 − e− C1(t − to))  −  A2(1.0 − e− C2(t − to))     (1)

where A_X are the fit coefficients, t_o is the reference time for the mission, C₁ is the short-period time constant, and C₂ is the long-period time constant. Data analysis has shown that the optimum short-period time constant (C₁) is 400 days. As additional measurements have been added to the lunar time series, the optimum long-period time constant (C₂) has increased from 4,000 to 20,000 to 40,000 days. The long-period exponential is asymptotically approaching a linear function. Consequently, the fitting function has been changed to a short-period exponential plus a linear function for this reprocessing, with a short-period time constant (C₁) of 400 days. The new fitting function has the form:

F(t)  =  A0  −  A1(1.0 − e− C1(t − to))  −  A2(t − to)    (2)

Analysis of the Band 8 lunar time series shows that the exponential plus linear function (Eq. 2) provides the best fit to the data, and for the other bands, it fits the data as well as the dual exponentials (Eq. 1) do.