Exactly, the data don't correspond to photos @CyrilGio uploaded. The k and To coefficients may be easily estimated using lm function, because if we take y = diameter_3d_corrige - pupil_timestamp_secondes^(-0.5) our original problem is just y ~ pupil_timestamp_secondes. For the provided data the estimates are: k = 0.8734 and To = 761.7452. The term pupil_timestamp_secondes^(-0.5) oscilates around 0.03389, so it's very small. That's why the modeled line looks lika a straight line. The problem in Excel was different, indeed, in terms of data. So @CyrilGio, please provide valid data first.
The data don't follow the expected model formula -kt + To + t^(-0.5).
