 Pulse-to-pulse energy fluctuation

Pulse-to-pulse energy fluctuation is variation in the laser pulse energy of successive emitted pulses. For a stationary population with finite variance, its standard deviation is ${\sigma }_U=\sqrt{\mathbb{E}[(U-\mathbb{E}U{)}^2]}$. A finite record supplies an estimate, whose convention should be stated rather than being confused with the uncertainty of the record's mean.

For an original four-pulse record, take measured energies $9,11,11,9\mu \mathrm{J}$. Their mean is $10\mu \mathrm{J}$. The sample standard deviation isIts coefficient of variation is 11.55 percent. The root-mean-square deviation of this particular list, using divisor four rather than three, is instead $1\mu \mathrm{J}$ or 10 percent. The definition matters when comparing reported stability figures. The familiar $s_U/\sqrt{N}$ estimate of uncertainty in a mean additionally assumes independent, identically distributed observations; an ordered record alone does not establish that assumption.

A historical NIST stability assessment compared an internal excimer-laser pulse monitor with a pyroelectric laser-energy meter. Its calorimeter integrated a pulse train, so averaging and individual-pulse variation entered different parts of the analysis.^[ref]

Observed variability also includes readout noise. Separating detector noise from pulse-energy variance requires an appropriate measurement model and independent information about that noise. Detector saturation, drift and correlated pulse errors are not removed merely by collecting a longer record. An average power of a laser pulse train measurement by itself does not resolve this sequence.