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Baseline-drift bias in pulse-energy integration is the systematic energy error caused by using an inaccurate baseline over the integration gate. Relative to the true signal energy in the same gate,This error is separate from energy excluded by the gate. Historical NIST measurements bracketed each run with baseline observations and subtracted their average to compensate background and thermal drift.^[ref]

An original curvature example shows a limit of endpoint bracketing. On $-T/2\le t\le T/2$, suppose $b(t)=b_0+c{t}^2$. Both endpoint baselines equal $b_0+c{T}^2/4$, so their average and the straight interpolation between them coincide. However, the true integrated baseline is $b_{0}T+c{T}^3/12$. Subtracting the endpoint level over the whole gate therefore givesFor a $20\mu \mathrm{s}$ gate whose endpoints are $3\mathrm{mW}$ above its midpoint baseline, this bias is $-(2/3)(3\mathrm{mW})(20\mu \mathrm{s})=-0.040\mu \mathrm{J}$. A true gated signal energy of $1.00\mu \mathrm{J}$ would be reported as $0.960\mu \mathrm{J}$ under these assumptions.

Thus quadratic baseline curvature in gated energy integration survives a correction that is exact for a linear baseline. For fixed curvature, the error grows with the cube of gate duration. Additional pulse-free samples can test the baseline model, but pulse tails in those samples can themselves corrupt the estimate. Pulse energy baseline correction supplies the broader measurement context.