= Optical pulse pedestal
An \b[optical pulse pedestal] is lower-level optical power extending around a pulse's dominant short peak. It can precede the peak, follow it or extend on both sides. A broad pedestal can carry substantial <laser pulse energy> while barely changing the peak's <full width at half maximum>. <Optical pulse temporal contrast> describes the relative power levels; integrated energy also depends on how long each contribution persists.
For an original power-profile model, choose a central rectangular contribution of height $P_0$ and duration $\tau$, together with a pedestal of height $\alpha P_0$ and duration $T>\tau$, centred at the same time. Let $0<\alpha<1$. The peak power is $(1+\alpha)P_0$, while the pedestal lies below half of that value. The power FWHM is therefore still $\tau$, but
$$
U=P_0\tau+\alpha P_0T,\qquad
\frac{U_{\rm pedestal}}U=\frac{\alpha T}{\tau+\alpha T}.
$$
These are stipulated additive power contributions, not a rule for adding coherent electric fields.
Set $\alpha=10^{-3}$ and $T=1000\tau$. The pedestal then contains half the total energy even though its power is about a thousand times below the main peak. With $P_0=1\,\mathrm{MW}$ and $\tau=1\,\mathrm{ps}$, each contribution carries $1\,\mathrm{\mu J}$. The peak-to-pedestal power ratio is exactly $(1+\alpha)/\alpha=1001$ in this example. An inverse convention would quote a small pedestal-to-peak ratio instead; state which contrast definition is being used.
A measurement needs temporal range as well as dynamic range. A narrow scan can miss broad wings, while a readout that resolves only the peak can bury a pedestal in its own background. A commercial example is the Sequoia third-order <cross-correlation> instrument, whose manufacturer identifies temporal-contrast measurement as its purpose and separately specifies scan range and temporal resolution.<Sequoia temporal contrast measurement by Amplitude>[PDF pp. 1–2, measurement purpose, third-order cross-correlator, scan and resolution specifications]{ref} The cited instrument description establishes the measurement approach; the numerical profile above is an independent model.
A real optical pedestal must also be distinguished from <detector baseline subtraction> errors. Blocked-beam and reference measurements characterize the detector background, while a suitable optical measurement tests whether low-level light accompanies the pulse. A <detection time gate> that excludes a pedestal changes the admitted energy relative to a detector integrating the full waveform.
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