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A pulse-energy interval from incomplete tail measurements combines measured energy with bounds on optical power outside the acquisition window. It describes a set of compatible total energies, not automatically a standard uncertainty or confidence interval. The pulse-energy bounds from tail duration and pedestal height article treats a particular peak-and-width model; a window-based construction need not assume that pulse shape.

Suppose true radiant energy inside a measured window $G$ lies in a justified interval $[L,H]$, with $0\le L\le H$. Partition the unobserved times into regions of durations ${\Delta }_j$ with independently established nonnegative radiant power caps $M_j$. ThenFor an original measurement, let the observed-window energy lie between $48$ and $52\mathrm{nJ}$. An unobserved early region lasting $2\mathrm{ns}$ at most $0.50\mathrm{W}$ contributes at most $1\mathrm{nJ}$; a late region lasting $20\mathrm{ns}$ at most $0.20\mathrm{W}$ contributes at most $4\mathrm{nJ}$. The total interval is therefore $48$ to $57\mathrm{nJ}$. For these assumptions the fraction of optical energy outside a time gate equal to $G$ is at most $5/(48+5)\approx 9.43\%$.

A finite support cutoff is sufficient but not necessary for a finite bound. Bounding unobserved optical energy with an exponential tail model uses a validated cap $P(t)\le P_b{e}^{-(t-b)/\tau }$ after the window endpoint $b$, which integrates to $P_b\tau$. Without a justified duration or integrable envelope, one below-threshold reading cannot bound all later energy.

Establish the caps with characterized detector sensitivity, baseline and temporal coverage; do not identify detector ringing directly with optical tails. NIST's response analysis explicitly models the electrical trace as a convolution of the optical waveform with detector response.^[ref] The interval above follows from chosen optical bounds, not from an uncorrected finite-bandwidth detector trace.

Unbounded pulse energy at fixed peak and FWHM means there is no universal finite energy upper bound from those two quantities alone. Each pulse can still have finite duration and finite energy. The nonuniqueness of pulse energy at fixed peak power and FWHM article constructs a rectangular core of width $\tau$ and a below-half-maximum pedestal of height $\alpha P_{\mathrm{pk}}$ extending to total duration $D$.

For any desired energy above the core energy, chooseThis is finite for every finite desired $U$ while keeping the peak and power FWHM unchanged. For an original numerical case, take $P_{\mathrm{pk}}=3\mathrm{W}$, $\tau =4\mathrm{ns}$ and $\alpha =0.20$. An energy of $1\mu \mathrm{J}$ requires $D\approx 1.651\mu \mathrm{s}$ in this ideal profile. The core contributes only $12\mathrm{nJ}$.

Additional information changes the problem. If the signal support is bounded by $D_{\max }=20\mathrm{ns}$ and power outside the FWHM interval is at most $0.20P_{\mathrm{pk}}$, thenThese pulse-energy bounds from tail duration and pedestal height require independently justified tail constraints. A FWHM definition alone fixes a threshold width, not the below-threshold integral.^[ref] The construction concerns isolated ideal pulse profiles, not a claim that an actual laser or finite-period pulse train can have arbitrary tails.