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Let $P(t)$ be the pulse's power integrated over its transverse section, and $U$ its energy. Its peak power is ${\max }_{t}P(t)$. For a chosen Gaussian power envelope with full width at half maximum $\tau$,The numerical shape factor is approximately $0.9394$. It matters when comparing quoted peak powers; the estimate $U/\tau$ assumes a shape and a width convention.

If an otherwise unchanged pulse is stretched by a factor $S$ without loss, its energy stays fixed and its peak power falls by $S$. For energy gain $G$ and compressor energy transmission $\eta$, ideal restoration of the original shape givesThese relations require a specified shape and preserved spectrum; they do not model amplifier saturation. For the diagram's chosen $1\mathrm{nJ}$, $30\mathrm{fs}$ seed, $S=9.2959$, $G=1000$ and $\eta =0.8$, the successive peak powers are $31.31\mathrm{kW}$, $3.369\mathrm{kW}$, $3.369\mathrm{MW}$ and $25.05\mathrm{MW}$. The last pulse contains $0.8\mu \mathrm{J}$: the compressor increases peak power while losing some energy.

Fluence is time-integrated light intensity, $F(x,y)=\int I(x,y,t)dt$, measured in $\mathrm{J}{\mathrm{m}}^{-2}$. For a uniform beam of area $\mathcal{A}$, $F=U/\mathcal{A}$ and $I_{\mathrm{pk}}=P_{\mathrm{pk}}/\mathcal{A}$. At fixed transverse profile, lossless temporal stretching lowers peak light intensity but leaves fluence unchanged. Absorbed energy, heat removal, beam size, coatings and pulse duration still constrain optical components. For nonoverlapping identical pulses at repetition frequency $f_r$, the average power is $U{f}_r$; it is a different quantity from peak power.

For a beam at a specified surface, fluence is the time-integrated incident light intensity: $F=\int I(t)dt$, with units of energy per area. It records how much energy arrived during an exposure rather than the instantaneous rate of delivery.

For a constant rectangular pulse, $F=I_0\tau$. Two pulses can therefore have equal fluence and different peak intensities if their durations differ. This matters in nonlinear optics, where the response can depend strongly on instantaneous intensity, and in comparing exposure protocols. Photon fluence instead counts incident photons per area; converting it to energy fluence requires the photon energies.

Radiant exposure measures the radiant energy received per unit surface area during a specified interval. At a fixed surface point $\mathbf{x}$, it is the time integral of incident irradiance $E_{\mathrm{e}}$:The area belongs to the receiving surface: its orientation and location matter. An irradiance in $\mathrm{W}{\mathrm{m}}^{-2}$ specifies a rate, while radiant exposure in $\mathrm{J}{\mathrm{m}}^{-2}$ specifies the accumulated arrival of energy.^[ref]

For a uniform rectangular pulse, $H_{\mathrm{e}}=E_0\tau$, with constant irradiance $E_0$ and duration $\tau$. Stipulate one pulse at $20\mathrm{W}{\mathrm{m}}^{-2}$ for $1\mathrm{s}$, and another at $80\mathrm{W}{\mathrm{m}}^{-2}$ for $0.25\mathrm{s}$. Both deliver $20\mathrm{J}{\mathrm{m}}^{-2}$, but their peak irradiances differ by a factor of four. The two radiant exposures agree only after each complete pulse has arrived. A shorter observation window can intercept different fractions of them, and a nonlinear receiver can respond differently even to their complete pulses.

Integrating over a receiving patch gives its incident radiant energy:Here ${\overline{H}}_A$ is the spatially averaged radiant exposure, rather than necessarily the local maximum. Uniform illumination is the special case where this spatially averaged radiant exposure equals the local value everywhere on the patch. In the rectangular-pulse example, a uniformly illuminated $1\mathrm{c}{\mathrm{m}}^2=10^{-4}{\mathrm{m}}^2$ patch receives $20\times 10^{-4}=2\mathrm{mJ}$.

For an original spatial example, consider a circular Gaussian beam at a fixed transverse plane, with constant Gaussian beam radius $w$ throughout the pulse. Let $P(t)$ be its total radiant power and $U=\int P(t)dt$ its laser pulse energy. Integrating its transverse irradiance in time gives the radiant exposure of a Gaussian beam:The normalization follows by integrating $H(r)2\pi rdr$ from $0$ to $\infty$. The disk of radius $w$ contains only $U(1-e^{-2})$, so its actual spatially averaged radiant exposure is $U(1-e^{-2})/(\pi w^2)$, not $U/(\pi w^2)$. With stipulated $U=1\mu \mathrm{J}$ and $w=1\mathrm{mm}$, the peak is $0.6366\mathrm{J}{\mathrm{m}}^{-2}$, while the average inside that disk is $0.2752\mathrm{J}{\mathrm{m}}^{-2}$. State the Gaussian beam radius convention and the receiving area with any reported value.

An energy readout alone therefore does not specify a surface's radiant exposure. In an ideal linear model for pulse energy measurement with a photodiode, dark-subtracted photocurrent $i_{\mathrm{ph}}(t)=R{P}_{\det }(t)$ has constant spectral responsivity $R$ at the chosen wavelength. Integrating the electric current gives signal electric charge $Q_{\mathrm{sig}}=R{U}_{\det }$. If a known patch of area $A$ is uniformly illuminated and all of its incident energy is collected, thenAs a separate stipulated example, $Q_{\mathrm{sig}}=0.40\mathrm{nC}$ and $R=0.40\mathrm{A}{\mathrm{W}}^{-1}$ correspond to $U_{\det }=1.0\mathrm{nJ}$. Uniform illumination over $A=1.0\mathrm{m}{\mathrm{m}}^2$ gives $H_{\mathrm{e}}=1.0\mathrm{mJ}{\mathrm{m}}^{-2}$. Background subtraction, collection geometry, detector linearity and an integration window covering the full response are part of this measurement model. Continuous-wave responsivity alone does not establish linearity for a short pulse: silicon-photodiode experiments have observed pulse-dependent saturation.^[ref]

A historical NIST measurement calibration separates these operations experimentally. A modulator produces pulses from a continuous-wave laser; a calibrated beam splitter sends one beam to a slow thermal reference and another to the pulse detector. The reference records the accumulated energy, while the pulse repetition rate and injection duration determine the mean energy per pulse. The detector's integrating electronics provide a pulse-energy readout. Converting such a readout to radiant exposure additionally requires the illuminated area and its spatial distribution.^[ref]

The beam-use term fluence denotes the same time integral for a directed beam normal to the chosen surface. For light arriving from many directions, specify the angular geometry: planar irradiance and spherical irradiance are different quantities, so a value defined using one cannot simply be substituted for the other.^[ref]