= Pulse energy measurement with a photodiode
{title2=$Q_{\rm sig}=RU$}
\b[Pulse energy measurement with a photodiode] estimates incident <laser pulse energy> from collected signal <electric charge>. At fixed <wavelength>, suppose a <photodiode> has constant calibrated <spectral responsivity> $R$ in amperes per watt and remains in its linear operating range. If $P(t)$ is the incident <radiant flux>, the signal <photocurrent> is $i_{\rm sig}(t)=RP(t)$. Integrating over the complete response gives
$$
Q_{\rm sig}=\int i_{\rm sig}(t)\,dt
=R\int P(t)\,dt=RU,\qquad U=\frac{Q_{\rm sig}}R.
$$
The units agree because amperes per watt equal coulombs per joule. <Spectral responsivity> must apply at the measurement wavelength; a broadband pulse requires accounting for its spectrum.
In an original example, let $R=0.40\,\mathrm{A\,W^{-1}}$ and let the baseline-corrected collected charge be $Q_{\rm sig}=12\,\mathrm{nC}$. Then $U=30\,\mathrm{nJ}$. An ideal <charge amplifier> with feedback <capacitance> $C_f=100\,\mathrm{nF}$ would produce an output change of magnitude $Q_{\rm sig}/C_f=0.12\,\mathrm V$. The amplifier's polarity depends on its circuit convention.
A practical apparatus needs a calibrated detector, a charge-sensitive readout and a measurement window containing the full response. <Detector baseline subtraction> removes the estimated background, including <dark current>. A residual constant current of1microampere integrated over10microseconds contributes10picocoulombs; with the example responsivity this is a25picojoule energy error. Extending the window can capture a missing signal tail but also accumulate more background error.
<Photodiode saturation> invalidates the assumed constant response. <Robert E. Vest> and collaborators measured pulsed silicon-detector behavior and reported dependencies on applied <reverse bias> and illuminated area.<Measuring Pulse Energy With Solid-State Photodiodes by Robert E. Vest and others>[Abstract, nonlinear pulsed response and bias/area dependence]{ref} A low average optical power therefore does not by itself establish linear response to individual pulses.
<Rodney W. Leonhardt>'s calibration report describes a complementary reference method: a slow thermal standard measures accumulated energy, while pulse count and a calibrated <beam splitter> ratio determine average energy in the test beam.<Calibration Service for Low-level Pulsed-Laser Radiometers at 1.06 µm: Pulse Energy and Peak Power by Rodney W. Leonhardt>[§4, printed pp9–10]{ref} This connects a fast photodiode readout to an energy reference without requiring the thermal standard to resolve every pulse.
Collected charge measures energy under the stated assumptions; it does not alone determine <peak power>. A flat30nanojoule pulse lasting100nanoseconds has power0.30watts, whereas a flat pulse of the same energy lasting1microsecond has power0.030watts. Those stipulated rectangular profiles illustrate why pulse shape and <pulse duration> are additional information.
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