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Manufacturer datasheet, revision DE-DLPCA-200_R19/JM/02JAN2019, five pages. Page 1 shows the current-to-voltage converter and programmable gain stages; pp. 2–3 tabulate gain-dependent bandwidth, noise and linear input limits. These specifications describe an actual amplifier, rather than the illustrative optical-power ranges in dynamic range.

The dynamic range of a measurement procedure is the ratio between the largest and smallest positive inputs it can usefully distinguish under specified conditions. The quantity, bandwidth, observation interval, measurement calibration and acceptance criteria must accompany the number. An upper boundary might be set by amplifier clipping, while a lower boundary might require a specified signal-to-noise ratio. More displayed digits do not by themselves establish either boundary or better measurement precision.

Consider a photodiode responsivity measurement in which a photodiode produces electric current $i=R_{\lambda }P$ from optical power $P$, with spectral responsivity $R_{\lambda }$ in amperes per watt. A transimpedance amplifier with transimpedance $R_T$ produces an output electric potential difference $v=R_{T}i=KP$, where $K=R_T{R}_{\lambda }$ is expressed in volts per watt. If a chosen detection criterion is $k$ times the root mean square output noise ${\sigma }_v$, and the linear output ceiling is $v_{\max }$, the noise-limited dynamic range isIncreasing $K$ shifts this input interval toward smaller optical power; it does not enlarge its ratio when the stipulated output noise and output ceiling remain fixed. The corresponding input-referred noise is ${\sigma }_v/K$.

An original numerical example makes the distinction concrete. Stipulate ${\sigma }_v=0.5\mathrm{mV}$ in either setting, $k=5$, $v_{\max }=1\mathrm{V}$, and no other limiting effect. A high-sensitivity setting $K_H=10^{5}V/W$ covers $25\mathrm{nW}$ to $10\mu \mathrm{W}$; a lower-sensitivity setting $K_L=10^{3}V/W$ covers $2.5\mu \mathrm{W}$ to $1\mathrm{mW}$. Each interval has $D=400$. With compatible measurement calibration and range-overlap calibration in their common interval, gain ranging covers a contiguous union from $25\mathrm{nW}$ to $1\mathrm{mW}$: $D=40000$. These are optical power ratios, so their values in decibels are $10{\log }_{10}D$, approximately $26.02\mathrm{dB}$ and $46.02\mathrm{dB}$ respectively.

The equal-noise assumption isolates the geometric effect of gain ranging; it is not a specification for an actual instrument. A real transimpedance amplifier changes several properties together: its feedback network affects bandwidth, noise and allowable input electric current. The DLPCA-200 manufacturer sheet shows a current-to-voltage converter followed by programmable amplification and gives separate tables for these dependencies.^[ref] To test a combined dynamic range, vary a stable light source through the overlap, compare the two estimates of optical power, and allow the output to settle after switching. Agreement within the required measurement uncertainty is evidence that the two ranges can be joined; the mere presence of two gain switches is insufficient.

Gain ranging changes the sensitivity of a measuring signal path to keep its output within a useful interval as the input changes. A high-sensitivity setting resolves smaller inputs; a lower-sensitivity setting accommodates larger ones before amplifier clipping. Combining the settings can extend the instrument's usable dynamic range, provided their input intervals overlap and their measurement calibration is consistent.

A concrete apparatus is a switchable transimpedance amplifier converting electric current into an output electric potential difference. The DLPCA-200 manufacturer diagram separates a current-to-voltage stage from programmable amplification, and its performance tables give gain-dependent noise, input limits and bandwidth. The settings therefore change more than the decimal point of a display.^[ref]

For an original ideal calculation, suppose two settings follow $V_j=G_{j}I+b_j+n_j$, where $I$ is input current, $b_j$ the offset and $n_j$ zero-mean output noise. Stipulate a usable offset-corrected output from $5\mathrm{mV}$ to $1\mathrm{V}$ in either setting. With $G_H=10^{8}V/A$, the input interval is $50\mathrm{pA}$ to $10\mathrm{nA}$. With $G_L=10^{6}V/A$, it is $5\mathrm{nA}$ to $1\mu \mathrm{A}$. Each setting spans a ratio 200, but their overlapping union spans a current ratio 20000. These are stipulated intervals, not specifications for the cited amplifier.

Range-overlap calibration checks that both settings estimate the same current in their common $5$–$10\mathrm{nA}$ interval. A range-switching hysteresis rule can switch down in sensitivity above $8\mathrm{nA}$ and back up below $6\mathrm{nA}$, reducing repeated switching near one boundary. The output must settle before it is accepted as a new measurement indication.

An analog-to-digital converter that merely changes its printed units cannot recover an already clipped upstream signal. Likewise, increasing amplification does not automatically improve input-referred noise; the new setting may have different noise sources, bandwidth and drift. A meaningful combined range includes these effects and the required measurement uncertainty, rather than multiplying nominal gain settings without checking their usable intervals.

Optical pulse temporal contrast compares a pulse's peak with weaker light at another time. For a radiant power trace with peak $P_{\max }>0$, explicitly choose either the peak-to-local ratio $C(t)=P_{\max }/P(t)$ or its inverse $r(t)=P(t)/P_{\max }$. The first is at least one where the local power is positive; the second lies between zero and one. With a fixed transverse beam shape, the same ratio can be formed from light intensity. If the beam shape changes with time, specify the spatial sampling instead of identifying local intensity and total power.

A plateau at $10^{-3}$ of the peak has $r=10^{-3}$ and $C=1000$. Expressing this power ratio as optical contrast in decibels givesFor an amplitude ratio $A$ whose power ratio is $A^2$, the same definition gives $10{\log }_{10}(A^2)=20{\log }_{10}A$. Contrast also needs a delay or time range: an optical prepulse, an optical postpulse and a long optical pulse pedestal can have the same relative height but different positions and laser pulse energies. The pedestal energy fraction additionally requires integration over the contribution's duration.

A useful nonlinear measurement is third-order intensity autocorrelation. In an ideal instantaneous model, an input light intensity $I(t)$ generates a second-harmonic gate proportional to $I^2(t)$. Sum-frequency generation with a delayed fundamental replica gives a recorded signal proportional toThe instrument measures this cross-correlation, rather than simply reading $I(\tau )$. Finite gate width, phase matching, spatial overlap and detector response enter the interpretation.

The1998/99 instrument of J. Collier and colleagues used second-harmonic generation, a Wollaston prism and an optical biprism to form crossing fundamental and harmonic beams. A second crystal generated the sum-frequency signal, imaged through optical filters onto a charge-coupled device. Position encoded delay. An inserted glass etalon produced a delayed replica near $1.5\times 10^{-3}$ of the main signal, recorded on one side of the correlation peak. Figure4 combines window settings shifted with etalons.^[ref]

An independent ideal calculation explains both the asymmetry and a possible third-order pulse correlation ghost. Let $I(t)=g(t)+\epsilon g(t-d)$ represent two identical-shape pulses with well-separated supports and correlation lobes, with the second weaker and delayed. Squaring introduces no overlap term. If $A_g(\tau )=\int g^2(t)g(t+\tau )dt$, expansion givesThe delayed replica produces a lobe of relative order $\epsilon$, while the opposite-delay ghost has order ${\epsilon }^2$. For $\epsilon =0.01$, the scales are about $10^{-2}$ and $10^{-4}$ respectively. These values are predictions of the stated ideal model. Assigning every small correlation feature directly to a separate input pulse would miss this distinction.

A nondetection below the measurement floor establishes a bound under a detection model, rather than demonstrating that no light exists there. Finite dynamic range, detector baseline subtraction, delay coverage and resolution should accompany a reported contrast trace. The Sequoia manufacturer likewise distinguishes optical temporal resolution from the scan step; making that step smaller does not alone narrow the optical response.^[ref]