Photodetector

A photodetector converts incident light into a measurable signal, often an electric current or stored electric charge. A photodiode collects carriers produced by absorbed photons; a photomultiplier first releases photoelectrons and then amplifies their number.

A basic characterization measures the output with the beam blocked and with several known incident radiant powers. The slope gives spectral responsivity at the chosen wavelength; the blocked signal reveals offsets and dark current. Quantum efficiency, response speed and noise-equivalent power describe different limitations. Detecting a weak signal requires separating its contribution from both background photons and the detector's own fluctuations.

A photoconductor is a detector whose illuminated material changes electrical conductivity, allowing an external circuit to measure the change under applied bias. It uses photoconductivity: absorbed photons can produce mobile electrons and electron holes, changing the conductive path between contacts. A simple photoresistor reads this as a light-dependent resistance. Shimadzu’s primary description explains band-gap excitation and the resistance decrease in a PbS detector.^[ref]

An original uniform-bar model makes the signal mechanism quantitative. Let the contact separation be $\ell$, the conducting area $A$, electron and hole number densities $n,p$, and their mobilities ${\mu }_n,{\mu }_p$. In the low-field ohmic model,Here $e$ is the positive elementary charge and $V_b$ the actual detector electric potential difference. If illumination changes carrier densities while mobilities stay fixed,The assumptions exclude contact barriers, strongly nonuniform illumination and a bias changed by the readout; those effects require an expanded model.

For $\ell =1\mathrm{mm}$, $A=10^{-8}{\mathrm{m}}^2$, ${\mu }_n=0.10{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})$, ${\mu }_p=0.05{\mathrm{m}}^2/(\mathrm{V}\mathrm{s})$ and $\Delta n=\Delta p=10^{18}{\mathrm{m}}^{-3}$, the conductivity increment is about $0.0240S/m$. At fixed $V_b=5\mathrm{V}$, the predicted current increment is about $1.20\mu \mathrm{A}$. These stipulated parameters illustrate the conversion of extra carriers into a signal, rather than specifications of a named detector.

Readout loading can change that result. In a divider powered at $V_s$, with detector resistance $R_d$ in series with load $R_L$, the output across the load isFor $V_s=5\mathrm{V}$ and $R_L=10\mathrm{k\Omega }$, changing $R_d$ from $100$ to $10\mathrm{k\Omega }$ raises the output from about $0.455$ to $2.50\mathrm{V}$. The detector’s own bias falls from about $4.55$ to $2.50\mathrm{V}$. A light-dependent conductance and a measured divider voltage therefore need not have the same linearity. Record the actual bias and illuminated area when measuring spectral responsivity.

Photoconductor response time also depends on carrier storage and loss. A simple spatially uniform excess-carrier model is $d\Delta n/dt=g(t)-\Delta n/\tau$. After a step to constant generation $g_0$, initially zero excess density becomes $g_0\tau (1-e^{-t/\tau })$. Small sinusoidal modulation has response proportional to $(1+i2\pi f\tau {)}^{-1}$. With stipulated $\tau =100\mu \mathrm{s}$, the single-pole cutoff is about $1.59\mathrm{kHz}$. Real traps, contacts and electronic filters need not yield one such time constant.

A proposed characterization biases the detector through a known readout, measures dark and illuminated currents at controlled wavelength and temperature, then chops or modulates the light and measures amplitude and phase versus modulation frequency. Repeat at several powers and biases to separate detector behavior from circuit loading. Temperature control matters: the manufacturer notes that PbS spectral sensitivity, response speed and dark resistance all change with temperature.^[ref]

The name photoconductive mode for a reverse-biased photodiode describes an operating choice of a junction detector; it does not make every such device the bulk-resistance detector modeled above. Likewise, a detector’s signal increase is not by itself a claim of unlimited useful gain: background response, dark current, noise, saturation and response time remain distinct characterization questions.

Photoconductor response time describes how quickly the electrical signal follows a change in illumination under stated bias, temperature, background and readout conditions. A rise time, fall time and modulation bandwidth summarize different features and require definitions. The manufacturer’s PbS description notes that sensitivity, response speed and dark resistance vary with temperature, so a timing number is not independent of operating conditions.^[ref]

An original one-lifetime model takes excess carrier density $n_e$ to obeyWith constant mobility and fixed detector bias, suppose the excess current is proportional to $n_e$. After a step from zero to generation $g_0$, the normalized signal is $1-e^{-t/\tau }$. The times to reach ten and ninety percent of its final value are $-\tau \ln 0.9$ and $-\tau \ln 0.1$, givingThe time from zero to ninety percent is instead $\tau \ln 10$. A quoted rise time without its thresholds is therefore incomplete.

For small sinusoidal generation changes, the normalized frequency response isThe half-power frequency is $f_c=1/(2\pi \tau )$, so this single-pole model gives $t_{10\text{–}90}{f}_c=\ln 9/(2\pi )\approx 0.3497$. This relationship is a consequence of the stated model, not a universal identity for arbitrary detectors.

For $\tau =100\mu \mathrm{s}$, the rise time is about $219.7\mu \mathrm{s}$ and the cutoff about $1.592\mathrm{kHz}$. At $1\mathrm{kHz}$, the signal amplitude is about $0.8467$ of its low-frequency value and its phase lags by $32.14^{\circ }$. The signal can therefore have a substantial phase delay before reaching the half-power point.

A readout adds its own dynamics. If the detector response is cascaded with a separate first-order electronic response of the same time constant, the overall magnitude is $1/[1+(2\pi f\tau {)}^2]$. Its half-power frequency is $\sqrt{\sqrt{2}-1}/(2\pi \tau )$, about $0.6436$ times the single-pole cutoff. Assigning that combined bandwidth entirely to the material would give an incorrect carrier-lifetime estimate.

Photoconductor rise and fall asymmetry tests another limitation of the simple model: linear one-lifetime dynamics predict equal normalized rise and fall behavior, but trap occupancy, changing background or a nonlinear circuit can produce different transients. A long relaxation tail should be measured rather than compressed into an unsupported single time constant.

A proposed experiment switches or modulates a monitored optical source, records detector current and actual bias, and measures ten-to-ninety and ninety-to-ten crossings after settling the initial illumination state. Repeat the modulation sweep with a characterized faster readout or independently measured amplifier response. Vary temperature and optical background while holding the wavelength and spot fixed. Agreement between step and frequency-response fits tests the one-pole approximation; disagreement identifies missing dynamics without by itself proving which physical mechanism caused them.

Photoconductor rise and fall asymmetry means that a photoconductor's normalized turn-on and turn-off transients have different shapes or threshold-crossing durations under stated illumination and electrical conditions. Define the levels first: a ten-to-ninety-percent rise and a ninety-to-ten-percent fall exclude different portions of a long tail than a zero-to-ninety-percent measurement. Detector temperature is an essential condition because the primary PbS description reports changes in response speed, dark resistance and spectral sensitivity with temperature.^[ref]

The simplest linear carrier model predicts symmetry. For excess carrier density $n$ satisfying $\dot{n}=g-n/\tau$, a step to $g_0$ gives $n/n_{\infty }=1-e^{-t/\tau }$; switching off after equilibration gives $n/n_{\infty }=e^{-t/\tau }$. Both threshold durations equal $\tau \ln 9$. Thus different measured durations are evidence against that complete one-pole measurement model, rather than a result it already predicts.

A photoconductor transient with quadratic recombination supplies an illuminating alternative model. Stipulate constant mobility, fixed detector bias, zero dark excess density andUnder constant $g_0$, let $n_{\infty }=\sqrt{g_0/\beta }$ and ${\tau }_{\ast }=1/(\beta n_{\infty })$. Starting at zero gives $n/n_{\infty }=\tanh (t/{\tau }_{\ast })$. Starting at $n_{\infty }$ and setting $g=0$ gives $n/n_{\infty }=(1+t/{\tau }_{\ast }{)}^{-1}$. Direct substitution verifies both solutions.

For an output proportional to $n$, the resulting durations areWith stipulated ${\tau }_{\ast }=1\mathrm{ms}$, the rise takes $1.372\mathrm{ms}$ and the fall $8.889\mathrm{ms}$, despite having no separate fitted rise and fall constants. This is a derived nonlinear electron-hole recombination model, not measured behavior or a specification of the cited PbS or CdS detector. Its long algebraic tail also shows why a single exponential fit may depend strongly on the fitted interval.

The readout can itself introduce asymmetry. A resistance divider has output $V_s{R}_{L}G/(1+R_{L}G)$ as a function of detector electrical conductance $G$. Equal exponential rise and fall in $G$ need not give equal normalized threshold durations after this nonlinear conversion. Carrier dynamics, the electrical transfer curve and an amplifier's response must therefore be separated before assigning a material lifetime.

A proposed experiment switches a monitored optical source between two reproducible levels, measures actual detector bias and current, waits for the same initial equilibrium, and repeats in both directions. Compare current-derived conductance with divider output, then vary background, temperature and step size. A slow reference source or readout can imitate a detector tail. Asymmetry alone does not uniquely identify trapping or any other microscopic mechanism.

A photoconductor transient with quadratic recombination is a carrier-density model in which the loss rate grows as the square of the mobile excess density. It explains how nonlinear loss can produce different turn-on and turn-off waveforms without assigning unrelated exponential lifetimes to the two directions. A photoconductor converts illumination-dependent electrical conductivity into a signal under external bias; the manufacturer's primary PbS description establishes that conversion mechanism.^[ref] The quadratic loss law below is an explicitly stipulated model, not a fitted specification of that detector.

Assume a spatially uniform excess density $n\ge 0$, generation rate $g\ge 0$, constant coefficient $\beta >0$ and an output proportional to $n$ at fixed mobility and bias:Density has units ${\mathrm{m}}^{-3}$, $g$ has units ${\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$ and $\beta$ has units ${\mathrm{m}}^3/s$. A two-carrier recombination rate proportional to the product of equal electron and hole densities motivates a quadratic term in an appropriate regime. Background carriers, other loss processes, contacts and trapping can invalidate that specialization.

For constant $g>0$, set $n_{\infty }=\sqrt{g/\beta }$ and $k=\beta n_{\infty }$. Separating variables, or differentiating the following expression, gives the solution for any finite nonnegative initial density $n_0$:For $n_0=0$ it reduces to $n_{\infty }\tanh (kt)$. For $n_0=n_{\infty }$ it stays at equilibrium, and for $n_0>n_{\infty }$ it approaches the same equilibrium from above. In the dark, $g=0$ instead yieldsThe reciprocal-density plot is linear in this model, while a semilogarithmic decay plot is curved. The dark half-decay time is $1/(\beta n_0)$, so it depends on the starting illumination.

The small-signal lifetime under quadratic recombination is different again. Linearize about a nonzero background $\overline{n}=\sqrt{\overline{g}/\beta }$:A locally exponential small-signal response can therefore coexist with a strongly nonexponential large dark transient. One measured time constant cannot be substituted for all three quantities.

For an original example, stipulate $\beta =10^{-15}{\mathrm{m}}^3/s$ and $\overline{n}=10^{18}{\mathrm{m}}^{-3}$. Then $\overline{g}=10^{21}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$, dark half-decay time $1\mathrm{ms}$, small-signal lifetime $0.5\mathrm{ms}$ and small-signal half-power frequency about $318.3\mathrm{Hz}$. Four times the background generation doubles equilibrium density and doubles that frequency in this model.

A proposed test measures small modulation about several backgrounds separately from complete turn-off traces, while controlling actual detector bias, temperature and readout response. Examine reciprocal-density linearity only after justifying how the measured current maps to density. A successful fit supports the tested rate-law approximation; it does not uniquely identify the microscopic electron-hole recombination mechanism. Temperature and spectral sensitivity also vary in real PbS detectors and must be held or measured independently.^[ref]

A photoresistor, also called a light-dependent resistor or LDR, is a two-terminal component whose resistance changes with incident light. A common photoconductive implementation uses an illuminated semiconductor between contacts; an external circuit converts its resistance change into a voltage or current signal. A manufacturer’s CdS datasheet explicitly identifies these names and describes resistance decreasing with visible illumination.^[ref]

The photoconductor mechanism is a change in conductivity through generated mobile carriers. A photoresistor’s resistance is consequently not a calibrated unit of optical power by itself. Material, wavelength distribution, temperature, illumination history and the measuring circuit help determine the observed response.

For an original illustrative model over a limited range, let $R(P)=R_0(P/P_0{)}^{-\gamma }$ with $\gamma >0$, fixed spectrum and geometry. Choose $R_0=20\mathrm{k\Omega }$ and $\gamma =0.7$. Four times the reference optical input gives $R\approx 7.579\mathrm{k\Omega }$, rather than one quarter of the original resistance. This stipulated power law illustrates a nonlinear response, not a fitted specification for the cited part.

In a divider with supply $V_s$ and fixed resistor $R_L$, measuring across $R_L$ givesAt $V_s=3.3\mathrm{V}$ and $R_L=10\mathrm{k\Omega }$, the model output rises from $1.10\mathrm{V}$ at $P_0$ to about $1.877\mathrm{V}$ at $4P_0$. The logarithmic sensitivity is greatest when $R(P)=R_L$, where it is $\gamma V_s/4$. Choosing a resistor therefore selects an operating region; it does not remove the material’s response law.

The electrical input must also be characterized. The divider seen at its output has Thevenin resistance $R(P)\parallel R_L$. A finite-input-resistance voltmeter or an analog-to-digital converter with a switched input can change the reading. Self-heating depends on the detector’s actual voltage and resistance, while photoconductor response time can make a rapidly sampled value differ from its settled value.

Photoresistor spectral calibration is essential when interpreting an illumination reading. Lux is photometrically weighted, so equal illuminance from different spectra need not produce equal absorption or equal resistance. The cited manufacturer specifies source conditions for light-resistance measurements, a waiting time for dark resistance and light-adaptation preconditioning before its tests.^[ref] Those conditions describe what was tested; they should not be silently omitted from a comparison.

A proposed characterization uses a stable monitored light source, fixed detector position and a controlled spectrum, stepping illumination in both directions and recording the settled resistance and transient. Measure actual bias and temperature, then test the intended readout separately. A component can work well as a light/dark threshold sensor while requiring substantially more characterization to estimate optical power quantitatively.

Photoresistor spectral calibration determines how a photoresistor's electrical reading depends on the illumination spectrum under specified geometry, background, temperature, bias and adaptation history. A resistance-versus-lux curve measured with one lamp is not automatically valid for another spectrum. The manufacturer's primary CdS datasheet specifies a $2854\mathrm{K}$ source for its light-resistance tests and preconditions cells with light before electrical measurements.^[ref]

The distinction is between irradiance and illuminance. With spectral irradiance $E_{\lambda }(\lambda )$, illuminance is approximatelywhere $V$ is the photopic luminous efficiency function. The detector weights wavelengths according to its own physical response, which need not be proportional to $V$. NIST's detector-based photometric realization measures that spectral response, rather than assuming an arbitrary detector reproduces the photometric weighting.^[ref]

For a locally linear small-signal model about a fixed operating state, writeHere $s_G$ is the differential spectral responsivity of electrical conductance, including the stated illumination geometry. It is not automatically a global, illumination-independent material constant. A background-dependent photoresistor spectral response requires rechecking this derivative when the operating point changes.

An original two-band example makes the mismatch quantitative. Stipulate relative photometric weights $V_a=0.8$, $V_b=0.2$ and equal detector generation weights $s_a=s_b$ for two narrow bands. Equal illuminance requires four times as much irradiance in band $b$, so its detector-weighted generation is four times greater. If, over this illustrative range, $R\propto g^{-0.7}$, the resistance ratio is $R_b/R_a=4^{-0.7}\approx 0.379$. These weights and exponent are stipulated, not measured specifications or tabulated values for named wavelengths. Equal lux can produce substantially unequal resistance.

A proposed spectral characterization uses narrow-band sources or a monochromator, a reference detector to measure incident irradiance, fixed beam geometry and controlled detector temperature. Record resistance or conductance after a defined settling time at several background levels. A separate calibrated photometer can establish illuminance; it cannot by itself establish the photoresistor's spectral weighting. Keep electrical loading and self-heating fixed while changing the source.

For a broadband transfer, characterize the reference and test spectra and test whether the measured spectral-response model predicts their relative readings. Existing spectral mismatch correction methods address the analogous transfer problem for photometers, but a nonlinear photoresistor first needs a justified operating-point model.^[ref] The result is a calibration valid for stated conditions, not a universal conversion from resistance to optical power.

A background-dependent photoresistor spectral response is the differential change of a photoresistor's output with wavelength-specific illumination, evaluated at a stated background state. It can depend on illumination level, spectral composition, bias, temperature and prior adaptation. The primary CdS datasheet specifies light-adaptation preconditioning before electrical tests, demonstrating that a measurement condition includes more than the instantaneous lux value.^[ref]

Let the steady electrical conductance be a functional $G=\mathcal{F}[E_{\lambda }]$ of incident spectral irradiance. About a background $E_{\lambda ,0}$, define the local response byThis derivative concerns small changes after specifying the operating state. A finite change or rapid modulation needs further nonlinear or dynamic characterization. Photoresistor spectral calibration establishes the required optical and electrical conditions.

An original separable model makes a useful distinction. Suppose $g=\int a(\lambda )E_{\lambda }(\lambda )d\lambda$ and $G=G_d+\kappa g^{\gamma }$, with positive $g,\kappa ,\gamma$. ThenThe amplitude changes with background, but the normalized spectral shape remains $a(\lambda )$. With $\gamma =0.7$, quadrupling $g_0$ multiplies the absolute differential response by $4^{-0.3}\approx 0.6598$. For a small one-percent generation increment, the leading fractional conductance change above the dark contribution is $0.7\%$; the exact model gives $(1.01{)}^{0.7}-1\approx 0.69895\%$.

A change in spectral shape requires more than that single separable nonlinearity. For an illustrative two-band response in dimensionless input coordinates, letThe derivatives are $\partial G/\partial E_a=1/(2\sqrt{E_a})$ and $\partial G/\partial E_b=1$. Changing the first-band background from $E_a=1$ to $4$ changes their ratio from $1/2$ to $1/4$. This toy model shows how relative spectral sensitivity can change; it is not measured behavior of a named component. Separable and nonseparable photoresistor spectral-response models should consequently be distinguished in a calibration analysis.

Resistance readout adds another operating-point factor: since $R=1/G$, $\delta R=-\delta G/G_0^2$. A resistance-divider output has yet another derivative. Comparing raw electrical slopes without converting to the same output variable can imitate a change in material response. Likewise, equal illuminance need not mean equal detector excitation, because the photopic luminous efficiency function supplies a different spectral weighting.^[ref]

A proposed apparatus combines a stable background source with a weak wavelength-selectable probe beam, a monitored reference detector and a fixed illumination geometry. At each background, measure the output derivative while decreasing probe amplitude to test the small-signal regime, then repeat after the prescribed settling or adaptation period. Normalize spectra only after retaining their absolute scale. This separates a changing overall gain from a changing spectral shape and from readout loading; it does not assume that a curve measured at one background transfers to every illumination condition.

A detector linearity test checks whether changes in a detector's output remain proportional to changes in its incident signal over a stated operating range. For a photodetector with a fixed wavelength, geometry and readout gain, a linear response model iswhere $P$ is radiant power, $b$ is the baseline and $R$ is the appropriate response coefficient. A detector baseline subtraction removes the offset before comparing $y-b$ with $P$. Linearity concerns the shape of that relation; an incorrectly calibrated constant $R$ can still give a linear detector.

A documented apparatus uses a beam splitter to illuminate two photodiodes at approximately a ten-to-one intensity ratio. NIST's measurement at $633\mathrm{nm}$ compared responsivity with its low-power value, with the aperture filled and uniformly irradiated. The report explicitly notes dependence on irradiation geometry.^[ref] A detector's response to a small concentrated spot need not reproduce its response to the same total power spread over the aperture.

For an original numerical example, stipulate baseline-corrected electric currents of $0.500$, $0.990$ and $1.940\mu \mathrm{A}$ at input powers $1$, $2$ and $4\mu \mathrm{W}$. Normalizing the apparent spectral responsivity to the first point givesThe last point has three percent less response per unit power than the first. A straight line through the origin with slope $0.500A/W$ would predict $2.000\mu \mathrm{A}$ there instead of $1.940\mu \mathrm{A}$.

A useful test varies incident power while monitoring source stability and holding the beam position, illuminated area and electronic settings fixed. Record blocked-beam readings as well as illuminated readings. A residual that exceeds the combined measurement uncertainty identifies a departure from the tested model; it does not by itself locate the cause in the photodiode rather than an amplifier or other readout stage.

For pulses, average power alone may hide a nonlinear response to high peak power. A continuous-illumination test therefore does not automatically validate pulse energy measurement with a photodiode at a different pulse duration or spot size. Test the illumination and electrical range actually used, and distinguish a change in slope from a change in baseline.

A detection time gate is a selected interval during which a photodetector's output contributes to a measurement. Its start delay and duration $T_g$ are measured relative to a trigger or another time reference. The gate may control an integrating amplifier, an electronic counter or a software selection of recorded events; it need not physically switch off the light.

A gated integrator supplies a concrete apparatus. Stanford Research Systems' SR250 uses a triggerable gate generator, a fast integrator and a readout normalized by gate width. Its gate monitor can be displayed alongside the signal on an oscilloscope to check their relative timing.^[ref] An integrated area and a gate-averaged amplitude are different output quantities: dividing an area by $T_g$ changes its units.

An original photon counting example shows the gate-width tradeoff. Suppose an ideal decaying signal has expected count rate $s(t)=S_{\infty }{e}^{-t/\tau }/\tau$ for $t\ge 0$, and a constant background has rate $b$. A gate from0 to $T_g$ collects expected countsIf signal and background counts are independent Poisson distributions and the background mean is known exactly, the background-corrected count has variance $S+B$. Its signal-to-noise ratio is $S/\sqrt{S+B}$. With chosen values $S_{\infty }=100$ and $b\tau =100$, a gate of width $\tau$ gives about63.2signal counts,100background counts and ratio4.95. A gate of width $3\tau$ collects95.0signal counts but300background counts, reducing that ratio to4.78. More collected signal alone does not guarantee a better measurement.

This example assumes ideal event registration; detector dead time, non-Poisson backgrounds or an estimated rather than known background alter the calculation. Gate timing jitter can also vary the admitted part of a rapidly changing signal. Gate placement and duration should therefore be checked against the actual waveform, background and measurement objective, rather than chosen solely from the nominal pulse width.

A gate-normalized detector output reports an integrated detector signal divided by the duration of the detection time gate. For an input electric potential difference waveform $v(t)$ and a gate from $t_0$ to $t_0+T_g$, the input-referred average isIts units are those of electric potential difference, whereas the integral has units of electric potential difference times time. The SR250 gated integrator implements integration followed by gate-width normalization and an adjustable amplification stage.^[ref]

For an original idealized detector pulse, take $v(t)=2\mathrm{mV}$ from0 to4nanoseconds and zero outside that interval. A gate covering0–4nanoseconds integrates $8\mathrm{mV}\mathrm{ns}$ and reports an average of2millivolts. A gate covering0–8nanoseconds integrates the same area but reports1millivolt. Thus unchanged admitted pulse area need not give an unchanged normalized output.

The gate average also differs from the average over a full repetition period. For the same pulse repeated once per microsecond, the full-period mean is only8microvolts. Comparing instruments therefore requires knowing whether the reported quantity is pulse area, within-gate average or full-period average.

A constant baseline $b$ contributesGate-width normalization does not remove that baseline. A separate reference or subtraction measurement is needed to distinguish it from the desired signal.

An apparatus check overlays the gate monitor and detector waveform on an oscilloscope, then varies the gate width while keeping its start fixed. A flat plateau should retain its input-referred average while the gate remains inside it; a short pulse diluted by additional quiet time behaves like the example above. Gate timing jitter and gate-width jitter can alter which signal portion is admitted and which duration is used for normalization.^[ref]

Gate timing jitter is shot-to-shot variation in the timing of a detection time gate relative to the signal being measured. It differs from a fixed delay error: repeated gates may have the correct mean delay while admitting different portions of a rapidly varying detector signal. The SR250 catalogue describes a trigger-controlled gate, finite delay jitter and a gate-monitor output that can be overlaid with the signal on an oscilloscope.^[ref]

For an original sensitivity derivation, let a reproducible baseline-corrected electric current waveform be $i(t)$ and the intended integrated electric charge beSmall edge errors giveIf both edges shift by the same amount, the gate width is unchanged butThus a gate translating within a flat plateau has little first-order sensitivity, while a gate whose edges intersect different signal levels can be sensitive even at fixed width.

For stipulated edge currents $i(t_0)=100\mathrm{nA}$ and $i(t_1)=20\mathrm{nA}$, a common timing error with standard deviation $2\mathrm{ns}$ contributes approximately $0.16\mathrm{fC}$ charge standard deviation. This calculation assumes smooth waveform values near both edges and timing excursions small enough for linearization. A gate crossing an abrupt onset requires the actual waveform integral.

Gate-width jitter is a separate effect. For a constant plateau current $I$, $Q=I(t_1-t_0)$, so $\delta Q=I\delta T_g$ even though a common gate translation would cancel. More generally, the edge-error contribution has varianceThe covariance determines whether two individually noisy edges largely preserve the width.

An apparatus check records both the gate monitor and signal waveform over many triggers, using the same time reference, to estimate relative delay and width distributions. A single aligned trace establishes neither distribution. Timing motion shared by the pulse and gate can cancel in their relative delay; the uncertainty relevant to the measured charge is their relative timing, not solely a gate generator's standalone specification.

Gate-width jitter is shot-to-shot variation in the duration of a detection time gate. If its opening and closing times are $t_0,t_1$, then $T_g=t_1-t_0$. Both edges can have substantial gate timing jitter while their difference remains stable. A common shift changes delay without changing width.

For small timing fluctuations,With equal edge standard deviations ${\sigma }_e$ and correlation coefficient $\rho$, this becomes ${\sigma }_T={\sigma }_e\sqrt{2(1-\rho )}$. The covariance identity is exact whenever those variances exist. It separates width stability from the jitter of either edge measured alone.

For an original example, let both edges have standard deviation $100\mathrm{ps}$. Independent edge errors give ${\sigma }_T=141.4\mathrm{ps}$; correlation $\rho =0.99$ instead gives $14.14\mathrm{ps}$. At nominal width $10\mathrm{ns}$, those are relative width fluctuations of about 1.414 percent and 0.1414 percent. Assuming independence would overestimate the second width uncertainty by a factor of ten.

If a flat, baseline-corrected electric current $I$ fills the gate, the integrated electric charge is $Q=I{T}_g$, so ${\sigma }_Q=|I|{\sigma }_T$. At $I=2\mu \mathrm{A}$ the nominal charge is $20\mathrm{fC}$, with respective standard deviations $0.2828$ and $0.02828\mathrm{fC}$. A varying waveform also introduces sensitivity to where the edges fall; the gate timing jitter article gives the general edge-current formula.

A gate-normalized detector output can report $Q/T_g$ instead of charge. For an exactly constant current and accurately known actual width, that ratio is $I$ despite width variation. Dividing by a fixed nominal width instead retains the width-induced variation. The SR250 documentation describes integration followed by gate-width normalization, and provides a gate monitor for checking timing.^[ref]

An apparatus check measures both edges relative to a common reference over repeated triggers and computes their difference for each shot. Measuring the two edge jitter distributions separately without their covariance cannot determine width jitter. Readout time resolution and the threshold used to define an edge are also part of that measurement.

Detector baseline subtraction estimates the non-signal level of a photodetector readout and subtracts it before interpreting the desired signal. The baseline can include electronic offset, dark current and background light. Subtracting its estimated mean removes a bias contribution; it does not remove the random fluctuations that occurred in the measurement.

For a current readout over a detection time gate, a constant baseline estimate $\hat{b}$ givesIf the true constant baseline is $b$, its contribution to the charge error is $(b-\hat{b})T_g$. An original example has $T_g=10\mu \mathrm{s}$ and a baseline overestimate of1nanoampere. The corrected charge is then10femtocoulombs too low. A longer gate amplifies this fixed baseline-estimation error linearly.

A finite baseline record also adds uncertainty. Suppose $n$ equally spaced signal-window samples and $N$ separate baseline samples each have independent zero-mean noise of variance ${\sigma }^2$, and the baseline estimate is their arithmetic mean. With spacing $\Delta t$,The same estimated baseline is subtracted from every signal sample, so its error is shared rather than independently redrawn $n$ times. For $n=N=100$, $\sigma =1\mathrm{nA}$ and $\Delta t=1\mu \mathrm{s}$, the standard uncertainty is about14.1femtocoulombs. Treating the baseline as known would give only10femtocoulombs. These are stipulated independent-noise values, not a detector specification.

Baseline drift motivates measuring the baseline near the signal in time. The SR250's active subtraction mode alternates signal-present and signal-absent triggers, reversing the baseline sample's sign before averaging.^[ref] Cancellation depends on how well those samples represent the baseline during the signal; a source-correlated artifact need not cancel.

In pulse energy measurement with a photodiode, charge-to-energy conversion propagates this baseline error through $U=Q/R$, where $R$ is spectral responsivity. Baseline characterization is therefore part of the energy measurement, not merely a cosmetic shift of a plotted trace.

Baseline drift is a change with time in the non-signal level of a measurement readout. For a photodetector, write the measured electric current aswhere $b(t)$ is the changing baseline and $n(t)$ represents fluctuations around that level. Detector baseline subtraction using one fixed value can leave a time-dependent residual even when it correctly removes the initial offset.

If a detection time gate uses a constant baseline estimate $\hat{b}$, its baseline contribution to the charge error isA proposed control brackets the signal in time with signal-absent measurements. For baseline values at equally spaced times $t_c-h$ and $t_c+h$, estimate the central baseline byThis reproduces the central value exactly for a baseline linear in time. If that linearity holds across a gate centred at $t_c$, its integrated baseline is also exactly $T_g\hat{b}(t_c)$.

For an original example, choose baseline readings $2$ and $6\mathrm{nA}$ before and after the signal, with linear drift between them. The central baseline is $4\mathrm{nA}$. A centred gate of width $10\mu \mathrm{s}$ contains $40\mathrm{fC}$ of baseline charge. Subtracting only the earlier reading removes $20\mathrm{fC}$ and leaves a false positive contribution of $20\mathrm{fC}$.

Bracketing is not an unconditional drift correction. For $b(t_c+s)=b_0+vs+c{s}^2/2$, the two-point estimate of the central level is $b_0+c{h}^2/2$, so curvature introduces an error. Random baseline-readout errors also contribute measurement uncertainty. Taking reference readings close to the signal limits some drift effects, but does not remove a source-correlated artifact or compensate for all changes in the measurement conditions.

A real gated-integrator implementation alternates signal-present and signal-absent triggers and reverses the latter contribution before averaging. The manufacturer's stated purpose is active baseline subtraction.^[ref] Its effectiveness depends on whether the signal-absent readings represent the baseline during the signal. Plotting those readings against time, as well as reporting their average, can distinguish a changing zero from uncorrelated measurement noise.

A photodetector capable of registering an individual absorbed photon as a distinguishable event. The detection record may include a click time and an output-channel label. Such a detector need not resolve the number of photons in a pulse: an ordinary single-pixel single-photon avalanche diode produces essentially the same saturated avalanche pulse when one or several photons trigger the same detection interval. Detector efficiency, dark counts and detector dead time affect the observed photon counting statistics.

A registered detector event occurring without an incident signal photon. For a single-photon avalanche diode, internally generated carriers can trigger the same avalanche as an absorbed photon. The dark-count rate $r_{\mathrm{dark}}$ is the mean number of these events per unit time under specified operating conditions. Such events can contaminate coincidence counting and increase the quantum bit error rate in quantum key distribution.

Noise-equivalent power expresses detector noise as an equivalent incident radiant power. In a bandwidth-normalized convention, divide the output amplitude amplitude spectral density by spectral responsivity; the units are $\mathrm{W}\mathrm{H}{\mathrm{z}}^{-1/2}$. It is the incident signal scale giving unit signal-to-noise ratio in a $1\mathrm{Hz}$ noise-equivalent detection bandwidth.^[ref]

For approximately white noise, a bandwidth $B$ gives equivalent rms radiant power $\mathrm{NEP}\sqrt{B}$. Thus $10^{-12}\mathrm{W}\mathrm{H}{\mathrm{z}}^{-1/2}$ over $100\mathrm{Hz}$ corresponds to $10^{-11}\mathrm{W}$. State the wavelength, operating conditions and bandwidth: a bandwidth-normalized specification is not itself a universal minimum detectable energy.

Noise-equivalent radiance is the incident radiance change producing signal-to-noise ratio one for a specified spectral and electrical bandwidth. A linear radiometer with voltage response $G=dV/dB$ and RMS voltage noise ${\sigma }_V$ has $\mathrm{NER}={\sigma }_V/|G|$. Its convention must distinguish per-sample noise from a noise amplitude per square-root bandwidth.

The ratio between a stated upper usable detector signal and a lower detectable or resolvable signal under specified measurement conditions. Exposure duration, read noise, saturation, digitization and the required linearity can all affect the quoted value. It is not determined by full well capacity alone.

The charge that an integrating detector well can hold within its stated operating specification before saturation or overflow compromises the response. It differs from the digitizer limit and from the largest signal that is accurately linear. In a charge-coupled device, excess charge can cause blooming into adjacent pixels.

Two or more photons detected within one unresolved spatial and temporal event cell can be registered as one event, have their energies combined, or be rejected by event grading. In an X-ray CCD, low mean occupancy per event island per frame is needed for reliable individual-photon spectroscopy. Reducing frame time or spreading the image can reduce this effect.

A photodetector in which light releases electrons from a cathode into a vacuum, and an anode collects them. A positive collecting-anode bias relative to the emitting cathode drives collection across the vacuum gap.

A bolometer detects absorbed electromagnetic radiation through the resulting change in temperature, often read as a change in electrical resistance. Its response depends on absorbed power, so interpreting an optical spectrum requires accounting for the incident wavelength band and detector calibration.

A microbolometer is a miniaturized bolometer in which absorbed electromagnetic radiation heats a thermally isolated sensing element and the readout detects the resulting change in electrical resistance. Arrays of microbolometers can form an infrared image without cryogenic detector cooling. A pixel commonly has an absorbing membrane suspended above its readout circuit on narrow supports.^[ref]

An elementary small-signal heat transfer model writesHere $C$ is the sensing element's heat capacity, $G$ its thermal conductance to a fixed-temperature substrate $T_b$, $P$ incident radiant power and $\eta$ its absorbed fraction. The model treats the element as having a single temperature and neglects changes in readout self-heating. A step to constant incident power $P_0$ givesThe thermal time constant therefore connects sensitivity to response speed. Lowering $G$ increases the steady temperature rise, but at fixed $C$ also lengthens the response.^[ref]

For an original example, choose $C=10^{-9}\mathrm{J}{\mathrm{K}}^{-1}$, $G=10^{-7}\mathrm{W}{\mathrm{K}}^{-1}$, $\eta =0.8$ and $P_0=1\mathrm{nW}$. Then $\tau =10\mathrm{ms}$ and the final sensing-element rise is $8\mathrm{mK}$; after $30\mathrm{ms}$ it has reached about $95\%$ of that rise. If the initial resistance is $100\mathrm{k\Omega }$ and the temperature coefficient of resistance is $\alpha =-0.02{\mathrm{K}}^{-1}$, the linear approximation $\Delta R\approx \alpha R\theta$ gives $\Delta R=-16\Omega$ at steady state. These stipulated values illustrate the model, not a particular camera's specification.

The sensing element's temperature rise is not the observed object's temperature rise. Inferring object temperature from the measured infrared signal additionally depends on emissivity, reflected radiation, the optical path and measurement calibration. “Uncooled” also permits temperature stabilization of the array; it describes the absence of required cryogenic operation, not the absence of thermal design.

For a photodiode in its linear regime, spectral responsivity is the dark-subtracted electric current per incident radiant flux in a narrow band at wavelength $\lambda$, measured in $\mathrm{A}{\mathrm{W}}^{-1}$. More generally a photodetector's readout can be electrical voltage or another quantity, with corresponding units. A broad-band readout weights the incoming optical spectrum by the detector's spectral responsivity; it is not the unweighted total incident power. ^[ref].

A photodetector bias frame is an exposure of effectively zero integration time used to estimate the electronic offset and read noise. For independent identical bias reads, the variance of their difference is twice the single-read variance; subtracting an estimated mean bias removes the offset but adds the uncertainty of that estimate.

Flat-field correction compensates stable multiplicative variations in photodetector response using calibrated illumination. Identically illuminated exposure ratios cancel the stable response in their mean, but their photon shot noise remains signal dependent.

An analogue-to-digital unit is a unit of a digitized photodetector output after electronic conversion. Its relation to collected electrons is set by the detector conversion gain; an additive electronic offset must be removed before interpreting a count as a light signal.

Detector conversion gain is the number of collected electrons per analogue-to-digital unit. With independent Poisson distribution photoelectron counts, the shot-noise variance in count units is the mean count divided by the gain. Detected-photon and electron conventions agree only when each detected photon contributes one electron.

Let independent exposure sums $A,B$ have mean $N$ ADU at each detector pixel, with pure Poisson distribution noise and fixed gain $g$. The delta method gives $A/B\simeq 1+(A-N)/N-(B-N)/N$, so $\mathrm{Var}(A/B)\simeq 2/(gN)$ and $g\simeq 2/(N{E}^2)$. For nonuniform detector pixel means $N_i$, an unweighted spatial ratio variance is instead $(2/g)⟨1/N_i⟩$. This high-count approximation requires linear unsaturated data, bias subtraction and negligible read noise.

For stable positive detector pixel means $N_i$ and uniform detector conversion gain $g$, high-count independent Poisson distribution noise gives $\mathrm{Var}(A_i/B_i)\simeq 2/(g{N}_i)$. Thus substituting a global mean in the equal-signal formula yields $g_{\mathrm{naive}}=g/[⟨N_i⟩⟨1/N_i⟩]\le g$, by the Jensen inequality. Equality holds for uniform means. The flat-field correction pattern cancels from the ratio mean but not from the signal-dependent noise. Local signal bins, or a variance fit after normalization of differences by the square root of their local mean, avoid this leading bias.

An optical photodetector detector pixel is a spatially sampled photosensitive element. Counts from distinct detector pixels have independent photon shot noise in the ideal model, but charge transfer, electrical coupling and resampling can produce covariance.

A photodiode is a semiconductor diode producing photocurrent from photon absorption. Exciting an electron across the band gap leaves an electron hole. The depletion region's electric field separates the charge carriers; others can arrive by diffusion before electron-hole recombination. Contacts complete the electrical circuit.^[ref]

The useful bridge is from light to a measurable electric current: spectral responsivity converts incident radiant flux into photocurrent, while quantum efficiency counts collected signal charge carriers per incident photon. These answer different questions: how much electric current one watt produces, and how many incident photons contribute to the signal. The worked calculation below makes their relationship explicit.

Photodiode saturation is a departure from the intended proportional response of a photodiode as incident radiation becomes too large for the detector's operating conditions. The simple relation $i=RP$, or its pulse-integrated counterpart $Q=RU$, then fails with a constant spectral responsivity $R$. The observed readout can also be limited by amplifier clipping or other circuit effects, so a flattened trace alone does not locate the nonlinearity inside the diode.

Robert E. Vest and collaborators characterized silicon-photodiode response under pulsed illumination, reporting dependence on reverse bias and illuminated area. Their study extends pulse-length characterization and compares a pulsed-radiation calibration with continuous-wave conditions at a synchrotron.^[ref] Low average optical power does not by itself ensure that an individual pulse remains within the detector's proportional-response range.

An original toy response makes the energy bias explicit. Suppose the collected pulse charge isThis chosen compression law is not Vest's detector model. At low pulse energy it approaches $RU$; at high energy it approaches $R{U}_s$. With $R=0.40\mathrm{C}{\mathrm{J}}^{-1}$, $U_s=100\mathrm{nJ}$ and true $U=100\mathrm{nJ}$, it gives $Q=20\mathrm{nC}$. Blindly applying the low-level calibration $U=Q/R$ would infer50nanojoules, only half the stipulated energy.

A detector linearity test varies incident energy while holding wavelength, illumination geometry, bias and readout settings fixed. In the toy law, halving the true energy from100to50nanojoules changes charge from20toabout13.3nanocoulombs, rather than to10nanocoulombs. Comparing these ratios with known optical changes can expose compression. Actual attenuation and reference measurements require their own measurement calibration.

The appropriate limit depends on pulse shape, area, bias and readout, not on one universal optical-power number. Detector baseline subtraction can correct an additive offset but cannot reconstruct charge lost through an unknown nonlinear response. Establishing linear operation or characterizing that response is therefore a prerequisite for trustworthy pulse energy measurement with a photodiode.

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 $i_{\mathrm{sig}}(t)=RP(t)$. Integrating over the complete response givesThe 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 $R=0.40\mathrm{A}{\mathrm{W}}^{-1}$ and let the baseline-corrected collected charge be $Q_{\mathrm{sig}}=12\mathrm{nC}$. Then $U=30\mathrm{nJ}$. An ideal charge amplifier with feedback capacitance $C_f=100\mathrm{nF}$ would produce an output change of magnitude $Q_{\mathrm{sig}}/C_f=0.12\mathrm{V}$. 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.^[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.^[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.

A photodiode with a strong internal electric field in which photogenerated charge carriers undergo impact ionization, amplifying the initial signal. Linear multiplication below breakdown and saturated single-event operation above breakdown are distinct operating regimes. A single-photon avalanche diode uses the latter.

A single-photon detector based on a reverse-biased photodiode operated above its breakdown voltage. A carrier generated by photon absorption can trigger a self-sustaining impact ionization avalanche. Quenching lowers the bias to stop that avalanche; recovery creates detector dead time. Random internally generated carriers can also trigger indistinguishable pulses, producing dark counts. Single-photon avalanche diodes ordinarily detect an event rather than resolve the incident photon number. ^[ref]

Subtracting two photocurrents can suppress a shared classical intensity fluctuation when the optical responses and electronic gains are matched. Independent shot noise contributions do not cancel: their variances add in the difference. With equal charge $q$ and mean currents $I_1,I_2$, the independent-arrival one-sided current power spectral density is $2q(I_1+I_2)$. Correlated optical inputs require their covariance as well.

A photodiode divided into four independently read segments. Differences of opposite segment signals can encode a light distribution's displacement after measurement calibration.

Photocurrent is the electric current attributable to illumination. Here $I_{\mathrm{ph}}\ge 0$ denotes its magnitude after background subtraction. For a photodiode without internal multiplication, let $P$ be incident radiant flux concentrated at wavelength $\lambda$, and let $\eta$ be external quantum efficiency, including losses before collection. An incident photon has energy $E_{\gamma }=hc/\lambda$, with Planck constant $h$ and speed of light $c$. Dividing energy per second by energy per photon gives the incident photon rate ${\Phi }_{\gamma }$. Multiplying by $\eta$ gives the mean collected pair rate ${\dot{N}}_{\mathrm{pair}}$; multiplying by elementary charge $q$ givesThe factor is $q$: each collected pair replenishes an electron at one contact and removes an electron at the other. A cross-section of the external wire therefore counts one transferred electron per completed pair, consistent with charge conservation. The electron and electron hole are two internal charge carriers, not two independent transfers through that wire.

Choose an illustrative photodiode model with $\lambda =650\mathrm{nm}$, $\eta =0.75$ and $P=1.00\mu \mathrm{W}$. Using the exact SI values $h=6.62607015\times 10^{-34}\mathrm{J}\mathrm{s}$, $c=299792458\mathrm{m}{\mathrm{s}}^{-1}$ and $q=1.602176634\times 10^{-19}\mathrm{C}$ givesA mean fraction $0.75$ does not require each fourth photon to be lost in a repeating pattern. It specifies a mean conversion rate. Nor does $0.75$ mean $0.75\mathrm{A}{\mathrm{W}}^{-1}$: quantum efficiency is dimensionless, whereas spectral responsivity compares electric current with power.

At fixed radiant flux, longer-wavelength photons have less energy, so more arrive per second. This explains the rising straight line when quantum efficiency is held constant. A real photodiode's quantum efficiency varies with wavelength; the plotted assumption cannot be extended past its band gap absorption cutoff. At fixed incident photon rate instead, $I_{\mathrm{ph}}=\eta q{\Phi }_{\gamma }$ has no additional factor of $\lambda$.

Photovoltaic mode uses no external reverse bias: a transimpedance amplifier can hold zero terminal electric potential difference, while an open electrical circuit develops a photovoltage. Photoconductive mode biases the diode cathode positive relative to the diode anode, generally reducing junction capacitance and increasing speed and dark current.^[ref]

A simple calculation separates the readout from the conversion. If a linear transimpedance amplifier has feedback electrical resistance $R_f=1.00\mathrm{M\Omega }$, the $650\mathrm{nm}$ model above produces an output change of magnitude $R_f{I}_{\mathrm{ph}}=0.393195\mathrm{V}$. The output sign depends on the connection. Increasing $R_f$ increases that electric potential difference, but does not create more collected charge carriers.

For a reverse-biased photodiode feeding an electrical load $R_L$, Ohm's law gives a readout magnitude $V_L\simeq I_{\mathrm{ph}}{R}_L$ while the response remains linear. With negligible dark current and other series drops, the remaining reverse bias is $V_R\simeq V_b-I_{\mathrm{ph}}{R}_L$, where $V_b$ is the supply magnitude. Thus the chosen electrical load can consume the available bias: a larger readout does not automatically reduce measurement uncertainty. For the same constructed example, $V_b=5\mathrm{V}$ and $R_L=1\mathrm{M\Omega }$ leave about $4.60680\mathrm{V}$; this algebra alone does not establish a real device's linear range.

Thorlabs' silicon FDS100 experiment sends a collimated, fibre-coupled laser beam through a beam splitter to the photodiode and a reference optical power meter. Varying reverse bias and electrical load tests linearity. The measured readout approaches saturation when its electric potential difference consumes the bias.^[ref] A separate low-signal setup uses a $637\mathrm{nm}$ laser, polarizers, an optical chopper, optical attenuators and a lock-in amplifier inside a light-tight enclosure. These are actual apparatus choices, not the parameters of the constructed example above.^[ref]

For an independent dark current check, Thorlabs enclosed a photodiode in nested metal boxes to exclude light and suppress interference, used a Keithley 6487 ammeter supplying reverse bias, and monitored temperature. Only one specimen per type was tested; the nearby temperature sensor did not directly contact the semiconductor. Such a dark control measures the baseline but cannot certify spectral responsivity.^[ref]

To infer spectral responsivity at a selected wavelength, measure the radiant flux actually reaching the test photodiode, rather than just the reference arm. A reference-arm measurement calibration must include the beam splitter ratio and path losses. With signed readouts in one fixed orientation, subtract a beam-blocked baseline and usefor direct electric current readout or a calibrated linear transimpedance amplifier, respectively. Repeating at several incident powers tests whether this ratio is constant. Blocking only the source estimates ambient light plus electronic baseline; covering the detector excludes ambient light too. Their difference distinguishes optical background from dark current and readout offset. For a broad optical spectrum, the ratio is a spectrum-weighted response, not generally $R$ at one wavelength.

For independent Poisson distribution collection, the root mean square shot noise in a one-sided rectangular frequency band of signal bandwidth $B>0$ isHere $I_d$ is reverse dark current; thermal electrical noise and amplifier noise also contribute.^[ref]

Subtracting a mean dark current removes its offset, not its fluctuations: subtracting a constant leaves the variance unchanged. Consequently $I_{\mathrm{ph}}\gg I_d$ makes dark current shot noise small relative to signal shot noise; it does not by itself establish high signal-to-noise ratio. With an independently measured baseline, the variance of that estimate must also be propagated. Increasing the measurement signal bandwidth raises the admitted noise. Calibration of wavelength, reference radiant flux, readout gain and collection geometry, together with drift and linearity, determines what measurement uncertainty can be claimed.

Dark current is charge produced in a detector without illumination, often by thermally excited carriers. Cooling reduces it, although cooling requirements also depend on the wavelength range and thermal background.

Correlated double sampling differences a signal reading and its associated reset or baseline reading. It suppresses correlated offsets and reset noise, while the noise of the two measurements must still be propagated.

A hybrid infrared detector bonds a photosensitive semiconductor array to a separate silicon readout circuit. Each pixel has its own electrical connection; charge need not be transferred across the array as in a charge-coupled device.

A detector reference pixel has no illuminated photosensitive connection and samples readout offsets. Reference-pixel subtraction can suppress common electronic drifts but does not measure the sky background or all pixel-dependent errors.

A nondestructive read samples a pixel’s accumulated signal without resetting it. Repeated samples permit Fowler sampling and up-the-ramp sampling, and can help identify saturation and cosmic-ray charge steps.

Up-the-ramp sampling measures accumulated charge repeatedly through an exposure and estimates flux from its slope. Cosmic-ray steps, saturation and nonlinearity must be identified or modelled.

Fowler sampling averages several nondestructive reads near the start and end of an integration and differences the two averages. For independent equal read noise, averaging lowers the read-noise variance; correlated noise limits the improvement.

The HAWAII-2RG architecture has a $2048\times 2048$ grid with an 18-micrometre pitch. For infrared work its readout circuit is normally bonded to a mercury cadmium telluride absorber. Reference pixels track electronic offsets and an independently addressed guide window can be read alongside the science array.

Background subtraction estimates a source contribution by removing a sky or detector-background measurement. An independent background estimate adds photon shot noise; a mismatched background adds bias of an estimator.

If emitted power obeys $P=A{T}^4$ with known constant $A$, then small relative temperature uncertainty is one quarter of relative net-power uncertainty. For measured quantities $X,Y$ with covariance $C_{XY}$, $\mathrm{Var}(X-Y)={\sigma }_X^2+{\sigma }_Y^2-2C_{XY}$. A weak net signal obtained by subtracting a large background can therefore have poor relative precision even when both original powers are measured accurately. Correlated standard uncertainties and worst-case error bounds require different propagation rules.