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Detector responsivity relates a detector's output to the incident radiant input under stated conditions. For a photodiode illuminated at a specified wavelength, current spectral responsivity iswhere $I_0$ is the background current and $P_{\lambda }$ is incident optical power. Its units are $\mathrm{A}{\mathrm{W}}^{-1}$. NIST's detector-calibration publication develops spectral radiant-power responsivity as the quantity transferred from optical standards to photodetectors.^[ref]

For an original example, $20\mu \mathrm{W}$ incident power produces $10\mu \mathrm{A}$ net photocurrent, giving $R_{\lambda }=0.5\mathrm{A}{\mathrm{W}}^{-1}$. If readout electronics convert that current to $1\mathrm{V}$, the complete system's voltage responsivity is $50,000\mathrm{V}{\mathrm{W}}^{-1}$. A value without its output quantity and units can therefore be misleading.

For a photodiode with no internal multiplication, let quantum efficiency $\eta$ be collected electrons per incident photon. A photon has energy $hc/\lambda$, with Planck constant $h$, speed of light $c$ and elementary charge $e$. Thus a photon arrival rate $\Phi$ gives $P=\Phi hc/\lambda$ and net current $I=\eta e\Phi$. ThereforeAt $800\mathrm{nm}$, the original $0.5\mathrm{A}{\mathrm{W}}^{-1}$ example corresponds to $\eta \simeq 0.775$. This relation assumes the stated charge-collection model; internal gain changes the interpretation.

Responsivity can depend on wavelength, irradiation geometry, bias and temperature. Detector linearity tests whether a response ratio stays constant as input level changes; detector saturation can make it strongly level-dependent. In a nonlinear response, the ratio of corrected output to input and the local transducer sensitivity are different quantities. Retain the wavelength, beam conditions, readout convention and measurement uncertainty when reporting a responsivity measurement.

Detector saturation occurs when increasing the input no longer produces the response expected from the detector's lower-input calibration. The limitation may arise in the sensing element, its load circuit, an amplifier or the digitizing stage of the measuring chain. A nearly flat output then represents many different inputs, so the lost amplitude information cannot be recovered by applying the original linear conversion.

A primary physical example is Thorlabs' silicon-photodiode saturation study. It varies reverse bias and load resistance and examines the resulting saturation limit and noise floor. Its stated limitations include testing one FDS100 photodiode with a continuous-wave source; those observations do not establish a universal limit for every detector or pulsed illumination condition.^[ref]

For an original idealized output-limit model, let incident optical power be $P\ge 0$ andThe linear branch reaches its limit at $P=0.5\mathrm{mW}$. Inputs $0.5$, $1$ and $2\mathrm{mW}$ all produce $2.5\mathrm{V}$ in this model. Interpreting that output as $P=V/a$ therefore reports $0.5\mathrm{mW}$ for each, hiding the differences. The abrupt limit is a teaching model; real response can depart from linearity gradually.

An optical attenuator placed before the detector can provide a check while retaining usable input information. For transmission $T=1/4$ and original $P=1\mathrm{mW}$, the detector receives $0.25\mathrm{mW}$ and gives $1.25\mathrm{V}$ on the linear branch. Correcting the known attenuation recovers $P=V/(aT)=1\mathrm{mW}$. Scaling a clipped stored value after detection cannot perform the same recovery.

To test detector linearity, vary calibrated attenuation or source power while monitoring stability and keeping geometry and wavelength fixed. Compare output ratios, including the background contribution, rather than assuming every output plateau is a constant source. Thorlabs also identifies reverse bias, load and bandwidth as relevant system conditions.^[ref] In the flat part of the ideal response, transducer sensitivity is zero, and the inverse measurement model is no longer unique.

Double substitution weighing determines the difference between an unknown mass and a reference through repeated substitutions on the same comparator, with a small known sensitivity mass used to determine response under load. NIST's SOP4 compares standard and unknown twice, rather than relying on the balance to establish their entire masses from its zero.^[ref]

For the source's sequence A, let S denote the standard, X the unknown and sw the added sensitivity mass. With optional tare masses omitted, the four pan loads areproducing measurement indications $O_1,O_2,O_3,O_4$. The standard remains the reference; the small addition probes transducer sensitivity close to the actual working load.^[ref]

An original simplified model neglects buoyancy, tare differences and drift, and assumes a common linear response coefficient $a$. Write $\Delta m=m_X-m_S$ and $m_{\mathrm{sw}}$ for the added mass. Relative to the standard load, the readings areThe two comparison differences estimate the same quantity; averaging them gives $D=[(O_2-O_1)+(O_3-O_4)]/2=a\Delta m$. The sensitivity step is $O_3-O_2=a{m}_{\mathrm{sw}}$, soFor original $m_{\mathrm{sw}}=10\mathrm{mg}$ and readings $(100,106,126,120)$, this gives $\Delta m=3\mathrm{mg}$. The offset $b$ and the unknown response coefficient cancel under the model.

Practical weighing records timing and environmental conditions, keeps settings fixed through the comparison, and controls handling and equilibration. The full NIST procedure supplies buoyancy corrections, uncertainty contributions and a comparison using a check standard.^[ref] For equally spaced readings, a linear additive drift cancels from $D$, but can still affect the sensitivity step $O_3-O_2$. Neither the simplified equation nor the method's name guarantees immunity to drift, contamination, nonlinear response or uncertainty in the measurement standard.

Input-referred resolution expresses an output increment or distinguishable output change in units of the quantity applied to a measuring system. For local response $y=f(x)$ with nonzero transducer sensitivity $S=dy/dx$, an output increment $q_y$ corresponds approximately toState what output criterion is being referred: one converter-code step, a noise-based threshold and a repeatably distinguishable input change are different specifications. Walt Kester's converter tutorial distinguishes code transitions, input-referred noise and noise-based resolution measures.^[ref]

For an original pressure readout, suppose a transducer has $S=5\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, followed by an ideal 12-bit analog-to-digital converter spanning $2.048\mathrm{V}$. Its code step is $q_V=2.048/4096=0.0005\mathrm{V}$, corresponding to $q_p=0.1\mathrm{kPa}$. This arithmetic specifies a nominal increment, rather than demonstrating that two pressures separated by that amount can be reliably distinguished.

Place an ideal amplifier of gain ten before the converter. The combined sensitivity becomes $50\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, so the converter step corresponds to $0.01\mathrm{kPa}$. With zero offset in this model, the pressure span mapping onto the converter simultaneously shrinks from $409.6$ to $40.96\mathrm{kPa}$. Gain trades converter coverage against nominal input increments; it does not create an unlimited input range.

Suppose the transducer itself contributes $0.25\mathrm{mV}$ rms output noise. That is $0.05\mathrm{kPa}$ input-referred noise. The added ideal gain scales both that signal and that noise, leaving this pressure-noise contribution unchanged. More display digits therefore need not improve the useful measurement resolution.

For a nonlinear response, repeat the conversion at the relevant operating point and account for the actual observation bandwidth and processing. Near detector saturation, sensitivity can approach zero and the local conversion becomes uninformative. A complete measurement result also includes measurement uncertainty, which contains calibration and other contributions beyond the chosen resolution criterion.

A measurement indication is the value supplied by a measurement instrument or measuring system. It may appear as a pointer position, displayed number, printed output or transmitted code. The indication and the corresponding measurand value need not be values of the same kind of quantity.^[ref]

For an original mechanical readout, suppose the indicated pointer position is a length $z$, related to input pressure $p$ byThe measurement indication $z=21.00\mathrm{mm}$ then corresponds to $p=(z-z_0)/S=100.0\mathrm{kPa}$ under this measurement model. The position is observable; the pressure value is inferred using the response relation. A printed pressure scale could carry out part of that conversion physically without changing the underlying distinction.

If the pointer position is uncertain by $0.10\mathrm{mm}$, that contribution corresponds to $0.50\mathrm{kPa}$ in this stipulated linear model. Uncertainty in the zero $z_0$, transducer sensitivity $S$, temperature response and instrumental drift can add further contributions. Closely spaced scale markings therefore do not establish the total measurement uncertainty.

Record the original indication and instrument settings when applying corrections. A corrected measured quantity value can change after improved measurement calibration even though the recorded indication remains the same. For example, revising the assumed zero from $1.00$ to $1.20\mathrm{mm}$ changes the inferred pressure from $100.0$ to $99.0\mathrm{kPa}$. The complete measurement result accompanies the inferred value with its uncertainty and relevant conditions; the raw measurement indication alone cannot supply that information.

A measuring transducer is a device whose output quantity has a specified relation to its input quantity and is used in measurement. VIM examples include a thermocouple, a strain gauge and a Bourdon tube.^[ref] A measuring transducer provides a link in a measuring chain; it need not itself display a finished measurement result.

For an original pressure readout, choose a linear modelwith pressure $p$, output electric potential difference $V$, transducer sensitivity $S=2\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$, and offset $V_0=1\mathrm{mV}$. An output $V=201\mathrm{mV}$ then corresponds to $p=100\mathrm{kPa}$. An amplifier, analog-to-digital converter and display can follow the transducer, each contributing to the whole measuring system.

The inverse calculation $p=(V-V_0)/S$ exposes distinct uncertainty contributions. Holding the other inputs fixed, a small output change $\delta V$ changes inferred pressure by $\delta V/S$; a small offset error changes it by $-\delta V_0/S$. An output increment $0.2\mathrm{mV}$ corresponds to $0.1\mathrm{kPa}$ for the stipulated sensitivity, but does not establish a total measurement uncertainty of that size.

Characterize the relevant range, temperature conditions, response time and possible instrumental drift during measurement calibration. The relation can be nonlinear, in which case local transducer sensitivity is the appropriate derivative rather than one gain valid everywhere. The definition also allows input and output quantities of the same kind; it does not require changing from a mechanical quantity to an electrical one. A sensor denotes the part directly affected by the phenomenon being sensed, whereas a complete measuring chain can contain further measuring transducers.

Transducer sensitivity describes how much the output of a measuring transducer changes when its input changes. For an output $y$ responding smoothly to input $x$, a local model usesVIM defines sensitivity of a measuring system through the quotient of corresponding indication and input changes, noting that sensitivity can depend on the input value and that the changes used must be appreciable relative to resolution.^[ref] The derivative is the smooth local limit of that response ratio.

For an original pressure-to-potential transducer, stipulateIts transducer sensitivity isAt $p=100\mathrm{kPa}$, the output is $0.310\mathrm{V}$ and the sensitivity is $4\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Across the finite interval from $100$ to $110\mathrm{kPa}$, output changes by $41\mathrm{mV}$, so the measured response ratio is instead $4.1\mathrm{mV}\mathrm{kP}{\mathrm{a}}^{-1}$. Specify the operating point or interval rather than treating these two slopes as contradictory.

An output increment $q=0.2\mathrm{mV}$ corresponds locally to input-referred resolution $q/|S|=0.05\mathrm{kPa}$ at the first operating point. This conversion is not a complete uncertainty statement. Increasing electronic gain can enlarge output noise as well as the signal; detector saturation can flatten the response and destroy local invertibility.

Estimate transducer sensitivity with known input steps, repeated outputs and checks for changing zero, loading and temperature. In a linear response $y=Sx+b$, a constant offset $b$ cancels from differences; a changing offset does not. Retain both the sensitivity relation and its uncertainty in measurement calibration, and propagate the relevant contributions when reporting a measurement result.