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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.

An interlaboratory comparison organizes measurements of the same or similar items by at least two laboratories under agreed conditions. Its purpose may be to compare measurement reproducibility, evaluate a measurement procedure, or assess participants through proficiency testing. The last purpose evaluates performance against criteria specified beforehand; it is one use of interlaboratory comparison, not a synonym for every such study.^[ref]

A comparison begins with its experimental design. When the aim is to compare laboratory analysis, the organizer needs evidence of reference material homogeneity and reference material stability: unequal or changing test items would otherwise be confounded with differences between laboratories. If collection is part of the measurement procedure, the design must instead include analytical sampling explicitly. In a 2002 collaborative study, several samplers collected wheat and green coffee from bulk lots. The reported between-sampler variation was significant for two wheat analytes; for coffee, a significant repeatability contribution was detected without a significant sampling-reproducibility contribution. Thus even the importance of collection differences depended on the material and analyte.^[ref]

For a common proficiency-test z-score, let laboratory $i$ report $x_i$, let the assigned value in proficiency testing be $x_{\mathrm{pt}}$, and let the standard deviation for proficiency assessment be ${\sigma }_{\mathrm{pt}}>0$. ThenThe denominator describes the scheme's assessment scale. It is not automatically the laboratory's own measurement uncertainty or the observed standard deviation of participants. The guide distinguishes this proficiency-test z-score from scores incorporating uncertainty, and discusses choosing the assessment scale to match the intended use.^[ref]

An original hypothetical example shows why the assigned value matters. Suppose three laboratories report $9.8$, $10.0$ and $10.2$ in the same units, with a stipulated assessment scale ${\sigma }_{\mathrm{pt}}=0.2$. Using their arithmetic mean as an interlaboratory consensus value gives $x_{\mathrm{pt}}=10.0$ and scores $(-1,0,1)$. An independently established assigned value of $11.0$, with the same assessment scale, instead gives $(-6,-5,-4)$. Close agreement between participants is compatible with a shared displacement from an independent reference.

The identifiability issue is visible in a simple model,where $\theta$ is the reference quantity value, $b$ is a common systematic error, and ${\epsilon }_i$ describes laboratory-specific deviations. Pairwise differences eliminate both $\theta$ and $b$. Moreover, replacing $(\theta ,b)$ by $(\theta +c,b-c)$ leaves every predicted $x_i$ unchanged. Consequently agreement alone cannot identify a common bias. Evidence from an independently characterized certified reference material or an independent measurement calibration can help resolve this ambiguity. Its own measurement uncertainty and any shared dependencies must then enter the comparison model; one should not silently interpret the simple proficiency-test z-score as a full uncertainty calculation. This is the practical importance of distinguishing measurement precision, measurement trueness and shared bias in an interlaboratory consensus.

Intermediate measurement precision is measurement precision under declared intermediate precision conditions of measurement. The measurement procedure and location remain the same, measurements extend over a longer period, and specified changes can include operators, measuring systems or measurement calibration. It lies between a tightly restricted measurement repeatability study and a comparison across locations for measurement reproducibility.^[ref]

For a concrete study, one laboratory could measure the same stable reference block each working day with a differential length comparator, taking four complete placements per day. Keep the procedure fixed, record temperature and operator, and retain the day labels. The labels let the study distinguish variation between days from rapid reading-to-reading variation.

An original measurement model makes that distinction explicit:Here $D_d$ is a shared daily offset, while ${\epsilon }_{dj}$ varies between placements. Assume zero-mean independent random variables, independent also between days. A single measurement then has standard deviation $\sqrt{{\tau }^2+{\sigma }^2}$. For stipulated $\tau =0.30\mu \mathrm{m}$ and $\sigma =0.10\mu \mathrm{m}$, this is $0.316\mu \mathrm{m}$, even though within-day scatter reflects only $0.10\mu \mathrm{m}$.

For four readings from one day, the daily arithmetic mean hasAveraging four such means from independent days reduces that modelled standard deviation to $0.152\mu \mathrm{m}$. Four same-day readings do not average away their shared daily offset. The numbers illustrate the model, not measured comparator performance. A real study must estimate its components from enough days and investigate trends: deterministic instrumental drift is not automatically an independent daily offset.

Measurement precision describes agreement among repeated indications or measured values obtained under stated conditions. It is commonly characterized using a standard deviation, variance or coefficient of variation, which describe the observed spread. Measurement repeatability is precision under a particular restricted set of conditions; intermediate measurement precision and measurement reproducibility concern other specified conditions.^[ref]

For an original balance example, take three repeat readings of a reference object: $100.100$, $100.080$ and $100.120\mathrm{g}$. Their arithmetic mean and sample standard deviation areSuppose the reference object's assigned mass is $100.000\mathrm{g}$ with standard uncertainty $0.002\mathrm{g}$. The observed mean differs from that reference by $0.100\mathrm{g}$, much more than the within-series scatter. These chosen readings therefore illustrate why close repeat readings do not establish agreement with a reference. They do not determine the true systematic offset from only three trials.

Measurement accuracy and measurement trueness answer different questions from precision. A common additive offset leaves the deviations $x_j-\bar{x}$, and hence $s$, unchanged. Averaging more independent readings can reduce random uncertainty in the mean but does not by itself remove that common offset.^[ref]

A useful physical study repeatedly removes and replaces the reference object while recording load procedure, environmental conditions and elapsed time. Specify which parts of the measurement were repeated: repeated display readings alone may omit placement variation or instrumental drift. The statistic describes the stated experiment, not an unconditional property of the instrument.

Measurement repeatability is measurement precision under a declared set of repeatability conditions. The VIM's repeatability condition of measurement includes the same procedure, operators, measuring system, operating conditions and location, with repeated measurements over a short time.^[ref] The complete measurement cycle must be specified before its repeatability can be assessed.

For an original length-comparator study, one operator measures the same reference block using the same differential length comparator over a short session. Three readings without disturbing the setup happen to be $20.000,20.000,20.000\mathrm{mm}$. Their sample spread is zero. In a separate series, the operator removes and reseats the block for every trial, obtaining $19.980,20.000,20.020\mathrm{mm}$. That series givesThe two procedures repeat different parts of the experiment. The first data cannot establish the repeatability of the full remove-and-reseat procedure, nor does its zero observed spread prove an absence of readout noise or finite measurement resolution.

A repeatability experiment keeps the declared conditions stable and records each completed trial, including placement and settling when those belong to the procedure. Positioning repeatability applies this reasoning to repeated returns of a moving stage. Repeating a study over longer periods with selected changes can instead assess intermediate measurement precision; studies changing locations, operators and measuring systems concern measurement reproducibility.^[ref] Report those changes rather than describing every repeated experiment as the same repeatability test.

Measurement reproducibility is measurement precision under specified reproducibility conditions of measurement. These include changed locations, operators and measuring systems; the measurement procedures may also differ. The comparison must state what changed and what remained common.^[ref] This is a metrological use of reproducibility, concerned with agreement of measured values under declared conditions.

An original comparison sends a stable reference block to three laboratories. Each laboratory uses its own differential length comparator and operator, measures the same specified measurand, and reports three length errors relative to the common reference, in micrometres:Each laboratory has sample standard deviation $1\mu \mathrm{m}$, yet their arithmetic means differ by as much as $6\mu \mathrm{m}$. Relative to the grand mean $2/3\mu \mathrm{m}$, the total squared deviation separates into within-laboratory and between-laboratory terms:Consequently the nine chosen values have pooled sample standard deviation $\sqrt{62/8}\approx 2.78\mu \mathrm{m}$. This is a descriptive statistic for these observations, not a universal estimator prescribed by the definition of measurement reproducibility. Reporting only the three within-laboratory spreads would conceal the disagreement.

The physical comparison must also monitor transport damage, reference stability and temperature corrections. A changing reference block could imitate a laboratory difference. Measurement reproducibility alone does not establish measurement trueness: all laboratories could share the same erroneous reference value or correction. The changed apparatus and conditions belong alongside the reported statistic.

Measurement trueness describes how closely the mean of indefinitely many replicate measured values would agree with a reference value. It concerns systematic error, rather than the random spread described by measurement precision. The VIM treats measurement trueness as qualitative: a numerical error or bias estimate is not itself a numerical value of trueness.^[ref]

An original measurement model separates the two issues:Here $b$ is a fixed offset from the stipulated reference and $\epsilon$ is random measurement error. Thus $\mathbb{E}[X]-x_{\mathrm{ref}}=b$, while the standard deviation of individual readings is $\sigma$. For $n$ independent random variables following this same model, averaging givesMore readings reduce the random scatter of the mean without removing $b$.

For a stipulated length example, instrument A has $b=0.40\mathrm{mm}$ and $\sigma =0.10\mathrm{mm}$; instrument B has $b=0$ and $\sigma =0.50\mathrm{mm}$. A is more precise, while B's limiting mean agrees better with the reference. With 25 independent readings each, the means have standard deviations $0.02\mathrm{mm}$ and $0.10\mathrm{mm}$ respectively, and their expected offsets remain $0.40\mathrm{mm}$ and zero. These are chosen model parameters, not experimental determinations.

Experimentally, compare repeated readings of a stable measurement standard with its assigned value under specified conditions. A finite observed mean difference estimates an offset; its interpretation includes sampling variation and the reference's measurement uncertainty. Determine an appropriate correction through measurement calibration, apply it in the measurement model, and check it with further reference measurements. Neither a small sample spread nor a single reading equal to the reference establishes measurement trueness.

Positioning repeatability describes the scatter of positions reached when a motion system repeatedly returns to the same commanded position under specified conditions. It is an application of measurement repeatability, a form of measurement precision. A system may return to almost the same wrong position each time, so small scatter does not establish measurement accuracy.^[ref]

The approach direction belongs in the test description. Unidirectional positioning repeatability keeps it fixed; bidirectional positioning repeatability includes returns from both directions. To measure the assembled stage, independently observe its final position rather than only the motor's rotary encoder count. Physik Instrumente describes a static test that lets the platform stop before reading it, using an interferometer for displacement and an autocollimator for angular error, with two reflecting mirrors on the stage.^[ref]

For an original numerical example, repeatedly command $x_{\ast }=10.000\mathrm{mm}$. Suppose an independent position readout with known measurement calibration gives the errors $e_j=x_j-x_{\ast }$, in micrometres,Each direction has the same sample standard deviation,Yet their arithmetic means are 0 and $2.0\mu \mathrm{m}$. The magnitude of their mean difference, a positioning reversal error at this target, is 2.0 micrometres, far larger than the within-direction scatter. Pooling all eight values gives a sample standard deviation of $\sqrt{8.04/7}\approx 1.149\mu \mathrm{m}$; that statistic mixes the directional shift with the smaller return-to-return variation.

The calculation uses a declared sample standard deviation, not an unspecified manufacturer's tolerance or a universal repeatability convention. A positioning specification must state its approach directions, target positions, settling/readout procedure, load, environmental conditions, statistic and measurement uncertainty. A single target does not establish performance over the travel range. The manufacturer's method explicitly separates directional means from scatter and combines information from multiple targets when forming axis-level specifications.^[ref]

Backlash is one possible cause of direction-dependent behavior, while thermal expansion and instrumental drift can move the apparent target over time. A repeatability experiment must distinguish those effects from random scatter. Measuring small returns to one target also answers a different question from minimum incremental motion, which asks whether a small commanded change can actually be executed.

A reference material is established as suitable for a specified measurement use because the relevant properties are sufficiently homogeneous and stable. The requirement concerns particular properties and an intended use, rather than every possible attribute of the material.^[ref] Reference material homogeneity concerns variation within or between the portions used; reference material stability concerns maintaining the relevant properties over time and under stated conditions.

Reference materials can support measurement precision control even without an assigned quantity value. An assigned value is needed when the material serves in measurement calibration or a check of measurement trueness.^[ref] A certified reference material adds authoritative documentation specifying property values with associated uncertainties and traceabilities obtained through valid procedures.^[ref]

A concrete physical example is the archived 2009 certificate for National Institute of Standards and Technology SRM 1922, a mineral oil characterized for refractive index. Its characterization used a precision spectrometer and goniometer arrangement with the minimum deviation method, oil in a hollow optical prism, and water-bath temperature control. Measurements covered several wavelengths and temperatures; multiple portions were examined to assess homogeneity.^[ref]

The certificate's Table 1 reports, at wavelength 589.3 nm and temperature $20{}^{\circ }\mathrm{C}$, refractive index 1.46945 with expanded uncertainty $6\times 10^{-5}$ and coverage factor 2. This wavelength's value was obtained through a dispersion fit. The listed temperature coefficient is $-3.68\times 10^{-4}{\mathrm{K}}^{-1}$.^[ref]

An original calculation using that linear coefficient predictsThe predicted change, $0.000736$ in magnitude, is larger than the quoted expanded uncertainty at the reference conditions. Temperature therefore belongs with the assigned optical value; it is not an incidental label. This calculation illustrates the certificate's model, rather than supplying a new certified value or uncertainty.

Record the material identity, certificate version, property, wavelength, temperature and handling history with a measurement result. The archived certificate supplies a documented example of those links, rather than a claim about a currently available product or the validity of a particular bottle today.