How Does an Instrument Know What It Is Reading? Measuring the Knowns First
By the BrainSnail editorial team. How these articles are written and checked, and how to tell us when one is wrong.
Most instruments produce a signal rather than a quantity, and converting one into the other requires measuring samples whose value is already known. That curve is where much of the accuracy and most of the error lives.
The problem being solved
An instrument rarely measures the thing you want directly. A spectrophotometer measures how much light a sample absorbs, a chromatograph produces a peak with an area, a pH electrode produces a voltage, a thermocouple produces a small potential difference, and in each case the quantity of interest is related to the output by a relationship that is not known in advance and that varies with the instrument, the conditions and the day. The remedy is to measure a series of samples whose values are known, plot the output against those values and use the resulting relationship to convert future readings. Everything downstream depends on that curve being right, which is why calibration is not preparation for the measurement but a substantial part of the measurement itself.
How a curve is built
The procedure is standardised and each step exists for a reason:
- •Prepare standards of known value spanning the range the samples will fall in
- •Include a blank containing everything except the substance being measured
- •Measure the standards, ideally in random order rather than ascending
- •Fit a line or curve through the points, recording how well it fits
- •Check that unknown samples fall inside the range covered rather than beyond it
- •Re-run standards periodically during a long batch to detect drift
Where the errors come from
The mistakes that matter are mostly systematic rather than random. Extrapolating beyond the highest standard assumes a relationship continues where it has not been checked, and detectors commonly saturate at high values so the real curve flattens while the fitted line does not, which produces confident and badly wrong results. Preparing standards from a stock solution means an error in that stock propagates to every point identically, which no amount of replication reveals. The sample may contain something that interferes with the measurement and the standards may not, so the two are not being measured on the same footing, which is the argument for adding known amounts to the sample itself rather than preparing separate standards. Drift over a long run makes early and late samples incomparable. And forcing the fit through zero when the blank is not zero biases every low result.
The limit of what can be detected
The lower end of a curve raises a question that gets asked constantly and answered loosely. A signal near zero is indistinguishable from the noise of the instrument, so there is a concentration below which a result cannot be reported as a measurement, and the convention defines it from the scatter of blank measurements rather than from a single reading. The limit of detection is the level at which a substance can be said to be present with reasonable confidence, and the limit of quantification, set higher, is the level at which a number can be reported with a stated precision. Reporting a value between the two as though it were a measurement overstates what was found, and reporting nothing at all loses information, which is why results are conventionally reported as being below a stated limit rather than as zero or as absent.
How the chain reaches back
The standards used in a laboratory have to be known accurately, which raises the question of how, and the answer is a chain of comparisons reaching back to defined references. A working standard is calibrated against a certified reference material, which is characterised by a national measurement institute, which maintains its own realisation of the unit traceable to its international definition. Since 2019 all the base units are defined in terms of fixed values of physical constants rather than artefacts, which means any sufficiently equipped laboratory can in principle realise a unit from first principles rather than by comparison with a master object kept elsewhere. Documenting that chain with stated uncertainty at each link is what traceability means, and it is required for measurements used in trade, in medicine and in legal contexts.
The takeaway
Instruments produce a signal rather than a quantity, so a set of known samples is measured to establish the relationship and convert readings. Errors are mostly systematic, including extrapolating past the highest standard, a bad stock solution affecting every point, and interference present in samples but not standards. Standards trace back through a documented chain to units now defined by physical constants.