= Instrument calibration
<Instrument calibration> applies <measurement calibration> to a particular measuring instrument: reference inputs with known <measurement uncertainty> are compared with its indications to obtain a relation for interpreting later readings. It determines a response and its <measurement uncertainty>; physically adjusting the instrument is a separate operation.<International vocabulary of metrology by JCGM>[VIM3 entry 2.39, definition and notes 1–3]{ref}
For an original <balance> example, an empty pan indicates $0.020\,\mathrm{g}$ and a reference mass of $100.000\,\mathrm{g}$ indicates $100.220\,\mathrm{g}$. An assumed linear <measurement model> is
$$
r=am+b,\qquad a=1.002,\quad b=0.020\,\mathrm{g}.
$$
A later indication $r=50.120\,\mathrm{g}$ gives
$$
\boxed{m=\frac{r-b}{a}=50.000\,\mathrm{g}.}
$$
The correction here is $-0.120\,\mathrm{g}$; subtracting only the <measurement zero offset> leaves the scale error uncorrected. These illustrative readings are exact arithmetic inputs, not a claim of zero <measurement uncertainty>.
In a real comparison, apply several reference loads across the working range, remove and replace them, and repeat points while increasing and decreasing the load. Two points alone fit a line exactly and cannot establish linear response. Record environmental conditions, reference values and their <measurement uncertainties>, scatter and <instrumental drift>. Subsequent results inherit uncertainties in the indication and fitted parameters, including their <covariance>. Recheck after adjustment because the original response relation may have changed.
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