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<ImageJ> is a <Java> program for viewing, processing and measuring image data. Its official feature description includes <image stacks>, selections, calibrated measurements, <image thresholding>, plugins and recorded macros.<ImageJ Features>[Java implementation; Selections, Analysis, Stacks and Macros sections]{ref} <Wayne Rasband> and <Tiago Ferreira>'s user guide documents how acquisition metadata and analysis settings affect those measurements.<ImageJ User Guide by Tiago Ferreira and Wayne Rasband>[Title-page authors; sections28.4,30.1 and30.7–30.8]{ref}

For an original numerical measurement example, suppose a selected $2\times2$ <image region of interest> contains gray values 10, 20, 30, 40. Set square <pixel pitch> to $0.25\,\mathrm{\mu m}$. The selection has four pixels, so its calibrated <area> and mean <image signal> are
$$
A=4(0.25\,\mathrm{\mu m})^2=0.25\,\mathrm{\mu m^2},\qquad\bar I=\frac{10+20+30+40}{4}=25.
$$
Changing only the spatial calibration to $0.50\,\mathrm{\mu m}$ per pixel changes the reported <area> to $1.00\,\mathrm{\mu m^2}$ while the mean remains 25. Spatial calibration changes the coordinate interpretation, not the stored gray values. An <image thresholding> rule retaining values at least 25 selects two pixels, whose total calibrated <area> under the original scale is $0.125\,\mathrm{\mu m^2}$.

A reproducible analysis records the original image, selection, spatial calibration, threshold rule and measurement settings. The guide separates spatial Set Scale from intensity Calibrate, and warns that global calibration can affect other open images.<ImageJ User Guide by Tiago Ferreira and Wayne Rasband>[Sections30.8–30.9, Set Scale and Calibrate; numbered note24, Global Calibrations]{ref} The arithmetic above is stipulated test data, not a screenshot measurement or a result from an unspecified plugin.


 ImageJ (source code)