The Influence of Magnification on Measurement Accuracy

This article presents an experimental and statistical investigation of how optical magnification influences calibration constants, measurement results, and uncertainty in a digital optical microscope. Measurements were performed on reference gauge blocks with nominal lengths from 1.0 mm to 1.5 mm at five magnification levels (1×–5×) to quantify the effect of magnification on dimensional accuracy. A combined statistical methodology integrating non-parametric hypothesis testing and bootstrap-based uncertainty analysis was developed to evaluate data distributions and validate the use of a normal coverage factor (k = 2) for expanded uncertainty. The results showed that magnification has a statistically significant effect on the measured lengths for most standards, with the smallest combined standard uncertainty achieved at approximately 4× magnification. The uncertainty budget analysis revealed that the dominant component arises from the microscope’s declared Maximum Permissible Error (MPE), while type A and reference-standard components contribute only marginally. All expanded uncertainties remained within the declared MPE limits, confirming the reliability and traceability of the measurement process. Practical recommendations were proposed for selecting optimal magnification and for implementing calibration verification procedures at each zoom level. The presented methodology provides a validated framework for minimizing uncertainty in image-based dimensional measurements using digital optical microscopes.