linearity

**Linearity** in metrology is the **consistency of measurement bias across the entire measurement range** — a linear measurement system has the same bias (systematic error) whether measuring small values, large values, or values in the middle of the range. Non-linearity means the bias changes with the measured value. **Linearity Assessment** - **Method**: Measure reference standards spanning the full measurement range — compare bias at each level. - **Plot**: Plot bias vs. reference value — the slope and scatter indicate linearity. - **Regression**: Fit a linear regression: $Bias = a + b imes ReferenceValue$ — ideal is $a = 0, b = 0$ (constant zero bias). - **Acceptance**: Both the slope and intercept should be statistically insignificant (p > 0.05). **Why It Matters** - **Range-Dependent Accuracy**: Non-linear gages give accurate results in one part of the range but inaccurate results elsewhere. - **Correction**: Non-linearity can be corrected with a calibration curve — but requires characterization first. - **Semiconductor**: CD-SEM linearity across feature sizes (5nm to 50nm) must be characterized — different CD ranges may have different biases. **Linearity** is **consistent accuracy everywhere** — verifying that measurement bias is uniform across the entire range of measured values.