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: $Bias = a + b \times ReferenceValue$ — 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.