Unambiguous measurement range and error tolerance in dual-wavelength interferometry

Area of Science:

• Optical Metrology
• Interferometry
• Precision Measurement

Background:

• Traditional equivalent wavelength methods in dual/multiwavelength interferometry enlarge the unambiguous measurement range (UMR).
• These methods neglect crucial single-wavelength phase information (size and sign), limiting UMR extension.
• The theoretical maximum UMR is half the least-common multiple (LCM) effective wavelength, often larger than the equivalent wavelength.

Purpose of the Study:

• To investigate why the larger, LCM-based UMR is seldom used in practice.
• To quantitatively analyze and describe the impact of single-wavelength phase errors on the actual UMR.
• To provide a deeper understanding beyond theoretical UMR limits.

Main Methods:

• Graphical analysis to illustrate the relationship between phase errors and UMR.
• Quantitative description of error effects on UMR.
• Simulation experiments to validate the analytical findings.

Main Results:

• The actual UMR is significantly influenced by measurement errors in single-wavelength wrapped phases.
• Half the LCM effective wavelength represents a theoretical UMR, not always achievable in practice.
• The study provides a quantitative understanding of how these errors constrain the practical UMR.

Conclusions:

• Error analysis is critical for determining practical UMR in multiwavelength interferometry.
• The limitations of the equivalent wavelength method stem from ignoring error impacts.
• This research offers a more realistic assessment of UMR capabilities by considering phase error quantification.