Systematic errors in small deformations measured by use of shadow-moiré topography

Area of Science:

• Optical metrology
• Surface topography measurement
• Computational imaging

Background:

• Phase-shift shadow-moiré topography is a noncontact optical technique.
• Artifactual bands, resembling isoheight contours, appear during measurements of minor shape changes.

Purpose of the Study:

• To investigate the cause of artifactual bands in phase-shift shadow-moiré topography.
• To test the hypothesis that height-dependent terms in the fringe pattern model cause systematic errors.

Main Methods:

• Simulated fringe patterns using a mathematical model with and without height-dependent terms.
• Reconstructed surface shapes from simulated fringe patterns.
• Computed shape-error curves by comparing reconstructed and known shapes.

Main Results:

• Systematic shape errors were observed only when using a model that included height-dependent terms.
• Simulated shape-error curves showed increased error with surface height and contained ripples, matching experimental data.
• Errors, though small, can manifest as noticeable bands in small deformation measurements.

Conclusions:

• The artifactual bands in phase-shift shadow-moiré topography are caused by ignoring height-dependent terms in the fringe pattern model.
• Refining the mathematical model by including these terms can improve accuracy, especially for small deformation analysis.
• The findings provide insights into error sources in optical metrology techniques.