Fringe projection profilometry with nonparallel illumination: a least-squares approach

Area of Science:

• Optical Metrology
• Phase Measurement Techniques
• Digital Image Processing

Background:

• Nonparallel illumination in fringe projection causes unequal fringe spacing.
• This unequal spacing introduces a nonlinear carrier phase component, complicating phase analysis.
• Conventional methods for carrier removal can magnify phase uncertainty and require geometric parameter estimation.

Purpose of the Study:

• To develop a nonlinear carrier removal technique for fringe projection under nonparallel illumination.
• To offer an alternative to conventional methods that avoids magnifying phase uncertainty.
• To eliminate the need for direct estimation of system geometrical parameters.

Main Methods:

• A least-squares approach is employed for nonlinear carrier phase removal.
• A theoretical expression for the carrier phase function is derived and expanded into a power series.
• Unknown coefficients of the power series are determined using the least-squares method.

Main Results:

• The proposed algorithm effectively removes the nonlinear carrier phase component.
• Phase measurement uncertainty is not magnified by the developed technique.
• Accurate object profile phase distribution is obtained by subtracting the calculated carrier phase from the unwrapped phase map.

Conclusions:

• The least-squares-based nonlinear carrier removal technique is effective and robust.
• This method offers advantages over conventional approaches by simplifying the process and improving accuracy.
• The technique is suitable for phase measurement applications with nonparallel illumination conditions.