Coherence scanning interferometry: linear theory of surface measurement.

Area of Science:

• Optics and Photonics
• Metrology
• Surface Science

Background:

• Optical surface topography measurement instruments are crucial for 3D surface characterization.
• Comparing the performance of different instruments like interferometry and microscopy is essential.
• Understanding the underlying imaging principles aids in instrument selection and data interpretation.

Purpose of the Study:

• To establish a framework for comparing the 3D performance of optical surface topography measuring instruments.
• To analyze the applicability and equivalence of different theoretical approximations in describing imaging systems.

Main Methods:

• Characterizing imaging methods as three-dimensional (3D) linear filtering operations.
• Defining imaging systems using the point spread function (PSF) and transfer function (TF).
• Investigating the Born and Kirchhoff approximations for surface scattering scenarios.

Main Results:

• The study demonstrates that optical surface topography instruments can be effectively modeled as 3D linear filters.
• Differences in filter characteristics arise from the Born and Kirchhoff approximations.
• Equivalence between these approximations is established for weakly scattering objects.

Conclusions:

• The 3D linear filtering framework provides a unified approach to compare optical surface topography instruments.
• The Born and Kirchhoff approximations, despite initial differences, are equivalent for weakly scattering surfaces.
• This research facilitates a deeper understanding of instrument performance and limitations.