Polarization-based coherent gradient sensing systems and methods

Polarization-based coherent gradient-sensing systems and methods for measuring at least one surface-shape property of a specularly reflective surface are disclosed. The method includes: reflecting a first circularly polarized laser beam from a sample surface to form a second circularly polarized laser beam that contains surface-shape information; converting the second circularly polarized laser beam to a linearly polarized reflected laser beam; directing respective first and second portions of the linearly polarized reflected laser beam to first and second relay assemblies that constitute first and second interferometer arms. The first and second relay assemblies each use a pair of axially spaced-apart gratings to generate respective first and second interference patterns at respective first and second image sensors. Respective first and second signals from the first and second image sensors are processed to determine the at least one surface-shape property.