Flexible lateral shearing interferometry based on polarization gratings for surface figure metrology

•A compact lateral shearing interferometer based on polarization gratings, which can dynamically obtain the phase map and conveniently adjust the lateral shear distances.•Theoretical and practical implementation of a lateral shearing interferometer based on a polarization grating.•Capability of the measurement of the shape with only two x- and y-images of shearing interferograms.•Experimental verification of various surface shapes from spherical to freeform surfaces. A lateral shearing interferometer based on polarization gratings to measure surface figures is proposed and experimentally verified. The birefringent, polarizing beam splitting characteristics of polarization gratings make the optical configuration compact and flexible to adjust the lateral shear. The use of a polarization camera does not require sequential measurements, enabling single shot phase derivative characterization. In the experimental results, various specimens including freeform surfaces were measured with less than 100 nm deviations from the references.