Single-frame fringe pattern analysis with synchronous phase-shifting based on polarization interferometry phase measuring deflectometry (PIPMD)

In the domain of phase measuring deflectometry (or fringe projection profilometry), utilizing only a single-frame fringe pattern to achieve high-precision three-dimensional reconstruction has emerged as a focal point of ongoing research. To achieve four-step phase-shifting demodulation from a single-frame fringe pattern, this paper proposes a Polarization Interferometry Phase Measuring Deflectometry (PIPMD). This method primarily relies on a Michelson polarization interferometry structure to produce projected polarization interference fringes, which are then captured by a polarization camera as modulated single-frame deformed fringe patterns. These single-frame fringe patterns enable pixelated four-step phase shifting with adjacent 2 x 2 pixel units. To validate the proposed method, a series of experiments has been conducted, including surface shape detection of a concave spherical mirror and an off-axis parabolic mirror, as well as dynamic deformation measurements of a deformable mirror. All experimental results consistently indicate that the polarization interference-based fringe projection technique can achieve synchronized phase-shifting demodulation of single-frame fringe patterns, thereby facilitating high-precision reconstruction of the fringe patterns captured in a single frame. This synchronous phaseshifting technique can overcome the influence of air disturbances in traditional four-step phase-shifting methods, thereby enhancing the accuracy of phase demodulation. Additionally, this polarization interference-based Phase Measuring Deflectometry exhibits promising application prospects in dynamic measurements.