A quadriwave lateral shearing interferometry (QWLSI) is proposed based on double birefringent crystals of a beam displacer (DBCs-BD). The DBCs-BD is formed by adopting two birefringent crystals of a polarization beam displacer (PBD), which can generate the lateral shearing interference waves of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer, and the direction of the transmission axis is set as 45° or 135°, the QWLSI’s polarization interferogram can be obtained. The high-precision phase can be obtained by simple spectrum denoising and performing the Fourier transform of the resulting interferogram. We deduce the principle of QWLSI in detail, and the wavefront distribution can be achieved by the phase calculation. The experiment shows that the DBCs-BD-QWLSI exhibits feasibility and high precision.

Quadriwave lateral shearing interferometry (QWLSI) is based on double birefringent crystals of a beam displacer (DBCs-BD), which can generate the lateral shearing interference wavefront of four beams of overlapped replicas in the DBCs-BD orthogonal directions. When the replica waves are overlapped incident to the analyzer and the direction of the transmission axis is set as 45° or 135°, the QWLSI’s polarization interferogram can be obtained. This paper deduces the principle of QWLSI based on the DBCs-BD and presents the analysis of orthogonal error influence based on the DBCs-BD and the phase retrieval error of QWLSI when shear displacement by tilted incident on the DBCs-BD. In our investigation, we have established the correction range of the PBD’s orthogonal angle error is within −0.5^∘−0.5^∘, the maximum error in PV is 0.0012λ, and the maximum error in RMS is 1.3789×10⁻⁴λ in wavefront reconstruction. Moreover, when the testing light tilts to incident on the PBD in the range of −0.4^∘−0.4^∘, correction of the shear distance is used for wavefront reconstruction to achieve a high-precision wavefront testing result. Finally, the experiment shows that QWLSI based on the DBCs-BD exhibits feasibility and high precision.

A novel simultaneous two-step phase-shifting lateral shearing interferometry for aspherical surface based on an orthogonal shear displacer (OSD) is proposed, it is an effective technological measure of aspherical surface measurement, to effectively solve the non-uniformity of light intensity and limited transmission order caused by the beam displacer device. The OSD system is formed by the adoption of two-crystal polarization parallel beam displacers (PBDs), which makes it achieve the orthogonal shearing in the x- and y-directions simultaneously. A quarter-wave plate (QWP) is used to generate the desired phase-shifting, and four beam lateral shearing interference waves are simply generated in OSD orthogonal directions without any bulky and complicated optical components. The phase maps of the aspherical surface can be instantly obtained using the spatial phase-shifting technique with a polarization pixelated mask (or called micro-polarization array: MPA) integrated into CCD. In this study, the proposed method was theoretically described and simulation results were analyzed. The simultaneous two-step phase-shifting lateral shearing interference fringes can be extracted in real-time with the MPA. The experiment results compared with the ZYGO interferometer were performed, and proved that the measurement error is not more than 2%. This interferometry has made it possible to improve the stability and feasibility of aspherical surface testing experiments.

To overcome the limitations of phase sampling points in testing aspherical surface wavefronts using traditional interferometers, we propose a high-spatial-resolution method based on multi-directional orthogonal lateral shearing interferometry. In this study, we provide a detailed description of the methodology, which includes the theoretical foundations and experimental setup, along with the results from simulations and experiments. By establishing a relational model between the multi-directional differential wavefront and differential Zernike polynomials, we demonstrate high-spatial-resolution wavefront reconstruction using multi-directional orthogonal lateral shearing interferometry. Theoretical calculations and simulations of aspherical surface wavefront testing are followed by experimental verification on an aspherical surface with a known asphericity. Comparing the measurement results with those from the LuphoScan profilometer, we achieve a relative measurement error with an RMS precision better than λ/100.

This paper explores a multi-directional (multiple directional) shearing synchronous polarization phase-shifting interferometer that utilizes a birefringent crystal displacer. This design effectively mitigates nonlinear issues and environmental influences commonly encountered in synchronous phase-shifting interferometry. Additionally, it enables the acquisition of shear wavefront information from multiple directions. By solving for the coefficients of the measured wavefront using multi-directional differential wavefront data, the system performs coefficient fitting to reconstruct the wavefront. The characteristics of crystal birefringence beam modulation, phase grating diffraction, and the polarization phase-shifting array for synchronous phase-shifting interferometry are investigated, based on the specific implementation methods of multi-directional shearing and synchronous polarization phase-shifting. The preprocessing method for the multi-directional shearing phase-shifting interferogram is then presented, followed by a detailed explanation of the spatial position registration technique for the shearing interferogram and the calculation method for the shear amount. The interferometer’s construction system was experimentally tested using a spherical optical component, and the results were compared with those obtained from ZYGO to verify its accuracy and testing reliability.