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.
Polarization cameras integrated with conventional four-channel micro-polarization arrays (MPA) are usually used as phase shift devices in focal plane-type interferometric systems to achieve simultaneous phase shifts. However, such phase shift devices suffer from low sampling rates and a lack of mature resolution reconstruction techniques to resolve pixel-level alignment errors. To solve such problems and further improve the phase reconstruction accuracy of the focal plane interferometric system, this paper proposes to apply the "Bayer-like" three-channel MPA to the interferometric system to realize the simultaneous phase shift. The arrangement of the three-channel MPA can reduce the processing complexity of the element and improve the inter-channel sampling rate. In addition, this structure can better utilize the resolution reconstruction idea of color filter array (CFA) to solve the inherent pixel-level alignment error problem between simultaneous phase shift interferograms. Taking lateral shearing interferometry as an example, the process of acquiring simultaneous phase-shifted interferograms and phase reconstruction in an interferometric system with threechannel MPA is verified by simulation. The experiment results shows that the proposed three-channel MPA structure performs better than the traditional four-channel MPA structure in terms of visual reconstruction effect and quantitative index of phase reconstruction.
In a simultaneous phase-shifted lateral shearing interferometry, a division of focal plane polarization camera is generally used as the phase-shifting device. However, acquiring simultaneous phase-shift interferograms in a single frame suffers from a lack of spatial resolution, significantly affecting the phase reconstruction accuracy. A polarization redundant sub-region interpolation (PRSI) method is proposed to solve this problem. This interpolation method distinguishes smooth regions from stripe fringe regions by calculating the polarization redundancy error of the synchronous phase shift interferogram. After sub-regional processing, resolution reconstruction is performed in the smoothed area using a fast convolutional bilinear interpolation method. In the streak detail region, the resolution reconstruction is performed based on the strength of the correlation between the orthogonal and non-orthogonal polarization channels crossing the streak region. The PRSI method can quickly reconstruct the lost pixels and accurately recover the stripe detail information. Experiment results show that the proposed interpolation method outperforms the existing dominant methods in terms of visual reconstruction effect and quantitative index of phase reconstruction.
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