Fringe projection profilometry (FPP) is a widely used non-contact optical method for 3D profiling of objects. The commonly used linear fringe pattern in FPP has periodic intensity variations along the lateral direction. As a result, the linear fringe pattern used in FPP cannot uniquely represent the lateral shift induced by the objects having surface discontinuities. Thus, unambiguous surface profiling of objects, especially with surface discontinuities, using a single linear fringe image having a single fringe frequency, is unfeasible. This paper proposes using a radially symmetric circular fringe pattern as the structured light pattern for accurate unambiguous surface profiling of sudden height-discontinuous objects. To the best of our knowledge, this is the only method that can reconstruct discontinuous height profiles with the help of a single fringe image having a single frequency. The performance of the proposed algorithm is evaluated on several synthetic and real objects having smooth variations and discontinuities. Compared to the well-known fringe projection methods, the results depict that for a tolerable range of error, the proposed method can be applied for the reconstruction of objects with 4 times higher dynamic range and even at much lower fringe frequencies.

中文翻译：

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单次圆形条纹投影，用于对具有表面不连续性的物体进行轮廓分析

边缘投影轮廓测量法 (FPP) 是一种广泛使用的非接触式光学方法，用于对象的 3D 轮廓分析。FPP 中常用的线性条纹图案沿横向具有周期性的强度变化。因此，FPP 中使用的线性条纹图案不能唯一地表示由具有表面不连续性的物体引起的横向位移。因此，使用具有单个条纹频率的单个线性条纹图像对物体进行明确的表面轮廓分析是不可行的，尤其是具有表面不连续性的对象。本文建议使用径向对称的圆形条纹图案作为结构光图案，用于对突然高度不连续的物体进行准确、明确的表面轮廓分析。据我们所知，这是唯一一种可以借助具有单一频率的单个条纹图像重建不连续高度轮廓的方法。所提出算法的性能在几个具有平滑变化和不连续性的合成和真实对象上进行了评估。与众所周知的条纹投影方法相比，结果表明，对于可容忍的误差范围，所提出的方法可以应用于重建动态范围高 4 倍甚至在低得多的条纹频率下的物体。