饱和模式下高精度三维形状测量新方法

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本文探讨了一种利用饱和模式的高精度三维形状测量方法，针对光学计量学领域的一项挑战——如何准确测量表面对比度高的三维物体。研究发现，当数字相位移的莫尔条纹周期（P）是偶数时，如P=2k（k=1,2,3...），采用步长为N=P/2×k的算法可以精确恢复相位，即使条纹图案已饱和。同样，如果P为奇数，采用步长为N=P×k的算法也能在饱和情况下准确地进行相位测量。这一发现对于解决由于物体表面细小凹凸导致的饱和问题具有重要意义，能够极大地缓解由于物体微观结构引起的测量误差。作者通过模拟和实验证明了这种方法的有效性。研究的关键技术包括莫尔投影（Fringeprojection）、条纹分析（Fringeanalysis）以及高动态范围（Highdynamicrange）的应用，这些都是实现高质量三维形状测量的基础。论文的主题集中在高动态范围的3D形状测量上，特别是在处理表面细节丰富、对比度强烈的对象时，通过巧妙地利用饱和模式和适当的算法，确保了在实际应用中的精度和鲁棒性。该研究成果对于精密工程、制造业、光学设计以及其他对三维形貌敏感领域的实践者具有显著的价值，可能推动相关技术的发展并提高测量效率。

This paper argues that the saturated camera images can be used to perform high-

quality 3D shape measurement for digital fringe projection (DFP) methods pro-

vided that 1) proper phase-shifting algorithms are used, 2) fringe patterns are gen-

erated discretely, and 3) there is no phase-shift error. Both simulation and experi-

mental results will be presented to validate the proposed idea.

Section 2 discusses the principle behind N-step phase-shifting algorithm. Section 3

shows simulation results. Section 4 presents experimental validation, and Sec. 6

summarizes this paper.

2 Principle

Phase-shifting-based algorithms are extensively used in practical 3D shape mea-

surement systems due to their speed, accuracy, resolutions, and other merits over

other methods. In general, N equally phase-shifted fringe pattern can be mathemat-

ically described as

(x,y) = I

(x,y) + I

(x,y)cos(φ + 2kπ/N), (1)

where I

(x,y) represents the average intensity, I

(x,y) the intensity modulation, and

φ(x,y) the phase to be solved for. Simultaneously solving these N equations leads

φ(x,y) = − tan

−1



∑

k=1

sin(2kπ/N)

∑

k=1

cos(2kπ/N)



. (2)

This equation produces wrapped phase whose value ranges [−π, +π). A spatial or

temporal phase-unwrapping algorithm can be adopted to remove 2π discontinuities

and obtain a continuous phase map. The continuous phase can then be used to

reconstruct (x,y,z) coordinates.

Typically, close-to-ideal sinusoidal patterns and accurate phase shifts are required

to obtain accurate phase, and thus the community has been striving to produce as

high-quality sinusoidal patterns as possible, and as accurate phase shifts as possible.

In a DFP system, phase shifts can be accurately generated due to digital fringe

generation nature, and thus the sinusoidality is the major concern. As a result, fringe

pattern saturation should always be avoided because saturation means the use of

non-sinusoidal fringe patterns. Therefore, it is a common belief that it is difﬁcult

to accurately measure high-contrast surfaces (e.g., shiny surface) at once because

it is difﬁcult to obtain high-quality sinusoidal patterns across the whole surface

with a single exposure. As such, it drives the development HDR and shiny surface

measurement techniques in the community, as discussed in Sec. 1.

This paper argues that the saturated patterns can be used to recover accurate phase

and thus to perform high-accuracy 3D shape measurement provided that 1) a proper

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