Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry

Han-Yen Tu; Ssu-Chia He

doi:10.3788/COL201816.101202

Journals >Chinese Optics Letters >Volume 16 >Issue 10 >Page 101202 > Article

Chinese Optics Letters
Vol. 16, Issue 10, 101202 (2018)

Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry

Han-Yen Tu^* and Ssu-Chia He

Author Affiliations

Department of Electrical Engineering, Chinese Culture University, Taipei 11114, Taiwan, China

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DOI: 10.3788/COL201816.101202 Cite this Article Set citation alerts

Han-Yen Tu, Ssu-Chia He. Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry[J]. Chinese Optics Letters, 2018, 16(10): 101202 Copy Citation Text

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Abstract

This study describes a novel fringe-shaping technique developed to alleviate the fringe truncation problem engendered by the acquired saturated and/or weak fringe images from high-/low-reflectance surfaces of three-dimensional (3D) objects in phase-shifting profilometry. The particle swarm optimization algorithm is employed to perform the recovery of the truncated fringes with optimal fitting for compensation after single-trial acquisition. The results show that the proposed method improves phase recovery accuracy to accomplish 3D surface reconstruction with only one set of phase-shifting fringes under different truncation sceneries.

I_{n} (x, y) = A (x, y) + B (x, y) \cos [φ (x, y) + 2 n π / N],

(1)

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φ (x, y) = - a r c \tan^{} \frac{\sum_{n = 1}^{N} I_{n} (x, y) \sin (\frac{2 n π}{N})}{\sum_{n = 1}^{N} I_{n} (x, y) \cos (\frac{2 n π}{N})} .

(2)

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I_{n, tru} (x, y) = {\begin{matrix} 0, & if I_{n} is small than lower limit \\ I_{n} (x, y), & if 0 < I_{n} (x, y) < 2^{m} - 1 \\ 2^{m} - 1, & if I_{n} is large than upper limit \end{matrix} .

(3)

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I_{tru}^{PSO} (x, y) = A_{tru}^{PSO} (x, y) + B_{tru}^{PSO} (x, y) \cos Φ_{tru}^{PSO} (x, y),

(4)

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A_{tru}^{PSO} (x, y) = \sum_{m = 0}^{p} \sum_{k = 0}^{m} a_{k + \frac{1}{2} [m (m + 1)]} x^{k} y^{m - k},

(5)

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B_{tru}^{PSO} (x, y) = \sum_{m = 0}^{q} \sum_{k = 0}^{m} b_{k + \frac{1}{2} [m (m + 1)]} x^{k} y^{m - k},

(6)

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Φ_{tru}^{PSO} (x, y) = \sum_{m = 0}^{r} \sum_{k = 0}^{m} c_{k + \frac{1}{2} [m (m + 1)]} x^{k} y^{m - k} .

(7)

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v_{i} (t + 1) = χ \cdot {v_{i} (t) + s_{1} \cdot ξ_{1} \cdot [p {best}_{i} (t) - p_{i} (t)] + s_{2} \cdot ξ_{2} \cdot [g best - p_{i} (t)]},

(8)

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p_{i} (t + 1) = p_{i} (t) + v_{i} (t + 1),

(9)

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F (x, y) = \sum_{(x, y \in N_{s})} {[I_{n, tru} (x, y) - I_{tru}^{PSO} (x, y)]}^{2},

(10)

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I_{n, com} = {\begin{cases} A (x, y) + B (x, y) \cos Φ (x, y), & 0 < I_{n} (x, y) < 2^{m} - 1 \\ I_{tru}^{PSO} (x, y), & otherw ise \end{cases} .

(11)

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Han-Yen Tu, Ssu-Chia He. Fringe shaping for high-/low-reflectance surface in single-trial phase-shifting profilometry[J]. Chinese Optics Letters, 2018, 16(10): 101202

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