Reflectance transformation imaging of 3D detection for subtle traces

Jie Dai; Lihua Huang; Kai Guo; Liqing Ling; Huijie Huang

doi:10.3788/COL202119.031101

Journals >Chinese Optics Letters >Volume 19 >Issue 3 >Page 031101 > Article

Chinese Optics Letters
Vol. 19, Issue 3, 031101 (2021)

Reflectance transformation imaging of 3D detection for subtle traces

Jie Dai^1、2, Lihua Huang^1、2、*, Kai Guo¹, Liqing Ling¹, and Huijie Huang^1、2

Author Affiliations

¹Laboratory of Information Optics and Optoelectronic Technology, Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, China

²Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.3788/COL202119.031101 Cite this Article Set citation alerts

Jie Dai, Lihua Huang, Kai Guo, Liqing Ling, Huijie Huang. Reflectance transformation imaging of 3D detection for subtle traces[J]. Chinese Optics Letters, 2021, 19(3): 031101 Copy Citation Text

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Abstract

This paper reports a detection method of two-dimensional (2D) enhancement and three-dimensional (3D) reconstruction for subtle traces with reflectance transformation imaging, which can effectively locate the trace area of interest and extract the normal data of this area directly. In millimeter- and micron-scale traces, during 3D construction, we presented a method of data screening, conversion, and amplification, which can successfully suppress noise, improve surface and edge quality, and enhance 3D effect and contrast. The method not only captures 2D and 3D morphologies of traces clearly but also obtains the sizes of these traces.

Keywords

2D enhancement 3D reconstruction size subtle traces

L = a_{0} (u, v) l_{u}^{2} + a_{1} (u, v) l_{v}^{2} + a_{2} (u, v) l_{u} l_{v} + a_{3} (u, v) l_{u} + a_{4} (u, v) l_{v} + a_{5} (u, v),

(1)

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[\begin{matrix} l_{u 0}^{2} & l_{v 0}^{2} & l_{u 0} l_{v 0} & l_{u 0} & l_{v 0} & 1 \\ l_{u 1}^{2} & l_{v 1}^{2} & l_{u 1} l_{v 1} & l_{u 1} & l_{v 1} & 1 \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ l_{u 53}^{2} & l_{v 53}^{2} & l_{u 53} l_{v 53} & l_{u 53} & l_{v 53} & 1 \end{matrix}] [\begin{matrix} a_{0} \\ a_{1} \\ ⋮ \\ a_{5} \end{matrix}] = [\begin{matrix} L_{0} \\ L_{1} \\ ⋮ \\ L_{53} \end{matrix}] .

(2)

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{\begin{matrix} l_{u 0} = \frac{a_{2} a_{4} - 2 a_{1} a_{3}}{4 a_{0} a_{1} - a_{2}^{2}} \\ l_{v 0} = \frac{a_{2} a_{3} - 2 a_{0} a_{4}}{4 a_{0} a_{1} - a_{2}^{2}} \\ \overset{⇀}{N} = (l_{u 0}, l_{v 0}, \sqrt{1 - l_{u 0}^{2} - l_{v 0}^{2}}) \end{matrix} .

(3)

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{\begin{matrix} Z_{x} = \frac{\partial Z}{\partial x} = p, Z_{x x} = \frac{\partial Z_{x}}{\partial x} = p_{x} \\ Z_{y} = \frac{\partial Z}{\partial y} = q, Z_{y y} = \frac{\partial Z_{y}}{\partial y} = q_{y} \end{matrix} .

(4)

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E (Z; p, q) = {(Z_{x} - p)}^{2} + {(Z_{y} - q)}^{2} + λ [{(Z_{x x} - p_{x})}^{2} + {(Z_{y y} - q_{y})}^{2}] .

(5)

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const = \iint E (Z; p, q) d x d y .

(6)

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{\begin{matrix} p = \frac{- n_{x}}{n_{z}} + w \times (\frac{- n_{x}}{n_{z}} + n_{x}) \\ q = \frac{- n_{y}}{n_{z}} + w \times (\frac{- n_{y}}{n_{z}} + n_{y}) \end{matrix} .

(7)

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{\begin{matrix} p' = p + k [p - \frac{1}{d^{2}} (\sum_{d} p_{i})] \\ q' = q + k [q - \frac{1}{d^{2}} (\sum_{d} q_{i})] \end{matrix} .

(8)

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{\begin{matrix} \tilde{P} = [\begin{matrix} P (x, y) & - P (N - x, y) \\ P (x, M - y) & - P (N - x, M - y) \end{matrix}] \\ \tilde{Q} = [\begin{matrix} Q (x, y) & Q (N - x, y) \\ - Q (x, M - y) & - Q (N - x, M - y) \end{matrix}] \end{matrix} .

(9)

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R^{2} = 1 - \frac{\sum_{i} {(z_{i} - {\hat{z}}_{i})}^{2}}{\sum_{i} {(z_{i} - \bar{z_{I}})}^{2}},

(10)

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Jie Dai, Lihua Huang, Kai Guo, Liqing Ling, Huijie Huang. Reflectance transformation imaging of 3D detection for subtle traces[J]. Chinese Optics Letters, 2021, 19(3): 031101

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