Wrapping phase repair method based on Tsallis Relative Entropy evaluation

Leqian KANG; Pengcheng YANG; Qiujuan LÜ; Liping LIAN; Xindong ZHU

doi:10.37188/OPE.20243208.1130

Journals >Optics and Precision Engineering >Volume 32 >Issue 8 >Page 1130 > Article

Optics and Precision Engineering
Vol. 32, Issue 8, 1130 (2024)

Wrapping phase repair method based on Tsallis Relative Entropy evaluation

Leqian KANG¹, Pengcheng YANG^1,*, Qiujuan LÜ², Liping LIAN^1,3, and Xindong ZHU⁴

Author Affiliations

¹School of Mechanical and Electrical Engineering， Xi'an Polytechnic University，Xi'an70048， China

²Department of Basic， Rocket Force University of Engineering， Xi'an71005， China

³College of Optoelectronic Engineering， Chongqing University， Chongqing400040， China

⁴Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter， School of Physics， Xi'an Jiaotong University， Xi'an71009， China

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DOI: 10.37188/OPE.20243208.1130 Cite this Article

Leqian KANG, Pengcheng YANG, Qiujuan LÜ, Liping LIAN, Xindong ZHU. Wrapping phase repair method based on Tsallis Relative Entropy evaluation[J]. Optics and Precision Engineering, 2024, 32(8): 1130 Copy Citation Text

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Abstract

In the laser interferometric measurement of gear tooth flank topography， the collected wrapped phase map can be influenced by various sources of noise. These areas of poor phase quality in the wrapped phase map can lead to unwrapping errors and reduces measurement accuracy. This paper proposed a wrapped-phase repair method to address the problem. It utilized Tsallis relative entropy as an evaluation criterion， based on the probability distribution characteristics of the interference fringe image. The method first fitted the thresholded image using Gaussian distribution， then evaluated the phase quality by Tsallis relative entropy， finally patched the poor quality regions to improve the quality of phase unwrapped. The experimental results show that the method can reduce the phase residue points by 40% and effectively improve the phase quality. The proposed method is user-friendly and highly accurate. It can be applied to other fields related to phase-shifting optics.

Keywords

image repair interferometry phase unwrapping Tsallis relative entropy wrapped phase map

V (m, n) = \frac{\sqrt[]{\sum_{i = (m - k) / 2}^{(m + k) / 2} \sum_{j = \frac{n - k}{2}}^{\frac{n + k}{2}} {(∆_{i, j}^{x} - \bar{∆_{k, k}^{x}})}^{2}} + \sqrt[]{\sum_{i = (m - k) / 2}^{(m + k) / 2} \sum_{j = \frac{n - k}{2}}^{\frac{n + k}{2}} {(∆_{i, j}^{y} - \bar{∆_{k, k}^{y}})}^{2}}}{k \times k}

(1)

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\begin{matrix} M (x, y) = \\ \frac{2}{N} \sqrt[]{{(\sum_{i = 1}^{N} I_{i} (x, y) s i n δ_{i})}^{2} + {(\sum_{i = 1}^{N} I_{i} (x, y) c o s δ_{i})}^{2}}, \end{matrix}

(2)

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D (A | B) = \frac{1}{q - 1} [\sum_{i = 1}^{n} b_{i} {(a_{i} / b_{i})}^{q} - 1]

(3)

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R = \{r_{i} | r_{i} = \frac{P_{B} ∙ p_{B}^{i} + P_{O} ∙ p_{O}^{i}}{\sum_{j = 0}^{L - 1} (P_{B} ∙ p_{B}^{i} + P_{O} ∙ p_{O}^{i})}, i = 0,1, \dots, L - 1\},

(4)

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\begin{matrix} J_{q} (H | R) = \\ \frac{1}{q - 1} \{\sum_{i = 0}^{L - 1} [h_{i} {(r_{i} / h_{i})}^{q} + r_{i} {(h_{i} / r_{i})}^{q}] - 2\}, \end{matrix}

(5)

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t^{*} = m i n_{t \in G} [J_{q} (H | R)]

(6)

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I (x, y) = \{\begin{matrix} 0, I (x, y) < t^{*} \\ 255, I (x, y) \geq t^{*} \end{matrix}

(7)

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φ (i, j) = - a r c t a n \frac{I_{2} (i, j) - I_{4} (i, j)}{I_{1} (i, j) - I_{3} (i, j)}

(8)

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μ = \frac{r_{b} - r_{a}}{p} \times 100 %

(9)

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Leqian KANG, Pengcheng YANG, Qiujuan LÜ, Liping LIAN, Xindong ZHU. Wrapping phase repair method based on Tsallis Relative Entropy evaluation[J]. Optics and Precision Engineering, 2024, 32(8): 1130

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