Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity

Xiaomeng Liu; Shuguang Dai

doi:10.3788/COL201513.101202

Journals >Chinese Optics Letters >Volume 13 >Issue 10 >Page 101202 > Article

Chinese Optics Letters
Vol. 13, Issue 10, 101202 (2015)

Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity

Xiaomeng Liu^* and Shuguang Dai

Author Affiliations

School of Optical Electrical and Computer Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

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DOI: 10.3788/COL201513.101202 Cite this Article Set citation alerts

Xiaomeng Liu, Shuguang Dai. Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity[J]. Chinese Optics Letters, 2015, 13(10): 101202 Copy Citation Text

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Abstract

A method for isochromatic determination in three-fringe photoelasticity is presented. It combines the phase-shifting method with cubic polynomial curve-fitting technology to eliminate the errors caused by color repetition. We perform a demonstration of the method on a circular disc subjected to compressive loading and an injection-molded cover with residual stresses. The test results compare well with the theoretical results.

I_{d} = I_{b} + \frac{1}{λ_{2} - λ_{1}} \int_{λ_{1}}^{λ_{2}} F (λ) T (λ) I_{0} (λ) \sin^{2} \frac{δ (λ)}{2} (1 - \cos^{2} 2 θ \sin^{2} ε) d λ,

(1)

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I_{p} = I_{b} + [\frac{1}{λ_{2} - λ_{1}} \int_{λ_{1}}^{λ_{2}} F (λ) T (λ) I_{0} (λ) \sin^{2} \frac{δ (λ)}{2} d λ] \sin^{2} 2 (θ - β_{r}),

(2)

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I_{w} = \frac{1}{λ_{2} - λ_{1}} \int_{λ_{1}}^{λ_{2}} F (λ) T (λ) I_{0} (λ) \sin^{2} \frac{δ (λ)}{2} d λ .

(3)

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I_{p} = I_{b} + I_{w} \sin^{2} 2 (θ - β_{r}) .

(4)

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I_{w j} = \sqrt{(I_{2, j} - I_{0, j})^{2} + (I_{3, j} - I_{1, j})^{2}} (j = R, G, B) .

(5)

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e_{i} = \sqrt{(R_{i} - R_{e})^{2} + (G_{i} - G_{e})^{2} + (B_{i} - B_{e})^{2} + (N_{p} - N)^{2} \times K^{2}},

(7)

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e_{i} = \sqrt{(R_{i} - R_{e})^{2} + (G_{i} - G_{e})^{2} + (B_{i} - B_{e})^{2}}; i \in [i_{c} - Δ i, i_{c} + Δ i],

(8)

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Xiaomeng Liu, Shuguang Dai. Cubic polynomial curve-guided method for isochromatic determination in three-fringe photoelasticity[J]. Chinese Optics Letters, 2015, 13(10): 101202

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