Six-Step Hybrid Phase Shift Technique in Digital Photoelasticity

Chuan Qiu; Niannian Chen; Ling Wu; Yong Fan; Guanghai Liu

doi:10.3788/AOS221978

Journals >Acta Optica Sinica >Volume 43 >Issue 10 >Page 1026001 > Article

Acta Optica Sinica
Vol. 43, Issue 10, 1026001 (2023)

Six-Step Hybrid Phase Shift Technique in Digital Photoelasticity

Chuan Qiu¹, Niannian Chen¹, Ling Wu^1、*, Yong Fan^1、**, and Guanghai Liu²

Author Affiliations

¹School of Computer Science and Technology, Southwest University of Science and Technology, Mianyang 621010, Sichuan , China

²Sichuan Physcience Optics and Fine Mechanics Co., Ltd., Mianyang 621010, Sichuan , China

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DOI: 10.3788/AOS221978 Cite this Article Set citation alerts

Chuan Qiu, Niannian Chen, Ling Wu, Yong Fan, Guanghai Liu. Six-Step Hybrid Phase Shift Technique in Digital Photoelasticity[J]. Acta Optica Sinica, 2023, 43(10): 1026001 Copy Citation Text

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Fig. 1. Polarization optical system. (a) Planar polarization optical system; (b) circular polarization optical system

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Isoclinic images. (a) Six-step phase shift with monochromatic light; (b) ten-step phase shift with monochromatic light; (c) ten-step phase shift with white light

Fig. 2. Isoclinic images. (a) Six-step phase shift with monochromatic light; (b) ten-step phase shift with monochromatic light; (c) ten-step phase shift with white light

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Fig. 3. Digital photoelastic image acquisition system

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Fig. 4. Wrapped isoclinic images. (a)(d)(g) F=200 N, D=50 mm; (b)(e)(h) F=350 N, D=50 mm; (c)(f)(i) F=200 N, D=40 mm

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Fig. 5. Unwrapped isoclinic images. (a) Ten-step phase shift; (b) proposed method

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Fig. 6. Isochromatic images. (a) Ten-step phase shift; (b) proposed method

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Fig. 7. Plot of isochromatic difference. (a) Location 1 of disc; (b) location 2 of disc

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Fig. 8. Wrapped isochromatic images. (a)(d) F=300 N, D=50 mm; (b)(e) F=350 N, D=50 mm; (c)(f) F=200 N, D=40 mm

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Number	α	φ	γ	β	Intensity
I₁	π/2	π/4	-π/4	0	$I_{1} = I_{b} + \frac{I_{c}}{2} (1 - c o s δ)$
I₂	π/2	π/4	-π/4	π/2	$I_{2} = I_{b} + \frac{I_{c}}{2} (1 + c o s δ)$
I₃	π/2	π/4	0	π/2	$I_{3} = I_{b} + \frac{I_{c}}{2} (1 - s i n δ s i n 2 θ)$
I₄	π/2	π/4	π/4	3π/4	$I_{4} = I_{b} + \frac{I_{c}}{2} (1 + s i n δ c o s 2 θ)$
I₅	π/2	π/4	0	0	$I_{5} = I_{b} + \frac{I_{c}}{2} (1 + s i n δ s i n 2 θ)$
I₆	π/2	π/4	π/4	π/4	$I_{6} = I_{b} + \frac{I_{c}}{2} (1 - s i n δ c o s 2 θ)$

Table 1. Intensity equations of six-step phase shift

Number	α	β	Intensity
I_w1	π/2	0	$I_{w 1} = I_{b} + I_{s} s i n^{2} \frac{δ}{2} s i n^{2} 2 θ$
I_w2	5π/8	π/8	$I_{w 2} = I_{b} + \frac{I_{s}}{2} s i n^{2} \frac{δ}{2} (1 - s i n 4 θ)$
I_w3	3π/4	π/4	$I_{w 3} = I_{b} + I_{s} s i n^{2} \frac{δ}{2} c o s^{2} 2 θ$
I_w4	7π/8	3π/8	$I_{w 4} = I_{b} + \frac{I_{s}}{2} s i n^{2} \frac{δ}{2} (1 + s i n 4 θ)$

Table 2. Intensity equations of four-step phase shift technique

One image	Two images
One image	I_w1 and I_w3	I_w2 and I_w4
I_w1	0	1
I_w2	1	0
I_w3	0	1
I_w4	1	0

Table 3. Three images of planar polarized light field

One image	Two images
One image	I₁and I₂	I₃ and I₅	I₄ and I₆
I₁	0	1	1
I₂	0	1	1
I₃	1	0	0
I₄	1	0	0
I₅	1	0	0
I₆	1	0	0

Table 4. Three images of circularly polarized optical field

Images SNR /dB	Deviation results of isoclinic B /rad		Deviation results of isochromatic B /rad
Images SNR /dB	Proposed method	Ten-step phase shift	Proposed method	Ten-step phase shift
40	0.0173	0.0141	0.0286	0.0199
45	0.0097	0.0098	0.0170	0.0120
50	0.0058	0.0046	0.0098	0.0079

Table 5. Average deviation results of isoclinic and isochromatic before and after noise of each method

Azimuth deviation	Deviation of isoclinic B /rad
Azimuth deviation	Proposed method	Ten-step phase shift
Δα=0.4°，Δβ=0.4°	0.0127	0.0127
Δα=-0.4°，Δβ=-0.4°	0.0127	0.0127
Δα=-0.4°，Δβ=0.4°	1.318×10^-13	1.318×10^-13
Δα=0°，Δβ=0.4°	0.0064	0.0064
Δα=0.4°，Δβ=0°	0.0064	0.0064

Table 6. Deviation results of isoclinic caused by azimuth of polarizer and analyzer

Azimuth deviation	Deviation of isochromatic B /rad
Azimuth deviation	Proposed method	Ten-step phase shift
Δγ=0.4°，Δβ=0.4°	6.647×10^-17	4.664×10^-17
Δγ=-0.4°，Δβ=0.4°	0.0322	0.0171
Δγ=0°，Δβ=0.4°	0.0160	0.0085
Δγ=0.4°，Δβ=0°	0.0159	0.0085
Δγ=-0.4°，Δβ=0°	0.0170	0.0085

Table 7. Deviation results of isochromatic caused by the azimuth of the second quarter wave and the analysis mirror

Diameter D /mm	Loading F /N	Deviation of isoclinic B /rad	Deviation of isochromatic B /rad
50	200	0.0106	0.0802
50	250	0.0086	0.0934
50	300	0.0099	0.0926
50	350	0.0117	0.0960
40	200	0.0090	0.0919

Table 8. Average deviation results of the isoclinic and isochromatic

Chuan Qiu, Niannian Chen, Ling Wu, Yong Fan, Guanghai Liu. Six-Step Hybrid Phase Shift Technique in Digital Photoelasticity[J]. Acta Optica Sinica, 2023, 43(10): 1026001

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