Six-Step Hybrid Phase Shift Technique in Digital Photoelasticity

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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Table 1. Intensity equations of six-step phase shift

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Table 1. Intensity equations of six-step phase shift

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 2. Intensity equations of four-step phase shift technique
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Table 2. Intensity equations of four-step phase shift technique
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 3. Three images of planar polarized light field
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Table 3. Three images of planar polarized light field
One image Two images
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 4. Three images of circularly polarized optical field
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Table 4. Three images of circularly polarized optical field
One image Two images
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 5. Average deviation results of isoclinic and isochromatic before and after noise of each method

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

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

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

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

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

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 8. Average deviation results of the isoclinic and isochromatic
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Table 8. Average deviation results of the isoclinic and isochromatic
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

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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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Paper Information

Category: Physical Optics

Received: Nov. 14, 2022

Accepted: Jan. 16, 2023

Published Online: May. 9, 2023

The Author Email: Wu Ling (wuling751@126.com), Fan Yong (419595203@qq.com)

DOI:10.3788/AOS221978

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Intensity equations of six-step phase shift

Table 1. Intensity equations of six-step phase shift

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

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

Table 3. Three images of planar polarized light field

Table 3. Three images of planar polarized light field

Table 4. Three images of circularly polarized optical field

Table 4. Three images of circularly polarized optical field

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

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

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

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

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

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

Table 8. Average deviation results of the isoclinic and isochromatic

Table 8. Average deviation results of the isoclinic and isochromatic