Encoding technology of an asymmetric combined structured light for 3D measurement

Zhirui Cao; Hanbing Jiang

doi:10.1364/AO.400307

Applied Optics
Vol. 59,
Issue 33,
pp. 10253-10263
(2020)
•https://doi.org/10.1364/AO.400307

Encoding technology of an asymmetric combined structured light for 3D measurement

Zhirui Cao and Hanbing Jiang

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Zhirui Cao and Hanbing Jiang, "Encoding technology of an asymmetric combined structured light for 3D measurement," Appl. Opt. 59, 10253-10263 (2020)

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Abstract

Sinusoidal phase-shifting symmetrically combined with cyclic code is one of the most important encoding methods in the field of 3D measurement. Due to the modulation of the object surface and the influence of the noise of the image acquisition system, the periods of the cyclic code and the sinusoidal phase-shifting in the intensity image do not coincide completely, and they lead to large absolute phase decoding errors near the cycle boundaries, which are called cycle dislocation errors. In order to eliminate these errors in principle, the concept and method of region encoding for four-step sinusoidal phase-shifting are proposed, and the sinusoidal phase-shifting is combined with cyclic code asymmetrically. Under the premise that the cyclic code and the region code change at different times, the cycle dislocation error is reduced from one cycle of cyclic code to one pixel by the dual constraint of cyclic code and region code. The simulation measurement results of 3 ds max and the physical measurement results show that the asymmetric combination encoding method effectively eliminates the cycle dislocation errors; the maximum measurement error is reduced by an order of magnitude, and the root mean square measurement error is reduced by 70%.

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Region Code	Conditions
$N = 0$	$I_{4} - I_{2} ⩾ 0$ , $I_{1} - I_{3} > 0$
$N = 1$	$I_{4} - I_{2} > 0$ , $I_{1} - I_{3} ⩽ 0$
$N = 2$	$I_{4} - I_{2} ⩽ 0$ , $I_{1} - I_{3} < 0$
$N = 3$	$I_{4} - I_{2} < 0$ , $I_{1} - I_{3} ⩾ 0$

$k$	Cyclic Code Boundary	$N$
0	left boundary	0
	right boundary	3
1	left boundary	3
	right boundary	2
2	left boundary	2
	right boundary	1
3	left boundary	1
	right boundary	0
4	…	…

$φ = \arctan (\frac{I_{4} - I_{2}}{I_{1} - I_{3}}) + fix (\frac{N + 1}{2}) \times π$ , $\arctan (\frac{I_{4} - I_{2}}{0}) = - \frac{π}{2}$
Error location	$Δ N$	$Δ φ$
One pixel to the left of the 0-1 region boundary	$N = 0 \to N^{'} = 1$	$φ = \frac{π}{2} - \frac{2 π}{32} = \frac{7 π}{16}$ , $φ^{'} = - \frac{π}{2} + f i x (\frac{1 + 1}{2}) \times π = \frac{π}{2}$ , $Δ φ = \frac{- π}{16}$
0-1 region boundary	$N = 1 \to N^{'} = 0$	$φ = \frac{π}{2}$ , $φ^{'} = \frac{π}{2} - \frac{2 π}{32} + f i x (\frac{0 + 1}{2}) \times π = \frac{7 π}{16}$ , $Δ φ = \frac{π}{16}$
One pixel to the left of the 1-2 region boundary	$N = 1 \to N^{'} = 2$	$φ = π - \frac{2 π}{32} = \frac{15 π}{16}$ , $φ^{'} = 0 + f i x (\frac{2 + 1}{2}) \times π = π$ , $Δ φ = \frac{- π}{16}$
1-2 region boundary	$N = 2 \to N^{'} = 1$	$φ = π$ , $φ^{'} = 0 - \frac{2 π}{32} + f i x (\frac{1 + 1}{2}) \times π = \frac{15 π}{16}$ , $Δ φ = \frac{π}{16}$
One pixel to the left of the 2-3 region boundary	$N = 2 \to N^{'} = 3$	$φ = \frac{3 π}{2} - \frac{2 π}{32} = \frac{23 π}{16}$ , $φ^{'} = - \frac{π}{2} + f i x (\frac{3 + 1}{2}) \times π = \frac{3 π}{2}$ , $Δ φ = \frac{- π}{16}$
2-3 region boundary	$N = 3 \to N^{'} = 2$	$φ = \frac{3 π}{2}$ , $φ^{'} = \frac{π}{2} - \frac{2 π}{32} + f i x (\frac{2 + 1}{2}) \times π = \frac{23 π}{16}$ , $Δ φ = \frac{π}{16}$

Error Location	$Δ k$ and $Δ N$	$Δ Φ$
Left boundary of the cyclic code	$k = 0 \to k^{'} = 1$ ;	$Φ = 2 π \times [0 - f i x (\frac{0 + 3 + 0.5}{4})] + φ$ ,
	$N = 3 \to N^{'} = 3$	$Φ^{'} = 2 π \times [1 - f i x (\frac{1 + 3 + 0.5}{4})] + φ^{'}$ $\| Δ Φ \| = \| Δ φ \|$
	$k = 0 \to k^{'} = 0$ ;	$Φ = 2 π \times [0 - f i x (\frac{0 + 3 + 0.5}{4})] + φ$ ,
	$N = 3 \to N^{'} = 2$	$Φ^{'} = 2 π \times [0 - f i x (\frac{0 + 2 + 0.5}{4})] + φ^{'}$ $\| Δ Φ \| = \| Δ φ \|$
Right boundary of the cyclic code	$k = 1 \to k^{'} = 2$ ;	$Φ = 2 π \times [1 - f i x (\frac{1 + 2 + 0.5}{4})] + φ$
	$N = 2 \to N^{'} = 2$	$Φ^{'} = 2 π \times [2 - f i x (\frac{2 + 2 + 0.5}{4})] + φ^{'}$ $\| Δ Φ \| = \| Δ φ \|$
	$k = 1 \to k^{'} = 1$ ;	$Φ = 2 π \times [1 - f i x (\frac{1 + 2 + 0.5}{4})] + φ$ ,
	$N = 2 \to N^{'} = 1$	$Φ^{'} = 2 π \times [1 - f i x (\frac{1 + 1 + 0.5}{4})] + φ^{'}$ $\| Δ Φ \| = \| Δ φ \|$

Methods	Maximum Error (mm)	Root-Mean-Square Error (mm)	Time Consumption (s)
Symmetric combination encoding with correction method	0.317 mm	0.058 mm	3.51
Asymmetric combination encoding method	0.032 mm	0.014 mm	2.39

Methods	Maximum Error (mm)	Root-Mean-Square Error (mm)	Time Consumption (s)
Symmetric combination encoding with correction method	0.651 mm	0.103 mm	3.64
Asymmetric combination encoding method	0.097 mm	0.032 mm	2.58

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Applied Optics