Fast single fringe-pattern processing with graphics processing unit

Haixia Wang; Hongxiang Zeng; Peng Chen; Ronghua Liang; Li Jiang

doi:10.1364/AO.58.006854

Applied Optics
Vol. 58,
Issue 25,
pp. 6854-6864
(2019)
•https://doi.org/10.1364/AO.58.006854

Fast single fringe-pattern processing with graphics processing unit

Haixia Wang, Hongxiang Zeng, Peng Chen, Ronghua Liang, and Li Jiang

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Haixia Wang, Hongxiang Zeng, Peng Chen, Ronghua Liang, and Li Jiang, "Fast single fringe-pattern processing with graphics processing unit," Appl. Opt. 58, 6854-6864 (2019)

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Table of Contents Category
- Imaging Systems, Image Processing, and Displays
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About this Article
History
- Original Manuscript: May 10, 2019
- Revised Manuscript: July 9, 2019
- Manuscript Accepted: July 24, 2019
- Published: August 28, 2019

Abstract

Optical interferometric techniques provide noncontact, full-field, and high-precision measurements that are very attractive in various research and application fields. Single fringe-pattern processing (SFPP) is often required when measuring fast phenomena, which contain multiple steps including noise removal, phase demodulation, and unwrapping. However, several difficulties are encountered during SFPP, among which the processing time is of interest due to the increasing computational load brought by the large amount and high-resolution fringe patterns in recent years. In this paper, we propose a general and complete graphics processing unit (GPU)-based SFPP framework to perform a systematic discussion on SFPP acceleration. Typical methods from the spatial domain, the transform-based, and the path-related are chosen to have a variety of methods in the framework for better parallelization demonstration, namely, coherence-enhancing diffusion for denoising, spiral phase quadrature transform for demodulation, and quality-guided phase unwrapping. To the best of our knowledge, this is the first time a complete GPU-based framework has been proposed for SFPP. The advantages of performing the analysis and parallelization in framework level are demonstrated, where processing redundancy can be identified and reduced. The proposed framework can be used as an example to demonstrate the GPU-based parallelization in SFPP. Methods in the framework can be replaced but the framework level analysis, the parallel design, and the involved functions are always good references. Experiments are performed on simulated and experimental fringe patterns to demonstrate the effectiveness of the proposed work and achieve at most 29.8 times speedup compared with CPU-based sequential processing.

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Description	Calculation Details
Structure tensor in Eq. (4)	Multiplication × 3
Structure tensor in Eq. (4)	Convolution × 5
Diffusion tensor in Eq. (3)	Addition × 2
	Subtraction × 2
	Multiplication × 5
	Division × 2
	Square Root × 1
The div operator in Eq. (2)	Addition × 26
	Subtraction × 13
	Multiplication × 17
	Absolute × 16
	Matrix padding × 4
Iterative updating in Eq. (2)	Addition × 1
Iterative updating in Eq. (2)	Multiplication × 1

Description	Calculation Details
$j_{11}$ , $j_{12}$ and $j_{22}$ from CED	NA
Eigenvalues $μ_{1}$ and $μ_{2}$ in Eq. (13)	addition × 3
	subtraction × 2
	multiplication × 5
	square root × 1
Quality $Q (x, y)$ in Eq. (12)	addition × 1
	subtraction × 1
	multiplication × 3
	division × 1
Orientation $θ (x, y)$ in Eq. (10)	subtraction × 1
	multiplication × 2
	arctangent × 1
Orientation unwrapping	pixel-level sequential processing
SPQT $V (\cdot)$ in Eq. (8)	FFT × 1, IFFT × 1
	complex multiplication × 2
	exponential × 1
Wrapped phase $φ_{W}$ in Eq. (9)	arctangent × 1

Fringe Patterns with Different Sizes	${MSE}_{1}$	${MSE}_{2}$	${MSE}_{3}$
Fig. 5(a) $256 \times 256$	0.005	0.005	$5.752 e - 13$
Fig. 5(b) $512 \times 512$	0.005	0.005	$4.040 e - 12$
Fig. 5(c) $1024 \times 1024$	0.004	0.004	$2.290 e - 11$
Fig. 5(d) $256 \times 256$	0.007	0.007	$4.532 e - 13$
Fig. 5(e) $512 \times 512$	0.004	0.004	$1.739 e - 12$
Fig. 5(f) $1024 \times 1024$	0.004	0.004	$6.953 e - 12$
Fig. 5(g) $256 \times 256$	0.033	0.033	$2.437 e - 13$
Fig. 5(h) $512 \times 512$	0.019	0.019	$4.842 e - 13$
Fig. 5(i) $1024 \times 1024$	0.010	0.010	$2.636 e - 12$

Fringe Patterns with Different Sizes	E1	E2	E3	E4	Speedup E1 versus E4
Fig. 5(a) $256 \times 256$	2.399	1.235	0.378	0.322	7.442
Fig. 5(b) $512 \times 512$	7.269	1.567	0.678	0.442	16.436
Fig. 5(c) $1024 \times 1024$	29.690	4.279	2.913	1.053	28.186
Fig. 5(d) $256 \times 256$	2.377	1.474	0.380	0.333	7.133
Fig. 5(e) $512 \times 512$	6.985	1.798	0.759	0.456	15.334
Fig. 5(f) $1024 \times 1024$	28.961	3.901	2.636	0.970	29.860
Fig. 5(g) $256 \times 256$	2.428	1.494	0.407	0.307	7.907
Fig. 5(h) $512 \times 512$	7.235	1.959	0.828	0.450	16.079
Fig. 5(i) $1024 \times 1024$	30.733	5.222	4.091	1.041	29.523

Fringe Patterns with Different Sizes	WFF	CED	WFR	CED+SPQT
Fig. 5(a) $256 \times 256$	0.172	0.269	0.639	0.275
Fig. 5(b) $512 \times 512$	0.547	0.328	1.504	0.353
Fig. 5(c) $1024 \times 1024$	2.088	0.490	6.633	0.600
Fig. 5(d) $256 \times 256$	0.160	0.288	0.597	0.294
Fig. 5(e) $512 \times 512$	0.554	0.330	1.509	0.357
Fig. 5(f) $1024 \times 1024$	2.097	0.485	6.607	0.599
Fig. 5(g) $256 \times 256$	0.165	0.268	0.594	0.274
Fig. 5(h) $512 \times 512$	0.564	0.295	1.514	0.320
Fig. 5(i) $1024 \times 1024$	2.097	0.493	6.475	0.602

Abstract

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Applied Optics