A Composite Grating Phase-Measuring Profilometry Based on Mixed Filtering Window

An Haihua; Cao Yiping; Li Hongmei; Wu Haitao

doi:10.3788/CJL202047.0604007

Chinese Journal of Lasers, Volume. 47, Issue 6, 604007(2020)

A Composite Grating Phase-Measuring Profilometry Based on Mixed Filtering Window

An Haihua¹, Cao Yiping^1、*, Li Hongmei^1,2, and Wu Haitao¹

Author Affiliations

¹Department of Opto-Electronics, Sichuan University, Chengdu, Sichuan 610064, China

²College of Physics and Engineering, Chengdu Normal University, Chengdu, Sichuan 611130, China

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Figures & Tables(11)

Fig. 1. Process of composite grating formation. (a) PMP gratings; (b) carrier gratings; (c) composite grating

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Fig. 2. Measurement principle of CGPMP. (a) Original composite pattern; (b) object to be measured;(c) deformed composite pattern; (d) spatial spectrum; (e) demodulated 3- step-phase shift pattern; (f) restructured object

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Fig. 3. Distribution of σ_RM at different noise sources. (a) Single noise effect; (b) compound noise effect

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Fig. 4. Spectrum with 3% amplitude noise

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Fig. 5. Selection of window width

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Fig. 6. Relationship between window width and σ_RM. (a) Width in horizontal direction; (b) width in vertical direction

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Fig. 7. Mixed window measurement results. (a) Mixed window; (b) error distribution

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Fig. 8. Plane measurement (h₀=10.000 mm). (a) Experimental device; (b) captured pattern;(c) spatial spectrum; (d) restructured plane

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Fig. 9. Comparison of reconstruction results. (a) Object to be measured: pentagram; (b) captured deformed pattern;(c) reconstruction results; (d) cutaway views of the 600th row

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Table 1. Measurement errors of different windows
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Table 1. Measurement errors of different windows
Error Rectangular (k=1) Triangular (k=2) Blackman (k=3) Hanning (k=4) Mixed (k=5)
e_k /mm 1.494 0.448 0.436 0.422 0.383
Δe_k /% 74.36 14.51 12.16 9.24 0
$\begin{matrix} {σ^{k}}_{RM} \end{matrix}$ /mm 0.115 0.095 0.092 0.091 0.081
Δ $\begin{matrix} {σ^{k}}_{RM} \end{matrix}$ /% 29.57 14.74 11.96 10.99 0

Table 2. Comparison of measurement results at different planes with known height

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Table 2. Comparison of measurement results at different planes with known height

h₀ /mm	Window	$\begin{matrix} {\bar{h}}_{k} \end{matrix}$ /mm	Δh_k /mm	$\begin{matrix} {σ^{k}}_{RM} \end{matrix}$ /mm	Δ $\begin{matrix} {σ^{k}}_{RM} \end{matrix}$ /%
	Rectangular (k=1)	5.879	0.121	0.122	24.59
	Triangular (k=2)	5.887	0.113	0.114	19.30
6.000	Blackman (k=3)	5.896	0.104	0.105	12.38
	Hanning (k=4)	5.897	0.103	0.102	9.80
	Mixed (k=5)	5.907	0.093	0.092	0
	Rectangular (k=1)	9.899	0.103	0.103	27.18
	Triangular (k=2)	9.907	0.093	0.094	20.21
10.000	Blackman (k=3)	9.920	0.080	0.086	12.79
	Hanning (k=4)	9.921	0.079	0.083	9.64
	Mixed (k=5)	9.928	0.072	0.075	0
	Rectangular (k=1)	12.876	0.124	0.125	20.40
	Triangular (k=2)	12.894	0.106	0.107	18.69
13.000	Blackman (k=3)	12.903	0.097	0.098	11.22
	Hanning (k=4)	12.904	0.096	0.097	10.31
	Mixed (k=5)	12.913	0.087	0.087	0

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An Haihua, Cao Yiping, Li Hongmei, Wu Haitao. A Composite Grating Phase-Measuring Profilometry Based on Mixed Filtering Window[J]. Chinese Journal of Lasers, 2020, 47(6): 604007

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