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数字散斑干涉术和时空三维相位解包裹用于非连续表面动态变形测量

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为解决传统相位解包裹法不能够用于非连续表面的动态变形测量的缺点,在详细阐述基于时空三维相位解包裹技术的数字散斑干涉术的工作原理和测量步骤基础上,应用数字散斑干涉术和时空三维相位解包裹测量非连续表面动态变形.实验证明,当采用每秒70帧的普通相机拍照时,可实现最快形变速率为25.12μm/s的非连续表面动态变形测量.本文所提方法扩展了数字散斑干涉术的测量范围,增强其应用能力.


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47  
2
期
光
子
学
报
第
卷第  
Vol．47 No．2  
February 2018  
2018  
2
年
月
ACTA PHOTONICA SINICA  
doi: 10．3788 /gzxb20184702．0212002  
数字散斑干涉术和时空三维相位解包裹用于非  
连续表面动态变形测量  
1
1
2
1
3
， ， ， ，  
吴思进 杨靖 潘思阳 李伟仙 杨连祥  
( 1  
，
北京信息科技大学 仪器科学与光电工程学院 北京  
100192)  
( 2 ， 100083)  
大唐移动通信设备有限公司 北京  
( 3  
，
奥克兰大学 机械工程系 美国 罗彻斯特  
48309)  
: ，  
要 为解决传统相位解包裹法不能够用于非连续表面的动态变形测量的缺点 在详细阐述基于时空  
摘
，
三维相位解包裹技术的数字散斑干涉术的工作原理和测量步骤基础上 应用数字散斑干涉术和时空三  
．
，
70  
，
帧的普通相机拍照时 可实现最快形  
维相位解包裹测量非连续表面动态变形 实验证明 当采用每秒  
25．12 m/s ． ，  
的非连续表面动态变形测量 本文所提方法扩展了数字散斑干涉术的测量范围 增  
变速率为  
μ
．
强其应用能力  
: ; ; ; ; ; ;  
关键词 电子散斑干涉术 变形测量 动态测量 相位分布 振动测量 相位解包裹 非连续表面  
: O439  
: A : 1004-4213( 2018) 02-0212002-9  
文章编号  
中图分类号  
文献标识码  
Dynamic Deformation Measurement of Discontinuous Surfaces Using  
Digital Speckle Pattern Interferometry and Spatiotemporal  
Three-dimensional Phase Unwrapping  
1
1
2
1
3
WU Si-jin ，YANG Jing ，PAN Si-yang ，LI Wei-xian ，YANG Lian-xiang  
( 1 School of Instrumentation Science and Opto-electronics Engineering，Beijing Information Science and  
Technology University，Beijing 100192，China)  
( 2 Datang Mobile Communications Equipment Co．，Ltd，Beijing 100083，China)  
( 3 Department of Mechanical Engineering，Oakland University，Rochester，Michigan 48309，USA)  
Abstract: Digital Speckle Pattern Interferometry ( DSPI) with a Spatiotemporal Three-dimensional Phase  
Unwrapping ( STPU) is used to measure the dynamic deformation distributions with the presence of object  
discontinuities． It overcomes the phase unwrapping failure of traditional DSPI in such conditions． Elaborate  
description of the measurement priciple and procedure of the DSPI with STPU is given． The experiments  
exibited that dynamic deformation of discontinuous surface，with a maximum deformation rate of 25．12 m/s，  
μ
can be determined perfectly by the proposed method while an ordinary camera with 70 fps was used． The  
research benefits the enlargement of the application areas of DSPI and the improvement of its applicability．  
Key words: Electronic Speckle Pattern Interferometry ( ESPI ) ; Deformation measurements; Dynamic  
measurements; Phase distribution; Vibration measurement; Phase unwrapping; Discontinuous surface  
OCIS Codes: 120．6160; 100．5088; 100．3175; 120．2880; 120．7280  
0 Introduction  
Digital Speckle Pattern Interferometry ( DSPI) ，also known as Electronic Speckle Pattern Interferometry  
Foundation item: The National Natural Science Foundation of China ( Nos．51675055，11672045) and the National Major Scientific Instrument and  
Equipment Development Project of China ( No．2016YFF0101801)  
－
First author: WU Si-jin ( 1979 ) ，male，associate professor，Ph． D． mainly focuses on digital speckle pattern interferometry and digital  
shearography． Email: swu@ bistu．edu．cn  
Received: Jul．25，2017; Accepted: Oct．23，2017  
http: www．photon．ac．cn  
∥
0212002-1  
光
子
学
报
( ESPI) ，is a full-field，non-contact，high-accuracy optical measurement technique for micro /nano-deformation  
［1-3］  
measurement，which has been widely used in manufacturing，aerospace，biomedicine，and so on  
． Precise  
measurement of deformation by DSPI depends on quantitative determination of interferometric phase． The obtained  
raw phase is wrapped and varies within the range of ［0，2 ) because of the use of an inverse tangent calculation，  
π
［4-5］  
an essential process in phase determination  
removed before the calculation of deformation． The process of phase discontinuity removal is called as phase  
unwrapping．  
． This wrapped form causes phase discontinuities which should be  
Traditionally，Spatial Phase Unwrapping ( SPU) is the dominant phase unwrapping algorithm that is used in  
DSPI． It demodulates phase along a two-dimensional spatial path which is either a predetermined or varying path．  
［6］  
Distinguished by strategies of routing，a variety of SPUs have been proposed，including row-by-point algorithm  
，
［7］  
［8］  
［9］  
p
［10］  
quality-guided algorithm ，least-squares algorithm ，branch-cut algorithm ，minimum L -norm algorithm  
，
etc． These SPUs can generate high-quality unwrapped phase maps in most cases，due to the use of modern image  
sensor with millions of pixels． The high-density image sensor allows an over sampling of the wrapped phase map，  
avoiding fault in phase unwrapping． However，in the presence of object surface discontinuity，abrupt phase change  
appears，causing local ultrahigh frequency phase variation which is over the image sensor sampling frequency． The  
local ultrahigh frequency blocks the path of phase unwrapping，resulting in the failure of real phase distribution  
obtainment． The dependence on continuous phase unwrapping path leads to the failure of using DSPI with SPU to  
determine phases of discontinuous surfaces．  
An alternate to solve the problem is the utilization of Temporal Phase Unwrapping ( TPU) in DSPI． TPU  
demodulates the phase through the time axis，so it can neglect the spatial relation between areas of the object  
［11］  
surface  
． Object discontinuity is not a handicap any longer when phase unwrapping． Another advantage is the  
［12］  
determination of absolute phase value which is realized by recording the initial phase map before loading  
． The  
disadvantage of TPU is high demand of camera speed which defines the sampling rate of TPU． Unfortunately，the  
sampling rate cannot satisfy the sampling theory in most situations，even if high-speed cameras are used． This makes  
DSPI with TPU an unpractical tool in engineering．  
Recently， we have proposed a Spatiotemporal Three-dimensional Phase Unwrapping ( STPU ) which  
［13］  
demodulates the phase not only along the two-dimensional spatial path but also through the time axis ． The  
combination of phase unwrapping in spatial and temporal domains makes DSPI able to determine the absolute phase  
by using an ordinary camera． The ability of the new algorithm in deformation measurement of discontinuous surfaces  
is also briefly introduced but has not been demonstrated clearly yet． In this article，the principle and procedure of  
using DSPI with STPU to measure deformation of discontinuous surface are demonstrated in detail． The capability of  
STPU is further revealed by theoretical explanation as well as experiments．  
1 Principle of spatiotemporal three-dimensional phase unwrapping  
The original phases obtained by DSPI are wrapped as modulo 2 of the true phases． The relation between the  
π
original and true phases is mathematically formulated as  
=
=
+
2n  
Φ
mod ( ，2 )  
Φ π  
( 1)  
π
where  
［0，2 ) is the original phase， is the true phase，and n is an integer．  
∈ π Ф  
The process of changing the original phase to the real phase is called as phase unwrapping which is  
traditionally classified as SPU and TPU，depending on phase unwrapping in spatial or temporal domain respectively．  
1．1 Spatial phase unwrapping  
SPU compares the phase values at neighboring pixels and adds or subtracts 2 if the phase jumps exist． The  
π
unwrapping path is predetermined or varied． Distinguished by strategies of routing，many SPUs have been proposed．  
For simplicity，row-by-point algorithm，the simplest SPU，is chosen to explain the basic principle of SPU． Row-by-  
point algorithm takes the first pixel，usually locating at the lower left corner of the phase map，as a start point． Then  
from this point，it demodulates the phase along the first column． The phase values at the first column are expressed  
by  
－
m
1
=
+
( i，0)  
(0，0)  
W[  
( i，0) ]  
( 2)  
Φ
Δ  
∑
=
i
1
where (0，0) is the phase at the start point，  
Δ  
is the difference between two neighboring pixels along the  
0212002-2  

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