小波變換在太赫茲三維成像探測(cè)內(nèi)部缺陷中的應(yīng)用?

代冰 王朋 周宇 游承武 胡江勝 楊振剛 王可嘉 劉勁松?

1)(華中科技大學(xué),武漢光電國(guó)家實(shí)驗(yàn)室,武漢430074)2)(華中科技大學(xué)機(jī)械科學(xué)與工程學(xué)院,武漢430074)

小波變換在太赫茲三維成像探測(cè)內(nèi)部缺陷中的應(yīng)用?

代冰1)王朋2)周宇1)游承武1)胡江勝1)楊振剛1)王可嘉1)劉勁松1)?

1)(華中科技大學(xué),武漢光電國(guó)家實(shí)驗(yàn)室,武漢430074)2)(華中科技大學(xué)機(jī)械科學(xué)與工程學(xué)院,武漢430074)

(2016年11月30日收到;2016年12月23日收到修改稿)

采用Syn View Head 300對(duì)內(nèi)部有膠和空氣孔的樣件進(jìn)行了太赫茲二維掃描(xy軸方向),系統(tǒng)通過(guò)線性調(diào)頻連續(xù)波技術(shù)得到樣件內(nèi)部的三維信息.檢測(cè)薄層時(shí),由于太赫茲源的波長(zhǎng)在亞毫米量級(jí),薄層的上下表面反射峰相距太近而難以辨別.為了提高太赫茲探測(cè)的縱向分辨率,采用小波變換對(duì)探測(cè)信號(hào)進(jìn)行處理,對(duì)小波系數(shù)進(jìn)行三維重構(gòu),獲得的三維小波系數(shù)圖像比原始三維探測(cè)信號(hào)更加精確.該方法有效提高了太赫茲成像的縱向檢測(cè)精度,縱向分辨率可達(dá)1mm.

太赫茲,無(wú)損檢測(cè),小波變換

1 引言

太赫茲(terahertz,THz)波是介于紅外和微波之間頻率為0.1—10 THz的電磁輻射[1,2],不僅擁有與光相同的直進(jìn)性,還具有與電波相似的穿透性和吸收性[3].隨著THz輻射源及THz探測(cè)技術(shù)的發(fā)展,THz在無(wú)損探傷、質(zhì)量監(jiān)測(cè)、內(nèi)容提取、油畫(huà)鑒別、THz成像、安檢等領(lǐng)域得到了越來(lái)越廣泛的應(yīng)用[4?11].THz波對(duì)非導(dǎo)電材料(如泡沫、陶瓷、玻璃、樹(shù)脂、涂料、橡膠和復(fù)合物等)具有良好的穿透性[12],采用THz波對(duì)這些材料的樣件進(jìn)行檢測(cè)成像,成像精度高于X射線成像,空間分辨率高于超聲波成像[13,14].由于THz源的功率較低,對(duì)人體沒(méi)有傷害,近年來(lái),一些運(yùn)用太赫茲成像原理的安檢產(chǎn)品已開(kāi)始進(jìn)入市場(chǎng)[15].由于太赫茲波位于微波和遠(yuǎn)紅外相交疊的波長(zhǎng)范圍,相比X射線和紅外光,波長(zhǎng)較長(zhǎng),使得檢測(cè)樣品的成像縱向分辨率較低.如何提高THz成像的縱向分辨率是目前亟需解決的問(wèn)題.

近年來(lái)小波變換的應(yīng)用越來(lái)越廣泛,其特有的數(shù)學(xué)特性可以有效地分辨出信號(hào)中的特征峰[16?18].本文采用小波變換對(duì)THz波探測(cè)的數(shù)據(jù)進(jìn)行處理,并將處理之后的小波系數(shù)進(jìn)行三維重構(gòu),采用小波系數(shù)代替原始光強(qiáng)信號(hào)進(jìn)行成像,有效地提高了THz成像的縱向分辨率.

2 基本理論

2.1 TH z三維成像原理

采用Syn View Scan 300在常溫下對(duì)樣品進(jìn)行THz成像,光源/探測(cè)器頻率為調(diào)頻0.23—0.32 THz.由于系統(tǒng)采用的是相干光成像,存在衍射極限,根據(jù)衍射極限的公式d/f=1.22λ/D,如果采用THz源成像,成像最低分辨率為1 mm.為了避開(kāi)衍射極限的限制,將THz源放置在步進(jìn)電機(jī)控制的平臺(tái)上,對(duì)檢測(cè)樣件進(jìn)行逐點(diǎn)掃描成像,系統(tǒng)在x-y平面的成像分辨率可達(dá)0.2mm×0.2mm.

系統(tǒng)的探測(cè)原理如圖1所示,圖中BS為分束鏡,從THz源出射的光被分為兩束,各占50%,L2,L3為準(zhǔn)直透鏡,L1,L4為聚焦透鏡,L4可以根據(jù)檢測(cè)需求進(jìn)行調(diào)整,系統(tǒng)采用的是焦距50 mm的L4透鏡.為了檢測(cè)樣件內(nèi)部結(jié)構(gòu),即獲得距離信息,需要獲得檢測(cè)信號(hào)的相位信息.系統(tǒng)采用線性的調(diào)頻連續(xù)波(frequency modulated continuous wave,FMCW)方式,一束光通過(guò)分束鏡到達(dá)探測(cè)器,另一束光通過(guò)樣品后反射到達(dá)探測(cè)器,在調(diào)頻帶寬ω和調(diào)頻周期T一定的條件下,混頻器輸出的中頻信號(hào)頻率ωb與目標(biāo)物體的距離R(兩束光到達(dá)探測(cè)器的時(shí)間差?t)成正比,因此,得到信號(hào)的頻率ωb即可計(jì)算出目標(biāo)物體的距離,如圖2所示.通過(guò)探測(cè)回波信號(hào)與發(fā)射信號(hào)的差拍信號(hào)可實(shí)現(xiàn)目標(biāo)物體的振幅和相位成像[19,20].

圖1 對(duì)樣件進(jìn)行三維THz掃描成像的系統(tǒng)原理圖Fig.1.ScheMatic of the experiMental setup for th reed iMensional THz iMaging.

圖2 線性的調(diào)頻連續(xù)波探測(cè)原理圖Fig.2.ScheMatic of the linear FMCW detection theory.

由圖2中的比例關(guān)系可得

基于這種方法,可以對(duì)檢測(cè)樣品的每個(gè)點(diǎn)進(jìn)行掃描探測(cè),得到樣品各點(diǎn)的縱向信息,實(shí)現(xiàn)對(duì)檢測(cè)樣件的三維成像.

2.2 小波變換原理

待處理信號(hào)為探測(cè)方向(z軸)上的信號(hào),由于信號(hào)的反射峰處對(duì)應(yīng)樣件的交界面,為了更好地對(duì)應(yīng)交界面信號(hào),采用高斯小波基的二階導(dǎo)數(shù)(Gaus2)對(duì)信號(hào)f(x)進(jìn)行連續(xù)小波變換.

對(duì)于任意函數(shù)f(x)∈L2(R)(L2(R)為能量有限的信號(hào)空間),連續(xù)小波變換定義為[21]

式中ψu(yù),s(x)由小波基函數(shù)ψ(x)經(jīng)過(guò)尺度因子s和時(shí)間平移因子u變化后得到,小波基函數(shù)ψ(x)必須滿足容許條件

即

圖3 z軸方向上的光強(qiáng)信號(hào)及其對(duì)應(yīng)的小波變換Fig.3.The z-direction intensity signal and the corresponding continuous wavelet transforMsignal.

3 實(shí)驗(yàn)對(duì)比與討論

將帶有預(yù)埋缺陷的樣件背面向上,放在吸波材料上,采用Syn View Scan 300對(duì)樣品進(jìn)行逐點(diǎn)掃描,探測(cè)其內(nèi)部結(jié)構(gòu),如圖4(a)所示.為了使檢測(cè)得到的圖像更加清晰,樣品盡量放置在探測(cè)系統(tǒng)的焦平面(即z=0mm,焦平面往上1 mm則表示為z=1 mm)附近.檢測(cè)樣品的內(nèi)部結(jié)構(gòu)如圖4(b)所示,樣品是大小為50 mm×50 mm×5 mm的光敏聚合物3D打印模型,設(shè)置4組大小不同的缺陷,缺陷孔的直徑為4 mm,缺陷深度(孔深)分別為4 mm(第1和5行),3 mm(第2和6行),2 mm(第3和7行),1.5 mm(第4和8行).將第1行的6個(gè)孔設(shè)置為3組對(duì)照組,如圖5(b)所示,組(I)填充完好,組(II)填充半完好,組(III)只填充表層,孔底部全部為空氣.對(duì)比這3組實(shí)驗(yàn)結(jié)果來(lái)辨別THz成像在x-y平面的橫向分辨率.在第2—4行用膠將所有孔完全填滿,與未填充膠的第5—8行作為參考組.待膠干燥之后,對(duì)樣品進(jìn)行掃描.

進(jìn)行2組實(shí)驗(yàn)對(duì)比:1)第1行中的組(I)、組(II)、組(III);2)填充膠水組第2—4行和空氣組第6—8行.樣件的實(shí)物圖如圖5(a)所示,通過(guò)逐點(diǎn)掃描成像,可以得到樣件不同z軸位置處的圖像,在z=5mm處得到的THz圖像如圖5(b)所示,從圖中可以清楚地辨別出第1行孔中的空氣部分(黃色區(qū)域)與第5行空氣孔一致,通過(guò)對(duì)比可以判斷組(I)黏貼完好,無(wú)空氣,組(II)只有部分黏貼較好,一半孔為空氣,組(III)的膠層中有空氣層.黏貼完好的第2—4行一直與光敏材料成像顏色保持一致,而空氣孔在相應(yīng)的分界面處呈現(xiàn)黃色.從THz圖可以準(zhǔn)確讀出孔的直徑為4mm.

圖4 (a)將帶有預(yù)埋缺陷的樣件背面向上放在吸波材料上進(jìn)行掃描成像;(b)樣件的結(jié)構(gòu)示意圖Fig.4.(a)Position the saMp lew ith eMbedded defects back-side-up on an absorbing Material and conduct iMage scanning;(b)scheMatic of the saMp le.

圖5 (網(wǎng)刊彩色)(a)樣件實(shí)物圖;(b)z=5 mm處的太赫茲切片圖;(c)圖(b)中標(biāo)注處放大圖Fig.5.(color on line)(a)The p ictu re of the saMp le;(b)the THz slice iMage at z=5 mm;(c)the en larged iMage of the position Marked in(b).

4 小波變換對(duì)實(shí)驗(yàn)結(jié)果的改進(jìn)

樣件的上下表面太赫茲圖像如圖6所示,上下表面分別位于z=8 mm和z=0 mm處,光敏聚合物的折射率no為1.6,檢測(cè)結(jié)果中無(wú)孔處板的光程為8mm,計(jì)算厚度與實(shí)際厚度5mm相符.在計(jì)算樣件厚度的時(shí)候,光敏聚合物材料厚度分別為5,3.5,3,2mm時(shí),檢測(cè)結(jié)果與實(shí)際樣件完全符合,由于太赫茲探測(cè)的光束在z=0 mm處聚焦,離聚焦平面越遠(yuǎn)的面可能存在越多干擾,因此z=6 mm處的太赫茲圖像中明顯存在較多噪聲.當(dāng)光敏聚合物材料厚度為1 mm時(shí),在z=6,5,4mm處都能看到該行孔,即在3 mm的區(qū)域內(nèi)都有該分界面信號(hào)而難以辨別該行孔的分界面位置.產(chǎn)生這個(gè)結(jié)果的主要原因在于檢測(cè)過(guò)程中太赫茲自身波長(zhǎng)較長(zhǎng)(系統(tǒng)中心頻率處波長(zhǎng)為1 mm),檢測(cè)薄層時(shí)薄層的上下表面反射峰相距太近因而難以分辨,為了解決這個(gè)問(wèn)題,采用小波變換進(jìn)行處理.

分別對(duì)光敏聚合物材料厚度為1,2,3,3.5mm處的反射光強(qiáng)信號(hào)進(jìn)行分析,結(jié)果如圖7所示,從圖中可以看到,孔深為3,2,3.5 mm處曲線的反射峰值易于判定,在孔深為4mm處,樣件的頂部和底部相差1 mm光敏聚合物,波峰并不明顯.為了更加精確方便地定位該分界面位置,采用Gaus2小波對(duì)孔深為4mm處的信號(hào)進(jìn)行處理,結(jié)果如圖7(b)所示.進(jìn)行小波變換之后,信號(hào)極大值點(diǎn)剛好對(duì)應(yīng)于原始信號(hào)的反射峰,且相應(yīng)的峰寬度被壓縮,將尺度2的小波系數(shù)再進(jìn)行三維重構(gòu),可以增強(qiáng)信號(hào)中的特征信息.

圖6 (網(wǎng)刊彩色)(a)z=0 mm時(shí)的太赫茲圖像,對(duì)應(yīng)樣件的下表面;(b)z=8 mm處的太赫茲圖像,對(duì)應(yīng)樣件的上表面;(c)z=4 mm處的太赫茲圖像;(d)z=5 mm處的太赫茲圖像;(e)z=6 mm處的太赫茲圖像Fig.6.(color on line)(a)The THz slice iMage at z=0 mm,corresponding to the back side of the saMp le;(b)the THz slice iMage at z=8 mm,correspond ing to the front side of the saMp le;(c)the THz slice iMage at z=4 mm;(d)the THz slice iMage at z=5 mm;(e)the THz slice iMage at z=6 mm.

圖7 (網(wǎng)刊彩色)(a)光敏材料厚度分別為1,2,3,3.5 mm(孔深分別為4,3,2,1.5 mm)時(shí)的反射峰對(duì)比;(b)光敏材料厚1 mm處信號(hào)及其對(duì)應(yīng)的小波變換Fig.7.(color on line)(a)Fou r z-direction intensity signals correspond ing to photosensitive Materials w ith thickness of 1,2,3,3.5 mm,respectively;(b)the z-direction intensity signal froM1 mMthick photosensitive Material and the corresponding continuous wavelet transforMsignal.

圖8 (網(wǎng)刊彩色)(a)截取圖中紅色虛線框區(qū)域中的z軸數(shù)據(jù)進(jìn)行三維重構(gòu);(b)原始檢測(cè)數(shù)據(jù)的三維重構(gòu);(c)對(duì)應(yīng)小波系數(shù)的三維重構(gòu)Fig.8.(color on line)(a)Select the z-direction data w ithin the dotted red line region for 3D reconstruction;(b)3D reconstruction of the original data froMpart of the saMp le;(c)3D reconstruction of the wavelet coeffi cients.

為了更清楚地對(duì)比1 mm厚光敏材料的THz三維成像信息,選圖8(a)所示紅色虛線區(qū)域數(shù)據(jù)進(jìn)行重構(gòu),沿L2邊的xz截面對(duì)應(yīng)1 mm厚光敏材料的上下表面.對(duì)該區(qū)域的信號(hào)進(jìn)行三維重構(gòu),重構(gòu)結(jié)果如圖8(b)所示,孔的頂部反射信號(hào)與樣件上表面的反射信號(hào)連在一起,難以辨別.將該區(qū)域的z軸信號(hào)進(jìn)行小波變換之后再重構(gòu)的三維圖像如圖8(c)所示,4 mm孔的上表面與樣件的上表面能夠清晰地辨別開(kāi)來(lái).從小波系數(shù)重構(gòu)的三維圖中可以準(zhǔn)確地判斷缺陷孔的頂部與樣件上表面的距離為1 mm.采用探測(cè)小波變換對(duì)該系統(tǒng)的探測(cè)數(shù)據(jù)進(jìn)行處理,分辨率可以達(dá)到系統(tǒng)的中心波長(zhǎng).這種方法提高了探測(cè)物質(zhì)內(nèi)部結(jié)構(gòu)的縱向探測(cè)精度.

5 結(jié)論

對(duì)THz波在無(wú)損檢測(cè)領(lǐng)域的應(yīng)用做了一系列研究工作,通過(guò)THz成像系統(tǒng),可以很好地獲得物質(zhì)內(nèi)部的結(jié)構(gòu)變化信息.本文采用小波系數(shù)的三維重構(gòu)提高了THz成像的縱向精度,這為以后的太赫茲計(jì)算機(jī)斷層掃描成像和太赫茲無(wú)損探測(cè)研究提供了新的思路.

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(Received 30 NoveMber 2016;revised Manuscrip t received 23 DeceMber 2016)

PACS:87.50.U–,81.70.Fy,43.60.H jDOI:10.7498/aps.66.088701

*Pro ject supported by the National Natu ral Science Foundation of China(G rant Nos.11574105,61475054,61405063,61177095)and the Science and Technology Condition Resources DevelopMent Project of Hubei Province,China(Grant No.2015BCE052).

?Corresponding author.E-Mail:jsliu4508@vip.sina.com

W avelet transforMin the app lication o f th ree-d iMensional terahertz iMaging for in ternal defect detection?

Dai Bing1)Wang Peng2)Zhou Yu1)You Cheng-Wu1)Hu Jiang-Sheng1)Yang Zhen-Gang1)Wang Ke-Jia1)Liu Jin-Song1)?

1)(W uhan National Laboratory for Op toelectronics,Huazhong University of Science and Technology,W uhan 430074,China)2)(College ofMechanical Science and Engineering,Huazhong University of Science and Technology,W uhan 430074,China)

Spatial resolution and spectral contrast are two Major bottlenecks for non-destructive testing of coMp lex saMp les w ith current imaging technologies.We use a three-dimensional terahertz(THz)imaging systeMto obtain the internal structure of the saMp le,and exp loit the wavelet transforMalgorithMto iMp rove the spatial resolution and the spectral contrast.W ith thisMethod,the longitudinal resolution of terahertz iMaging systeMcan be iMproved to the wavelength coMparable thickness,while the x-y p lane resolution can be as high as 0.2mm×0.2mm,which benefi ts froMthe pointto-point scanning on the x-y p lane.In this three-diMensional terahertz iMaging system,the Syn V iew Head 300 w ith light source/detector frequency of 0.3 THz is used for two-diMensional scanning(x-y direction)of the saMp le,and the linear frequencymodu lated continuouswave technique isused to obtain the reflected terahertz light intensity at diff erent dep ths(z axis)of the saMp le.W hen the saMp le is thin,the upper and lower interface refl ection peaks are diffi cu lt to distinguish due to broad peak w id th of the THz source.To solve this probleMeffi ciently,continuouswavelet transform(CW T)is used.In recent years,CW T is app lied w idely because of its particu larMatheMatical p roperties in the feature signal recognition.Since the Gaus2 wavelet basis is better to highlight the peak signal,we choose it for CW T.A fter CW T,one scale of the wavelet coeffi cients is chosen for three-dimensional data reconstruction,for which the w id ths of the reflection peaks are narrower and the noise signals are weaker.That Means if we reconstruct the three-diMensional wavelet coeffi cient data on the chosen scale,the three-diMensional iMage of the tested saMp le w ill be enhanced.In order to demonstrate that,the three-dimensional images reconstructed by wavelet coeffi cients are coMpared w ith those by original data.The tested saMp le has holes inside w ith diff erent depths.Based on the original three-diMensional THz iMage,it is hard to locate the top of 4 mMdeep hole(1 mMdeep photosensitiveMaterial p late),while the top of the inner 4 mMdeep holes(the bottoMof the 1 mMdeep photosensitivematerial p late)can be distinctly located and the noises are greatly reduced based on the three-diMensional iMages reconstructed by wavelet coeffi cients.W ith this method,the longitudinal resolution of terahertz detection systeMs can be iMproved to 1mMthat is coMparab le to the wavelength,which deMonstrates advantages of thisMethod.

terahertz,non-destructive testing,wavelet transform

10.7498/aps.66.088701

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào):11574105,61475054,61405063,61177095)和湖北省科技條件資源開(kāi)發(fā)項(xiàng)目(批準(zhǔn)號(hào):2015BCE052)資助的課題.

?通信作者.E-Mail:jsliu4508@vip.sina.com

?2017中國(guó)物理學(xué)會(huì)C h inese P hysica l Society

http://w u lixb.iphy.ac.cn