剪切光束成像技術(shù)對(duì)縱深目標(biāo)的成像

蘭富洋 羅秀娟 陳明徠 張羽 劉輝

1)(中國(guó)科學(xué)院西安光學(xué)精密機(jī)械研究所,西安 710119)

2)(中國(guó)科學(xué)院大學(xué),北京 100049)

剪切光束成像技術(shù)對(duì)縱深目標(biāo)的成像

蘭富洋1)2)?羅秀娟1)陳明徠1)張羽1)劉輝1)

1)(中國(guó)科學(xué)院西安光學(xué)精密機(jī)械研究所,西安 710119)

2)(中國(guó)科學(xué)院大學(xué),北京 100049)

剪切光束成像,散斑成像,目標(biāo)縱深,相位延遲

剪切光束成像技術(shù)是一種能透過(guò)大氣湍流對(duì)遠(yuǎn)距離目標(biāo)實(shí)現(xiàn)高分辨率成像的主動(dòng)成像技術(shù).現(xiàn)有相關(guān)研究中所采用的目標(biāo)均為二維平面目標(biāo),然而現(xiàn)實(shí)中的目標(biāo)一般都具有三維形貌,目標(biāo)縱深對(duì)回波信號(hào)產(chǎn)生的延遲或?qū)Τ上褓|(zhì)量產(chǎn)生不利影響.從剪切光束成像理論出發(fā),在二維目標(biāo)成像模型的基礎(chǔ)上建立了三維縱深目標(biāo)成像模型,并利用該模型研究了兩剪切光與參考光間的頻差及目標(biāo)縱深對(duì)成像的影響.仿真結(jié)果表明,隨著拍頻的增大,重構(gòu)圖像質(zhì)量逐漸下降.剪切光束成像技術(shù)可通過(guò)減小拍頻來(lái)提高真實(shí)目標(biāo)成像質(zhì)量.

1 引 言

在空間態(tài)勢(shì)感知、衛(wèi)星遙感和空天對(duì)地觀測(cè)等遠(yuǎn)距離成像探測(cè)領(lǐng)域,大氣湍流使光傳輸特性發(fā)生隨機(jī)變化,這常常會(huì)導(dǎo)致成像分辨率下降、像質(zhì)變差甚至用傳統(tǒng)方法無(wú)法直接成像等問(wèn)題[1,2].剪切光束成像(sheared-beam imaging,SBI)技術(shù)[3,4]是一種相干照明主動(dòng)成像技術(shù),利用三束激光剪切照射目標(biāo),通過(guò)探測(cè)器接收被測(cè)目標(biāo)反射回波的散斑場(chǎng)進(jìn)行計(jì)算成像,不受湍流擾動(dòng)和快速運(yùn)動(dòng)目標(biāo)多普勒頻移的影響[5?7],無(wú)需自適應(yīng)光學(xué)和成像透鏡就能達(dá)到衍射極限分辨率[8],突破了傳統(tǒng)光學(xué)成像瓶頸,具有重要的科學(xué)研究意義.

為了驗(yàn)證剪切光束成像技術(shù)的可行性及其克服大氣湍流成像的能力,全世界范圍內(nèi)多家研究機(jī)構(gòu)相繼開(kāi)展了理論仿真和實(shí)驗(yàn)研究[9?11],所采用的目標(biāo)均為二維平面目標(biāo).考慮到實(shí)際應(yīng)用中目標(biāo)具有三維形貌,目標(biāo)不同縱深區(qū)域的成像距離不同,這將導(dǎo)致不同區(qū)域的反射回波到達(dá)探測(cè)器陣列時(shí),彼此間存在相位延遲,對(duì)成像質(zhì)量產(chǎn)生不利影響.本文從成像基本原理著手推導(dǎo)了SBI對(duì)縱深目標(biāo)的成像公式,對(duì)目標(biāo)三維形貌引入的相位延遲情況進(jìn)行了研究,結(jié)合計(jì)算機(jī)仿真分析了SBI對(duì)縱深目標(biāo)的成像能力,最后給出SBI系統(tǒng)在實(shí)際應(yīng)用中拍頻設(shè)計(jì)的依據(jù).

2 原理分析

用激光照射遠(yuǎn)程目標(biāo),反射回波經(jīng)遠(yuǎn)距離傳播后到達(dá)接收面時(shí)發(fā)生夫瑯禾費(fèi)衍射.由于夫瑯禾費(fèi)衍射可近似看作對(duì)光場(chǎng)進(jìn)行的一次傅里葉變換[12],探測(cè)器接收到的回波光場(chǎng)中包含目標(biāo)的傅里葉頻譜信息[13].若直接利用強(qiáng)度探測(cè)器陣列接收目標(biāo)的傅里葉頻譜,僅能獲取強(qiáng)度信息而損失相位信息,難以據(jù)此重構(gòu)目標(biāo)圖像.SBI基于振幅干涉測(cè)量方法,利用三束以L形式剪切排布、具有不同頻差的激光照射目標(biāo),將目標(biāo)頻譜相位信息調(diào)制到三束光形成的拍頻信號(hào)中,之后對(duì)強(qiáng)度探測(cè)器陣列采集的反射回波信號(hào)進(jìn)行解調(diào)和循環(huán)迭代[14,15],恢復(fù)得到目標(biāo)頻譜相位,最后進(jìn)行傅里葉逆變換重構(gòu)目標(biāo)圖像[16,17].圖1為SBI原理示意圖.

圖1 SBI原理示意圖Fig.1.Schematic of sheared-beam imaging principle.

探測(cè)器陣列平面上反射回波可表示為[18]

式中U(x,y)為接收平面上的反射回波;t為時(shí)間;(x,y)為接收平面坐標(biāo);(x′,y′)為目標(biāo)平面坐標(biāo);O(x′,y′)為目標(biāo)表面反射率分布;φ(x′,y′)為目標(biāo)表面粗糙引起的隨機(jī)相移,其偏移量在[?π,π]間隨機(jī)選取[19];E0和ω0為0光的振幅及角頻率;Ex,Ey和ωx,ωy分別為X光和Y光的振幅及角頻率;sx和sy為剪切量;λ為激光波長(zhǎng);R為成像距離.(1)式為三束激光反射回波的疊加,第一項(xiàng)為0光攜帶的目標(biāo)頻譜,后兩項(xiàng)為X光和Y光攜帶的目標(biāo)頻譜,U(x,y)實(shí)質(zhì)上是目標(biāo)頻譜的錯(cuò)位疊加.

對(duì)縱深目標(biāo)成像時(shí),可將目標(biāo)看作是由多個(gè)具有不同縱深的面元oi構(gòu)成,目標(biāo)基面到接收平面的距離為R,不同面元到基面的縱深為di,如圖2所示.

接收平面處的反射回波U(x,y)可表示為目標(biāo)各面元單獨(dú)產(chǎn)生的反射回波Ui(x,y)的相干疊加,即

式中c為光速;N為目標(biāo)面元個(gè)數(shù);oi(x′,y′)為各面元的反射率分布;φi(x′,y′)為各面元產(chǎn)生的隨機(jī)相移.

圖2 縱深目標(biāo)成像示意圖Fig.2.Imaging schematic of object with depth information.

目標(biāo)縱深對(duì)一部分反射回波造成2di/c的時(shí)間延遲,使得不同縱深表面所產(chǎn)生的反射回波到達(dá)接收平面時(shí)存在不同相位偏移.將相位偏移項(xiàng)移入積分式內(nèi)有

式中d(x′,y′)為目標(biāo)縱深分布. 由于φ(x′,y′)和exp[jω02d(x′,y′)/c]的乘積仍為[?π,π]區(qū)間內(nèi)的隨機(jī)相移,將二者的乘積用φ′(x′,y′)表示,(3)式可寫(xiě)為

式中Δω1=ωx?ω0,Δω2=ωy?ω0分別為X光、Y光與0光的角頻率差.(4)式后兩項(xiàng)頻譜的每個(gè)復(fù)振幅分量都引入了與拍頻和縱深有關(guān)的相位偏移,如圖3所示.圖3(a)中每個(gè)實(shí)線箭頭代表目標(biāo)頻譜的一個(gè)復(fù)振幅分量(以3個(gè)為例),虛線箭頭代表相位偏移后的復(fù)振幅分量,各分量疊加之后得到的頻譜相位將產(chǎn)生Δφ的偏差,如圖3(b)所示.可見(jiàn)對(duì)縱深目標(biāo)成像時(shí),探測(cè)器陣列接收到的頻譜不再是目標(biāo)的準(zhǔn)確頻譜,而是存在一定的誤差,且該誤差隨拍頻和縱深的增大愈發(fā)嚴(yán)重.

SBI重構(gòu)的目標(biāo)圖像實(shí)為目標(biāo)表面反射率分布O(x′,y′)與隨機(jī)相移的乘積,受隨機(jī)相移的影響,單次重構(gòu)圖像中存在較嚴(yán)重的散斑現(xiàn)象[15].為提升成像質(zhì)量,通常需要連續(xù)進(jìn)行多次成像,利用多幅重構(gòu)圖像疊加平均的方法消除圖像中的散斑[20],如圖4所示.

圖3 頻譜相位偏移示意圖 (a)理想目標(biāo)頻譜分量和相位偏移后的頻譜分量;(b)頻譜分量疊加形成的理想頻譜和有誤差的頻譜Fig.3.Schematic of phase shift:(a)Ideal Fourier spectrum components and Fourier spectrum components with their phase shifted;(b)ideal Fourier spectrum and Fourier spectrum with phase-shift errors.

圖4 圖像疊加平均去除散斑Fig.4.Frame averaging to reduce speckle noise.

3 仿真驗(yàn)證與分析

3.1 拍頻對(duì)成像結(jié)果的影響

SBI對(duì)縱深目標(biāo)成像時(shí),拍頻和縱深的作用使得到的目標(biāo)頻譜與真實(shí)值產(chǎn)生偏差,且該偏差隨拍頻和縱深的增大而增大.一般空間目標(biāo)的縱深不超過(guò)10 m[21],而拍頻的取值范圍較大,可從赫茲量級(jí)到兆赫茲量級(jí),因此拍頻的設(shè)置對(duì)成像結(jié)果的影響更為顯著.下面通過(guò)仿真分析拍頻取值對(duì)成像結(jié)果的影響.

為對(duì)成像質(zhì)量做出客觀描述,通常采用Strehl比來(lái)衡量重構(gòu)圖像與目標(biāo)圖像的相似度.對(duì)于兩幅圖像fa(m,n),fb(m,n),Strehl比定義為

圖5 (網(wǎng)刊彩色)拍頻對(duì)重構(gòu)圖像Strehl比值的影響Fig.5.(color online)Strehl ratios of reconstructed images at different beat frequencies.

式中“·”表示內(nèi)積.兩幅圖像越相似,Strehl比越趨近于1,當(dāng)兩圖像強(qiáng)度值相等或只相差一個(gè)常數(shù)因子時(shí)Strehl比為1[22].

選用分辨率為128 pixel×128 pixel的三種衛(wèi)星灰度圖像作為目標(biāo),激光波長(zhǎng)為1064 nm,X光和Y光相對(duì)于0光的頻差分別為Δνx和Δνy,成像距離為3.6×104km,探測(cè)器陣列維數(shù)為80×80.為簡(jiǎn)單起見(jiàn),仿真中將目標(biāo)區(qū)域均勻分成兩部分,設(shè)定兩種不同的縱深,深度差設(shè)為10 m.仿真中所有成像結(jié)果均為30次重構(gòu)圖像的疊加平均.拍頻Δνx,Δνy的取值對(duì)成像質(zhì)量的影響如圖5所示.圖中Δνy的取值范圍為5—106Hz,Δνx的取值范圍為10—1.25×106Hz,不同顏色的曲線具有固定的Δνy值.從圖5可以看出,當(dāng)Δνy取值固定時(shí),不同目標(biāo)的重構(gòu)圖像質(zhì)量均隨Δνx的增加而下降,該過(guò)程中X光產(chǎn)生的目標(biāo)頻譜相位誤差逐漸增大.當(dāng)Δνy同時(shí)增大后,Y光產(chǎn)生的目標(biāo)頻譜相位誤差增加使得成像質(zhì)量進(jìn)一步下降,如圖5中縱向分布的不同顏色曲線所示,部分成像結(jié)果如圖6所示.圖6中Δνy固定取值為2 kHz,Δνx增大后目標(biāo)細(xì)節(jié)逐漸變得模糊,最終無(wú)法識(shí)別.仿真結(jié)果表明為獲得較高質(zhì)量的圖像,應(yīng)盡量選用較小的拍頻.

3.2 目標(biāo)縱深分布對(duì)成像結(jié)果的影響

上述仿真將目標(biāo)簡(jiǎn)化為僅有兩種深度,但真實(shí)目標(biāo)一般由多個(gè)具有不同深度的面元構(gòu)成.為了推廣到一般情況,為同一目標(biāo)圖像賦予不同數(shù)目的面元深度,驗(yàn)證目標(biāo)縱深分布對(duì)成像的影響.仍選用分辨率為128 pixel×128 pixel的三種衛(wèi)星灰度圖像作為目標(biāo),依次將目標(biāo)區(qū)域均勻分成2,4,9,16個(gè)小塊,每小塊賦予不同的縱深值,使小塊間深度呈連續(xù)梯度變化,最大縱深為10 m.設(shè)置兩組拍頻:一組取值為Δνx=500 Hz,Δνy=300 Hz;另一組拍頻為Δνx=500 kHz,Δνy=300 kHz.其余成像仿真參數(shù)與3.1節(jié)相同,重構(gòu)結(jié)果如圖7所示.

圖6 Δνx取不同值時(shí)的重構(gòu)圖像及其Strehl比值Fig.6.Reconstructed target images and corresponding Strehl ratios at different Δνxvalues.

圖7 具有不同縱深分布的目標(biāo)的成像結(jié)果 (a)拍頻為300和500 Hz時(shí)目標(biāo)在不同縱深分布情況下的成像結(jié)果;(b)拍頻為300和500 kHz時(shí)目標(biāo)在不同縱深分布情況下的成像結(jié)果Fig.7.Reconstructed images of objects with different depth distributions:(a)Imaging results when beat frequencies are 300 and 500 Hz;(b)imaging results when beat frequencies are 300 and 500 kHz.

從圖7(a)成像結(jié)果看出,當(dāng)拍頻較小時(shí),目標(biāo)表面的不同縱深分布對(duì)成像質(zhì)量并無(wú)明顯影響,這是由于此時(shí)拍頻值遠(yuǎn)小于光速值,加之目標(biāo)縱深范圍有限,縱深變化對(duì)相位偏移量2dΔω/c的影響十分微弱.但當(dāng)拍頻值較大時(shí),對(duì)于最大縱深一定的目標(biāo),不同深度面元分塊數(shù)目越多,重構(gòu)圖像的Strehl值越大,如圖7(b)所示.根據(jù)目標(biāo)縱深對(duì)成像質(zhì)量影響的原理可知,縱深越大的面元產(chǎn)生的回波造成的頻譜相位偏移量越大,因此當(dāng)分塊數(shù)為2時(shí),有一半的回波信號(hào)存在最大相位偏移[21],導(dǎo)致頻譜畸變較為嚴(yán)重.隨著不同深度面元分塊數(shù)目的增多,目標(biāo)表面變得平滑,目標(biāo)上最大縱深面元所占比例逐漸變小,偏移量最大的回波對(duì)頻譜影響的權(quán)重也變小,成像質(zhì)量提升.綜上可知,使用SBI技術(shù)對(duì)縱深目標(biāo)成像時(shí)拍頻是影響成像質(zhì)量的主要因素,因此為獲得質(zhì)量較好的圖像,應(yīng)在保證信號(hào)能夠順利解調(diào)和信噪比較高的前提下盡可能選取較小的拍頻.

4 結(jié) 論

本文研究了剪切光束成像技術(shù)對(duì)縱深目標(biāo)的成像原理,對(duì)成像公式進(jìn)行了推導(dǎo)和分析,發(fā)現(xiàn)實(shí)際目標(biāo)的反射回波信號(hào)間存在大量不同程度的相位偏移,使獲得的目標(biāo)頻譜相位與理想頻譜相位間存在偏差,這些相位偏移主要由激光拍頻決定.理論和仿真結(jié)果均表明,拍頻增大會(huì)導(dǎo)致成像質(zhì)量下降.因此在實(shí)際應(yīng)用中,為了對(duì)復(fù)雜縱深目標(biāo)重構(gòu)得到質(zhì)量較好的圖像,需根據(jù)探測(cè)器的性能,在信噪比最佳的響應(yīng)頻段內(nèi)選擇盡可能小的拍頻.同時(shí),拍頻設(shè)計(jì)應(yīng)避開(kāi)探測(cè)器的低頻噪聲,即拍頻設(shè)計(jì)的下限定量分析需結(jié)合探測(cè)器實(shí)際參數(shù)進(jìn)行進(jìn)一步研究與論證.

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Sheared-beam imaging of object with depth information

Lan Fu-Yang1)2)?Luo Xiu-Juan1)Chen Ming-Lai1)Zhang Yu1)Liu Hui1)

1)(Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi’an 710119,China)
2)(University of Chinese Academy of Sciences,Beijing 100049,China)

3 March 2017;revised manuscript

15 May 2017)

Sheared-beam imaging technique is a non-conventional imaging method which can be used to image remote objects through atmospheric turbulence without needing any adaptive optics.In this imaging technique,the target is coherently illuminated by three laser beams which are laterally sheared at the transmitter plane and arranged into an L shape.In addition,each beam is modulated by a slight frequency shift.The speckle intensity signals scattered from the target are received by a detector array,and then the image of target can be reconstructed by computer algorithm.By far,most of studies in this fi eld have focused on two-dimensional imaging.In real conditions,however,the surface of targets we are concerned about reveals that different depths introduce various phase delays in the scattering signal from target.This delay causes the phase-shift errors to appear between the ideal target Fourier spectrum and the Fourier spectrum received by detector array.Finally,this would result in poor image quality and low resolution.In this study,a three-dimensional target imaging model is established based on the two-dimensional target imaging model.The in fl uence of modulated beat frequency between sheared beam and reference beam is studied on the objects with depth information,and the result shows that large beat frequency may have an adverse e ff ect on reconstructed images.The simulation we have developed for this three-dimensional imaging model uses three targets with different shapes.Each target is divided into several sub-blocks,and we set different depth values(within 10 m)for these blocks.Then beat frequencies are increased from 5 Hz to about 1 MHz,respectively.At each pair of frequencies,the reconstructed image is recorded.Strehl ratio is used as the measure of the imaging quality.Computer simulation results show that the Strehl ratio of reconstructed images descends with the increase of beat frequency,which is fully consistent with the theory of three-dimensional target imaging proposed before.Meanwhile,we fi nd that the depth distribution of target also has an e ff ect on imaging quality.As for actual space targets,the maximum depth is usually not more than 10 m.Compared with the in fl uence caused by beat frequencies,the e ff ect produced by depth distribution is negligible.Therefore when a space target is imaged,beat frequencies play the major role in reconstructing high-quality image.The results presented in this paper indicate that in order to achieve better imaging quality in the practical application,it is necessary to select the smallest beat frequency according to the detector performance and keep the candidate frequencies away from the low-frequency noise of the detector.

sheared-beam imaging,speckle imaging,depth of target,phase delay

(2017年3月3日收到;2017年5月15日收到修改稿)

10.7498/aps.66.204202

?通信作者.E-mail:lanfuyang@opt.cn

?2017中國(guó)物理學(xué)會(huì)Chinese Physical Society

http://wulixb.iphy.ac.cn

PACS:42.25.Fx,42.30.–d,42.30.KqDOI:10.7498/aps.66.204202

?Corresponding author.E-mail:lanfuyang@opt.cn