四光束剪切相干成像目標(biāo)重構(gòu)算法研究

陸長(zhǎng)明陳明徠羅秀娟張羽劉輝蘭富洋2)曹蓓

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)

3)(北京跟蹤與通信技術(shù)研究所,北京 100049)

四光束剪切相干成像目標(biāo)重構(gòu)算法研究

陸長(zhǎng)明1)2)3)陳明徠1)?羅秀娟1)張羽1)劉輝1)蘭富洋1)2)曹蓓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)

3)(北京跟蹤與通信技術(shù)研究所,北京 100049)

(2016年12月12日收到;2017年3月17日收到修改稿)

針對(duì)傳統(tǒng)剪切光束成像技術(shù)的準(zhǔn)實(shí)時(shí)性問題,提出用口字形排布的四束光代替?zhèn)鹘y(tǒng)L形三束剪切光照射目標(biāo),研究了四光束剪切相干成像目標(biāo)重構(gòu)算法.只需單次測(cè)量就能同時(shí)重構(gòu)出四幅目標(biāo)圖像,減少了用于降低散斑噪聲、獲取高質(zhì)量圖像所需的測(cè)量次數(shù),同時(shí)大大減少了多組發(fā)射時(shí)的光束切換次數(shù),提高了成像效率.在算法實(shí)現(xiàn)中,通過最小二乘法恢復(fù)出四組波前相位,利用散斑幅值的簡(jiǎn)單代數(shù)運(yùn)算恢復(fù)波前幅值,從而重構(gòu)出目標(biāo)圖像.仿真結(jié)果表明,與傳統(tǒng)方法相比,在圖像質(zhì)量相同的前提下,本文方法所需的數(shù)據(jù)采集時(shí)間減少了至少1/2,不但提高了目標(biāo)重構(gòu)效率,還可為遠(yuǎn)程運(yùn)動(dòng)目標(biāo)的成像識(shí)別提供更好的手段.

剪切相干成像,四光束,目標(biāo)重構(gòu),成像效率

1 引言

剪切光束成像技術(shù)是一種非傳統(tǒng)相干無透鏡成像技術(shù),利用被測(cè)目標(biāo)返回光束的散斑場(chǎng)進(jìn)行計(jì)算成像,在技術(shù)機(jī)理上能最大限度地克服大氣湍流等擾動(dòng)介質(zhì)對(duì)成像分辨率的影響,可實(shí)現(xiàn)對(duì)遠(yuǎn)距離目標(biāo)的高分辨率成像.該技術(shù)在遠(yuǎn)程暗弱目標(biāo)監(jiān)視、地形地貌觀測(cè)、石油勘探及天文觀測(cè)等領(lǐng)域有潛在的應(yīng)用前景[1?3].

傳統(tǒng)的剪切光束成像系統(tǒng)采用振幅干涉測(cè)量方法,用三束在發(fā)射平面以L形排列的橫向剪切同源激光同時(shí)照射目標(biāo)[4?14],三束激光的光頻率稍有變化,但波前幾乎相同,在目標(biāo)上形成三個(gè)不同頻差的拍頻信號(hào).用探測(cè)器陣列接收從目標(biāo)散射回來的調(diào)制光,獲得散斑強(qiáng)度和相位差信息,進(jìn)而計(jì)算重構(gòu)出一幅目標(biāo)圖像.將一系列這樣的圖像進(jìn)行平均,即可得到一幅質(zhì)量較好的圖像.要進(jìn)一步抑制大氣湍流對(duì)成像的影響,需發(fā)射多組三束相干光照射目標(biāo)[11],光束切換次數(shù)也會(huì)相應(yīng)增多.

本文改進(jìn)了傳統(tǒng)剪切光束成像技術(shù),提出四光束剪切相干成像方法.同時(shí)發(fā)射四束以口字形排布的激光照射目標(biāo),等同于同時(shí)發(fā)射四組三光束激光對(duì)目標(biāo)成像,不但提高了成像效率,而且達(dá)到單次多組發(fā)射的目的,減小了大氣湍流在最終成像中的影響.利用快速傅里葉變換(FFT)提取四組散斑相位差和幅值,通過迭代算法恢復(fù)目標(biāo)頻譜,重構(gòu)目標(biāo)圖像.最后利用仿真驗(yàn)證了提出的四光束圖像重構(gòu)算法的有效性.

2 四光束剪切相干成像理論

圖1為四光束剪切相干成像系統(tǒng)示意圖,發(fā)射四束空間位置、頻率互不相同的口字形激光束照射目標(biāo),產(chǎn)生四個(gè)形狀相同且相互之間具有一定剪切量的散斑場(chǎng),并利用探測(cè)器陣列接收拍頻回波信號(hào).利用FFT提取散斑相位差和強(qiáng)度,重構(gòu)四組波前,通過傅里葉逆變換重構(gòu)四幅目標(biāo)圖像.

圖1 四光束成像系統(tǒng)示意圖Fig.1.Schematic of the four-beam imaging system.

發(fā)射平面與目標(biāo)平面的幾何關(guān)系如圖2所示,四束激光照射目標(biāo)發(fā)生漫反射產(chǎn)生的散斑場(chǎng)在接收平面的分布為[5]

(1)式中的四個(gè)散斑場(chǎng)發(fā)生干涉產(chǎn)生的拍頻信號(hào)強(qiáng)度分布為

圖2 發(fā)射平面與目標(biāo)平面的幾何關(guān)系Fig.2.Geometric relationship between transmitter plane and target plane.

由(2)式可知,波前A0(u,v)和?(u,v)隱含在散斑拍頻信號(hào)中,通過求解四組散斑相位差——??01和??03,??01和??12,??12和??23,??03和??23——可恢復(fù)四幅目標(biāo)散斑圖.

剪切相干成像的空間分辨率取決于探測(cè)器接收陣列最大間距D,可表示為λR/D.當(dāng)目標(biāo)尺寸為Dobj,探測(cè)器間距應(yīng)滿足的約束條件,接收陣列單向維數(shù)m應(yīng)滿足m>D/d[15].

傳統(tǒng)剪切光束成像技術(shù)發(fā)射三束光(圖1中的激光0,1,3),產(chǎn)生三個(gè)散斑場(chǎng),單次測(cè)量只能重構(gòu)一幅目標(biāo)散斑圖像[4?14].本文所述方法發(fā)射四束光,可排列組合成四組散斑場(chǎng)(三光束為一組),等同于同時(shí)發(fā)射四組傳統(tǒng)三光束激光(圖1中的激光0,1,3;0,1,2;1,2,3;0,2,3)對(duì)目標(biāo)成像.單次測(cè)量數(shù)據(jù)可同時(shí)重構(gòu)出四幅目標(biāo)散斑圖像.為獲得一幅高質(zhì)量圖像,通常需將一系列這樣的散斑圖像進(jìn)行平均.因此,與傳統(tǒng)方法相比,四光束方法所需的測(cè)量次數(shù)更少,數(shù)據(jù)采集時(shí)間更短.此外,為進(jìn)一步克服大氣湍流對(duì)成像的影響,傳統(tǒng)方法用12組三光束的不同組合方法照射目標(biāo)(圖3)[11],本文方法只需三組不同四光束組合發(fā)射方式就能達(dá)到相同的湍流效應(yīng)抑制效果(圖4),大大減少了光束切換次數(shù),進(jìn)一步縮短了數(shù)據(jù)采集時(shí)間,提高了成像速度.

圖3 傳統(tǒng)三光束算法光束照明方式Fig.3.The manner of illumination for traditional three-beam algorithm.

圖4 四光束算法光束照明方式Fig.4.The manner of illumination for four-beam algorithm.

3 四光束圖像復(fù)原算法

回波信號(hào)數(shù)據(jù)預(yù)處理、波前相位重構(gòu)和幅值復(fù)原是研究算法的三個(gè)關(guān)鍵要素.首先對(duì)拍頻信號(hào)進(jìn)行預(yù)處理,設(shè)置置信區(qū)間對(duì)信號(hào)進(jìn)行頻域?yàn)V波,準(zhǔn)確提取主譜線處的散斑相位差和幅值.運(yùn)用最小二乘法推導(dǎo)波前相位求解公式并采用高斯賽德爾(Gauss-Seidel)松弛法進(jìn)行迭代求解進(jìn)而復(fù)原波前相位;利用復(fù)原出的波前相位和幅值重構(gòu)目標(biāo)圖像.對(duì)多幅圖像進(jìn)行平均處理,可得目標(biāo)清晰圖像.

3.1 波前相位恢復(fù)

由(2)式的散斑相位差??01和??03,可得波前相位相鄰點(diǎn)之間的關(guān)系為

根據(jù)最小二乘法[16,17],將求解?(xi,yj)的問題轉(zhuǎn)化為如下優(yōu)化問題:

求(4)式關(guān)于?(xi,yj)的偏導(dǎo)數(shù),并令其等于0,整理可得波前相位的求解公式為[18,19]

同理,由??01和??12可得

由??12和??23可得

由??03和??23可得

根據(jù)(5)—(8)式,利用Gauss-Seidel數(shù)值計(jì)算方法可復(fù)原出四幅相位頻譜面.

3.2 波前幅值恢復(fù)

通過散斑幅值的代數(shù)運(yùn)算可得波前幅值,令

由此可得波前幅值為

結(jié)合上述求得的A0(x,y)和?(x,y),通過(10)式,即傅里葉逆變換[20,21]可重構(gòu)四幅目標(biāo)圖像:

上述圖像重構(gòu)算法與傳統(tǒng)三光束方法類似,復(fù)雜度并未提高.

4 仿真驗(yàn)證

利用仿真驗(yàn)證四光束成像方法的有效性,并利用斯特列爾比(Strehl ratio)評(píng)價(jià)重構(gòu)圖像質(zhì)量,具體計(jì)算公式為[20]

式中OT(x,y)為無誤差重建圖像的強(qiáng)度分布,OR(x,y)為有誤差重建圖像的強(qiáng)度分布,*表示共軛.斯特列爾比越接近1,重建圖像與目標(biāo)圖像越相似,圖像質(zhì)量越好.

仿真參數(shù)設(shè)為:激光波長(zhǎng)λ為532 nm,采樣頻率為4200 Hz,采樣點(diǎn)數(shù)為8400.四束光之間的頻率差分別為10,20,30,40,50,70 Hz,目標(biāo)大小為4 m×4 m,剪切量sx,sy均為0.1 m,成像距離R為1000 km,接收陣列維數(shù)為82×82.頻率置信區(qū)間設(shè)為8—12 Hz,18—22 Hz,28—32 Hz,38—42 Hz,48—52 Hz和68—72 Hz,對(duì)回波信號(hào)進(jìn)行頻域?yàn)V波.利用測(cè)量次數(shù)、光束切換次數(shù)和圖像重構(gòu)算法處理時(shí)間衡量成像速度,對(duì)四光束和傳統(tǒng)三光束方法的成像效率進(jìn)行驗(yàn)證.

圖510 次測(cè)量重構(gòu)圖像(a)原始圖像;(b)四光束算法;(c)傳統(tǒng)三光束算法Fig.5.Reconstructed images via 10 measurements:(a)Original target image;(b)four-beam algorithm;(c)traditional three-beam algorithm.

表1 四光束與傳統(tǒng)算法數(shù)據(jù)采集次數(shù)比較Table 1.Comparison of data acquisition amount between four-beam and conventional algorithms.

1)測(cè)量次數(shù)相同時(shí)的成像效果

四光束和傳統(tǒng)方法10次測(cè)量數(shù)據(jù)平均后的成像結(jié)果分別如圖5(b)和圖5(c)所示,斯特列爾比分別為0.8348和0.8025.當(dāng)測(cè)量次數(shù)相同時(shí),四光束算法的重構(gòu)圖像質(zhì)量比傳統(tǒng)算法好,散斑噪聲明顯降低.

2)重構(gòu)圖像斯特列爾比相同時(shí)的成像效率

在圖像質(zhì)量相同時(shí),對(duì)四光束與傳統(tǒng)算法數(shù)據(jù)采集次數(shù)進(jìn)行比較,結(jié)果如表1所示.可以看出,傳統(tǒng)方法的測(cè)量次數(shù)至少是四光束方法的2—3倍.因此,四光束剪切相干成像技術(shù)的數(shù)據(jù)采集速度至少為傳統(tǒng)方法的兩倍以上.其中,斯特列爾比為0.835和0.854的重構(gòu)圖像分別如圖6和圖7所示.

圖6 重構(gòu)圖像(斯特列爾比為0.835)(a)四光束算法;(b)傳統(tǒng)三光束算法Fig.6.Reconstructed images(Strehl ratio is 0.835):(a)Four-beam algorithm;(b)traditional three-beam algorithm.

圖7 重構(gòu)圖像(斯特列爾比為0.854)(a)四光束算法;(b)傳統(tǒng)三光束算法Fig.7.Reconstructed images(Strehl ratio is 0.854):(a)Four-beam algorithm;(b)traditional three-beam algorithm.

仿真過程中同時(shí)對(duì)算法處理時(shí)間進(jìn)行統(tǒng)計(jì).對(duì)于單次測(cè)量,傳統(tǒng)三光束平均處理時(shí)間約為四光束算法的1/2.根據(jù)前述仿真結(jié)果,傳統(tǒng)方法的測(cè)量次數(shù)至少是四光束方法的2—3倍.綜合兩方面因素可知,四光束算法的處理時(shí)間不超過傳統(tǒng)算法.

此外,四光束算法還減少了克服大氣湍流所需的光束切換次數(shù),進(jìn)一步縮短了數(shù)據(jù)采集時(shí)間.

綜上,四光束剪切相干成像技術(shù)的成像效率優(yōu)于三光束方法.

雖然本文方法的硬件成本略高,比傳統(tǒng)方法多了一路小孔徑激光發(fā)射裝置,但是其數(shù)據(jù)采集時(shí)間卻為傳統(tǒng)方法的1/2,成像效率更高,對(duì)遠(yuǎn)程運(yùn)動(dòng)目標(biāo)的成像識(shí)別有顯著優(yōu)勢(shì),便于在短時(shí)間內(nèi)正確反映目標(biāo)姿態(tài)的變化.

5 結(jié)論

本文針對(duì)改進(jìn)的剪切光束成像技術(shù),進(jìn)行了成像理論公式推導(dǎo),提出了一種四光束剪切相干成像算法.通過最小二乘法和簡(jiǎn)單的代數(shù)運(yùn)算,單次測(cè)量能恢復(fù)四組波前相位和幅值,重構(gòu)四幅目標(biāo)圖像,減少了成像所需的數(shù)據(jù)測(cè)量次數(shù)和光束切換次數(shù).仿真結(jié)果表明,本文所提方法的數(shù)據(jù)采集時(shí)間比傳統(tǒng)方法減少了至少1/2,成像效率更高,更適合對(duì)遠(yuǎn)程運(yùn)動(dòng)目標(biāo)的成像識(shí)別.

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PACS:42.25.Fx,42.30.Rx,42.30.KqDOI:10.7498/aps.66.114201

Target reconstruction algorithm for four-beam sheared coherent imaging

Lu Chang-Ming1)2)3)Chen Ming-Lai1)?Luo Xiu-Juan1)Zhang Yu1)Liu Hui1)Lan Fu-Yang1)2)Cao Bei1)
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)(Beijing Institute of Tracking and Telecommunications Technology,Beijing 100049,China)

12 December 2016;revised manuscript

17 March 2017)

Sheared-beam imaging,which is a nonconventional coherent laser imaging technique,can be used to better solve the problem of taking pictures with high resolution for remote targets through turbulent medium than conventional optical methods.In the previous research on this technique,a target was illuminated by three coherent laser beams that were laterally arranged at the transmitter plane into an L pattern.In order to obtain a high quality image,a series of time-varying scattered signals is collected to reconstruct speckled images of the same object.To overcome atmospheric turbulence,multiple sets of three-beam laser should be emitted,which increases data acquisition time.

In this paper,aiming at the quasi real-time problem of conventional sheared beam imaging technique,we use four-beam laser with rectangular distribution instead of the traditional L type sheared three-beam laser to illuminate the target.According to this,we propose a target reconstruction algorithm for four-beam sheared coherent imaging to reconstruct four target images simultaneously in one measurement,which can acquire high quality images by reducing the amount of measurement and the speckle noise.Meanwhile,it can greatly reduce the amount of beam switching in multi-group emission and improve the imaging efficiency.Firstly,the principle of the four-beam sheared coherent imaging technique is deduced.Secondly,in the algorithm,the speckle amplitude and phase di ff erence frames can be extracted accurately by searching for the accurate positions of the beat frequency components.Based on the speckle phase di ff erence frames,four sets of wavefront phases can be demodulated by the least squares method,and wavefront amplitude can be obtained by algebraic operation of speckle amplitude.The reconstructed wavefront is used for inverse Fourier transform to yield a two-dimensional image.A series of speckled images is averaged to form an incoherent image.Finally,the validity of the proposed technique is veri fi ed by simulations.From the simulation results,the image quality of the proposed method is better than that of the traditional method in the same amount of measurement.Furthermore,on the premise of the same image quality,the data acquisition amount of the proposed method is 2-3 times as large as that of the traditional method.In other words,compared with that of the traditional method,the data acquisition time of the proposed method is reduced at least by half and the algorithm processing time is less.It can be concluded that the proposed imaging technique can not only improve the efficiency of target reconstruction,but also present a better way of imaging the remote moving targets.

sheared coherent imaging,four-beam,target reconstruction,imaging efficiency

10.7498/aps.66.114201

?通信作者.E-mail:shuxuemlchen@163.com

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

http://wulixb.iphy.ac.cn

?Corresponding author.E-mail:shuxuemlchen@163.com