陳明徠 羅秀娟 張羽 蘭富洋 劉輝 曹蓓 夏愛利

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

基于全相位譜分析的剪切光束成像目標(biāo)重構(gòu)?

陳明徠?羅秀娟 張羽 蘭富洋 劉輝 曹蓓 夏愛利

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

(2016年8月1日收到;2016年10月28日收到修改稿)

剪切光束成像技術(shù)是一種非傳統(tǒng)散斑成像技術(shù),能透過(guò)擾動(dòng)介質(zhì)對(duì)遠(yuǎn)距離目標(biāo)進(jìn)行高分辨率成像.本文提出了一種基于全相位譜分析的圖像重構(gòu)算法,利用全相位譜分析對(duì)回波信號(hào)數(shù)據(jù)進(jìn)行預(yù)處理,可有效抑制頻譜泄露,校正散斑頻譜,消除多種因素引起的頻率漂移誤差,得到準(zhǔn)確的散斑強(qiáng)度和相位差,提高實(shí)際成像環(huán)境的系統(tǒng)成像能力.仿真結(jié)果表明：該圖像重構(gòu)算法有效抑制了頻率漂移對(duì)成像質(zhì)量的影響,當(dāng)信號(hào)存在頻率誤差時(shí),其成像效果大大優(yōu)于基于傳統(tǒng)傅里葉變換譜分析的重構(gòu)算法.

剪切光束成像,散斑,全相位譜分析,目標(biāo)重構(gòu)

1 引 言

剪切光束成像技術(shù)[1,2]是一種新型相干照明主動(dòng)成像技術(shù),用三束經(jīng)頻率調(diào)制的同源激光以橫向剪切方式照射目標(biāo),再利用被測(cè)目標(biāo)返回光束的散斑場(chǎng)進(jìn)行計(jì)算成像,能克服大氣湍流擾動(dòng)和快速運(yùn)動(dòng)目標(biāo)多普勒頻移對(duì)成像的影響,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.在探潛、地形地貌觀測(cè)、天文觀測(cè)、醫(yī)學(xué)成像以及遠(yuǎn)程運(yùn)動(dòng)目標(biāo)監(jiān)視與跟蹤等領(lǐng)域有巨大的應(yīng)用潛力[3,4].

針對(duì)剪切光束成像技術(shù),Hutchin[5]提出了成像概念和波前恢復(fù)的方法,并闡述了消除大氣畸變的機(jī)理;Voelz等[6]用仿真和室內(nèi)實(shí)驗(yàn)對(duì)成像原理進(jìn)行了可行性驗(yàn)證,用基于Knox-Thompson的指數(shù)重建算法重構(gòu)出了目標(biāo)圖像;此后,Stahl等[7]研究了一種新的圖像重構(gòu)算法,解決了由于缺少目標(biāo)先驗(yàn)信息很難重構(gòu)圖像的問(wèn)題;Olson等[8]對(duì)兩種波前重構(gòu)算法進(jìn)行了比較,分析了兩種方法的優(yōu)劣,推動(dòng)了對(duì)原有圖像重構(gòu)算法的分析與改進(jìn).目前,剪切光束成像技術(shù)主要采用“復(fù)合指數(shù)重建算法”來(lái)處理整個(gè)散斑場(chǎng)和重構(gòu)目標(biāo)圖像[1].總之,上述算法均采用傳統(tǒng)傅里葉變換(FFT)譜分析對(duì)信號(hào)進(jìn)行處理,沒有考慮回波信號(hào)中頻率漂移誤差對(duì)成像質(zhì)量的影響.

事實(shí)上,目標(biāo)回波信號(hào)的實(shí)際頻率會(huì)受到大氣湍流擾動(dòng)、移頻器的移頻誤差以及目標(biāo)快速運(yùn)動(dòng)等多種因素的影響而出現(xiàn)漂移,使得解調(diào)后的相位數(shù)據(jù)產(chǎn)生誤差,從而直接影響目標(biāo)圖像的重構(gòu)質(zhì)量.傳統(tǒng)FFT譜分析存在譜泄露的缺陷,嚴(yán)重影響了譜分析的性能[9],無(wú)法準(zhǔn)確提取回波信號(hào)的頻譜.而基于全相位FFT(all-phase FFT,apFFT)譜分析[9-12]的信號(hào)處理技術(shù),具有“相位不變”的良好性質(zhì),具有更優(yōu)良的抑制譜泄露的性能,能更好地抑制頻率誤差對(duì)成像質(zhì)量的影響[12,13].因此,本文針對(duì)剪切光束成像技術(shù),提出基于全相位譜分析的目標(biāo)重構(gòu)算法.對(duì)回波信號(hào)進(jìn)行全相位處理,提取散斑頻譜.采用最小二乘法推導(dǎo)波前相位的方程,用高斯-賽德爾法進(jìn)行迭代計(jì)算,并通過(guò)散斑幅值之間的代數(shù)運(yùn)算得到波前幅值.這種方法不依賴于回波信號(hào)拍頻的精確估計(jì),即使頻率發(fā)生漂移,也能對(duì)目標(biāo)清晰成像,有效地抑制了頻率漂移對(duì)重構(gòu)圖像質(zhì)量的影響.

2 剪切光束主動(dòng)成像原理

圖1為剪切光束成像原理示意圖,發(fā)射三束具有一定剪切量的“L”形、頻率有微小差別的激光照明目標(biāo)產(chǎn)生三個(gè)相同的散斑場(chǎng),并在探測(cè)器陣列表面發(fā)生干涉形成拍頻信號(hào),最終由探測(cè)器陣列接收,實(shí)現(xiàn)了將目標(biāo)的空間頻率信息在時(shí)域上編碼[5,6,14,15].利用FFT提取每個(gè)探測(cè)器單元的回波信號(hào)拍頻處散斑的振幅和相位差,從而恢復(fù)目標(biāo)整個(gè)頻譜面,通過(guò)傅里葉逆變換可重構(gòu)目標(biāo)圖像,對(duì)多幅圖像平均處理,得到目標(biāo)清晰圖像.

由于返回的三個(gè)散斑場(chǎng)透過(guò)大氣湍流時(shí)經(jīng)過(guò)相同路徑到達(dá)探測(cè)器陣列,產(chǎn)生相同的相位畸變,散斑場(chǎng)之間的相位差不變,剪切光束成像技術(shù)利用雙向剪切照明、光瞳面相位差測(cè)量和時(shí)域信息編碼等方法,在技術(shù)機(jī)理上可最大限度克服大氣湍流擾動(dòng)對(duì)成像質(zhì)量的影響[5].

圖1 剪切光束成像原理示意圖Fig.1.Schematic of sheared-beam imaging principle.

根據(jù)夫瑯禾費(fèi)衍射原理,O光、X光和Y光照射目標(biāo)通過(guò)漫反射產(chǎn)生的散斑場(chǎng)分別為[6]：

其中u=x/(λR),v=y/(λR).λ為激光波長(zhǎng),R為成像距離,sx,sy分別為O光與X光、Y光之間的剪切量.Ei,ωi(i=0,1,2)分別為O,X,Y光的振幅、角頻率.A0(u,v)為波前幅值,φ(u,v)為波前相位.

三個(gè)散斑場(chǎng)在探測(cè)器陣列表面發(fā)生干涉產(chǎn)生的拍頻信號(hào)強(qiáng)度分布為

圖2 全相位FFT譜分析圖像重構(gòu)算法實(shí)現(xiàn)框圖Fig.2.Schematic diagram of image reconstruction algorithm based on apFFT.

由(2)式可知,波前振幅A0(u,v)和相位φ(u,v)隱含在回波信號(hào)I(x,y,t)中,以往算法通過(guò)傳統(tǒng)FFT直接提取.然而,當(dāng)頻率發(fā)生漂移時(shí),即頻差Δωi(i=1,2,3)不準(zhǔn)確時(shí),使用FFT譜分析方法會(huì)發(fā)生數(shù)據(jù)截?cái)嘈?yīng),引起頻譜泄露,提取的波前相位不準(zhǔn)確,影響了圖像重構(gòu)質(zhì)量.本文采用全相位譜分析的目標(biāo)重構(gòu)算法解決該問(wèn)題.

3 基于全相位譜分析的目標(biāo)重構(gòu)算法

算法實(shí)現(xiàn)框圖如圖2所示.當(dāng)回波信號(hào)頻率存在漂移時(shí),較傳統(tǒng)FFT,基于全相位FFT的數(shù)據(jù)預(yù)處理方法能抑制各頻率因數(shù)據(jù)截?cái)喽斐傻呐宰V泄露,使譜間干擾減小,可準(zhǔn)確搜索主譜線位置,精確估計(jì)散斑相位差和幅值,從而恢復(fù)高質(zhì)量波前,通過(guò)傅里葉逆變換重構(gòu)目標(biāo)圖像,這種方法有效抑制了頻率漂移對(duì)重構(gòu)圖像質(zhì)量的影響.

3.1 全相位數(shù)據(jù)預(yù)處理

對(duì)于測(cè)量數(shù)據(jù)為包含(2N-1)個(gè)元素的數(shù)據(jù)向量,全相位處理就是完成從長(zhǎng)度為(2N-1)的數(shù)據(jù)向量到長(zhǎng)度為N的數(shù)據(jù)向量的映射[9].對(duì)于如下數(shù)據(jù)向量

其預(yù)處理過(guò)程分為如下步驟：

1)對(duì)上述向量進(jìn)行如下周期延拓

2)對(duì)上述周期延拓之后的序列進(jìn)行豎直方向的求和形成新的周期序列,可得全相位數(shù)據(jù)向量

假設(shè)探測(cè)器陣列維數(shù)為L(zhǎng)×M,用上述預(yù)處理方法,對(duì)每個(gè)探測(cè)器接收到的時(shí)域數(shù)據(jù)進(jìn)行全相位預(yù)處理,得到向量然后分別進(jìn)行N階傅里葉變換,可得全相位FFT輸出,從而解調(diào)出散斑相位差和幅值[16].

3.2 波前相位

已知探測(cè)器陣列維數(shù)為L(zhǎng)×M,則由(2)式可得：

利用最小二乘法[17],求解φ(xi,yj)的問(wèn)題可轉(zhuǎn)化為如下優(yōu)化問(wèn)題：

求上式關(guān)于φ(xi,yj)的偏導(dǎo)數(shù),并令其等于0,通過(guò)整理可得[18]

根據(jù)(4)式,利用Gauss-Seidel數(shù)值計(jì)算方法可求解相位頻譜面.

3.3 波前振幅

通過(guò)多幅重構(gòu)圖像平均處理,可得目標(biāo)清晰圖像.

4 仿真驗(yàn)證

設(shè)置仿真參數(shù)：激光波長(zhǎng)為532 nm,三束光之間的頻率差分別為20,40和60 Hz,采樣頻率為1200 Hz,采樣點(diǎn)數(shù)為9600.剪切量sx,sy均為0.1 m,成像距離為1000 km,目標(biāo)大小為3.5 m,接收陣列維數(shù)為80×80.

當(dāng)回波信號(hào)不存在頻率漂移時(shí),基于apFFT譜分析和傳統(tǒng)FFT譜分析兩種重構(gòu)算法的成像結(jié)果如圖3所示(10幅圖像平均).由圖可知,兩種算法均能對(duì)目標(biāo)進(jìn)行成像,圖像質(zhì)量相同.

移頻器的移頻誤差、大氣湍流擾動(dòng)和運(yùn)動(dòng)目標(biāo)的多普勒效應(yīng)等因素都會(huì)引起頻率漂移,這些誤差中,既有固定誤差也有隨機(jī)誤差.一般漂移誤差在最大頻差的5%以內(nèi),給三束光的頻率都設(shè)定0-3 Hz的隨機(jī)誤差,為搜索主譜線位置,利用拍頻信號(hào)與其他頻率信號(hào)的幅值差異性搜索主譜線位置.使用傳統(tǒng)FFT方法和本文提出的apFFT方法分別對(duì)圖3(a)目標(biāo)進(jìn)行五次成像,其對(duì)應(yīng)的成像結(jié)果如圖4和圖5所示,其中圖5(b)-圖5(e)為對(duì)10幅圖像進(jìn)行平均的結(jié)果,其他圖像為沒有平均的結(jié)果.可以看出,傳統(tǒng)方法無(wú)法抑制頻譜漂移誤差,不能重構(gòu)出目標(biāo)圖像;而本文方法五次均能對(duì)目標(biāo)成像.

因此,在回波信號(hào)存在頻率漂移時(shí),可采用本文提出的方法有效抑制頻率誤差對(duì)成像的影響.若想得到更高質(zhì)量的圖像,可對(duì)50-100幅圖像平均.

圖3 無(wú)頻率漂移時(shí)目標(biāo)重構(gòu)圖像 (a)原始圖像;(b)傳統(tǒng)FFT;(c)apFFTFig.3.The reconstructed images with no frequency error：(a)Original target image;(b)traditional FFT method;(c)apFFT method.

圖4 存在頻率漂移時(shí)傳統(tǒng)FFT方法重構(gòu)圖像Fig.4.The reconstructed images with frequency error based on traditional FFT method.

圖5 存在頻率漂移時(shí)apFFT方法重構(gòu)結(jié)果 (a)單幅散斑圖;(b)-(e)平均散斑圖Fig.5.The reconstructed images with frequency error based on apFFT method：(a)Single speckle image;(b)-(e)average speckle image.

5 結(jié) 論

本文提出了一種基于全相位譜分析的剪切光束成像技術(shù)目標(biāo)重構(gòu)算法,解決了傳統(tǒng)算法無(wú)法抑制頻率漂移對(duì)成像質(zhì)量的影響問(wèn)題.利用全相位譜分析對(duì)回波信號(hào)進(jìn)行預(yù)處理,更好地抑制了信號(hào)的頻譜泄露,準(zhǔn)確地提取散斑相位和幅值.采用最小二乘算法和高斯-賽德爾法恢復(fù)波前相位,并結(jié)合波前相位和幅值對(duì)目標(biāo)圖像進(jìn)行重構(gòu),并對(duì)多幅圖像平均處理得到清晰圖像.仿真驗(yàn)證了算法的有效性,較傳統(tǒng)FFT譜分析的方法,有更好的魯棒性.

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PACS:42.25.Fx,42.30.Kq,42.30.Rx DOI:10.7498/aps.66.024203

Sheared-beam imaging target reconstruction based on all-phase spectrum analysis?

Chen Ming-Lai?Luo Xiu-Juan Zhang Yu Lan Fu-Yang Liu HuiCao BeiXia Ai-Li
(Xi’an Institute of Optics and Precision Mechanics,Chinese Academy of Sciences,Xi’an 710119,China)

1 August 2016;revised manuscript

28 October 2016)

Sheared-beam imaging technique is considered to be a non-conventional speckle technique for remote imaging through turbulent medium.In this high resolution imaging technique,three beams are splitted from one laser source and illuminate a remote target simultaneously in shearing distribution.Each beam is modulated by a tiny frequency shift so that these beams can interfere and beat together.The returning speckle signals are received by an array of detectors.The primary algorithm for the signal processing and image reconstruction has been developed previously.However,the reconstructed image is deteriorated by the frequency drifting error and spectrum leakage.These frequency errors are always from the transmitter and scattered signals that are caused by spectrum-shift errors from acousticoptic modulators,atmospheric turbulence,Doppler effects of moving targets,etc.To solve the problems mentioned above,in this paper we propose a new image reconstruction algorithm based on the all-phase spectrum analysis theory.The all-phase fast Fourier transform(FFT)spectrum analysis theory,which can effectively inhibit spectral leakage and correct speckle spectrum,is used to process the scattered signals.By searching for the accurate positions of the beat frequency components in the transformed frequency domain data,the speckle amplitude and phase difference frames can be extracted accurately.Based on the speckle phase-difference frames,the phase distribution of the wavefront is derived by least-square algorithm.The phase distribution in grid is highly coherent,in which each point is related to the phases of its four nearest neighbors.If an initial phase map is given or preset,the phase map of the wavefront can be estimated accurately by Gauss-Seidel method.Meanwhile,the amplitude of wavefront is obtained by the algebraic operation of speckle amplitude frames.The reconstructed wavefront is inverse Fourier transformed to yield a two dimensional image.A series of speckled images of the same object are averaged to reduce the speckle noise.The proposed method improves the ability of system imaging in the actual imaging environment.Simulation experiments validate the effectiveness of the proposed algorithm,and simulation results show that the proposed image reconstruction algorithm can inhibit the frequency errors from influencing imaging quality when there exist frequency errors in scattered signals.Thus,the imaging quality of the algorithm based on the all-phase FFT method is much better than that of the algorithm based on the traditional FFT method.The substantial usage of this technique is widely spread after the reconstruction algorithm has been optimized.

sheared-beam imaging,speckle,all-phase spectrum analysis,target reconstruction

:42.25.Fx,42.30.Kq,42.30.Rx

10.7498/aps.66.024203

?國(guó)家自然科學(xué)基金(批準(zhǔn)號(hào)：61505248)資助的課題.

?通信作者.E-mail：shuxuemlchen@163.com

*Project supported by the National Natural Science Foundation of China(Grant No.61505248).

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