譜域光學(xué)相干層析系統(tǒng)的色散補(bǔ)償技術(shù)研究

姜盼秋，汪平河

譜域光學(xué)相干層析系統(tǒng)的色散補(bǔ)償技術(shù)研究

姜盼秋，汪平河*

電子科技大學(xué)光電科學(xué)與工程學(xué)院，電子薄膜與集成器件國(guó)家重點(diǎn)實(shí)驗(yàn)室，四川 成都 611731

對(duì)譜域光學(xué)相干層析系統(tǒng)(SD-OCT)采用色散補(bǔ)償方法進(jìn)行優(yōu)化，是提高系統(tǒng)成像質(zhì)量的重要方式。本文提出了一種基于數(shù)值多項(xiàng)式擬合的色散補(bǔ)償方法。該方法通過(guò)提取干涉信號(hào)的相位并解包裹，利用數(shù)值多項(xiàng)式對(duì)解包裹后的相位進(jìn)行擬合，然后根據(jù)擬合出的高階色散因子對(duì)干涉信號(hào)做相位補(bǔ)償。本文利用SD-OCT系統(tǒng)測(cè)量出不同光程差位置處的軸向分辨率和信噪比，通過(guò)比較分析色散補(bǔ)償前后系統(tǒng)的軸向分辨率及信噪比，來(lái)驗(yàn)證該方法的有效性和可靠性。結(jié)果表明，本文設(shè)計(jì)的色散補(bǔ)償技術(shù)可以使系統(tǒng)具有良好的軸向分辨率，三階多項(xiàng)式擬合相位的色散補(bǔ)償方法在約1.5 mm的成像深度范圍內(nèi)有明顯的優(yōu)化效果。

譜域光學(xué)相干層析系統(tǒng)；色散補(bǔ)償；分辨率；信噪比；成像質(zhì)量

1 引 言

光學(xué)相干層析(Optical coherence tomography，OCT)技術(shù)是一種重要的斷層成像技術(shù)，能夠?qū)ι锝M織和材料內(nèi)部微觀結(jié)構(gòu)進(jìn)行橫截面和三維成像，具有分辨率高、成像速度快、非接觸以及可實(shí)時(shí)成像等優(yōu)點(diǎn)[1-2]。OCT通過(guò)測(cè)量生物組織后向散射光的回波來(lái)檢測(cè)生物組織的斷層結(jié)構(gòu)，其軸向分辨率可以達(dá)到幾個(gè)微米[3-5]。早期的OCT系統(tǒng)采用時(shí)域探測(cè)的方式，通過(guò)參考臂平面鏡的軸向掃描實(shí)現(xiàn)對(duì)樣品深度信息的提取[6]。目前OCT成像通常在傅里葉域進(jìn)行檢測(cè)，與時(shí)域OCT相比，傅里葉域OCT的靈敏度和成像速度有了顯著提高，傅里葉域OCT(Fourier domain OCT，F(xiàn)D-OCT)分為譜域OCT(spectral domain OCT，SD-OCT)和掃頻OCT(swept source OCT，SS-OCT)[7-9]。

SD-OCT系統(tǒng)采用光譜儀和線陣相機(jī)測(cè)量干涉信號(hào)的光譜，并通過(guò)傅里葉變換重建深度信息。SD-OCT系統(tǒng)中導(dǎo)致靈敏度下降和成像質(zhì)量惡化的主要原因之一是色散[10]。光的傳播速度取決于材料的折射率。當(dāng)樣品臂和參考臂的光纖長(zhǎng)度不同時(shí)，會(huì)發(fā)生色散失配，此時(shí)系統(tǒng)的點(diǎn)擴(kuò)散函數(shù)(point spread function，PSF)不僅會(huì)展寬，而且其峰值強(qiáng)度也會(huì)降低[11]。色散補(bǔ)償是解決樣品臂與參考臂色散失配問(wèn)題的基礎(chǔ)。為了解決干涉儀兩臂之間色散失配導(dǎo)致的軸向分配率下降的問(wèn)題，許多基于硬件和軟件的色散補(bǔ)償方法被用于校正樣品臂和參考臂之間的色散失配[12-14]。基于硬件的色散補(bǔ)償方法可以同時(shí)對(duì)系統(tǒng)色散和樣品色散進(jìn)行矯正，只需要在干涉儀中的一個(gè)臂中添加補(bǔ)償材料，如色散棱鏡、光柵、光纖相位調(diào)制器等[15-16]。但是這些硬件補(bǔ)償方法補(bǔ)償程度較低，并且會(huì)提高系統(tǒng)的復(fù)雜度和成本?；谲浖纳⒀a(bǔ)償方法可矯正更高階的色散，如一種深度依賴的色散補(bǔ)償方法，基于相位校正信號(hào)的迭代調(diào)整來(lái)優(yōu)化圖像清晰度[17-19]。然而，基于迭代算法的數(shù)值補(bǔ)償方法計(jì)算量大，需要更多的計(jì)算時(shí)間。還可以通過(guò)去復(fù)共軛鏡像和解卷積等方法提高系統(tǒng)成像清晰度等[20-21]。本文提出了一種基于數(shù)值多項(xiàng)式擬合分析的方法來(lái)解決SD-OCT系統(tǒng)的色散問(wèn)題，通過(guò)消除樣品臂和參考臂之間色散失配引起的非線性相位項(xiàng)來(lái)實(shí)現(xiàn)色散補(bǔ)償，從而提升成像質(zhì)量。

2 理論推導(dǎo)

SD-OCT系統(tǒng)的軸向分辨率取決于光源的相干長(zhǎng)度，對(duì)于高斯型光源，系統(tǒng)的軸向分辨率可以表示為

在譜域光學(xué)相干層析成像技術(shù)中，光譜儀采集到的干涉信號(hào)光譜可以表示為

為了得到補(bǔ)償相位項(xiàng)()，在對(duì)波數(shù)空間進(jìn)行線性插值之后，頻譜通過(guò)傅里葉變換到波長(zhǎng)空間，在波長(zhǎng)空間移動(dòng)使得相干函數(shù)集中在原點(diǎn)。然后通過(guò)傅里葉逆變換得到波數(shù)空間的復(fù)數(shù)譜信號(hào)。相位項(xiàng)()等于虛部與實(shí)部比值的反正切函數(shù)。為了分析不同階次的擬合效果，對(duì)相位進(jìn)行了二階、三階和四階多項(xiàng)式擬合。為了計(jì)算出相位中的高階色散因子，采用多項(xiàng)式對(duì)相位進(jìn)行擬合，通過(guò)最小二乘法計(jì)算出多項(xiàng)式的系數(shù)。補(bǔ)償相位項(xiàng)()可以用相位補(bǔ)償方程表示：

調(diào)整系數(shù)–2以消除群速度色散不平衡，調(diào)整系數(shù)–3以消除三階色散不平衡。經(jīng)過(guò)色散補(bǔ)償后，利用快速傅里葉的逆變換將干涉信號(hào)從空間轉(zhuǎn)換到空間，得到點(diǎn)擴(kuò)展函數(shù)，點(diǎn)擴(kuò)展函數(shù)的半高寬對(duì)應(yīng)于SD-OCT軸向分辨率。

3 實(shí)驗(yàn)結(jié)果與討論分析

SD-OCT系統(tǒng)的示意圖如圖1所示。寬帶光源(D-840-HP SM fiber light source，Superlum)是由兩塊超輻射發(fā)光二極管(superluminescent diode，SLD)拼接而成，中心波長(zhǎng)為846 nm，帶寬為103.6 nm。寬帶光源發(fā)出的光首先經(jīng)過(guò)光隔離器，目的是防止光沿著光路返回進(jìn)入光源，對(duì)光源造成損傷。光纖耦合器使用中心波長(zhǎng)為850 nm，分光比為50: 50的寬帶耦合器。光束通過(guò)50/50光纖耦合器分別傳輸?shù)絽⒖急酆蜆悠繁?。參考臂由偏振控?PC)、準(zhǔn)直器、透鏡和反射鏡組成。樣品臂由偏振控制(PC)、準(zhǔn)直器、二維振鏡和透鏡組成，其中二維振鏡用于實(shí)現(xiàn)樣品的橫向掃描。樣品臂和參考臂返回的干涉信號(hào)由光譜儀接收。該光譜儀由光纖準(zhǔn)直器、中心波長(zhǎng)為840 nm的1200 線/mm透射光柵、焦距為150 mm的聚焦透鏡和線陣CCD組成。該線陣CCD相機(jī)(E2v，EV71YEM2CL2014-BA0)由2048個(gè)像素點(diǎn)組成，每個(gè)像素點(diǎn)的尺寸為14mm×14mm。CCD相機(jī)采用的A掃描頻率為5 kHz。最后通過(guò)圖像采集卡將數(shù)據(jù)傳輸?shù)接?jì)算機(jī)。數(shù)據(jù)處理由VC++和MATLAB編程實(shí)現(xiàn)。

圖1 SD-OCT系統(tǒng)示意圖

寬帶光源的半高寬103.6 nm，中心波長(zhǎng)為846 nm。相應(yīng)的理論軸向分辨率約為3.05 μm。然而，由于光譜的形狀不是高斯分布的，因此采用光譜整形的方法來(lái)優(yōu)化圖像質(zhì)量，導(dǎo)致測(cè)量的軸向分辨率降低。在樣品臂中放置一個(gè)反射鏡，每隔100mm在～1.5 mm的成像深度內(nèi)測(cè)量點(diǎn)擴(kuò)散函數(shù)。SD-OCT系統(tǒng)靈敏度的下降如圖2所示，SD-OCT系統(tǒng)未進(jìn)行色散補(bǔ)償時(shí)，在零光程差附近色散失配較小，點(diǎn)擴(kuò)散函數(shù)沒有明顯展寬，軸向分辨率較高。隨著光程差增大，色散失配變大，對(duì)應(yīng)的點(diǎn)擴(kuò)散函數(shù)脈寬增加且峰值強(qiáng)度降低，軸向分辨率顯著下降。

3.1 相位信息

用2048像素的線陣CCD相機(jī)可以采集到干涉信號(hào)。在樣品臂中放置一個(gè)反射鏡，并將光程差調(diào)整為0.32 mm。色散補(bǔ)償過(guò)程如圖3所示，去除自相關(guān)項(xiàng)和直流項(xiàng)，干涉光譜如圖3(a)所示。通過(guò)對(duì)干涉譜進(jìn)行Hilbert變換，利用復(fù)數(shù)干涉信號(hào)的虛部項(xiàng)除以實(shí)部項(xiàng)，再通過(guò)反正切函數(shù)解析干涉信號(hào)的相位信息。圖3(b)顯示了以單個(gè)反射鏡為樣本的波數(shù)空間中作為函數(shù)的相位項(xiàng)。相移限制在-π～π范圍內(nèi)，解包裹的相位信息如圖3(c)所示，解包裹后的相位與真實(shí)相位之間相差一個(gè)2π整數(shù)倍的初相位，這個(gè)初相位可以不用考慮，因?yàn)閮杀坶g的光程差只與相位曲線的斜率有關(guān)，曲線的斜率與兩臂間的光程差成正比。如果不進(jìn)行色散補(bǔ)償，相位中高階色散項(xiàng)的存在會(huì)使系統(tǒng)點(diǎn)擴(kuò)散函數(shù)發(fā)生展寬，降低系統(tǒng)的軸向分辨率。色散補(bǔ)償需要對(duì)相位中的高階項(xiàng)進(jìn)行補(bǔ)償，通過(guò)計(jì)算出相位中的高階色散因子來(lái)消除高階項(xiàng)的影響，提升系統(tǒng)的軸向分辨率。

圖2 SD-OCT系統(tǒng)未色散補(bǔ)償?shù)臐L降圖

圖3 測(cè)得的干涉信號(hào)的強(qiáng)度和相位。(a) 干涉信號(hào)；(b) 通過(guò)希爾伯特變換解析出的相位；(c) 解包裹后的相位

3.2 色散補(bǔ)償

圖4 不同色散補(bǔ)償方案對(duì)系統(tǒng)軸向分辨率和PSF的影響。(a) 在0～1.5 mm深度范圍的軸向分辨率；(b) 在1.02 mm處的點(diǎn)擴(kuò)散函數(shù)

圖5顯示了通過(guò)三階數(shù)值色散補(bǔ)償和通過(guò)迭代法優(yōu)化二階和三階項(xiàng)之后的點(diǎn)擴(kuò)散函數(shù)的比較。該方法使用迭代過(guò)程來(lái)測(cè)量和優(yōu)化圖像的銳度。圖中顯示的是成像深度為1.02 mm時(shí)的點(diǎn)擴(kuò)散函數(shù)。采用三階色散補(bǔ)償方法測(cè)得的半高寬約為～7.5 μm，采用數(shù)值迭代補(bǔ)償方法測(cè)得的半高寬為～7.0 μm。采用數(shù)值迭代補(bǔ)償方法得到的軸向分辨率略好于采用三階色散補(bǔ)償方法得到的軸向分辨率。但采用三階色散補(bǔ)償方法的計(jì)算量要小得多。

圖5 無(wú)色散補(bǔ)償、三階色散補(bǔ)償和數(shù)值迭代補(bǔ)償?shù)膶?shí)測(cè)點(diǎn)擴(kuò)散函數(shù)的比較

圖6給出了SD-OCT系統(tǒng)經(jīng)過(guò)色散補(bǔ)償后的滾降(roll-off)圖和色散補(bǔ)償前后點(diǎn)擴(kuò)散函數(shù)的峰值對(duì)比圖，從圖6(a)可以看出，SD-OCT系統(tǒng)進(jìn)行色散補(bǔ)償后，隨著光程差的增加，點(diǎn)擴(kuò)散函數(shù)的展寬基本保持不變，并且峰值強(qiáng)度同色散補(bǔ)償前相比也保持較高的水平，軸向分辨率得到很大提升。圖6(b)對(duì)比了色散補(bǔ)償前后點(diǎn)擴(kuò)散函數(shù)的峰值。從圖中可以看出，經(jīng)過(guò)色散補(bǔ)償后，點(diǎn)擴(kuò)散函數(shù)的峰值在成像深度為0～0.6 mm范圍內(nèi)差別不大，隨著成像深度逐漸增加，色散補(bǔ)償前后的點(diǎn)擴(kuò)散函數(shù)峰值差值逐漸增大，在深度為1.3 mm處達(dá)到最大值1.2 dB，而PSF 的峰值與底部噪聲功率的差值可以衡量圖像的信噪比，表明色散補(bǔ)償后信噪比得到有效提升，提升的最大值達(dá)到1.2 dB。

圖6 (a) SD-OCT系統(tǒng)色散補(bǔ)償后的滾降圖; (b) 色散補(bǔ)償前后PSF峰值對(duì)比圖

為了驗(yàn)證三階色散補(bǔ)償對(duì)樣品SD-OCT圖像的補(bǔ)償效果，分別對(duì)橡膠管和單層蓋玻片的圖像進(jìn)行了色散補(bǔ)償。圖7(a)和圖7(b)顯示了對(duì)橡膠管的OCT圖像的色散補(bǔ)償前后的效果，可以看出在成像深度較大的區(qū)域，圖像清晰度得到了提升。圖7(c)和圖7(d)顯示了色散補(bǔ)償前后蓋玻片樣品的OCT圖像，將蓋玻片上下表面的軸向信息提取出來(lái)后，并分別對(duì)這兩部分進(jìn)行相位補(bǔ)償?？梢钥闯鰧?duì)于軸線上樣品的展寬信息，色散補(bǔ)償能夠有效提升圖像的銳度，成像效果得到明顯提升。

圖7 橡膠管、蓋玻片樣品的OCT圖像。(a)，(c) 色散補(bǔ)償前；(b)，(d) 色散補(bǔ)償后

4 結(jié) 論

本文提出了一種基于三階多項(xiàng)式擬合的色散補(bǔ)償方法。在SD-OCT系統(tǒng)中，當(dāng)參考臂和樣品臂之間存在色散失配時(shí)，干涉信號(hào)的相位會(huì)出現(xiàn)高階項(xiàng)，進(jìn)而展寬系統(tǒng)的點(diǎn)擴(kuò)散函數(shù)，降低系統(tǒng)軸向分辨率。對(duì)于任意光程差位置的干涉信號(hào)，其相位可以通過(guò)泰勒級(jí)數(shù)展開，色散補(bǔ)償?shù)哪康木褪窍辔恢械母唠A項(xiàng)對(duì)系統(tǒng)的影響。干涉信號(hào)的相位通過(guò)希爾伯特變換提取，提取出的相位經(jīng)過(guò)解包裹后可以還原出相位與波數(shù)的關(guān)系，接著利用三階多項(xiàng)式擬合相位，得到的高階色散因子可用于消除相位中的高階項(xiàng)。實(shí)驗(yàn)使用平面鏡樣品測(cè)量系統(tǒng)在不同光程差位置的點(diǎn)擴(kuò)散函數(shù)，發(fā)現(xiàn)光程差越大，系統(tǒng)的點(diǎn)擴(kuò)散函數(shù)展寬越明顯。通過(guò)比較二階、三階和四階色散補(bǔ)償三種方案對(duì)系統(tǒng)軸向分辨率的影響，發(fā)現(xiàn)只需要將干涉信號(hào)的相位補(bǔ)償?shù)饺A項(xiàng)就可以達(dá)到較好的補(bǔ)償效果，最后通過(guò)對(duì)比色散補(bǔ)償前后蓋玻片和橡膠軟管的SD-OCT圖像，證明了該方法的有效性和可行性。

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Research on dispersion compensation technology for SD-OCT system

Jiang Panqiu, Wang Pinghe*

State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Science andEngineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

SD-OCT images of rubber hose and coverslip. (a), (b) Not compensated for dispersion; (c), (d) 3rd-order dispersion compensation

Overview:Optical coherence tomography (OCT) is an optical imaging modality that enables high-resolution, cross-sectional, and three-dimensional volumetric imaging of the internal microstructure in biological tissues and materials. SD-OCT system has a broadband source and a spectrometer with a line scan camera. One of the main problems of the SD-OCT system is that chromatic dispersion causes the decrease of sensitivity and imaging quality. Many different methods have been proposed, including hardware-based and software-based methods. Solutions include physically matching the dispersion in both arms by adding compensating materials, gratings, or fiber-stretchers in one of the interferometer arms. However, all these methods only compensate up to second-order dispersion and have the same pitfalls of complexity and cost. Various software-based methods have also been proposed to solve the problem of dispersion mismatch. Some rely on an iterative adjustment of a phase correction signal to optimize image sharpness.

We propose a dispersion compensation method based on the numerical polynomial fitting analysis in the spectral domain optical coherence tomography. This method obtains the dispersion factor by fitting the phase of the interference signal and removes the dispersion mismatch terms, which can significantly improve the system axial resolution compared with non-dispersion compensation.

To illustrate that the numerical dispersion compensation method has an optimized effect on the axial resolution of the SD-OCT system, we measured the axial resolution at different depths and compared the PSF of 2nd-order, 3rd-order, and 4th-order dispersion compensation. The results prove that the axial resolution obtained by 3rd-order dispersion compensation is in good agreement with it measured by 4th-order dispersion compensation, and is better than it measured by non-dispersion compensation and 2nd-order dispersion compensation. The third-order dispersion compensation has a visible optimization effect.

A comparison between the measured PSF by third-order numerical dispersion compensation and by the iterative dispersion compensation technique was carried out. The PSF is measured at the imaging depth of 1.02 mm. The measured FWHM with third-order dispersion compensation is ～7.5 μm and that with the iterative dispersion compensation technique is ～7.0 μm. The iterative dispersion compensation yields a little better resolution than the three-order dispersion compensation. However, it requires more computation.

The images of rubber hose and coverslip in the experiment are shown in the Figure. Using the method of the third-order dispersion compensation, two-dimensional imaging of rubber hose and coverslip are shown in Figure (c) and Figure (d), respectively. In order to contrast the effect of this method, the diagrams without dispersion compensation are shown in Figure (a) and Figure (b). The diagram with third-order dispersion compensation has a good sharpness in the deep position.

Jiang P Q, Wang P HResearch on dispersion compensation technology for SD-OCT system[J]., 2021, 48(10): 210184; DOI:10.12086/oee.2021.210184

Research on dispersion compensation technology for SD-OCT system

Jiang Panqiu, Wang Pinghe*

State Key Laboratory of Electronic Thin Films and Integrated Devices, School of Optoelectronic Science andEngineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Dispersion compensation for the data processing of the spectral domain optical coherence tomography (SD-OCT) system is an important way to improve the imaging quality of the system. A dispersion compensation method for spectral domain optical coherence tomography based on numerical polynomial fitting analysis is proposed in this paper. This method obtains the dispersion factor by fitting the phase of the interference signal and removes the dispersion mismatch terms, which can significantly improve the system axial resolution compared with non-dispersion compensation. The SD-OCT system is used to measure the axial resolution and signal-to-noise ratio (SNR) at different positions of the optical path difference, and the effectiveness and reliability of the method are verified by analyzing the axial resolution and the SNR of the system before and after the dispersion compensation technology. Finally, we found that the third-order dispersion compensation has a visible optimization effect within the imaging depth of ～1.5 mm.

SD-OCT; dispersion compensation; polynomial fitting; resolution; imaging quality

National Key R&D Program of China (2016YFF0102003, 2016YFF0102000)

10.12086/oee.2021.210184

O439

A

* E-mail: wphsci@uestc.edu.cn

姜盼秋，汪平河. 譜域光學(xué)相干層析系統(tǒng)的色散補(bǔ)償技術(shù)研究[J]. 光電工程，2021，48(10): 210184

Jiang P Q, Wang P H. Research on dispersion compensation technology for SD-OCT system[J]. Opto-Electron Eng, 2021, 48(10): 210184

2021-06-02；

2021-10-13

國(guó)家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2016YFF0102003，2016YFF0102000)

姜盼秋(1989-)，女，碩士，講師，主要從事光學(xué)相干層析成像技術(shù)的研究。E-mail：jiangpanqiu_1006@sina.com

汪平河(1976-)，男，博士，教授，主要從事光學(xué)相干層析成像技術(shù)和光纖激光器的研究。E-mail：wphsci@uestc.edu.cn

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