姜盼秋，汪平河

譜域光學(xué)相干層析系統(tǒng)的色散補償技術(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家重點實驗室，四川 成都 611731

對譜域光學(xué)相干層析系統(tǒng)(SD-OCT)采用色散補償方法進行優(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)值多項式擬合的色散補償方法。該方法通過提取干涉信號的相位并解包裹，利用數(shù)值多項式對解包裹后的相位進行擬合，然后根據(jù)擬合出的高階色散因子對干涉信號做相位補償。本文利用SD-OCT系統(tǒng)測量出不同光程差位置處的軸向分辨率和信噪比，通過比較分析色散補償前后系統(tǒng)的軸向分辨率及信噪比，來驗證該方法的有效性和可靠性。結(jié)果表明，本文設(shè)計的色散補償技術(shù)可以使系統(tǒng)具有良好的軸向分辨率，三階多項式擬合相位的色散補償方法在約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、非接觸以及可實時成像等優(yōu)點[1-2]。OCT通過測量生物組織后向散射光的回波來檢測生物組織的斷層結(jié)構(gòu)，其軸向分辨率可以達(dá)到幾個微米[3-5]。早期的OCT系統(tǒng)采用時域探測的方式，通過參考臂平面鏡的軸向掃描實現(xiàn)對樣品深度信息的提取[6]。目前OCT成像通常在傅里葉域進行檢測，與時域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測量干涉信號的光譜，并通過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度不同時，會發(fā)生色散失配，此時系統(tǒng)的點擴散函數(shù)(point spread function，PSF)不僅會展寬，而且其峰值強度也會降低[11]。色散補償是解決樣品臂與參考臂色散失配問題的基礎(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題，許多基于硬件和軟件的色散補償方法被用于校正樣品臂和參考臂之間的色散失配[12-14]。基于硬件的色散補償方法可以同時對系統(tǒng)色散和樣品色散進行矯正，只需要在干涉儀中的一個臂中添加補償材料，如色散棱鏡、光柵、光纖相位調(diào)制器等[15-16]。但是這些硬件補償方法補償程度較低，并且會提高系統(tǒng)的復(fù)雜度和成本。基于軟件的色散補償方法可矯正更高階的色散，如一種深度依賴的色散補償方法，基于相位校正信號的迭代調(diào)整來優(yōu)化圖像清晰度[17-19]。然而，基于迭代算法的數(shù)值補償方法計算量大，需要更多的計算時間。還可以通過去復(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)值多項式擬合分析的方法來解決SD-OCT系統(tǒng)的色散問題，通過消除樣品臂和參考臂之間色散失配引起的非線性相位項來實現(xiàn)色散補償，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度，對于高斯型光源，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光譜可以表示為

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

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)過色散補償后，利用快速傅里葉的逆變換將干涉信號從空間轉(zhuǎn)換到空間，得到點擴展函數(shù)，點擴展函數(shù)的半高寬對應(yīng)于SD-OCT軸向分辨率。

3 實驗結(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，中心波長為846 nm，帶寬為103.6 nm。寬帶光源發(fā)出的光首先經(jīng)過光隔離器，目的是防止光沿著光路返回進入光源，對光源造成損傷。光纖耦合器使用中心波長為850 nm，分光比為50: 50的寬帶耦合器。光束通過50/50光纖耦合器分別傳輸?shù)絽⒖急酆蜆悠繁邸⒖急塾善窨刂?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現(xiàn)樣品的橫向掃描。樣品臂和參考臂返回的干涉信號由光譜儀接收。該光譜儀由光纖準(zhǔn)直器、中心波長為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(E2v，EV71YEM2CL2014-BA0)由2048個像素點組成，每個像素點的尺寸為14mm×14mm。CCD相機采用的A掃描頻率為5 kHz。最后通過圖像采集卡將數(shù)據(jù)傳輸?shù)接嬎銠C。數(shù)據(jù)處理由VC++和MATLAB編程實現(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優(yōu)化圖像質(zhì)量，導(dǎo)致測量的軸向分辨率降低。在樣品臂中放置一個反射鏡，每隔100mm在～1.5 mm的成像深度內(nèi)測量點擴散函數(shù)。SD-OCT系統(tǒng)靈敏度的下降如圖2所示，SD-OCT系統(tǒng)未進行色散補償時，在零光程差附近色散失配較小，點擴散函數(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，對應(yīng)的點擴散函數(shù)脈寬增加且峰值強度降低，軸向分辨率顯著下降。

3.1 相位信息

用2048像素的線陣CCD相機可以采集到干涉信號。在樣品臂中放置一個反射鏡，并將光程差調(diào)整為0.32 mm。色散補償過程如圖3所示，去除自相關(guān)項和直流項，干涉光譜如圖3(a)所示。通過對干涉譜進行Hilbert變換，利用復(fù)數(shù)干涉信號的虛部項除以實部項，再通過反正切函數(shù)解析干涉信號的相位信息。圖3(b)顯示了以單個反射鏡為樣本的波數(shù)空間中作為函數(shù)的相位項。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相位之間相差一個2π整數(shù)倍的初相位，這個初相位可以不用考慮，因為兩臂間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。如果不進行色散補償，相位中高階色散項的存在會使系統(tǒng)點擴散函數(shù)發(fā)生展寬，降低系統(tǒng)的軸向分辨率。色散補償需要對相位中的高階項進行補償，通過計算出相位中的高階色散因子來消除高階項的影響，提升系統(tǒng)的軸向分辨率。

圖2 SD-OCT系統(tǒng)未色散補償?shù)臐L降圖

圖3 測得的干涉信號的強度和相位。(a) 干涉信號；(b) 通過希爾伯特變換解析出的相位；(c) 解包裹后的相位

3.2 色散補償

圖4 不同色散補償方案對系統(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處的點擴散函數(shù)

圖5顯示了通過三階數(shù)值色散補償和通過迭代法優(yōu)化二階和三階項之后的點擴散函數(shù)的比較。該方法使用迭代過程來測量和優(yōu)化圖像的銳度。圖中顯示的是成像深度為1.02 mm時的點擴散函數(shù)。采用三階色散補償方法測得的半高寬約為～7.5 μm，采用數(shù)值迭代補償方法測得的半高寬為～7.0 μm。采用數(shù)值迭代補償方法得到的軸向分辨率略好于采用三階色散補償方法得到的軸向分辨率。但采用三階色散補償方法的計算量要小得多。

圖5 無色散補償、三階色散補償和數(shù)值迭代補償?shù)膶崪y點擴散函數(shù)的比較

圖6給出了SD-OCT系統(tǒng)經(jīng)過色散補償后的滾降(roll-off)圖和色散補償前后點擴散函數(shù)的峰值對比圖，從圖6(a)可以看出，SD-OCT系統(tǒng)進行色散補償后，隨著光程差的增加，點擴散函數(shù)的展寬基本保持不變，并且峰值強度同色散補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)對比了色散補償前后點擴散函數(shù)的峰值。從圖中可以看出，經(jīng)過色散補償后，點擴散函數(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，色散補償前后的點擴散函數(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)色散補償后的滾降圖; (b) 色散補償前后PSF峰值對比圖

為了驗證三階色散補償對樣品SD-OCT圖像的補償效果，分別對橡膠管和單層蓋玻片的圖像進行了色散補償。圖7(a)和圖7(b)顯示了對橡膠管的OCT圖像的色散補償前后的效果，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后，并分別對這兩部分進行相位補償?？梢钥闯鰧τ谳S線上樣品的展寬信息，色散補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) 色散補償前；(b)，(d) 色散補償后

4 結(jié) 論

本文提出了一種基于三階多項式擬合的色散補償方法。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，干涉信號的相位會出現(xiàn)高階項，進而展寬系統(tǒng)的點擴散函數(shù)，降低系統(tǒng)軸向分辨率。對于任意光程差位置的干涉信號，其相位可以通過泰勒級數(shù)展開，色散補償?shù)哪康木褪窍辔恢械母唠A項對系統(tǒng)的影響。干涉信號的相位通過希爾伯特變換提取，提取出的相位經(jīng)過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。實驗使用平面鏡樣品測量系統(tǒng)在不同光程差位置的點擴散函數(shù)，發(fā)現(xiàn)光程差越大，系統(tǒng)的點擴散函數(shù)展寬越明顯。通過比較二階、三階和四階色散補償三種方案對系統(tǒng)軸向分辨率的影響，發(fā)現(xiàn)只需要將干涉信號的相位補償?shù)饺A項就可以達(dá)到較好的補償效果，最后通過對比色散補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

國家重點研發(fā)計劃項目(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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