Theoretical sensitivity calculation

Leitgeb’s paper1

% Sensitivity from [Performance of FD vs TD]
N = 2048;
rho = 0.4;                                                                % spectrometer efficiency rho
eta = 0.8;                                                                 % detector quantum efficiency
tau = 14.2 * 10^(-6);                                                             % exposure time / s 
h = 6.63 * 10^(-34);                                                       % planck constant / J * s
P_0 = 3 * 10^(-3);                                                      % power at the sample / Watt 
gamma_s = 1;                                                            % part of input power on sample arm 
gamma_r = 1;                                                            % part of input power on ref arm 
c = 2.99 * 10^(8);                                                          % light speed m/s
lambda_0 = 820 * 10^(-9);                                                  % center-wavelengt / m
delta_lambda = 120 * 10^(-9);                                               % FWHM bandwidth / m
nu_0 =  c / lambda_0;                                                      % center-frequency / hz
e = h * nu_0;                                                              % electron charge
delta_nu = (pi / (2 * log(2)))^(1/2) * c * delta_lambda /[(lambda_0)^(2)]; % effective line width
R_r = 1;                                                                   % reference arm reflectivity

% Sensitivity
a = 1/N * (rho*eta*tau*P_0/e)^2 * gamma_s * gamma_r * R_r;
b = (1/N*rho*eta*tau*P_0*gamma_r*R_r/e)*[1+1/2*(rho*eta/e)*(P_0/N)*gamma_r*R_r*(N/delta_nu)]+250*e;
sensitivity = 10*log10(a/b)
  • For parameters in paper, it’s 94.5020 dB
  • For our system, it’s 93.4097 dB

Choma’s paper2

%% Sensitivity from [Choma paper]
N = 2048;
rho = 0.6;                                                                % spectrometer efficiency rho
eta = 0.8;                                                                 % detector quantum efficiency
tau = 14.2* 10 ^(-6);                                                             % exposure time / s 
h = 6.63 * 10^(-34);                                                       % planck constant / J * s
P_0 = 3 * 10^(-3);                                                      % power at the sample / Watt 
c = 2.99 * 10^(8);                                                          % light speed m/s
lambda_0 = 820 * 10^(-9);                                                  % center-wavelengt / m
delta_lambda = 120 * 10^(-9);                                               % FWHM bandwidth / m
nu_0 =  c / lambda_0;                                                      % center-frequency / hz
e = h * nu_0;                                                              % electron charge
%% Sensitivity
a = rho * eta * P_0 * tau;
b = 2*e;
sensitivity = 10*log10(a/b)

  • For parameters in paper, it’s 120.1337 dB
  • For our system, it’s 106.2625 dB
  1. Leitgeb, R., Hitzenberger, C. & Fercher, A. F. Performance of fourier domain vs. time domain optical coherence tomography. Opt. Express 11, 889-894 (2003).
  2. Choma, M. A., Sarunic, M. V., Yang, C. & Izatt, J. A. Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Opt. Express 11, 2183-2189, doi:10.1364/OE.11.002183 (2003).

OCT Daily Mar 18, 2017//Extended-focus optical coherence microscopy

Curated Paper

Optical coherence microscopy with extended focus for in vivo embryonic imaging

Abstract:

Optical coherence microscopy (OCM) has unique advantages of high-resolution volumetric imaging without relying on exogenous labels or dyes. It combines the coherence-gated depth discrimination of optical coherence tomography (OCT) with the high lateral resolution of confocal microscopy, offering an excellent balance between the resolutions and imaging depth. However, as the lateral resolution becomes higher, the imaging depth of OCM decreases and its three-dimensional imaging capability is greatly degraded. To overcome this limitation, we used amplitude apodization to create quasi-Bessel beam illumination in order to extend the depth of focus. The lateral and axial resolutions of our OCM system were measured to be 1.6 μm and 2.9 μm in tissue. The imaging depth was extended by 3.0X (100 μm) beyond that of the standard Gaussian beam OCM. Using zebrafish embryos as a test system, we demonstrate extendedfocus OCM for structural imaging studies, which revealed the detailed anatomy deep in embryos. © (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Comments

首先,几个概念。

0.Gaussian 光束:

1.Bessel光束:

「无衍射光束」的概念是由美国Rochester大学的 J.Durnin 等人在1987年首次提出的,它是自由空间标量波动方程的一组特殊解,其场分布特点具有第一类零阶Bessel函数的表示形式。它以特殊的性质:在无界自由空间的传输过程中光强分布保持不变、中心光斑小、与传播方向垂直的各个平面上其光场分布保持相同,而且它的光强高度集中,也就是它的能量高度局域化,且不会在传播过程中遭受衍射扩散。

2.Fresnel菲涅尔透镜

相比传统的球面透镜,菲涅耳透镜通过将透镜划分出为一系列理论上无数多个同心圆纹路(即菲涅耳带)达到相同的光学效果,同时节省了材料的用量:

由于光的折射发生在介质的交界面,这里以玻璃与空气为例,若能去除光在玻璃中直线传播的部分而保留发生折射的曲面,便能省下大量材料同时达到相同的聚光效果。如图,菲涅耳透镜便是通过此法使透镜变薄。曲面划分得越细,透镜越能够做薄。

将普通透镜不参与折射的部分去掉,变成仅有参与折射的曲面的透镜。这个动画很有意思。菲涅尔透镜有一些列的环带组成,当平行光入射到菲涅尔透镜时,不同波长的光被聚焦到光轴上不同的点,实现光能量沿光轴的再分布。菲涅尔透镜的焦深是由波长所决定的焦点在光轴上所占的距离和单个波长的焦深之和,而波长所决定的焦点在光轴上所占的距离可以由最大波长的焦点与最小波长的焦点之间的确立来确定。

3.Axicon |AKSIKEN| 锥透镜

锥透镜通常也被称作轴对称棱镜,它是一种带一个圆锥面和一个平面的透镜。锥透镜常用来产生贝塞尔强度轮廓光束或者锥形非发散光束。当把准直光束转变为环形时,平的一面对着准直光源。

Based on above:

大多数OCT基本上是基于频域探测的谱域或者扫频光源OCT,研究全场OCT这样时域探测的很少。两者的区别在于,前者的探测是深度方向,而全场是面阵探测。本文在谱域探测的OCT中使用了全场OCT中惯用的显微物镜(跟我中国实验室一样的显微物镜),这样的使用无疑减小了焦深,焦深是什么详见这篇文章。为了维持深度方向的横向分辨率,主要原理:

  1. Bessel 光束代替 Gaussian 光束,然而由于有限能量和维数,通常是 Quasi-Bessel 光束
  2. 大多数采用轴锥棱镜,相位模板或者空间光调制器产生Quasi-Bessel 光束

但它们对宽带光源不友好(why?)(OCT使用宽带光源可得到高轴向分辨率该文章带宽为760-930 nm),故采用环状mask产生准Bessel光束来延长焦深,如图:

这篇文章的摘要说道:

To overcome this limitation, we used amplitude apodization(振幅变迹) to create quasi-Bessel beam illumination in order to extend the depth of focus.

从我的角度就是简单做了个圆环,模拟Bessel光束!

What can I learn from

1.这使我想起大师兄的博士论文的「基于菲涅尔透镜的SDOCT」:

横向分辨率与系统焦深之间的矛盾关系是目前SDOCT技术的一个热点问题。目前的SDOCT系统为了在横向分辨率和焦深之间达到一个平衡,一般在样品臂都使用低数值孔径的物镜,为了改善这一矛盾关系,通过对现有方法的大量分析与研究,在现有方法的基础上,提出了利用菲涅尔透镜替代普通物镜的方法,来改善这一问题。本章首先介绍了其它小组提出的改善这一矛盾关系的几种方法,接着介绍了基于菲涅尔透镜的SDOCT系统的原理,并用所搭建的系统对人体皮肤进行了在体成像,验证了系统的可行性,最后对色散问题进行了讨论。

基于菲涅尔透镜的SDOCT系统事实上是将传统SDOCT系统中的普通物镜换成菲涅尔透镜,利用菲涅尔透镜的一些性质实现焦深的增加。

2.和一篇新文章,使用 axicon lens 轴锥棱镜的SDOCT:

Extended focus depth for Fourier domain optical coherence microscopy

The Bessel beam was generated by the axicon lens and transferred to the object using a set of telescopes. The annular aperture was inserted in the first telescope to block unwanted residual rays coming from the imperfect axicon tip.

这篇新文章,使用锥透镜,还用圆环挡住不需要的残余光线。

3.和一篇新文章 Simultaneous dual-band ultra-high resolution full-field optical coherence tomography

The effective spectra are deduced from Fourier transform of the interferogram using a Hamming window for apodization

4.Bessel beam in FFOCT

5.可变焦棱镜(non scanning)Fast electrically tunable lens EL-10-30-TC

OCT Daily Mar 14, 2017, 08:15

Curated Paper

Integrated Local Binary Pattern Texture Features for Classification of Breast Tissue Imaged by Optical Coherence Microscopy

Abstract:

Highlights

• Texture analysis is applied on OCM images for human breast tissue classification.

• New variants of local binary pattern (LBP) are proposed to extract texture features.

• Using multi-scale and integrated image features improves classification accuracy.

• Achieved high sensitivity (100%) and specificity (85.2%) for cancer detection.

Comments

昨天的 OCT Daily Mar 13 写到了对乳腺癌成像结果分析以及初诊,今天这篇来自Fujimoto实验室,同样对乳腺癌进行纹理配对分析,值得注意的是在 Image Processing 部分,文章提到:

The images utilized in our experiments in this work are en face OCM images of ex vivo human breast tissue.

上图显示了邻域图案到量化的过程,下图是具体处理过程。

这里提及另一篇文章。因为FDOCT(大部分)是以一个A扫为单位的,也就是说必须使用振镜扫描才能得到所谓的 en face 结构。而这篇文献的主从模式干涉结构1

Conventional spectral domain interferometry (SDI) methods suffer from the need of data linearization. When applied to optical coherence tomography (OCT), conventional SDI methods are limited in their 3D capability, as they cannot deliver direct en-face cuts. Here we introduce a novel SDI method, which eliminates these disadvantages. We denote this method as Master – Slave Interferometry (MSI), because a signal is acquired by a slave interferometer for an optical path difference (OPD) value determined by a master interferometer. The MSI method radically changes the main building block of an SDI sensor and of a spectral domain OCT set-up. The serially provided signal in conventional technology is replaced by multiple signals, a signal for each OPD point in the object investigated. This opens novel avenues in parallel sensing and in parallelization of signal processing in 3D-OCT, with applications in high-resolution medical imaging and microscopy investigation of biosamples. Eliminating the need of linearization leads to lower cost OCT systems and opens potential avenues in increasing the speed of production of en-face OCT images in comparison with conventional SDI.

What can I learn from



全场OCT存在的必要性。医生诊断还是需要 en face image。全场OCT的缺点:

  1. 不稳定
  2. 灵敏度不如 FDOCT
  3. 成像深度浅 – 500$\mu m$

除此之外,也提供了识别癌症的一种思路。SensitivitySpecificity是判断癌症与否的两个指标。

  1. Bradu, A. & Podoleanu, A. G. Imaging the eye fundus with real-time en-face spectral domain optical coherence tomography. Biomed. Opt. Express 5, 1233-1249, doi:10.1364/BOE.5.001233 (2014).

OCT Daily Mar 13, 2017

这篇文章讲述了一个女性如何在自己的领域为乳腺癌的初诊做的事情。

Curated Paper

Visualization and tissue classification of human breast cancer images using ultrahigh-resolution OCT

Abstract:

Breast cancer is one of the leading cause of mortality in women. Optical coherence tomography (OCT) enables three dimensional visualization of biological tissue with micrometer level resolution at high speed, and can play an important role in early diagnosis and treatment guidance of breast cancer. In this study, we imaged human breast tissue using two spectral domain OCT systems at different wavelengths: a home-built ultra-high resolution (UHR) OCT system at 840nm (measured as 2.72 µm axial and 5.52 µm lateral) and a commercial OCT system at 1300nm with standard resolution (measured as 6.5 µm axial and 15 µm lateral). We found that detailed structures of basic units found in breast tissue, such as TDLUs, ducts, adipose and fibrous stroma, can be better delineated by UHR OCT. In addition, we added phyllodes, fibrotic focus and necrotic tumor to the UHR OCT image library of breast cancer. Moreover, by using regional features derived from OCT images produced by the two systems, we developed an automated classification algorithm based on relevance vector machine (RVM) to differentiate hollow-structured adipose tissue against solid tissue. We further developed B-scan based features for RVM to classify invasive ductal carcinoma (IDC) against normal fibrous stroma tissue amongst OCT datasets produced by the two systems. With a limited number of datasets, we showed that both OCT systems can achieve a good accuracy in identifying adipose tissue. Classification in UHR OCT images achieved higher sensitivity (94%) and specificity (93%) of adipose tissue than the sensitivity (91%) and specificity (76%) in 1300 nm OCT images. In IDC classification, similarly, we achieved better results with UHR OCT images, featured an overall accuracy of 84%, sensitivity of 89% and specificity of 71% in this preliminary study. Our work may open the door towards automatic intraoperative OCT evaluation of early-stage breast cancer.

Comments

Christine Hendon的实验室,虽然她当年压根没理我的信。Basic OCT scheme:

利用OCT对乳腺癌的成像和数据分析,Tissue classification algorithm flow/ 组织分类算法流程图如下:

定义灵敏度和确认度分析肿瘤结构,还跟Thorlabs OCT和传统病理学结果对比,部分成像结果如下:

诊断分类(阳性,阴性)分析对比结果如下:

In particular, ultra-high resolution (UHR) OCT provides images with better histological correlation.

What can I learn from

已经从对成像的改进进入到实用领域,像DeepMind这类公司利用Machine Learning 取代病理识别已经是趋势。该文章给我提供了一个流程,包括SBO LAB的文章1和FFOCT对乳腺癌的诊断2,试图解决这样一个问题:如何从成像结果变成可量化的结论。

具体为对图片有什么要求,比如:

All OCT images presented have a corresponding histology slides, which were annotated with the help of an experienced pathologist. The aspect ratio of UHR OCT images was scaled to match the dimension of the actual cross-sectional field of view in air (3 mm by 1.78 mm), and Thorlabs OCT images were presented in their original scale.

但目前如何以 Decent way 做组织病理学实验还需要专业病理科医生指导。

  1. Zarnescu, L. et al. Label-free characterization of vitrification-induced morphology changes in single-cell embryos with full-field optical coherence tomography. BIOMEDO 20, 096004-096004, doi:10.1117/1.JBO.20.9.096004 (2015).
  2. Assayag, O. et al. Large Field, High Resolution Full-Field Optical Coherence Tomography: A Pre-Clinical Study of Human Breast Tissue and Cancer Assessment. Technology in Cancer Research & Treatment 13, 455-468, doi:doi:10.7785/tcrtexpress.2013.600254 (2014).

OCT Daily Mar 10, 2017

Curated paper

Accurate wavelength calibration method for compact CCD spectrometer

Abstract:

Wavelength calibration is an important step in charge-coupled device (CCD) spectrometers. In this paper, an accurate calibration method is proposed. A model of a line profile spectrum is built at the beginning, followed by noise reduction, bandwidth correction, and automatic peak-seeking treatment. Experimental tests are conducted on the USB4000 spectrometer with a mercury-argon calibration light source. Compared with the traditional method, the results show that this wavelength calibration procedure obtains higher accuracy and the deviations are within 0.1 nm.

简评

这是一篇关于利用自动选择光谱OCT峰值信号,进行光谱标定的文章。没有太多新意,比较实用的算法文章。

内核分成三部分:

  1. 噪声分析与消噪算法
  2. 校正带宽
  3. 自动识别峰值信号

噪声(read out noise/dark noise/photoelectron noise/fixed pattern noise)消噪算法(平均算法,小波阈值算法)。

校正带宽用{Woolliams, 2011 #512}提出的差分算法1

自动识别峰值信号。方法一:将离散信号当作连续曲线,通过使用数值微分公式来计算每个点的导数。峰中心的位置是一阶导数的过零点的对应像素数。

What I can learn from

三种自动识别峰值的方法,目前我确实是手动选择,但仅仅一次就足够,如果自动识别,可能还是要筛选前后区域来重复。该文章仅仅提供一种可能性,

  1. Woolliams, E. R., Baribeau, R., Bialek, A. & Cox, M. G. Spectrometer bandwidth correction for generalized bandpass functions. Metrologia 48, 164 (2011).

焦深

这一节翻译自Depth of Field and Depth of Focus

当考虑光学显微镜的分辨率时,大部分重点放在垂直于光轴的平面中的点到点横向分辨率,如下图1所示:

而轴向分辨率的能力,是通过测量与光轴平行方向且大多数情况被视为景深。

轴向分辨率,是被显微物镜的数值孔径决定,如图2:

其中目镜仅放大被分辨并投影到中间像平面中的细节。传统摄像中,景深是从最近的聚焦物面到最远的聚焦物面的距离。显微镜景深非常短并且通常以微米为单位。术语焦深depth of focus,涉及的是像面空间,通常与景深(物空间)互换使用。

互换的命名系统则产生了困扰,尤其两者都在描述显微物镜的景深时。几何像面被期待对样品进行无穷远处的薄层成像的结果,但即使在无像差系统中,每个像点会产生各自的衍射图形,从而超出该平面。Airy斑,是由显微物镜产生的衍射图像的基本单元,表示通过中间像平面的中心的截面。这增加了略微不同的样品平面的Z轴Airy斑强度分布的有效焦深。

焦深随着显微物镜的数值孔径和放大倍率变化,在某些情况下,高数值孔径系统(通常有着更高的放大倍率)有更深的汇聚深度,相比较低数值孔径系统而言,尽管景深更小(见表1)。这在显微摄影中特别重要,因为胶卷乳剂或数码照相机的传感器必须落在聚焦区域内的平面中曝光或照射。焦点处的小误差在高倍率下不像在低倍率放大物镜中那么严重。表1示出了在具有增加的数值孔径和放大率的一系列物镜中的中间像平面中的景深和图像深度的计算变化。

高数值空间显微镜中,景深主要由波动光学方程确定,而在较低数值孔径处几何光学的弥散圆斑占主导。使用各自不同的标准来确定图形何时变得不可接受地尖锐,一些作者已经提出不同公式来描述显微镜中的景深。总景深由波函数和像场的几何光学景深之和:



$$d_{tot}=\frac{\lambda⋅n}{{NA}^2}+\frac{n}{M⋅NA}⋅e$$
$d_{tot}$表示景深,$\lambda$表示照明光波长,n为介质折射率($n_{air}=1$ 或者 $n_{oil}=1.515$),介质是放在显微物镜和样品之间的物质,$NA$等于物镜数值孔径。$e$表示可被放置在显微镜像面的探测器可分辨的最小距离,它的横向放大倍率为$M$。使用该方程,$d_{tot}$和波长$\lambda$必须使用同样单位。例如,微米。值得注意的是,景深的衍射极限(式子第一项)与数值孔径的平方相反地收缩,而横向分辨率极限以与数值孔径的反比的方式减小。因此,可以获得光学薄层的轴向分辨率和厚度受系统数值孔径的影响远大于横向分辨率。

人眼通常可对无限远到250mm明视距离成像,故景深范围可以比上述公式(目镜观察显微镜下物体的情况)大得多,另一方面,视频传感器或者照相乳剂在薄的固定平面中,故使用这些传感器的景深和轴向分辨率被方程中的参数给出。在这些情况下,轴向分辨率由惯例,定义为「沿着物镜产生的三维衍射图像光轴方向的『第一最小值(上下焦点)』距离的四分之一。

景深的数值和在三维衍射图案中的光强分布,是在非相干照明点光源情况下计算,此时聚光镜的数值孔径比物镜大,亦或相同。总体来讲,景深增加到两倍,照明相干性也随之增加(随着聚光镜数值孔径趋近于零)。然而,具有部分相干照明的三维点扩散函数(PSF)可由复杂方式出发,在孔径函数不均匀情况下进一步讨论。在许多基于相位的对比产生显微镜中,景深可能会出乎意料地比根据上述等式预测的更浅,并且可能产生非常薄的光学界面。

在数字视频显微镜中,相机晶体管或者CCD目标中的浅焦平面,在高倍率物镜和聚光镜数值孔径下实现的高对比度,以及在监视器上显示的图像的高放大倍率都导致景深变小。因此,通过视频,我们可以获得非常尖锐和薄的光学切片,并可以非常高的精度限定薄层样品的焦平面。

SDOCT系统表现

  1. 景深是物面清晰范围
  2. 焦深是像面清晰范围
  3. 任何薄层平面汇聚的不是一点,是弥散球,是三维PSF的最终呈现。
  4. OCT系统的轴向分辨率由光源带宽决定,即层析能力。

SD-OCT系统理论焦深(Depth of Focus, DOF)即共焦参数,是瑞利距离的两倍。焦深随着横向分辨率的提高而减小,大数值孔径下可以提高横向分辨率,但同时限制了焦深,导致在焦深外区域横向分辨率的迅速下降。在SD-OCT中,样品的深度信息通过傅里叶变化一次得到,无法实施时OCT中的动态聚焦1,因此在实际成像时需要权衡横向分辨率焦深。为了解决该矛盾,轴锥棱镜被使用在OCT系统中,实现大景深高横向分辨。

SD-OCT系统的轴向分辨率由光源的相干长度决定,相干长度是光源自相干函数包络的半高全宽。

OCT系统成像深度与光源的波长、功率以及待测样品的吸收和散射性质有关。除了光波的穿透深度,SD-OCT系统成像深度主要由光谱仪的分辨率决定。干涉信号可以看成是在波数K空间进行采样,波数变化频率来自于干涉信号余弦项。光谱分辨率对应的K空间采样间隔可从对波数K进行微分得到,采样率则为其倒数$F_k$。由采样定理,当采样频率$F_k$对干涉信号在K空间采样时,其能恢复的最大频率为$F_k/2$:

$$(f_K)_{max}=F_k/2$$
大师姐博士论文:

  1. 考虑理想抽样情况,根据采样定理,可得上述最大成像深度
  2. 考虑CCD像素宽度引起的非理想抽样以及实际的光谱分辨情况,即考虑灵敏度随深度下降因素。可知灵敏度下降6dB时成像深度为2

$$Z_{max}=\frac{2ln2}{\delta k’}$$
其中,$\delta k’$表示实际光谱分辨率

FFOCT系统表现

全场OCT的相干长度与焦深,横向分辨率与数值孔径的关系:

上图显示了焦深表达式,横向分辨率越高,焦深越小,导致成像深度变小,故TDOCT和FDOCT不能使用大数值孔径。而全场OCT直接对样品进行深度方向的扫描,所以大数值孔径不影响成像深度。因此,全场OCT系统成像深度取决于光源的中心波长、样品本身的散射能力以及全场OCT的动态范围。全场OCT系统的横向分辨率由显微物镜数值孔径决定,横向分辨率要大于CCD像素尺寸,否则就要被CCD限制。

在OCT中使用MO的可能性

  1. 全场OCT+面阵CCD
  2. FF-SS-OCT 低NA MO/会聚透镜+面阵CCD
  3. SD-OCT with MO 线阵CCD $1.6\mu m$的 Depth of Focal doesn’t make sense
  4. OCT MO in thorlabs
  1. Grebenyuk, A., Federici, A., Ryabukho, V. & Dubois, A. Numerically focused full-field swept-source optical coherence microscopy with low spatial coherence illumination. Appl. Opt. 53, 1697-1708, doi:10.1364/AO.53.001697 (2014).
  2. Schmitt, J. M. & Kumar, G. Optical scattering properties of soft tissue: a discrete particle model. Appl. Opt. 37, 2788-2797, doi:10.1364/AO.37.002788 (1998)

OCT Daily Mar 9, 2017

Curated paper

Full-Field Optical Coherence Tomography as a Diagnosis Tool: Recent Progress with Multimodal Imaging

Abstract:

Full-field optical coherence tomography (FF-OCT) is a variant of OCT that is able to register 2D en face views of scattering samples at a given depth. Thanks to its superior resolution, it can quickly reveal information similar to histology without the need to physically section the sample. Sensitivity and specificity levels of diagnosis performed with FF-OCT are 80% to 95% of the equivalent histological diagnosis performances and could therefore benefit from improvement. Therefore, multimodal systems have been designed to increase the diagnostic performance of FF-OCT. In this paper, we will discuss which contrasts can be measured with such multimodal systems …

What I can learn from

This is my goal in the near future

「 生物组织全场光学相干层析术研究」大纲1.0ver

本文用 Ulysses 发布,测试与 WordPress 的连接。

绪论

OCT技术研究概况

  1. 时域OCT
  2. 谱域OCT
  3. 扫频OCT
  4. 全场OCT

全场OCT技术的发展

全场OCT的生物应用领域

目前存在的问题

本文的主要研究内容和结构安排

全场OCT成像理论

全场OCT系统构成

  1. 光源
  2. 参考臂
  3. 样品臂
  4. 探测臂

干涉成像

  1. 时间相干性
  2. 空间相干性

全场OCT性能

  1. 横向分辨率
  2. 纵向分辨率
  3. 信噪比
  4. 灵敏度
  5. 成像深度

全场OCT信号解调原理

全场OCT系统搭建与改进完善

系统搭建与实验

实验结果

分离球差

  1. 产生原因
  2. 实验及结果

补偿离焦

  1. 产生原因
  2. 实验及结果

基于Hilbert变换的消色散移相方法

消色散移相原理

偏振移相

Hilbert移相

  1. 本章小结

基于全场OCT图像结构的快速诊断方法研究

分形参数研究

  1. 分形理论
  2. 肝组织分形统计结果与分析

智能识别方法研究

  1. 轮廓提取法
  2. 处理结果与分析

人体肝组织成像研究

  1. 肝组织病理学
  2. 肝组织病理结果
  3. 肝组织样品制备
  4. 全场OCT成像结果及对比

本章小结

频域OCT系统

扫频OCT实时成像系统设计

  1. 光谱标定
  2. 色散补偿
  3. 基于LabVIEW的实时软件界面设计
  4. 手指实时成像
  5. 谱域OCT成像系统对胚胎的成像结果
  6. …未完待续

总结与展望

研究工作

创新点

展望


参考文献

Sensitivity Measurement

Sensitivity Measurement

SNR is the ratio of the peak value of the A-scan with a reflector on the sample arm and rms of the noise floor with the sample arm blocked.

Note that in the OCT community, SNR and sensitivity are sometimes used interchangeably 可交换的 (although technically they should be different). In our group, we will agree that SNR refers to the base measurement and Sensitivity is determined by also considering what ND filters were used. We should also report what power was incident on the sample for the measurement that was made.

This measurement process assumes your system is well enough aligned to get an interferogram.
该测量是假设系统已调校好的情况下

To perform an SNR measurement:

  1. Make sure that your ND filters have been calibrated for the wavelength / light source you are using. The specifications are wavelength-dependent. To calibrate the ND filter, measure the power of a light source without a filter and after you add the filter. The decrease should tell you the actual OD of the filter for the wavelength you are using.
    校准NDF,测量放NDF前后的光强,记录衰减。必须记录实际OD值和对应波长。

  2. Add a reflector (mirror) in the sample arm.样品臂放置反射镜

  3. Align the sample arm with the calibrated ND filter in place (this ensures that your alignment is as good as possible when you make the measurement).样品臂放置NDF校准样品臂,同时确保数字转换器范围接近期待值来最小化数字噪声。(make sure you set your digitizer range to nearly what you expect to measure to minimize digitization noise)

  4. Adjust the reference arm power so that you are near to saturation with the current ND filter in the sample arm (this may require also having some sort of filter in the reference arm).调节参考镜功率接近饱和,此时样品臂有NDF,可能也需要NDF在参考臂。

  5. Take an A-scan and find the peak. The reflector should be placed close to the DC point to reduce errors from fall-off(脱落).记录信号,参考镜必须放置接近DC的地方来降低fall-off

  6. Block the sample arm and take a measurement of the noise floor. (where the peak would normally be; use many pixels about where the peak would be; you can also take pixels from the same location as a function of time)挡住样品臂测试噪声,在peak所在的地方取值,

  7. Take the ratio of the A-scan peak (linear scale) to the noise rms(root mean square均方根). This number is your SNR. When reported in dB you should multiply it by 20.SNR = 20*log10(peak / noise_rms).We use 20log10 instead of 10log10 because in the interferometric equation, the information that corresponds to the peak of the A-scan value is proportional to the electric field from the sample (i.e., proportional to sqrt(Rs)*Es), not the intensity.

  8. To calculate the sensitivity, add to the SNR the deficit caused by use of the ND filters. As mentioned above, the filter must be counted twice for double-passed light.

    Sensitivity = SNR + 20*OD

where OD = optical density. This is because OD is already expressed in log10 form.

计算系统灵敏度的程序:

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Wed Dec 14 18:45:30 2016

@author: zhuyue
"""

import matplotlib.pyplot as plt
import numpy as np
from scipy import signal
from scipy.fftpack import fft, fftshift

# %% Calibrate NDF 这是 放置NDF后光强 文件 和 原始光强 文件%%
INDF = 0.243 #uw
I0 = 294 #uw
OD = (np.log10(I0 / INDF))/2
#OD = max(od)
INDF_R = 44.4 #uw
I0_R = 294 #uw
OD_R = (np.log10(I0 / INDF_R))/2
# %% PEAK 这是 参考臂饱和样品臂NDF的干涉信号 文件%%

#%%initialization%%
SelRan = np.arange(0,2048,1)
window = signal.hann(SelRan.size)
ref = np.loadtxt(open("NKT_ND20_52us_REF.csv","rb"),delimiter=",",skiprows=0)
sam = np.loadtxt(open("NKT_ND20_52us_SAM.csv","rb"),delimiter=",",skiprows=0)
AveRef = ref + sam

#%% Read data %%
I = np.loadtxt(open("NKT__ND20_52us_0thou.csv","rb"),delimiter=",",skiprows=0)

#%% Reshape %%
I = I - AveRef
I = I * window
S = fft(I, I.size)
Signal = np.abs(S)
peak_range = np.arange(0,50,1)
peak = max(Signal[peak_range])

# %% NOISE 这是 noise floor 文件 %%
N = np.loadtxt(open("NKT_ND20_52us_BG.csv","rb"),delimiter=",",skiprows=0)
N = np.abs(fft(N, N.size))
noise_range = np.arange(500,1023,1)
Noise = N[noise_range]

# %% RMS %%
from math import sqrt
def qmean(num):
    return sqrt(sum(n*n for n in num)/len(num))
noise_rms = qmean(Noise)

sensi = 20 * np.log10 (peak / noise_rms) + 20 * OD + 20 * OD_R

What I learned from:

  • Optical power meter 要确定波长范围再读数据
  • Noise floor
    • Turn off the laser and make a reading
    • Turn on the laser and block the sample
    • Use a section of the FFT where there’s no signal as noise floor.

Reference

  1. Mike’s WeeklyUpdate
  2. NDF_Thorlabs
  3. RMS 的计算
  4. 任意语言下的RMS

Log_20160519_Sensitivity

  • Sensitivity in FF-OCT
    • Dubois, A., et al. (2002). “High-resolution full-field optical coherence tomography with a Linnik microscope.” Applied Optics 41(4): 805-812.
    • ZJH Dissertation
    • 系统灵敏度需要用参考臂
  • CCD的选择

Sensitivity in FF-OCT

Dubois, A., et al. (2002). “High-resolution full-field optical coherence tomography with a Linnik microscope.” Applied Optics 41(4): 805-812.

The sensitivity of the instrument characterizes its ability to detect a small coherent signal masked by the preponderant incoherent background.

  • 系统灵敏度
  • 样品灵敏度
  • Q1 Rmin和Rinc是如何求得?
  • A1 见 ZJH 大论文

ZJH Dissertation

量子井深指的是光敏元件能够容纳的电荷数的最大值,即饱和状态下的电荷数。而当光强的强度恰好使得光敏元件饱和,则光敏器件本身的噪声(电噪声,热噪声等)将远小于光子的散粒噪声。 一般来说,生物组织Rinc=0.4%~0.8%;(S+Setup)inc=1%;r=2%;

Reference: Sacchet, D., et al. (2008). “Simultaneous dual-band ultra-high resolution full-field optical coherence tomography.” Optics Express 16(24): 19434-19446.

Abstract: Ultrahigh-resolution full-field optical coherence tomography (FF-OCT) is demonstrated in the 800 nm and 1200 nm wavelength regions simultaneously using a Silicon-based (Si) CCD camera and an Indium Gallium Arsenide (InGaAs) camera as area detectors and a halogen lamp as illumination source. The FF-OCT setup is optimized to support the two broad spectral bands in parallel, achieving a detection sensitivity of ~ 90 dB and a micrometer-scale resolution in the three directions. Images of ex vivo biological tissues are presented (rabbit trachea and Xenopus laevis tadpole) with an increase in penetration depth at 1200 nm. A color image representation is applied to fuse both images and enhance spectroscopic property visualization.

理论动态范围

参考臂的反射率r=2%、生物样品对应的非相干部分的反射率Rinc=0.5%,无样品时实验装置的反射率0.2%、并用100次的叠加数,理论动态范围为67dB.

实际测量

为了测我们全场OCT系统实际的动态范围,我们对氟化钙晶体表面某一区域进行了纵向扫描(步长为 0.3um)。该晶体表面理论的反射系数为 0.13% (相当于衰减29dB)。我们对不同叠加数重复了上述测量,得到了不同叠加数对应的动态范围。图3.14 为理论与实测动态范围随叠加数变化的曲线。从该图中可以看出,实测与理论值比较相符,但都略小于理论值。这是由于理论推导时都用到了最理想的条件,而实测中只能尽量调到与理论值相符。 10*log(Rmax/Rmin)

系统灵敏度需要用参考臂

FFOCT测量某一样品灵敏度方法:

  • 1.载玻片作为样品;
  • 2.轴向扫描并求出en face图;
  • 3.取光强纵向拟合;
  • 4.取噪声为最小探测信号n,取最大值为强度信号I;
  • 5.动态范围为:10log10(I/n) + 样品本身的衰减系数, 例如:载玻片反射率为4%,则衰减系数为:10log10(0.04)=-14dB。

前辈郑京镐博士说:

系统灵敏度需要按照参考臂去求,样品是可以变化的,实际测量结果(跟参考臂反射率无关,此时的参考臂只起到匹配作用)为某一样品时的灵敏度。公式里是最理想的值,但结果应该能匹配,或者就差一些。

我要谢谢郑京镐博士。但是最近又遇到了问题,我们CCD是8位,那就可以不测灵敏度了,因为最多就是10log(255/1),这tm才多少呢?

CCD的选择

涉及到像素深度的概念,我们CCD是8bit,内部也是只能达到8bit。而ZJH用的CMOS像素深度12bit,内部取出的数据则为16bit。所以要选择新相机。

  • Imperx MDC-1004 48HZ 12bit
  • Dalsa 1M15 1024*1024 uncontinued
  • Dalsa 1.4M 1400*1024 100FPS up to 10 bits
  • PhotonFocus MV-D1024E-160-CL-12 1024*1024 150fps 12/10/8 bit