## 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).

## 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.

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

Based on above:

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

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.

## 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」：

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.

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

## 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.

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

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

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

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).

## 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.

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

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

## What can I learn from

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.

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).

## 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.

1. 噪声分析与消噪算法
2. 校正带宽
3. 自动识别峰值信号

## What I can learn from

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

$$d_{tot}=\frac{\lambda⋅n}{{NA}^2}+\frac{n}{M⋅NA}⋅e$$
$d_{tot}$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。

## 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$F_k/2$:

$$(f_K)_{max}=F_k/2$$

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

$$Z_{max}=\frac{2ln2}{\delta k’}$$

## 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)

## 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

1. 时域OCT
2. 谱域OCT
3. 扫频OCT
4. 全场OCT

1. 光源
2. 参考臂
3. 样品臂
4. 探测臂

1. 时间相干性
2. 空间相干性

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

1. 产生原因
2. 实验及结果

1. 产生原因
2. 实验及结果

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

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

## 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

# 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.

## 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.

#!/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)
AveRef = ref + sam

#%% 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.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

• 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

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.

## 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。

# CCD的选择

• 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