## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|EE262

statistics-lab™ 为您的留学生涯保驾护航 在代写三维成像Three-Dimensional Imaging方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写三维成像Three-Dimensional Imaging方面经验极为丰富，各种代写三维成像Three-Dimensional Imaging相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Effect of Pixel Pitch

Here, it is assumed the elemental image has a pixel structure, and the pitch is given by $P_{N P}$. The elemental image is sampled by the pixels on the elemental images. The maximum projected spatial frequency of the object is limited by the Nyquist frequency:
$$\alpha_{N P} \cong \frac{g}{2 P_{N P}} .$$
Visual spatial frequency $\beta_{N P}$ according to $\alpha_{\mathrm{NP}}$, is given by Eq. (1.39):
$$\beta_{N P}=\alpha_{N P} \frac{L_{O B}-Z_{s}}{\left|Z_{s}\right|}=\frac{g}{2 P_{N P}} \frac{L_{O B}-Z_{s}}{\left|Z_{s}\right|}$$
Here, assuming $-z_{s}$ is infinite, we obtain:
$$\beta_{N P}=\frac{g}{2 P_{N P}} .$$
Maximum visual spatial frequency $\beta_{M X}$ is given by the following equation:
$$\boldsymbol{\beta}{M X}=\min \left(\boldsymbol{\beta}{N P}, \boldsymbol{\beta}{D F}, \boldsymbol{\beta}{V L}, \boldsymbol{\beta}{N L}\right)$$ where $\beta{D F}$ is a spatial frequency that gives the null response by diffraction or the defocus described in the former section. When the diameter of the elemental lens is more than about $1.0 \mathrm{~mm}, \beta_{D F}$ is more than $\beta_{V L}$ under the condition in Eq. (1.42). If the pixel pitch of each elemental image $P_{N P}$ is too large, the MTF response depends mainly on the Nyquist frequency $\beta_{N P}$ by the pixel pitch.
The viewing zone is given by [19]
$$\boldsymbol{\phi}{V Z} \cong \frac{P{a}}{g}$$
A wide viewing zone requires small $\mathrm{g}$, but small $g$ degrades $\beta_{N P}$. To compensate for the degradation, $P_{N P}$ needs to be smaller.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Experimental System

To obtain moving pictures, an electronic capture device, such as a CCD or CMOS image sensor, is set on the capture plate and takes elemental images. For reconstruction, a display device such as an LCD panel or an EL panel is placed behind the lens array. Video signals are transmitted from the capture device to the display device.

The size of the lens array for capturing needs to be large enough to obtain a large parallax; however, it is difficult to develop a large capture device for moving pictures. In the actual system, a television camera using a pickup lens is set to capture all elemental images formed by the elemental lenses. In the future, a capture device of the same size as the lens array will need to be developed and set immediately behind the lens array.

Figure $1.6$ shows an experimental real-time integral imaging system. A depth control lens, a GRIN lens array [14, 15], a converging lens, and an EHR (extremely high resolution) camera with 2,000 scanning lines [23] are introduced for capturing. The depth control lens [10] forms the optical image of the object around the lens array, and the GRIN lens array captures the optical image. Many elemental lenses (GRIN lenses) form elemental images near the output plane of the array. An elemental GRIN lens acts as a specific lens forming an erect image for the object in the distant R.O. area to avoid pseudoscopic 3-D images. The converging lens [10], which is set close to the GRIN lens array, leads the light rays from elemental GRIN lenses to the EHR camera. The converging lens uses light rays efficiently, but is not an essential which are formed around the output plane of the GRIN lens.

Table $1.1$ shows the experimental specifications of the capture setup. Figure $1.7$ shows the two-dimensional arrangement of the GRIN lens array used in the experiment. The pitch between the adjacent elemental lenses corresponds to $21.3$ pixels of the EHR camera. The arrangement has a delta structure, which is more efficient than a grid structure. The horizontal pitch is considered $21.3 / 2$ and the vertical one is considered $21.3 \times \sqrt{3} / 2$, equivalently.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Effect of Pixel Pitch

$$\alpha_{N P} \cong \frac{g}{2 P_{N P}}$$

$$\beta_{N P}=\alpha_{N P} \frac{L_{O B}-Z_{s}}{\left|Z_{s}\right|}=\frac{g}{2 P_{N P}} \frac{L_{O B}-Z_{s}}{\left|Z_{s}\right|}$$

$$\beta_{N P}=\frac{g}{2 P_{N P}} .$$

$$\boldsymbol{\beta} M X=\min (\boldsymbol{\beta} N P, \boldsymbol{\beta} D F, \boldsymbol{\beta} V L, \boldsymbol{\beta} N L)$$

$$\phi V Z \cong \frac{P a}{g}$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|GRA3312

statistics-lab™ 为您的留学生涯保驾护航 在代写三维成像Three-Dimensional Imaging方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写三维成像Three-Dimensional Imaging方面经验极为丰富，各种代写三维成像Three-Dimensional Imaging相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Derivation of MTF in Capture and Display Stages

As shown in Fig. 1.1, spatial frequency $\alpha$ is normalized by the distance [19]. These have the following relationship between $v_{s}, v_{p}$, and $g$ :
$$\alpha=\frac{1}{\tan ^{-1}\left[1 /\left(v_{s}\left|z_{s}\right|\right)\right]} \cong v_{s}\left|z_{s}\right|=v_{p} \mathrm{~g} .$$
The MTF for the capture stage can be expressed as the product of the elemental lens’s MTF and the capture device’s MTF. Let $M T F_{p}(\alpha)$ represent the MTF for the capture stage. The MTF of the display stage can also be expressed as the product of the elemental lens’s and display device’s MTFs. Let $M T F_{d}(\alpha)$ represent the MTF for the display stage. In this section, we assume that the numbers of pixels of these capture and display devices are infinite, meaning the MTF of the elemental lens is the sole factor affecting the resolution. These MTFs are obtained by Eqs. (1.24) and (1.25) and are rewritten by $\alpha$.

MTF can be calculated as the Fourier transform of the squared amplitude of the point spread function. It is equal to calculating the autocorrelation function of the pupil function [20, 21], as is well-known. It is assumed that the pupil of each elemental lens is a two-dimensional circle. The pupil function $P_{f p}$ of the elemental lens for the capture stage, which includes the effect of the defocusing, is expressed as follows:
$$P_{f p}=\exp \left[i \pi\left(x_{i . m}^{2}+y_{i . m}^{2}\right) E_{p}\left(z_{s}\right) / \lambda\right],$$
where
$$E_{p}\left(z_{s}\right)=\left|1 / g-1 / z_{s}-1 / f\right|,$$
$\lambda$ is the wavelength, $f$ is the focal length of the elemental lens for capture and display, and $z_{s}$ is object distance or image distance, mentioned above. Coordinate $\left(x_{i, m}, y_{i, m}\right)$ is applied to the plane of the pupil.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Examples of MTF

The spatial frequency measured from the observer’s position, i.e., visual spatial frequency $\beta$ (cpr), is defined here to clarify the argument. Spatial frequencies $\alpha$ and $\beta$ have the following relationship [19]:
$$\beta=\alpha\left(L_{O B}-z_{s}\right) /\left|z_{s}\right|,$$
where $L_{O B}$ is the viewing distance between the lens array and the observer. This $\beta$ is originally defined in the display stage. It can be expanded in the capture stage and considered as a spatial frequency when an object is viewed from the observer’s position.

When the observer views the reconstructed image, it is being sampled at the elemental lens, as shown in Fig. 1.2. The maximum spatial frequency of reconstructed images is limited to the Nyquist frequency. With $P_{a}$ representing the pitch between elemental lenses, the Nyquist frequency can be expressed as follows based on the visual spatial frequency:
$$\beta_{N L}=L_{O B} / 2 P_{a} .$$
The sampling effect is conspicuous if the elemental lenses and observer’s pupil are pinholes. It is also clear when the image is located on the lens array. We assume the Nyquist frequency limitation is expanded when the elemental lenses and the pupil are lenses, not pinholes, or when the image is not located on the lens array.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Derivation of MTF in Capture and Display Stages

$$\alpha=\frac{1}{\tan ^{-1}\left[1 /\left(v_{s}\left|z_{s}\right|\right)\right]} \cong v_{s}\left|z_{s}\right|=v_{p} \mathrm{~g} .$$

MTF 可以计算为点扩散函数的平方幅度的傅里叶变换。它等于计算瞳孔函数的自相关函数[20, 21]，这是众所周知 的。假设每个基本透镜的光瞳是二维圆。瞳孔函数 $P_{f p}$ 包含散焦效果的捕捉阶段的基本镜头的表达如下:
$$P_{f p}=\exp \left[i \pi\left(x_{i . m}^{2}+y_{i . m}^{2}\right) E_{p}\left(z_{s}\right) / \lambda\right],$$

$$E_{p}\left(z_{s}\right)=\left|1 / g-1 / z_{s}-1 / f\right|,$$
$\lambda$ 是波长， $f$ 是用于捕捉和显示的基本镜头的焦距，并且 $z_{s}$ 是物距或像距，如上所述。协调 $\left(x_{i, m}, y_{i, m}\right)$ 应用于瞳孔平面。

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Examples of MTF

$$\beta=\alpha\left(L_{O B}-z_{s}\right) /\left|z_{s}\right|,$$

$$\beta_{N L}=L_{O B} / 2 P_{a} .$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|BMES621

statistics-lab™ 为您的留学生涯保驾护航 在代写三维成像Three-Dimensional Imaging方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写三维成像Three-Dimensional Imaging方面经验极为丰富，各种代写三维成像Three-Dimensional Imaging相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Geometric Approach

Though the principle of image formation is described above, a more thorough explanation must include a description of ray tracing by geometrical optics $[11,12]$. Figures 1.1(a) and (b) focus on around the $m$-th elemental lenses, many of which constitute an array. A point light source is placed at distance $L_{s}$ from the lens array and is expressed as a delta function $\delta\left(x_{m}-x_{s, m}\right)$, where $x_{s . m}$ represents the object’s position. $x_{i . m}$ and $x_{p . m}$ represent the positions in the incident plane of the lens array and capture plate, respectively. Subscript $m$ indicates the position on the coordinates where the intersection of an incident plane and its own optical axis is the origin for each elemental lens. The following $x$ can be obtained by adding $m P_{a}$ to $x_{m}$, that is, the distance from the origin of the whole array to the optical axis of the elemental lens:
$$x=x_{m}+m P_{a},$$
where $x_{s, m}, x_{i, m}$ and $x_{p, m}$ are converted to $x_{s}, x_{i}$ and $x_{p}$, respectively, by adding $m P_{a}$ in the same way. $P_{a}$ is the pitch between adjacent elemental lenses. Note that $z$ is not assigned a subscript because the coordinates of each elemental lens match those of the whole array. The origin of the $x$ and $z$ coordinates of the whole array is defined as the point where the optical axis crosses the incident plane of the central elemental lens. To simplify calculations, we use the two-dimensional coordinates $(x, z)$, defined by the $x$-axis and optical axis $z$.

Real objects in the capture stage can be located in the space with a negative value of $z$, which is called the real objects area (R.O. area). Real images in the display stage can be located in the space with a positive value of $z$, which is called the real images area (R.I. area). The following calculations can be applied to the three-dimensional coordinates $(x, y, z)$ defined by the optical axis and a plane that crosses it perpendicularly. There is a relationship between $x_{s . m}$ and $x_{p . m}$ in the capture stage shown in Fig. 1.1(a):
$$\frac{x_{s . m}}{z_{s}}=\frac{x_{p . m}}{g},$$
where $g$ is the gap between the elemental lens and the capture plate. As shown in Fig. 1.1(b), we assume the pitch of the elemental lenses and the gap in the display stage are the same as in the capture stage, respectively. $x_{d, m}$ is the position of the point light source in the display plate and $x_{m}$ represents the space in which the reconstructed image is formed. There is a similar relationship between $x_{d, m}$ and $x_{m}$ in the display stage:
$$-\frac{x_{d . m}}{g}=\frac{x_{m}}{z}$$

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Wave Optical Approach

By using wave optics the captured elemental images synthesize an optical image in the display stage $[16,17]$. We present the response of the $m$-th elemental lens on the pickup plate shown in Fig. 1.1(a). First, the wave (electric field) entering the elemental lens of the pickup stage is calculated by Fresnel’s approximation as
\begin{aligned} u_{i, m}\left(x_{i . m}\right)=& \frac{1}{j \lambda L_{s}} \exp \left(-j k \frac{x_{i, m}^{2}}{2 L_{s}}\right) \int_{o b j e c t} \delta\left(x_{m}-x_{s . m}\right) \exp \left(-j k \frac{x_{m}^{2}}{2 L_{s}}\right) \ & \exp \left(-j k \frac{x_{m} x_{i, m}}{L_{s}}\right) d x_{m} \ =& \frac{1}{j \lambda L_{s}} \exp \left(-j k \frac{x_{i, m}^{2}}{2 L_{s}}\right) \exp \left(-j k \frac{x_{s, m}^{2}}{2 L_{s}}\right) e\left(-j k \frac{x_{s, m} x_{i . m}}{L_{s}}\right) \end{aligned}
where $L_{s}=Z_{i}-Z_{s}, k$ is the wave number and equals $2 \pi / \lambda$, and $\lambda$ is the wavelength. The output wave from an elemental lens is a product of Eq. (1.8) and the phase shift function of the elemental lens:
$$u_{i, m}\left(x_{i, m}\right) \exp \left(x_{i, m}^{2} / 2 f\right) .$$
The wave on the capture plate is obtained by
\begin{aligned} &h_{p . m}\left(x_{p . m}\right)=\frac{1}{j \lambda g} \exp \left(-j k \frac{x_{p . m}^{2}}{2 g}\right) \int_{-w_{a / 2}}^{w_{a / 2}} u_{i . m}\left(x_{i . m}\right) \exp \left(\frac{x_{i, m}^{2}}{2 f}\right) \exp \left(-j k \frac{x_{i, m}^{2}}{2 g}\right) \ &\quad \exp \left(-j k \frac{x_{i, m} x_{p . m}}{g}\right) d x_{i . m}, \end{aligned}
where $f$ is the focal length of the elemental lens, and $w_{a}$ is the width of an elemental lens.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Geometric Approach

$\delta\left(x_{m}-x_{s, m}\right)$ ，在哪里 $x_{s . m}$ 表示对象的位置。 $x_{i . m}$ 和 $x_{p . m}$ 分别表示透镱阵列和捕获板在入射平面中的位置。下 标 $m$ 表示在坐标上的位置，其中入射平面和它自己的光轴的交点是每个元素透镜的原点。以下 $x$ 可以通过添加获得 $m P_{a}$ 至 $x_{m}$ ，即整个阵列的原点到基本透镜光轴的距离:
$$x=x_{m}+m P_{a},$$

$$\frac{x_{s . m}}{z_{s}}=\frac{x_{p . m}}{g},$$

$$-\frac{x_{d . m}}{g}=\frac{x_{m}}{z}$$

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Wave Optical Approach

$$u_{i, m}\left(x_{i . m}\right)=\frac{1}{j \lambda L_{s}} \exp \left(-j k \frac{x_{i, m}^{2}}{2 L_{s}}\right) \int_{\text {object }} \delta\left(x_{m}-x_{s . m}\right) \exp \left(-j k \frac{x_{m}^{2}}{2 L_{s}}\right) \quad \exp \left(-j k \frac{x_{m} x_{i, m}}{L_{s}}\right) d x_{r}$$

$$u_{i, m}\left(x_{i, m}\right) \exp \left(x_{i, m}^{2} / 2 f\right) .$$

$$h_{p . m}\left(x_{p . m}\right)=\frac{1}{j \lambda g} \exp \left(-j k \frac{x_{p, m}^{2}}{2 g}\right) \int_{-w_{a / 2}}^{w_{a / 2}} u_{i . m}\left(x_{i . m}\right) \exp \left(\frac{x_{i, m}^{2}}{2 f}\right) \exp \left(-j k \frac{x_{i, m}^{2}}{2 g}\right) \quad \exp (-j k .$$

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。