### 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
• Advanced Probability Theory 高等楖率论
• Advanced Mathematical Statistics 高等数理统计学
• (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

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