assignmentutor™您的专属作业导师

assignmentutor-lab™ 为您的留学生涯保驾护航 在代写光学Optics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。我们的专家在代写光学Optics代写方面经验极为丰富，各种代写光学Optics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

## 物理代写|光学代写Optics代考|An Example

Consider an experiment to check whether the electric field obeys the principle of linear superposition. To do this we could use a Michelson interferometer with monochromatic light of wavelength $\lambda$. Suppose $x$ is the distance moved by an end mirror of the interferometer while $y$ is proportional to the power seen at the output of the interferometer. We measure $y$ as a function of $x$ and compare the results to the expected response ${ }^{9}$ assuming $x \ll \lambda$.
$$y=\left(\frac{4 \pi}{\lambda}\right) x+1 .$$
The predicted relationship relies on the assumption that linear superposition of electric fields is exact. We now fit our measured data to a straight line: $y=a_{1}+a_{2} x$. If a straight line is not consistent with the data or if $a_{1}$ and $a_{2}$ are not consistent with the expected values, then something must be missing in our understanding.

Figure $2.14$ shows a simulated data set for such an experiment with the best-fit line included. To evaluate whether the data is consistent with this best-fit straight line, we need to check how far the best-fit line lies from the data points and how that compares with the uncertainties. One expects the data to be scattered about the fit due to measurement uncertainties but a “chi-square test” (see below) can tell us whether the scatter is greater or smaller than expected. If the variation of the data around the fit is too large and we are sure we understand our apparatus and the errors, then we have to consider that the fit function may be wrong. If that’s the case, the physics that leads to the fit function may need to be examined as well. And that’s ultimately what we want to discover when we do an experiment: whether or not the model representing our physical understanding agrees with the data. The lower the measurement uncertainties, the more stringently we can make that test.

I should emphasize here that usually it’s not the physics that’s found to be incorrect. Rather, there may be unaccounted for systematic errors that can explain a discrepancy with the model. However, if other, independent experimenters reproduce your result and also cannot identify any reason for the discrepancy, the case becomes stronger.

The steps required to do a fit, perform a chi-square test, and find the uncertainties in the fit parameters, are described below.

## 物理代写|光学代写Optics代考|Finding the best fit

Let’s assume we have taken $N$ data pairs $x_{i}$ and $y_{i},(i=1 . . N)$ perhaps arranged with uncertainties $\Delta y_{i}$ into a table as follows. ${ }^{10}$
\begin{tabular}{|c|c|c|}
\hline $\mathbf{x}$ & $\mathbf{y}$ & $\boldsymbol{\Delta y}$ \
\hline$x_{1}$ & $y_{1}$ & $\Delta y_{1}$ \
$x_{2}$ & $y_{2}$ & $\Delta y_{2}$ \
$\vdots$ & $\vdots$ & $\vdots$ \
$x_{N}$ & $y_{N}$ & $\Delta y_{N}$ \
\hline
\end{tabular}
Our task is then to evaluate whether the relationship between the $x_{i}$ ‘s and the $y_{i}$ ‘s is actually well described by our chosen fit function $f\left(x, a_{1}, a_{2}, \ldots, a_{m}\right)$. The idea is to vary the parameters $a_{1}, a_{2}, \ldots, a_{m}$ so that the mean square vertical distance between the data points and the fit function becomes as small as possible. For this reason, we call it a “least squares” fit. However, we’d like data points with low uncertainty to count more in defining the best fit than data points with large uncertainty. So, we will divide the vertical distance of each data point from the fit curve by the uncertainty $\Delta y_{i}$ thus reexpressing the distance in units of the uncertainty
$$d_{i} \equiv \frac{y_{i}-f\left(x_{i}, a_{1}, a_{2}, \ldots, a_{m}\right)}{\Delta y_{i}} .$$
The best fit is then given by minimizing the sum of the squared distances
$$\chi^{2}=\sum_{i=1}^{N} d_{i}^{2}$$
This quantity is known as the chi-square, $\chi^{2}$, and is pronounced “Kai-square.”

# 光学代考

## 物理代写|光学代写Optics代考|An Example

$$y=\left(\frac{4 \pi}{\lambda}\right) x+1 .$$

## 物理代写|光学代写Optics代考|Finding the best fit

$$d_{i} \equiv \frac{y_{i}-f\left(x_{i}, a_{1}, a_{2}, \ldots, a_{m}\right)}{\Delta y_{i}} .$$

$$\chi^{2}=\sum_{i=1}^{N} d_{i}^{2}$$

## 有限元方法代写

assignmentutor™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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师