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

Integral Harmonic Feedback In first- or second-harmonic feedback, described above, the correction signal is linearly proportional to the amplitude of the first or second harmonic with amplification constants $A$ and $B$, respectively. If there is a continuous phase shift drift during the exposition $\left(\varphi_N\right.$ increases continuously during the exposure), the PZT-supported mirror must be shifted continuously to compensate for the fringe drift. In this case, as the amplification is not infinity, $\varphi$ will shift further away continuously from its initial value of zero or $\frac{1}{2} \pi$ to provide the necessary voltage for the PZTsupported mirror. To correct this phase shift, $V_0$ must be manually changed during the exposure to compensate for the drift.

In this case, more efficient performance of the stabilization system may be obtained if an integral feedback is used by introducing a simple integrator device between the lock-in amplifier output and the PZT power supply. The effect of this integrator in the feedback loop may be understood by substituting the linear time-independent terms $A \sin (\varphi)$ and $B \cos (\varphi)$ in Eqs. $3.13$ and 3.17, respectively, by the integral voltages
\begin{aligned} &\frac{A}{\tau_i} \int_0^t \sin (\varphi) d t \ &\frac{B}{\tau_i} \int_0^t \cos (\varphi) d t \end{aligned}
with $\tau_i$ being the time constant of the integrator device and the $t$ the time elapsed since the instant that the loop is closed $(t=0)$.

In the integral feedback the correction signal may be much greater than the error signal, keeping the phase $\varphi$ close to its initial value.

The necessary amplification may be achieved by increasing the amplification factors $A$ or $B$ or by decreasing the integration time $\tau_i$.

This integral feedback is particularly interesting for compensating large and slowly varying perturbations like temperature drift and air current drafts, allowing the stabilization of nonstationary holograms.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Fringe Lock with Arbitrary Phase

Fringe Lock with Arbitrary Phase $\varphi$ To record self-stabilized stationary holograms in photorefractive crystals in the presence of an external electrical field [8], or even to self-stabilize holograms using the reflected waves [7], feedback using single-harmonic signals does not work because the phase shift $\varphi$ between the interfering waves must be different from $0, \pi$, or $\pm \frac{1}{2} \pi$.
By adequately processing and combining the first- and second-harmonic signals, before feedback of the PZT-supported mirror, it is possible also to lock the fringe pattern with an arbitrary phase shift $\varphi$. A discussion of this processing, described in detail in a recent paper [9], is presented below.
The electrical signal measured directly by the photodetector contains all harmonics of the dither frequency $\Omega$. The second-harmonic electrical signal may be represented by
$$V_{2 \Omega}(t)=4 k_2 J_2\left(\varphi_d\right) \sqrt{\eta_0 \eta_1 I_1 I_2} \cos (\varphi) \cos (2 \Omega t)$$
which is directly proportional to the light intensity $I_{2 \Omega}(t)$ of Eq. 3.12.
The first-harmonic signal, proportional to light intensity $I_{\Omega}(t)$ of Eq. 3.11, is separated from $I_{\mathrm{R}}$ (Eq. 3.9) using a bandpass filter. After the bandpass filter, the first-harmonic signal is frequency doubled, phase shifted in relation to the second-harmonic signal (Eq. 3.22), and amplified to generate a new electrical second-harmonic signal:
$$V_{\Omega 2}(t)=-4 k_1 J_1\left(\varphi_d\right) \sqrt{\eta_0 \eta_1 I_1 I_2} \sin (\varphi) \sin (2 \Omega t+\delta)$$

## 电子工程代写|三维成像代写三维成像代考|积分谐波反馈

\begin{aligned} &\frac{A}{\tau_i} \int_0^t \sin (\varphi) d t \ &\frac{B}{\tau_i} \int_0^t \cos (\varphi) d t \end{aligned}
，其中$\tau_i$是积分器的时间常数，$t$是自环路关闭的瞬间$(t=0)$经过的时间

## 电子工程代写|三维成像代写三维成像代考|条纹锁与任意相位

，与光强成正比 $I_{2 \Omega}(t)$ 式3.12的。

$$V_{\Omega 2}(t)=-4 k_1 J_1\left(\varphi_d\right) \sqrt{\eta_0 \eta_1 I_1 I_2} \sin (\varphi) \sin (2 \Omega t+\delta)$$

## 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。

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

Point-by-point holograms can be recorded sequentially as suggested above. Alternatively, the set of points can be used as a whole to generate a pattern that can be recorded as a whole. Obviously, then it will be a coherent recording of a line. However, if we take an imaginary point source to calculate its diffraction pattern and store this electronically, we can display it on a spatial light modulator (SLM) or write the information onto a diffractive optical element. Illuminating this element by coherent light will reconstruct the point source. Now, as before, we can assemble in the computer memory the diffraction patterns of the whole sequence of points in the trajectory and then we essentially have an electronic hologram of the world line. That is, we throw the time information away before recording rather than during recording. The now-traditional approach to doing this is to compute a Fresnel transform of the world line and then use some computer hologram method to record it. But there may be a way to record such holograms on line electronically. We review one way of doing this briefly here.

For historical reasons not of interest here, we began to work on the electronic evolution of holograms on SLMs. Given a way to measure and evaluate the holographically produced image, we can use optimization algorithms, such as genetic algorithms or projections-onto-constraint-sets algorithms to adjust the pixel values of the SLM to achieve optimum results $[12$, 13]. That is, we would evolve a hologram pattern electronically with the figure of merit being the closeness of correspondence of the reconstructed wave-front intensity to the target world line [14].

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

In principle, this chapter reviews an extremely narrow aspect of holography. However, looking at this issue in a broader context, the developments described here are significantly related to many other aspects of holography and may have an appreciable impact on holography in the third millenium. We may recall that holography was invented for microscopic purposes [15]. Very little was achieved in that field until now, but holography made the big strides forward when it was realized that real-looking 3D images can be recorded and reconstructed $[16,17]$. With these developments beautiful $3 \mathrm{D}$ display holograms of real objects could be made. This is where our first experiments came in: Can we record a drawing that physically does not exist? As described in this chapter, our success was quite limited. Much of the phenomena we observed at those early stages we did not exactly understand, and we even reinvented average-time holographic interferometry without realizing it.

The further development toward achieving our aim came when it was realized that a holographic recording is a “drawing” of interference fringes and, in principle, one may use a computer to calculate these fringes and plot them on a transparency [18]. Illuminating this transparency with the calculated reference wave will regenerate the object even if that object existed only in the computer memory. This was the beginning of what is referred to as computergenerated holography $(\mathrm{CGH})$.

The initial idea behind $\mathrm{CGH}$ was the design of objects for comparison in a production line or for decorative displays. It did, however, not take long to find other applications in a diverse list of areas. The reason is that, if we generalize the notion of the $\mathrm{CGH}$, it can be designed to generate any desired complex amplitude distribution as long as it does not contradict physical principles and technological limitations. This is really the basis for the more general field of diffractive optical elements (DOEs). Most DOEs are digitally designed, but from various aspects they function like optically recorded holograms. As indicated earlier, DOEs can now be designed for displaying line segments in 3D space [19-22] as well as much more complicated structures [23-25]. A specially interesting structure is an intensity distribution that rotates during propagation $[26,27]$. In this structure, light rays describe a helical trajectory (Fig. 2.2); they are helical rays. Obviously, as shown in this chapter, such a continuous trajectory cannot be recorded as a continuous-time exposure of a moving point source.

## 电子工程代写|三维成像代写三维成像代考|DISCUSSION

$\mathrm{CGH}$背后最初的想法是为了在生产线上进行比较或用于装饰展示而设计的对象。然而，它的确很快就在一系列不同的领域中找到了其他应用。原因是，如果我们推广$\mathrm{CGH}$的概念，只要不违背物理原理和技术限制，它就可以被设计成产生任何想要的复杂振幅分布。这实际上是衍射光学元件更一般领域的基础。大多数do是数字化设计的，但从各个方面来看，它们的功能就像光学记录的全息图。如前所述，现在可以设计do在3D空间中显示线段[19-22]，以及更复杂的结构[23-25]。一个特别有趣的结构是在传播过程中旋转的强度分布$[26,27]$。在这个结构中，光线描述了一个螺旋轨迹(图2.2);它们是螺旋射线。显然，如本章所述，这样的连续轨迹不能被记录为移动点源的连续时间曝光

## 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。

Posted on Categories:Three-Dimensional Imaging, 三维成像, 电子代写

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

Assume a point source of strength $A_0$ positioned at a point represented by $\boldsymbol{\rho}=\hat{x} \hat{\xi}+\hat{y} \eta+\hat{z} \zeta$ on the left of a recording plane with coordinates $\mathbf{r}=\hat{x} x+\hat{y} y+\hat{z}$, where the “hat” denotes a unit vector. The complex amplitude distribution on the recording plane (Fig. 2.1) is a spherical wave given by (see, e.g., Ref. 5),
$$u_0(\mathbf{r})=\frac{A_0}{j k|\mathbf{r}-\rho|} \exp (j k|r-\rho|)$$
where $k=2 \pi / \lambda$ is the wave number and $\lambda$ is the wavelength. If the point source moves, the vector $\rho$ is a function of time, which makes the complex amplitude on the observation plane also a function of time. If we wish to record a hologram, we need a reference beam, $u_r$, and expose a recording medium for a time $T$. That is, the recorded intensity pattern will be given by
$$I(\mathbf{r})=\int_0^T\left|u_r+u_o\right|^2 d t=\int_0^T\left(\left|u_r\right|^2+\left|u_o\right|^2+u_r^* u_o+u_r u_o^\right) d t$$ The first two terms constitute the so-called zero-order term, which is of no interest at this point, while the last two terms are responsible for the reconstruction of the recorded object. The fourth term reconstructs a phaseconjugate image that, if properly recorded, is spatially separated from the third term which represents the true image. Therefore, we shall concentrate now on the third term, which has the form $$I_t(\mathbf{r})=\int_0^T u_r^(\mathbf{r}) u_o(\mathbf{r}, t) d t$$
where we noted explicitly that the object wave depends on time while the reference wave is constant in time.

## 电子工程代写|三维成像代写Three-Dimensional Imaging代考|Longitudinal Translation with Constant Velocity

Since the transverse coordinate of the source remains constant in this case, we may choose the $z$ axis along the trajectory such that $\boldsymbol{\rho}_t=0$. Accordingly, Eq. $2.9$ reduces to
$$I_t(\mathbf{r})=C \int_0^T \exp [-j k \zeta(t)] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta(t)}\right] d t$$
Motion with constant velocity along the $z$ axis can be written as
$$\zeta=\zeta_0+v_z t$$
where $v_z$ is the velocity of the source and $\zeta_0$ is the starting point. Maintaining the paraxial approximation, we may assume $\zeta_0 \gg v_z t$ during the integration time, and then we may write
$$\frac{1}{\zeta(t)}=\frac{1}{\zeta_0+v_z t} \approx \frac{1}{\zeta_0}\left(1-\frac{v_z t}{\zeta_0}\right)$$
Returning to Eq. 2.10, we obtain
$$I_t(\mathbf{r}) \approx C \exp \left[-j k \zeta_0\right] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right] \int_0^T \exp \left[-j k v_z t\left(1-\frac{\left|\mathbf{r}_t\right|^2}{2 \zeta_0^2}\right)\right] d t$$

\begin{aligned} I_t(\mathbf{r}) \approx & \frac{C}{j k v_z\left(1-\left|\mathbf{r}_t\right|^2 / 2 \zeta_0^2\right)} \exp \left[-j k \zeta_0\right] \ & \times \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right]\left{1-\exp \left[-j k v_z T\left(1-\frac{\left|\mathbf{r}_t\right|^2}{2 \zeta_0^2}\right)\right]\right} \end{aligned}
With some rearrangement of factors, this can be written in the form
\begin{aligned} I_t(\mathbf{r}) \approx & \frac{C}{j k v_z\left(1-\left|\mathbf{r}_t\right|^2 / 2 \zeta_0^2\right)}\left{\exp \left[-j k \zeta_0\right] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right]\right.\ &\left.-\exp \left[-j k\left(\zeta_0+v_z T\right)\right] \exp \left[-\frac{j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\left(1-\frac{v_z T}{\zeta_0}\right)\right]\right} \end{aligned}
Apart from the constant amplitude and phase factors, this expression contains two quadratic phase factors and thus represents two spherical wave fronts. One of these originates at the initial position of the source while the second has a radius of curvature modified to $R=\zeta_0^2 /\left(\zeta_0-v_z T\right)$. This is an equivalent point source at some intermediate position between the starting point and the ending point of the trajectory. There is also an exposure-time and velocity-dependent phase difference between the two sources leading to interference effects that are also exposure and velocity dependent. As a result, the final reconstructed pattern cannot be uniquely predicted from a practical point of view. In any case, the source trajectory cannot be reconstructed unless the total displacement does not exceed a wavelength by much, where “much” is not too well defined.

## 电子工程代写|三维成像代写三维成像代考|数理分析

$$u_0(\mathbf{r})=\frac{A_0}{j k|\mathbf{r}-\rho|} \exp (j k|r-\rho|)$$
，其中$k=2 \pi / \lambda$是波数，$\lambda$是波长。如果点源移动，矢量$\rho$是时间的函数，这使得观测平面上的复振幅也是时间的函数。如果我们希望记录全息图，我们需要一个参考光束$u_r$，并曝光记录介质$T$。也就是说，记录的强度模式将由
$$I(\mathbf{r})=\int_0^T\left|u_r+u_o\right|^2 d t=\int_0^T\left(\left|u_r\right|^2+\left|u_o\right|^2+u_r^* u_o+u_r u_o^\right) d t$$给出。前两项构成所谓的零阶项，这在这里没有意义，而后两项负责对记录的对象进行重构。第四项重建相位共轭图像，如果正确记录，则在空间上与代表真实图像的第三项分离。因此，我们现在将集中于第三项，其形式为$$I_t(\mathbf{r})=\int_0^T u_r^(\mathbf{r}) u_o(\mathbf{r}, t) d t$$
，其中我们明确指出，对象波依赖于时间，而参考波在时间上是恒定的

## 电子工程代写|三维成像代写三维成像代考|纵向平移与恒速

$$I_t(\mathbf{r})=C \int_0^T \exp [-j k \zeta(t)] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta(t)}\right] d t$$

$$\zeta=\zeta_0+v_z t$$
，其中$v_z$是源的速度，$\zeta_0$是起点。保持近轴近似，我们可以在积分时间内假设$\zeta_0 \gg v_z t$，然后我们可以写
$$\frac{1}{\zeta(t)}=\frac{1}{\zeta_0+v_z t} \approx \frac{1}{\zeta_0}\left(1-\frac{v_z t}{\zeta_0}\right)$$

$$I_t(\mathbf{r}) \approx C \exp \left[-j k \zeta_0\right] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right] \int_0^T \exp \left[-j k v_z t\left(1-\frac{\left|\mathbf{r}_t\right|^2}{2 \zeta_0^2}\right)\right] d t$$

\begin{aligned} I_t(\mathbf{r}) \approx & \frac{C}{j k v_z\left(1-\left|\mathbf{r}_t\right|^2 / 2 \zeta_0^2\right)} \exp \left[-j k \zeta_0\right] \ & \times \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right]\left{1-\exp \left[-j k v_z T\left(1-\frac{\left|\mathbf{r}_t\right|^2}{2 \zeta_0^2}\right)\right]\right} \end{aligned}

\begin{aligned} I_t(\mathbf{r}) \approx & \frac{C}{j k v_z\left(1-\left|\mathbf{r}_t\right|^2 / 2 \zeta_0^2\right)}\left{\exp \left[-j k \zeta_0\right] \exp \left[\frac{-j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\right]\right.\ &\left.-\exp \left[-j k\left(\zeta_0+v_z T\right)\right] \exp \left[-\frac{j k\left|\mathbf{r}_t\right|^2}{2 \zeta_0}\left(1-\frac{v_z T}{\zeta_0}\right)\right]\right} \end{aligned}

## 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。