# 物理代写|高能物理代写High Energy Physics代考|PHY489

## 物理代写|高能物理代写High Energy Physics代考|CCDs in Optical Astronomy and High-Energy Astrophysics

One of the most important advances in optical astronomy, developed and popularized very rapidly since 1970, is the solid state detector known as a charge-coupled device or CCD [2]. The device consists of a large number of photon-sensitive zones called pixels, used to form a spatially accurate image of a region. It can also obtain the distribution of incoming photon energies and perform spectroscopic analysis that is essential to understanding the physics of the emission. Today most people are familiar with pixels because they actually own digital television sets and cameras. Although these commercial CCDs are much less reliable than the scientific ones and have many more defects, they work in the same way.

CCDs are made of a semiconductor (usually silicon), while the pixels are determined by the position of the electrodes above them, as indicated by I01, I02, and I03 in Fig. 3.4. A positive voltage is applied to the electrodes (as shown for I02 in the figure), and the resulting electric potential attracts electrons to the area below the electrode (little blue balls in the figure), while the positively charged holes are repelled (little red balls in the figure). Thus a potential well is generated where the electrons produced by the incoming photons accumulate. As more photons arrive, the well accumulates electrons until it fills up completely. It is important not to exceed this limit. The signal must be integrated (i.e., allowed to accumulate), but it must not exceed the capacity of the well, because the image to be generated would be distorted (astronomers speak of a saturated image). The most common type of CCD in astronomy has $1024 \times 1024$ pixels, although special configurations can be made. Taking into account the fact that an ordinary pixel is around $10-20 \mu \mathrm{m}$, the physical size is about $2 \mathrm{~cm}^2$. Depending on the application, the pixels can be made much larger and associated in large mosaics.

Each CCD pixel is affected by three electrodes (see Fig. 3.4). We have already talked about the need to create the potential well, but the other two are needed to transfer the accumulated charge out of the device. For this, each electrode is kept at high and low voltage alternatively, to transfer the charge to the neighboring pixel in row or column mode depending on how the electrodes are oriented. For this reason (the transfer of charge from one pixel to the next and so on until the end), it is said that the charges are coupled, and hence the name CCD. The final reading of each pixel is taken by means of an amplifier that converts the accumulated charge into voltage,typically a few $\mu \mathrm{V}$ for each one. This way, even a voltage of a few volts requires the reading of about 100,000 units in each pixel. A CCD camera thus consists not only of the CCD, but also of the associated electronics which reads all the pixels, removes noise (electrons that have nothing to do with the source), and digitizes the signal (the CCD is in fact an analog device), and software to analyze the data and create images from them.

## 物理代写|高能物理代写High Energy Physics代考|The Problem of Focusing (Imaging) High-Energy Photons and Its Solutions

When dealing with optical refracting telescopes there are several ways to focus the light, two of which are shown in Fig. 3.5. In fact, Newtonian and Cassegrain foci are widely used, and due to the relative scale of the wavelength of the observed light, there are no technological problems that prevent an accurate focus.

However, in the treatment of X-ray telescopes this issue takes on much greater importance, since the wavelength is much shorter and focusing is more difficult. In other words, an image of any X-ray object will be “out of focus” unless we can build telescopes that solve this focusing problem. For these purposes, it was necessary to explore the basic physical properties of hard photons and build new designs that allow efficient imaging.

The first physical property required is Snell’s reflection law. An incident ray from the vacuum with refractive index $n_1$ on top of a reflective material that has refractive index $n_2$ is subject to a geometric deviation in the transmission that satisfies
$$\sin \theta_{\mathrm{T}}=\frac{n_1}{n_2} \sin \theta_{\mathrm{i}},$$
where $\theta_{\mathrm{T}}$ and $\theta_1$ are the transmission and incidence angles, respectively. Since $n_1>n_2$ because photons arrive from the vacuum onto the reflective material, there will be real values for transmission only in the case of angles $\theta_{\mathrm{i}}<\arcsin \left(n_2 / n_1\right)$. Choosing the reflective material, e.g., gold with $n_2=0.99$, there will only be transmission for angles $\theta_{\mathrm{i}}<81.9^{\circ}$. If incidence occurs at a higher angle, Snell’s law will not be satisfied and there will be no transmission (see Fig. 3.6).

This feature is exploited by building a grazing incidence reflector arrangement, hereafter denoted by GI (Fig. 3.7). In each set of reflectors, light from the source is deflected until it can focus on the detector [5]. In fact, there are several complications in this design that we will not address here. The important thing is that this shows how the X-rays can be focused.

## 物理代写|高能物理代写高能物理代考|光学天文学和高能天体物理学中的ccd

. ccd . ccd . ccd . ccd

ccd是由半导体(通常是硅)制成的，而像素是由它们上面的电极位置决定的，如图3.4中的I01、I02和I03所示。在电极上施加正电压(如图中I02所示)，产生的电势将电子吸引到电极下方的区域(图中小蓝球)，而带正电的空穴则被排斥(图中小红球)。因此，当入射光子产生的电子聚集在一起时，就产生了势阱。当更多的光子到达时，阱会积累电子，直到它完全被填满。重要的是不要超过这个限制。信号必须被整合(即允许累积)，但不能超过井的容量，因为生成的图像会被扭曲(天文学家称之为饱和图像)。天文学中最常见的CCD有$1024 \times 1024$像素，尽管也可以做出特殊的配置。考虑到普通像素在$10-20 \mu \mathrm{m}$左右，物理尺寸大约是$2 \mathrm{~cm}^2$。根据应用程序的不同，像素可以做得更大，并在大的马赛克中关联

## 物理代写|高能物理代写高能物理代考|聚焦(成像)高能光子的问题及其解决方案

$$\sin \theta_{\mathrm{T}}=\frac{n_1}{n_2} \sin \theta_{\mathrm{i}},$$
，其中$\theta_{\mathrm{T}}$和$\theta_1$分别为透射角和入射角。由于$n_1>n_2$，因为光子从真空到达反射材料，只有在角度$\theta_{\mathrm{i}}<\arcsin \left(n_2 / n_1\right)$的情况下才会有真实的传输值。选择反光材料，例如带有$n_2=0.99$的金色，只有$\theta_{\mathrm{i}}<81.9^{\circ}$的角度才会有透射。如果入射角度较大，则不满足斯涅尔定律，也不会发生透射(见图3.6)

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