An astronomical detector is a device, typically located in the focal plane of a telescope or instrument, that has the ability to record the photons incident upon it. For imaging or spectroscopy(光谱学), a detector composed of a two-dimensional array of pixels is essential. Detectors must not waste photons - astronomical objects are faint and millions of pounds are spent on large telescopes to collect as many photons as possible. Throughout history many astronomical detectors have been used; perhaps the most important were the human eye and photographic plates. In 1969, however, Willard Boyle and George Smith invented the charge-coupled device or CCD, a discovery for which they were awarded a share of the 2009 Nobel Prize in Physics. CCDs are small and incredibly efficient, detecting almost all photons incident upon them. Astronomers pioneered the use of CCDs in the 1970s and nowadays you would find it extremely difficult to find any other type of detector in use at a major telescope. For this reason, we shall concentrate exclusively on CCDs in this lecture. CCDs are very complex electronic devices, and we shall discuss their operation in a simplified way. For the curious, much more detail on the operation and construction of CCDs is provided in Vik Dhillon's old notes. Figure:A photograph showing an CCD. The central, dark-bray region is the Silicon wafer where photons are recorded. It is surrounded by a package containing the readout electronics and wiring.

### 1.Semi-conductors

CCDs work by making use of semiconductors; the most common semi-conductor used for CCDs is Silicon. We saw in PHY104 that the energy levels of electrons around single atoms were restricted to discrete energy levels. When isolated atoms are brought together to form a solid, they interact and their energy levels are spread into a large number of closely spaced levels, creating a series of bands, as shown in figure 63, below. At temperatures of absolute zero, the highest energy band that contains electrons is called the valence band. Electrons in the valence band are unable to move between atoms in the solid, because nearly all the electron states at this energy are already occupied. The only way an electron can move, and thus conduct electricity is to gain energy. The electron then moves into the conduction band. Now there are unoccupied conduction band states available around nearby atoms and the electron can move through the solid. The difference between insulators and metals is explained by the difference in energy between the valence band and the conduction band, known as the band gap. In insulators these are very far apart in energy. As a result, there are almost no electrons in the conduction band and the electrical conductivity is poor. In metals, the valence and conduction bands overlap. Even at low temperatures, thermal excitation is able to create many conduction band electrons which are free to move through the solid. Metals are good conductors of electricity. Somewhere in between are the semi-conductors. Semi-conductors have small band gaps. Thermal excitation of electrons into the conduction band is small (but not zero). However, in a semi-conductor, electrons can be promoted into the conduction band by the absorption of energy from a photon. It is this property that allows semi-conductors to be used in CCDs as photon detectors. Figure 63 - Left: The band structure of electron energy levels in a solid. The valence band is the highest energy band occupied by electrons. The band above this is known as the conduction band. Right: The difference between conductors, metals and semiconductors is explained by the energy difference between the valence and conduction bands.

### 2.CCDs: Principles

All CCDs work via the same basic process. Photons excite electrons into the conduction band. These electrons are free to move through the CCD, and so can be moved to some readout electronics, where we count the number of electrons which have been excited. The number of electrons we count is proportional to the number of photons arriving at the detector. CCDs thus have to perform four jobs: 1)they must create photo-electrons; 2)they must store photo-electrons in pixels during an exposure; 3)they must move the photo-electrons to the readout electronics; 4)they must count the number of photo-electrons created in each pixel.

#### 2.1 Quantum Efficiency

The semi-conductor of choice for CCDs is silicon. It has a large band gap, reducing the importance of thermal excitation (more on this next lecture). Electrons that are elevated to the conduction band via the absorption of a photon are known as photo-electrons. Not all electrons will produce photo-electrons. The band gap of Silicon is 1.26 eV. Electrons with a lower energy, $$E=h\nu < 1.26$$ eV will not create photo-electrons. This means that CCDs based on Silicon can only detect photons with wavelengths shorter than $$λ=1100 nm$$. Photons with higher energies, e.g. optical photons, can of course produce photo-electrons, but not all do. The quantum efficiency (QE) of a detector is the fraction of incident photons which produce photo-electrons. Through clever design, the QE of CCDs can reach 90% at optical wavelengths. For comparison, the quantum efficiency of photographic film is around 10%, making it easy to see why CCDs have become the dominant detector in optical astronomy.

#### 2.2 Charge Coupling

How are the photo-electrons kept within a pixel during the exposure, and how are they moved to the readout electronics at the end of an exposure? The unique feature of CCDs, which give them their name, is the way photo-electrons are moved from the pixel in which they were created - a process known as charge-coupling. Once the CCD has been exposed to light for the required amount of time, each pixel will contain a charge packet of size proportional to the number of incident photons. To measure this charge, it is necessary to move these charge packets, one by one, off the chip. The easiest way of visualizing this process is by thinking of taking a CCD image as analogous to measuring the rain falling on a field, as shown in figure 64. The first step is to distribute a large number of buckets in a rectangular pattern of rows and columns over the field - these are the pixels. After it has stopped raining, you can measure the amount of water collected in each bucket, i.e. the amount of charge in each pixel, by shifting the entire array of buckets,** one row at a time**, on parallel conveyor belts towards a perpendicular(垂直的) conveyor belt(传送带) at one end of the field. When a single row has been transferred onto the conveyor belt at the end of the field, the row is shifted, one bucket at a time, towards a measuring point at the end of this conveyor belt, where the amount of water in each bucket is recorded. Once the whole row has been measured, the next row is shifted onto the conveyor belt at the end of the field, and the process is repeated until every bucket in the field has been measured. By plotting the amount of rain in each bucket as a two-dimensional grey-scale image, where white represents a full bucket and black an empty one, it is possible to visualise the pattern of rainfall over the field. Replacing the rain in this analogy by photons, this is how an image of the sky can be recorded. Figure 64 - Left: schematic showing how charge coupling moves the photo-electrons from each pixel to the readout electronics, by way of the rain-bucket analogy. Right: an animation showing the same process. How are the conveyor belts implemented electronically? In most CCDs, each pixel has three electrodes attached to it. A large positive voltage applied to one of these electrodes will attract the photo-electrons. We can also think of this voltage as creating a potential well which will fill with photo-electrons. This is the way CCDs keep photo-electrons in a single pixel during an exposure. The three electrodes are also used to move charge between pixels. The voltage in an electrode adjacent to the electrode holding the charge packet is raised to the same level. This allows the charge to flow, like water, and be shared between the two electrodes. Decreasing the voltage of the original electrode then completes the transfer, pushing all of the charge across to the adjacent electrode, which is held at the higher voltage level. Since there are three electrodes in each pixel, three of the above transfers are required to move the charge packet by one pixel. The process of raising and lowering the voltages to move charge is known as clocking, and is illustrated in figure 65. Figure 65: An animation showing the clocking of electrons in a CCD. By this process the photo-electrons are moved from one pixel to the next.

Looking again at figure 64, we can see that rows of pixels are shifted consecutively onto a horizontal serial register, which moves the charge from each pixel, one-by-one into the readout electronics. The job of the readout electronics is to measure the amount of charge collected in each pixel. The readout electronics for a CCD are quite complex, but they all operate on the same basic principle. The charge from each pixel, $$Q$$, is emptied into a capacitor of capacitance $$C$$. This causes a small change in the voltage across the capacitor given by $$V=Q/C$$. This analog voltage change can be measured. Finally, the voltage produced by each charge packet is digitized using an analogue-to-digital converter (ADC), producing the number of analogue-to-digital units (ADUs), or simply counts, in each pixel, which are then written to a computer disk.

In an ideal world, every photon striking the CCD would produce one electron in a pixel, which would be measured as one count by the ADC. Of course, we do not live in an ideal world. The voltage on the capacitor in the readout electronics is around one microvolt for each electron in the pixel, and this voltage cannot be measured with perfect accuracy. This introduces a readout noise in the charge measured in every pixel. In a well designed CCD the readout noise can be as small as 3e- per pixel. This means that, even if every pixel in the CCD actually contained the same number electrons, the measured number of counts would vary by about 3e- from pixel to pixel. We will see later that this is quite important for observations of faint astronomical objects.

#### 3.2 Well-Depth and Dynamic Range

Each CCD pixel has a maximum charge carrying ability, known as the full-well capacity. Typically, the full-well capacity of a pixel is hundreds of thousands of electrons. If more electrons are created, they spill vertically into adjacent pixels (structures in the CCD, known as channel stops prevent horizontal leakage). This leakage of charge into adjacent pixels is known as blooming, and is shown in figure 66. The full well depth sets an upper limit to how many electrons can be detected by one pixel. At the other end of the scale, the readout noise sets a lower limit to how many electrons each pixel can detect. With a readout noise of 3e-, how do you tell the difference between pixels which store 1, 2 or 3 e-? The ratio of the full-well capacity to the readout noise is known as the dynamic range of the CCD, and is typically of order 100,000:1.

#### 3.4Saturation

One consequence of using low gains to reduce quantization noise, however, is that the dynamic range of the CCD is defined not by the full-well capacity of a pixel but by the limits of the ADC. For example, a gain of 1.5 e-/ADU would mean that a 16-bit ADC is capable of counting 1.5 x 65535 = 98302 e- before running out of numbers to record higher pixel charges. We say that such a pixel is** saturated.** If the full-well capacity of the pixel is 200,000 e-, this means that the ADC would saturate well before the full-well capacity of the pixel is reached, i.e. the maximum number of electrons that can be counted is 98302, not 200,000. Obviously, a saturated pixel is not capable of accurately recording the amount of photons incident upon it. Figure 66 - Left: CCD images showing the effects of blooming, when the number of electrons in a pixel exceeds the full-well depth. Right: The profile from a saturated star. The central pixels should have values exceeding 65535 ADU, but the ADC cannot represent these. This results in a characteristic flat-topped profile. Saturation means we cannot accurately measure the brightness of this star. In the previous lecture, we covered the basics of how CCDs work. Once we have taken our CCD image we'd like to use it for some scientific purpose. For example, we might wish to perform relative or absolute photometry on the stars in the image. However, before we can do that, we must perform some additional processing on the image. To understand why, we need to look at some details of CCD operation.

### Bias Frames

Let's recall how a CCD measures the number of electrons $$N_e$$ in each pixel. These electrons have a total charge $$Q = eN_e$$. We measure this charge by dumping it onto a capacitor with capacitance $$C$$ and measuring the voltage $$V = Q/C$$. We can re-write the number of electrons in terms of this tiny, analog voltage as $N_e = CV/e.$ In other words, the voltage is proportional to the number of electrons. Because we need to store the data in digital format, the analog voltage is converted to a digital number of counts $$N_c$$, by an analog-to-digital converter (ADC). Since the value in counts is proportional to the voltage $$N_c \propto V$$, it follows that the number of counts is proportional to the number of photo-electrons, i.e $$N_e = GN_c$$, where $$G$$ is the Gain, measured in e-/ADU. The number of bits used by the ADC to store the count values limits the number of different count values that can be represented. For a 16-bit ADC, we can represent count values from 0 to 65,535. Now, imagine a relatively short exposure, taken from a dark astronomical site. Suppose that the gain, $$G=1$$ e-/ADU and that in our short exposure we create, on average, two photo-electrons from the sky in each pixel. Because of readout noise, we will NOT have 2 counts in each pixel. Instead, the pixel values will follow a Gaussian distribution, with a mean of 2 counts, and a standard deviation given by the readout noise, which may be of the order of 3 counts. It should be obvious that this implies that many pixels should contain negative count values. However, our ADC cannot represent numbers less than 0! This means our data has been corrupted by the digitisation process. If we didn't fix this, it would cause all sorts of problems: in this case it would lead us to over-estimate the sky level. The solution is to apply a bias voltage. This is a constant offset voltage applied to the capacitor before analog-to-digital conversion. The result is that, even if the pixel contains no photo-electrons, the ADC returns a value of a few hundred counts, nicely solving the issue of negative counts. However, it does mean that we must correct for the bias level when doing photometry! Each pixel in our image contains counts from stars, from the sky background and from the bias level. We must subtract the bias level before performing photometry. How do we know what the bias level is? The easiest way to do this is to take a series of images with zero exposure time. Because there is no exposure time, these images contain no photo-electrons, and no thermally excited electrons. These images, known as bias frames, allow us to measure the bias level, and subtract it from our science data. A bis frame is shown in figure 67. Several bias frames are needed because the value of any pixel in a given bias frame will differ from the bias level due to readout noise. Averaging several frames together reduces the impact of readout noise and gives a more accurate estimate of the bias level. The master bias frame produced from this averaging can be subtracted from all science images to remove the bias level from each pixel. Figure 67: A single bias frame, taken with the department's robotic telescope ROSA. The bias level in this image is 320 counts. Each pixel is scattered around this value due to read noise.

### Dark Frames

Recall that photo-electrons are produced in CCDs by photons exciting electrons from the valence band(价（电子）带) to the conduction band. However, this is not the only way to excite electrons into the conduction band. Thermal excitation( <物>（原子获得高能量的）激发（过程）) is also capable of producing electrons in the conduction band. Thermal excitation of electrons is known as dark current and the electrons produced by it are indistinguishable from photo-electrons. Dark current can be very substantial. At room temperature, the dark current of a standard CCD is typically 100,000 e-/pixel/s, which is sufficient to saturate most CCDs in only a few seconds! The solution is to cool the CCD. The typical operating temperatures of CCDs are in the range 150 to 263 K (i.e. -123 to -10oC). At major observatories, most CCDs are cooled to the bottom end of this range, generally using liquid nitrogen.The resulting dark current can be as low as a few electrons per pixel per hour. The CCDs on the Hicks telescopes are air-cooled to a few degrees below zero, and have dark currents of around 40 e-/pixel/hour. Neither of these values are negligible, especially for short exposures. Thus, every pixel in our image contains contributions from stars, sky background, bias level and dark current. The dark current must be measured, and subtracted from our science images for the same reasons as the bias level. For this purpose dark frames are taken. These are long exposures, taken with the shutter closed. These frames will have no contribution from photo-electrons, but they will contain dark current and the bias level. This means that dark frames must have the bias subtracted from them before use. Once the bias level has been subtracted off, several dark frames can be combined to make a master dark frame, which can be subtracted from your images. It is best to combine the dark frames using the median, rather than the mean. Dark frames are often long exposures, which can be affected by cosmic rays. Cosmic rays hitting the CCD will excite also excite electrons. Taking the median of the master dark will help remove cosmic rays from the master dark frame. Because the dark frame increases with time, it is easiest if the dark frames have the same exposure time as your science images. If they do not, it is possible to scale the dark frame by the ratio of exposure times, since dark current increases (roughly) linearly with time. Dark current is also a strong function of temperature - it is essential that dark frames are taken with the CCD at the same temperature as your science frame. Figure 68 shows an example dark frame. In this 300-sec exposure the dark current is about 50 counts. Note that not every pixel has the same value. Some of this is read noise, but it is also true that different pixels in a CCD show different levels of dark current. Some pixels show very high levels of dark current - these so called hot pixels can have a very serious effect on your photometry if your target star happens to lie on top of one. Figure 68: A single dark frame, with an exposure time of 300s, taken with the department's robotic telescope ROSA. The mean level in this image is 370 counts. 320 of these counts are bias level, giving a dark current of 50 counts.

### Flat Fields

Suppose we use our telescope and CCD to take an image of a perfectly uniform light source. Would every pixel have the same number of counts in it? No - as we have seen each pixel will have a varying contribution from dark current and readout noise. What if we ignored these effects? The answer is still no. Various effects combine to mean that the count level can vary significantly across the image. Figure 69 shows an image of the twilight sky taken with the ROSA telescope on the roof of the Hicks building. On the small image scale of a telescope, the twilight sky is an excellent approximation to a uniformly illuminated light source. However, figure 69 is far from uniform. Figure 69: An image of the twilight sky, taken using the ROSA telescope on the roof of the Hicks building. The overall illumination pattern is a result of vignetting. Pixel-to-pixel variations, and large donuts from out-of-focus dust spots can also be seen. There are three main reasons for the structure seen in figure 69.
##### (1)Vignetting(渐晕)
Consider the design of the Newtonian telescope shown in figure 41. If the secondary mirror is exactly the right size to fit the beam produced by an on-axis source, some fraction of the beam produced by an off-axis source will miss the secondary mirror. This light will be lost, and off-axis sources will appear dimmer than on-axis sources. This is vignetting, and its effect is clearly visible in figure 69. (wiki:In photography and optics, vignetting (/vɪnˈjɛtɪŋ/, UK also /vɪˈnɛt-/; French: vignette) is a reduction of an image's brightness or saturation toward the periphery(边缘) compared to the image center.)
##### （2）Pixel-to-Pixel variations
Each pixel in a CCD is not exactly the same size; manufacturing tolerances mean that some pixels are larger than others. If each CCD pixel is exposed to a constant flux, the variation in pixel area means that some pixels will capture more photons than others. This effect can also be seen in figure 69 if you look closely, and is often called flat field grain.
##### (3)Dust grains on optical surfaces
Dust grains on the window of the CCD, or on the filters will block out a small fraction of the light falling on the CCD. These grains appear as dark donuts, with the size of the donut depending on how far from the focal plane the dust grain is. Two such donuts are visible in figure 69.
##### (4)Flat field frames
It is essential to correct our images for these effects. If we did not, the number of counts from an object would vary depending upon its location in the image, ruining our photometry. Fortunately, we can correct these effects using flat field frames. These are images taken of the twilight sky, which is assumed to be uniform (this is a good assumption for most instruments). Any variation in the flat field is therefore due to the effects above. Because vignetting and the contribution from dust grains can depend on the filter, flat fields must be taken in the same filters as your science data. For small telescopes, it can be more convenient to use a specially constructed flat-field panel, such as the one shown in figure 70. These panels are carefully designed to provide a uniform light source. The advantage of a flat field panel over the twilight sky is that flat fields can be taken at any time, whereas twilight flats can only be taken in a narrow window after sunset. How should the flat field be used? First of all, we must realise that the flat field image must be bias subtracted. Dark frame subtraction is not normally necessary, since exposure times are short and the dark current will be very small. The count level of pixel (i,j) in the bias-subtracted flat field image can be written as $F_{ij} = \alpha_{ij} F,$ where $$F$$ is the uniform flux of the twilight sky, or flat field panel. The quantity $$\alpha_{ij}$$ represents the fraction of light lost to vignetting, pixel-to-pixel variations and dust grains. If we normalise our image, i.e. divide the flat field by the mean flux, $$F$$, we get an image whose brightness $$f$$ is given by $$f_{ij} = \alpha_{ij}$$. Our science image is given by the product of the flux falling on each pixel $$G_{ij}$$, and the flat field effects, giving an image in which the brightness of pixel (i,j) is given by Figure 70: A flat field panel placed at the aperture of a Newtonian telescope. The panel provides a roughly uniform illumination and can be placed at the aperture of a small telescope. The 16" Hicks telescope uses a panel like this for taking flat field frames.

### A worked example - M52

The calibration frames shown in the figures above were taken to support observations with ROSA of the nearby galaxy M52, by a first year student in 2012. A raw CCD image in the I-band is shown in figure 71. Five sets of each calibration frame were taken. The five biasses were median-combined to make a master bias. The darks were bias-subtracted and median-combined to make a master dark. The flat field images were bias subtracted and median-combined to make a master flat, which was normalised. The raw CCD image then had the master dark and bias frames subtracted, and was divided by the normalised master flat to make the calibrated CCD image, also shown in figure 71. Note that the calibrated image has had the dark current from hot pixels removed. If you look closely, you can also see that the illumination across the frame is even (as vignetting has been corrected), and that the pixel-to-pixel variations have been removed. Many science images in the BVI filters were taken, and calibrated as above. These were then aligned to correct for imperfections in telescope tracking, and combined into the colour image seen in figure 72. Figure 71 - Left: A raw CCD image of M51. This is a 200-sec exposure in the I-band taken using ROSA. Non-even illumination due to vignetting is visible, as are bright "hot pixels" which are scattered throughout the image. Right: a de-biassed, dark-subtracted and flat-fielded version of the same image. Note the correction for vignetting and removal of hot pixels. Figure 72: A colour image of M51, taken using ROSA. 18 images were taken in each of the B, V and I filters. These images were de-biassed, dark-subtracted and flat-fielded. They were then aligned to account for errors in auto guiding, and median-combined to create a master image in each filter. These were combined to make a colour image.

### Name:

##### 1.conduction band and valence band
1)导带（英语：conduction band），又名传导带，是指半导体或是绝缘体材料中，一种电子所具有能量的范围。这个能量的范围高于价带（valence band），而所有在导带中的电子均可经由外在的电场加速而形成电流。 2)In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level and thus determine the electrical conductivity of the solid. In non-metals, the valence band is the highest range of electron energies in which electrons are normally present at absolute zero temperature, while the conduction band is the lowest range of vacant electronic states. On a graph of the electronic band structure of a material, the valence band is located below the Fermi level, while the conduction band is located above it 3)The valence band is the band of electron orbitals(轨道) that electrons can jump out of, moving into the conduction band when excited. The valence band is simply the outermost electron orbital of an atom（原子的最外层轨道上） of any specific material that electrons actually occupy. This is closely related to the idea of the valence electron. The energy difference between the highest occupied energy state of the valence band and the lowest unoccupied state of the conduction band is called the band gapand is indicative of the electrical conductivity of a material.[3]A large band gap means that a lot of energy is required to excite valence electrons to the conduction band. Conversely, when the valence band and conduction band overlap as they do in metals, electrons can readily jump between the two bands (see Figure 1) meaning the material is highly conductive.[4] The difference between conductors, insulators, and semiconductors can be shown by how large their band gap is.[5] Insulators are characterized by a large band gap, so a prohibitively large amount of energy is required to move electrons out of the valence band to form a current.[6] Conductors have an overlap between the conduction and valence bands, so the valence electrons in such conductors are essentially free.[4] Semiconductors, on the other hand, have a small band gap that allows for a meaningful fraction of the valence electrons of the material to move into the conduction band given a certain amount of energy. This property gives them a conductivity between conductors and insulators, which is part of the reason why they are ideal for circuits as they will not cause a short circuit like a conductor.[2] This band gap also allows semiconductors to convert light into electricity in photovoltaic cells and to emit light as LEDs when made into certain types of diodes. Both these processes rely on the energy absorbed or released by electrons moving between the conduction and valence bands. Refer:https://energyeducation.ca/encyclopedia/Valence_band 1.In most CCDs, each pixel has three electrodes attached to it. 1.Because of readout noise, we will NOT have 2 counts in each pixel 2.It should be obvious that this implies that many pixels should contain negative count values. However, our ADC cannot represent numbers less than 0! 3.some fraction of the beam produced by an off-axis source will miss the secondary mirror

### Reference

1.Detectors http://slittlefair.staff.shef.ac.uk/teaching/phy217/lectures/instruments/L11/index.html 2.Dealing with CCD data http://slittlefair.staff.shef.ac.uk/teaching/phy217/lectures/instruments/L12/index.html#example 3.更加详细的参考阅读资料(未读) http://www.optique-ingenieur.org/en/courses/OPI_ang_M05_C06/co/Contenu_04.html