Electronic sensors represent one of the greatest technological advances for astronomy since the invention of the telescope. Starting in the 19th century, long-exposure film photography allowed astronomers to see deeper than the human eye, but typically only of the light reaching the film was ever registered in the image. In the late 20th century, electronic sensors improved this rate (the 'quantum efficiency') to levels as high as . Now, even a small telescope with a digital camera can reveal objects too dim to see visually in the largest telescopes. 电子传感器是天文学自望远镜发明以来最伟大的技术进步之一。从 19 世纪开始，长曝光胶片摄影技术让天文学家能够看到比人眼更深的东西，但通常只有 的光线能够到达胶片并记录在图像中。20 世纪末，电子传感器将这一比率（"量子效率"）提高到了 的水平。现在，即使是装有数码相机的小型望远镜，也能显示出在最大的望远镜中也无法看到的微弱物体。 Further, digital images can be subjected to sophisticated processing algorithms that can sharpen blurry features, reduce noise, or enhance contrast in the final image. 此外，数字图像还可以通过复杂的处理算法来锐化模糊的特征、减少噪音或增强最终图像的对比度。
From our vantage point on Earth, deep-sky objects range in size from distant galaxies only a few arcseconds across to gigantic nebulae many times larger than the full moon. Many are stunningly beautiful when imaged properly. 从我们在地球上的有利位置看，深空天体的大小不一，从只有几弧秒宽的遥远星系到比满月大许多倍的巨大星云。许多天体在正确成像后都美得令人惊叹。 All of them, however, are dim, and this is the main challenge of creating deep-sky images. Images produced by amateurs routinely reveal objects so faint that the total light collected for each pixel may have been only a handful of photons per minute. 然而，所有这些天体都很暗淡，这也是制作深空图像的主要挑战。业余爱好者拍摄的图像经常会显示出非常暗淡的天体，每个像素收集到的总光可能只有每分钟几个光子。 We are literally able to count photons from our backyards. 我们简直可以在自家后院数光子。
When faced with a dimly lit outdoor scene, a daylight photographer will use a faster focal ratio or take a longer exposure. In our case we'll do both, but faster optics can only take us so far. 面对光线昏暗的室外场景，日光摄影师会使用更快的焦距比或进行更长时间的曝光。在我们的情况下，我们会同时使用这两种方法，但更快的光学镜头只能帮我们到这里。 The defining characteristic of deep-sky imaging is that we must take very long exposures. Instead of measuring our exposure times in fractions of a second, we measure them in minutes and hours. 深空成像的显著特点是我们必须进行长时间曝光。我们的曝光时间不是以几分之一秒为单位，而是以分钟或小时为单位。 We synthesize many exposures together into one that incorporates hours of total exposure time. None of this was possible before digital imaging revolutionized photography. 我们将多次曝光合成一次曝光，总曝光时间长达数小时。在数码成像彻底改变摄影技术之前，这些都是不可能实现的。
Even as we conquer the challenge of dimness, there are additional challenges to overcome. Aside from being very dim, the sky rotates slowly over our heads, so we'll require accurate tracking. 即使我们战胜了昏暗的挑战，还有其他挑战需要克服。除了非常昏暗之外，天空在我们头顶上缓慢旋转，因此我们需要精确的跟踪。 We'll also find that while daytime photography is relatively forgiving when it comes to optics, the night sky (especially stars) seems designed to reveal even the slightest optical aberrations. Light pollution fills the sky for observers anywhere near civilization. 我们还会发现，虽然白天的摄影在光学方面相对宽容，但夜空（尤其是星星）似乎会暴露出最轻微的光学像差。对于文明附近的观测者来说，光污染充斥着整个天空。 And while most photographers give only passing thought to concepts like signal and noise, we'll see that they play a critical role in nearly every aspect of deep-sky imaging. 虽然大多数摄影师对信号和噪声等概念只是一带而过，但我们会发现它们在深空成像的几乎每个方面都起着至关重要的作用。
Fortunately, there are tools and techniques within the reach of amateurs to overcome every one of these challenges, and we'll cover all of them on our journey. But let's start with the tool that makes all of this possible: the sensor. 幸运的是，业余爱好者可以利用一些工具和技术来克服所有这些挑战，我们将在旅途中介绍所有这些工具和技术。不过，让我们从使这一切成为可能的工具开始：传感器。
Planets are very small, with all their light concentrated into that tiny area. Thus planetary imaging requires short exposure times at very high magnification. The light from deepsky objects is spread over much larger areas, requiring lon- ger exposures and less magnification. 行星非常小，其所有光线都集中在这一微小区域。因此，行星成像需要很短的曝光时间和很高的放大倍率。深空天体的光线散布在更大的区域内，需要更长的曝光时间和更小的放大倍率。 While both disciplines have some similarities, the equipment and processing techniques are quite different. This book focuses on deep-sky imaging 虽然这两个学科有一些相似之处，但设备和处理技术却大相径庭。本书重点介绍深空成像
How electronic sensors work 电子传感器如何工作
Photons are the fundamental particles of light, and at a high level, the job of an electronic sensor is to count them. Many sensors can discriminate between brightness levels with an accuracy down to a single-photon. 光子是光的基本粒子，在高层次上，电子传感器的工作就是对光子进行计数。许多传感器可以精确到单光子来区分亮度等级。 Sensors are composed of millions of these light-measuring elements arranged in a grid. These elements are referred to as photodetectors or photosites, each of which usually corresponds to a pixel in the final image. . 传感器由数百万个网格状的光测量元件组成。这些元件被称为光电探测器或光子，每个光子通常对应最终图像中的一个像素。.
There are several steps between photons striking the camera's sensor and an image you can view. While the technical details vary by sensor type, the process is schematically illustrated in Figure 1, which breaks it down into five steps: 从光子撞击照相机的传感器到您能看到图像之间有几个步骤。虽然技术细节因传感器类型而异，但图 1 对这一过程作了示意性说明，将其分为五个步骤：
Photons are guided through your optical system to strike the photodetector. 光子在光学系统的引导下穿过光电探测器。
The photons' energy frees electrons from the silicon, which are then held in the photosite's well. 光子的能量将电子从硅中释放出来，然后被保存在光子井中。
These electrons generate a charge, which is often amplified. When the exposure is over, circuitry in the camera called the Analog-to-Digital Converter (ADC) quantifies the charge at each photosite. 这些电子会产生电荷，电荷通常会被放大。曝光结束后，相机中被称为模数转换器（ADC）的电路会对每个光点的电荷进行量化。
This creates a digital value that is proportional to the number of photons that struck the photosite. The units for this digital value are referred to as Analog-to-Digital Units (ADUs). 这样就产生了一个数字值，该数字值与撞击光点的光子数量成正比。该数字值的单位称为模数转换单位（ADU）。
The camera then saves the ADU values from every photosite into an image file. 然后，照相机会将每个照相点的 ADU 值保存到图像文件中。
Not every photon that strikes the sensor generates an electron in the well. The proportion of incoming photons a sensor records is called its quantum efficiency, and this varies by wavelength of light. 并非每个撞击传感器的光子都能在井中产生电子。传感器记录入射光子的比例称为其量子效率，它因光的波长而异。 Infrared or longer wavelength photons do not carry enough energy to free an electron out of the silicon matrix, and those in the ultraviolet range are mostly reflected. 红外线或波长更长的光子所携带的能量不足以将电子从硅基质中释放出来，而紫外线范围内的光子大多会被反射。 The spectral response of a sensor can be altered adding other elements or compounds to the silicon, but the response range for most sensors is approximately 300 to 1000 nm . By comparison, the human eye can see wavelengths in the range of about 400 to 700 nm . 在硅中添加其他元素或化合物可以改变传感器的光谱响应，但大多数传感器的响应范围约为 300 到 1000 纳米。相比之下，人眼能看到的波长范围约为 400 到 700 纳米。
Another way to think about this process is to consider how the signal is transferred, as shown in Figure 2. Photons generate electrons, which create a charge that is amplified and then quantified into a digital value. 思考这一过程的另一种方法是考虑信号是如何传输的，如图 2 所示。光子产生电子，电子产生电荷，电荷被放大，然后量化为数字值。 Ideally, that final digital value would be exactly proportional to the number of photons that struck the sensor during an exposure, but each step in the chain is an opportunity for a degree of inaccuracy to be intro 理想情况下，最终的数字值与曝光过程中撞击传感器的光子数量完全成正比，但链条中的每一步都有可能造成一定程度的误差。
Figure 1. How electronic images are created (highly simplified) 图 1.电子图像是如何创建的（高度简化）
duced. We'll refer to these inaccuracies as noise, and the less noise we have, the better our image is likely to be. 我们将这些误差称为噪点。我们把这些不准确的地方称为噪点，噪点越少，图像就可能越好。
Sensor architecture: CCD vs CMOS 传感器结构：CCD 与 CMOS
There are two main types of imaging sensor technology: CCD (Charge-Coupled Device) and CMOS (Complementary Metal Oxide Semiconductor). 成像传感器技术主要有两种：CCD（电荷耦合器件）和 CMOS（互补金属氧化物半导体）。 Both technologies convert photons into an electrical charge, creating a signal that is proportional to the brightness of the light at each photosite The differences lie mostly in how and where the electrons from each photosite are quantified. 这两种技术都能将光子转化为电荷，产生与每个光点的光亮度成正比的信号。 This is known as the readout process. 这就是所谓的读出过程。
The most relevant difference is that on CMOS sensors, every photosite has its own readout electronics. In the CCD readout process, the charge from each photosite is passed across rows of photosites where it is then amplified and quantified by a single analog-to-digital converter. 最重要的区别在于，在 CMOS 传感器上，每个光点都有自己的读出电子元件。在 CCD 的读出过程中，每个光点的电荷都会穿过一排光点，然后由一个模数转换器进行放大和量化。 The common analogy for this process is that the electrons are passed along like water in a bucket brigade. 对这一过程的常见比喻是，电子就像水桶里的水一样被传递。 While this process was surprisingly effective, a defect in one photosite would affect all of those that were 'downstream' of it, leading to defects that span a row or column. The readout process could also be slow, taking several seconds to generate a final image. 虽然这一过程出奇地有效，但一个光点上的缺陷会影响到其 "下游 "的所有光点，从而导致跨行或跨列的缺陷。读出过程也很慢，需要几秒钟才能生成最终图像。 By putting an amplifier and ADC circuit in each photosite, CMOS sensors eliminate these issues. In early CMOS designs, these circuits blocked some of the light gathering area, leading to lower quantum efficiency. CMOS 传感器在每个光点上都安装了放大器和 ADC 电路，从而消除了这些问题。在早期的 CMOS 设计中，这些电路阻挡了部分聚光区域，导致量子效率降低。 They could also be inconsistent, leading to variations in sensitivity between photosites. As with CCDs, the technology improved over time, and they are now better than CCDs in most respects. 此外，它们还可能不一致，导致不同感光元件之间的灵敏度存在差异。与 CCD 一样，随着时间的推移，该技术也在不断改进，目前在大多数方面都优于 CCD。 By 2020, nearly all consumer camera sensors were CMOS designs, and the major sensor manufacturers had stopped making CCD sensors. The future clearly belongs to CMOS. 到 2020 年，几乎所有的消费类相机传感器都是 CMOS 设计，主要的传感器制造商已经停止生产 CCD 传感器。未来显然属于 CMOS。
For both CCD and CMOS sensors, you may hear about two technologies that have been key to improving sensitivity: microlenses and back-side illumination. Microlenses are exactly what they sound like: tiny lenses over each photosite. 对于 CCD 和 CMOS 传感器而言，您可能会听说有两种技术是提高灵敏度的关键：微透镜和背面照明。微透镜和它们听起来一样：每个光点上都有微小的透镜。 These redirect incoming light that would ordinarily fall on the space between photosites or on the CMOS amplifier. Backside illumination (BSI) is where the silicon on the back of the sensor is thinned, allowing it to be flipped around so that 这些装置可将通常落在光子之间的空间或 CMOS 放大器上的入射光重新定向。背面照明（BSI）是指将传感器背面的硅片削薄，使其可以翻转，以便
Figure 2. How the signal is transferred in electronic imaging 图 2.电子成像中的信号传输方式
incoming light strikes the back of the sensor. This positions the readout circuitry on the non-lit side, where they cannot block any incoming photons. As a result, some BSI sensors boast quantum efficiencies of over . 入射光会照射到传感器的背面。这样，读出电路就位于不发光的一侧，不会阻挡任何入射光子。因此，一些 BSI 传感器的量子效率超过 。
Well capacity and bit depth 井容量和钻头深度
Each photosite can capture only a certain number of photons before it becomes full of charge and ceases to register further strikes. This limit is called the full well capacity. 每个光点只能捕捉一定数量的光子，然后才会充满电荷，停止记录进一步的撞击。这个极限称为满井容量。 Typical full well capacities range from 20,000 to 200,000 electrons, and the capacity is roughly correlated with the surface area of the photosites. 典型的全孔容量在 20,000 到 200,000 个电子之间，容量与光敏材料的表面积大致相关。
When the analog-to-digital converter reads each photosite, it maps the voltage to a digital value within a predetermined range called the bit depth. 模数转换器读取每个光点时，会将电压映射到一个预定范围内的数字值，这个范围被称为位深度。 Eight bits means there are 256 possible values (two to the eighth power) that can be assigned, corresponding to the range of values expressed by eight binary digits (from 00000000 to 11111111). 八位意味着可以分配 256 个可能的值（2 到 8 的幂次），对应于八个二进制数字表示的值范围（从 00000000 到 11111111）。 In fact, 'bit' is short for 'binary digit.' Translated to normal base-10 numbers, no voltage is recorded as 0 , and the maximum voltage the photosite can hold (a 'full well') is recorded as 255 . Other common bit depths are shown in the table. 事实上，"比特 "是 "二进制位 "的简称。转换为普通的 10 进制数，无电压记录为 0，光敏元件能保持的最大电压（"满格"）记录为 255。其他常见的位深度如表所示。
Bit depth 比特深度
Range of discrete values 离散值范围
12
14
16
32
Most electronic cameras today have ADCs that generate 12- to 16-bit data. Having an ADC with a greater bit depth means that it can distinguish smaller voltage differences, yielding a more accurate assessment of the brightness of each pixel. 如今，大多数电子摄像头的 ADC 都能生成 12 至 16 位数据。ADC 的位深度越大，就越能分辨出更小的电压差，从而更准确地评估每个像素的亮度。
The bit depth of the ADC is not the end of the story for accuracy, though. Being able to resolve more discrete levels of brightness is only meaningful if the noise in the readout process can match that level of precision. 不过，ADC 的位深度并不是精度的全部。只有当读出过程中的噪声与精度水平相匹配时，能够分辨出更多离散的亮度水平才有意义。 In some cameras the random fluctuations in that process, known as read noise, limit the realized precision. 在某些照相机中，这一过程中的随机波动（即读取噪声）限制了实现的精度。
The trade-off between dynamic range and gain 动态范围与增益之间的权衡
Dynamic range is the ratio of the brightest and dimmest signals. There are two contexts where we talk about dynamic range: that of the scene and that of the sensor. 动态范围是指最亮和最暗信号的比率。我们在两种情况下谈论动态范围：场景和传感器。 For a deep-sky object, the empty sky background would be the dimmest part of a scene, and the brightest level is usually a bright star or galaxy core. 对于深空天体来说，空旷的天空背景是场景中最暗的部分，而最亮的层次通常是明亮的恒星或星系核心。 For a sensor's theoretical dynamic range, the well capacity defines the maximum possible signal, and the sensor's read noise defines the 'floor' for the lowest distinguishable signal. 对于传感器的理论动态范围，井容量定义了可能的最大信号，而传感器的读取噪声则定义了最低可分辨信号的 "底限"。 (Actual dynamic range will always be a little less than the theoretical value once other sources of noise, like the thermal noise, are accounted for in the noise floor.) (一旦将热噪声等其他噪声源计入本底噪声，实际动态范围总会比理论值小一些）。
The dynamic range of the sensor determines how much of a scene's dynamic range you can capture in one exposure. Dynamic range is often expressed in decibels (dB), a base-10 logarithmic unit. To convert a raw ratio to dB , the formula is 传感器的动态范围决定了一次曝光可以捕捉到多少场景的动态范围。动态范围通常用分贝（dB）来表示，这是一个以 10 为底的对数单位。将原始比率转换为 dB 的公式为
For a sensor, this translates to 对于传感器来说，这意味着
F-stops are another way to quantify dynamic range. This is borrowed from daylight photography, where an adjustable diaphragm allows a lens's effective aperture to be varied. This is a base-2 logarithmic scale: an increase of one corresponds to a doubling of dynamic range. 光圈是量化动态范围的另一种方法。这是从日光摄影中借用的，通过可调光阑可以改变镜头的有效光圈。这是一个以 2 为底的对数刻度：增加 1 相当于动态范围增加一倍。 For a sensor, this would be 对于传感器来说，这将是
For example, a sensor with a read noise of 10 electrons and a full well capacity of 500 electrons has a 50 -fold dynamic range. This would be expressed as 34 dB , or 5.6 stops. (If you already have the dynamic range in dB , you can simply divide by 6.02 to convert to f-stops.) 例如，一个读取噪声为 10 个电子、满井容量为 500 个电子的传感器，其动态范围为 50 倍。这可以用 34 dB 或 5.6 档来表示。(如果您已经有了以 dB 为单位的动态范围，则只需除以 6.02 即可转换为光圈）。
Most cameras have adjustable gain settings that allow the charge to be amplified before the ADC converts it to a digital value. This allows finer distinctions to be made between the brightness levels. 大多数摄像机都有可调增益设置，可在 ADC 将电荷转换为数字值之前对其进行放大。这样就能更精细地区分亮度等级。 Gain on consumer cameras is set with the ISO setting, mimicking the sensitivity levels of film, and most astronomical cameras have variable gain settings as well. 消费类相机的增益是通过 ISO 设置来设置的，模仿胶片的感光度级别，大多数天文相机也有可变增益设置。 Since the well capacity is fixed, however, increasing the gain means that fewer photons can be counted before the well is full. This reduces the dynamic range we can capture in a single exposure. 然而，由于井的容量是固定的，增益的增加意味着在井满之前可以计数的光子数量会减少。这就缩小了我们在一次曝光中可以捕捉的动态范围。
Applying gain reduces the dynamic range available because each photon will generate more charge at the ADC than it would without gain, filling up the well faster. 应用增益会减小可用的动态范围，因为每个光子在 ADC 上产生的电荷会比不应用增益时更多，从而更快地填满阱。 Therefore, the brightest value the ADC can register (corresponding to the maximum value of its bit depth) goes down as you apply more gain. Any part of the image brighter than gain allows will be clipped, leading to 'blown out' highlights. 因此，ADC 可记录的最亮值（对应于其比特深度的最大值）会随着增益的增加而降低。图像中任何亮度超过增益允许值的部分都会被削去，从而导致高光 "模糊"。 The benefit of gain is that it allows for faint signals to be better revealed, as they are now represented by more discrete ADU levels; the cost is that bright signals may be lost, as they will exceed the maximum ADU value. 增益的好处是可以更好地显示微弱信号，因为它们现在由更多离散的 ADU 电平表示；代价是可能会丢失明亮信号，因为它们会超过最大 ADU 值。
Figure 3 and the following simplified example illustrate the point. Arriving photons create the same number of electrons in the well for each of two exposures taken with a DSLR. 图 3 和下面的简化示例说明了这一点。在使用数码单反相机进行的两次曝光中，每次到达的光子都会在井中产生相同数量的电子。 The well on the left is set at ISO 100, which for this camera applies no gain amplification, and the well on the right is set at ISO 200, where a gain is applied. With no gain applied, this count of electrons is about of the well capacity, and the 12-bit ADC maps this to a value of 1600 , which will correspond to a dark gray in the image file. When gain is 左边的井设置为 ISO 100，对该相机而言，没有应用增益放大；右边的井设置为 ISO 200，应用了 增益。在不应用增益的情况下，电子计数约为井容量的 ，12 位 ADC 将其映射为 1600 的值，在图像文件中将对应于深灰色。当 增益为
applied, the charge is doubled before being quantified by the ADC, which finds a value of 3199 , corresponding to a light gray in the image. 在 ADC 进行量化之前，电荷会被加倍，ADC 会发现一个 3199 的值，对应于图像中的浅灰色。
So why bother with electronic gain? Why not just count the number of electrons then multiply the ADU number by two instead? Because without any gain, the ADC's bit depth may mean that it is essentially counting electrons by twos or threes or tens. 那么，为什么还要费力去计算电子增益呢？为什么不直接计算电子数，然后将 ADU 数乘以二呢？因为在没有任何增益的情况下，ADC 的比特深度可能意味着它基本上是在用二、三或十来计算电子数。 Amplifying the electrons before they are counted allows us to map all of the available ADU values across a smaller range of brightnesses. 在对电子进行计数之前对其进行放大，可以让我们在更小的亮度范围内映射所有可用的 ADU 值。
As an extreme example, imagine a hypothetical photosite with a well capacity of exactly 40,950 electrons and 12-bit ADC. Without any electronic gain applied, the full well capacity maps to the ADC's 12-bit range (0-4095) at a convenient 10 electrons per ADU. Now assume we take an exposure that generates 15,996 electrons in the well. 举个极端的例子，假设一个光斑的井容量正好为 40,950 个电子，ADC 为 12 位。在不应用任何电子增益的情况下，全井容量映射到 ADC 的 12 位范围 (0-4095)，每 ADU 10 个电子 。现在假设我们进行一次曝光，在井中产生 15,996 个电子。
Not applying any gain allows us to capture the greatest dynamic range from the scene, but we lose some resolution in our ability to count electrons, since it takes 10 electrons to increase the ADU by one. 不应用任何增益可以让我们捕捉到场景中最大的动态范围，但我们在电子计数能力方面会损失一些分辨率，因为 ADU 增加一个需要 10 个电子。 For this exposure where photons generated 15,996 electrons, the ADC outputs a value of 1600 ( 15,996 divided by 10 electrons per ADU, rounded to the nearest integer), but any electron count from 15,996 to 16,004 would also yield 1600 ADUs. 在这次曝光中，光子产生了 15,996 个电子，ADC 输出值为 1600（15,996 除以每 ADU 10 个电子，四舍五入为整数），但从 15,996 到 16,004 之间的任何电子计数也会产生 1600 ADU。 We just don't have the bit depth to distinguish between them. 我们只是没有足够的比特深度来区分它们。
If we apply a amplification, the charge from 15,996 electrons is doubled by the amplifier before being measured by the ADC. Let's say that the result is a charge equivalent to 31,991 electrons after a tiny bit of error. The ADC maps this to a value of 3199 . 如果我们使用 放大器，那么在 ADC 测量之前，来自 15 996 个电子的电荷会被放大器放大一倍。假设经过微小误差后，结果相当于 31991 个电子的电荷量。ADC 将其映射为 3199 的值。
With gain we can only use half the full well capacity, since any more electrons than that will cause the ADC to read out the maximum value. But we can now resolve smaller differences in the electron count, since each incremental change in 使用 增益时，我们只能使用全井容量的一半，因为任何超过该值的电子都会导致 ADC 读出最大值。但我们现在可以分辨电子计数中较小的差异，因为电子计数中的每一个增量变化，都会影响到我们的测量结果。
(no gain) (无收益）
the ADU now corresponds to five electrons instead of ten. Finer levels of brightness can be discerned, so intermediate shades are now available that were indistinguishable at a lower gain. We are trading dynamic range for precision. 现在，ADU 相当于五个而不是十个电子。可以分辨出更精细的亮度等级，因此现在可以获得在较低增益下无法分辨的中间色调。我们正在用动态范围换取精度。 If we know our target will be dim, we can use gain to avoid wasting a lot of our bit depth on unused levels at the brightest end of the dynamic range. However, if there are bright regions of the scene as well, they could be clipped. 如果我们知道我们的目标将是昏暗的，我们就可以使用增益来避免在动态范围最亮的一端浪费大量的比特深度在未使用的电平上。但是，如果场景中也有明亮的区域，则可能会出现削波。
The same logic applies to greater levels of gain with ever smaller fractions of the well capacity being mapped to the default bit depth through amplification of the charge. You can see that at gain (ISO 400 for this camera), our example exposure is too bright. Around 63,984 electrons would result, exceeding the full well capacity of 40,950 . The ADC will read out at the maximum value of 4095 no matter how many more photons arrive. 同样的逻辑也适用于更高的增益水平，通过电荷的放大，越来越小的井容量分数被映射到默认位深度。您可以看到，在 增益下（该相机的 ISO 值为 400），我们的曝光示例过于明亮。大约会产生 63,984 个电子，超过了 40,950 的全井容量。无论有多少光子到达，ADC 的读数都将达到最大值 4095。 We will never know the actual brightness of that part of the image. 我们永远不会知道图像中那部分的实际亮度。 However, for a dimmer area where fewer electrons were generated in the well, this level of gain would have mapped the smaller range of electron counts onto the same 12-bits, resolving increments of brightness four times finer than with no gain. 然而，对于井中产生电子较少的较暗区域，这种增益水平可以将较小范围的电子计数映射到相同的 12 位上，分辨亮度增量的精细程度是无增益时的四倍。
In DSLRs the extreme ISO settings (usually ISO 3200 and up) may be different from the others in that the final digital value from the ADC is simply multiplied to create a sort of imitation gain. 在数码单反相机中，极限 ISO 设置（通常为 ISO 3200 及以上）可能与其他设置不同，因为 ADC 的最终数字值会被简单地乘以，从而产生一种模拟增益。 Because there is no amplification to the analog signal going into the ADC, this reduces dynamic range without providing any additional precision. Check the pixel value in the image-if all the output values are even multiples, then synthetic gain has been applied. 由于进入 ADC 的模拟信号没有经过放大，因此动态范围会减小，但精度不会提高。检查图像中的像素值--如果所有输出值都是偶数倍，则表示已经应用了合成增益。 Also be cautious of the 'in-between' ISOs, like 500 or 1000, as those can be the result of either two-step amplification or simple multiplication of the ADC's output. 此外，还要小心 "介于 "之间的 ISO，如 500 或 1000，因为这些可能是两步放大或 ADC 输出简单相乘的结果。
Figure 3. Gain offers a trade-off between precision and dynamic range 图 3.增益在精度和动态范围之间进行权衡
Abstract 摘要
Worked Exercise Within a faint nebula sits a bright star. The nebula has a brightness of magnitude 14 per square arcsecond, while the star has a magnitude of 4 and covers approximately one square arcsecond when viewed through your optical system. 作业练习 在一个暗星云中，有一颗明亮的恒星。星云的亮度为每平方角秒 14 等，而恒星的亮度为 4 等，通过光学系统观察时，恒星的亮度约为 1 平方角秒。 (Five magnitudes constitute a 100 -fold difference in brightness.) How many decibels of dynamic range would your sensor need to have in order to capture this scene fully in a single exposure? And for your photographer friend who thinks in terms of -stops, how would you describe the dynamic range of the scene? (五倍等于 100 倍的亮度差异。）为了在一次曝光中完整捕捉这一场景，您的传感器需要多少分贝的动态范围？您的摄影师朋友的思维方式是 光圈，您如何描述场景的动态范围？
Since there are 10 magnitudes between the brightest and dimmest areas of the scene, and we know that five magnitudes are a difference, there is a factor of range in our scene. 由于场景中最亮和最暗的区域之间相差 10 个等级，而我们知道 5 个等级是 的差异，因此我们的场景中存在 的范围。
To calculate decibels, we use the formula provided: 计算分贝时，我们使用提供的公式：
This yields . 由此得出 .
In f-stops, it would be: 以光圈计算，应该是
stops 停止
This would be at the limit of most modern sensors to fully capture in a single exposure, but by taking and averaging many exposures, we can capture even greater dynamic ranges. 对于大多数现代传感器来说，这已经达到了单次曝光就能完全捕捉的极限，但通过多次曝光并取平均值，我们可以捕捉到更大的动态范围。
The importance of bit depth 比特深度的重要性
For daylight photography, even 8-bits (256 levels) of data for each color channel is more than the human eye can distinguish. If you see 'more than 16 million colors' or '24-bit color' advertised for a display, it is referring to 8-bit depth for each of the three color channels. 对于日光摄影来说，即使每个色彩通道的数据量为 8 位（256 级），也超过了人眼的分辨能力。如果你看到 "超过 1600 万色 "或 "24 位色彩 "的显示器广告，它指的是三个色彩通道中每个通道的 8 位深度。 There are 256 levels possible in each of red, green, and blue creates different color combinations. 红、绿、蓝各有 256 个等级，可产生 不同的颜色组合。
The possible shades from black to white encompassed by a range of bit depths from one bit (black and white) to eight bits (256 shades of gray) is shown in Figure 4. 图 4 显示了从一位（黑白）到八位（256 种灰度）的比特深度范围所包含的从黑到白的可能色调。
Just because 256 levels create a smooth gradient in a final image doesn't mean that this is adequate for our raw data, though. We'll usually capture image files with 16 bits per color channel, and we often use 32 bits for intermediate processing steps. 虽然 256 色阶能在最终图像中产生平滑的渐变效果，但这并不意味着这对我们的原始数据来说就足够了。我们通常会捕捉每个颜色通道 16 位的图像文件，而且我们通常会在中间处理步骤中使用 32 位。 Deep-sky objects are very faint. They live in narrow sliver of brightness levels, while stars in the same scene are likely orders of magnitude brighter. 深空天体非常暗淡。它们的亮度范围很窄，而同一场景中的恒星可能要亮上几个数量级。 To reveal the objects in our final image, we have to expand the darker levels of the dynamic range by mapping them to a wider range of values This leaves fewer values available for the brighter levels, so those are mapped to fewer values. 为了显示最终图像中的物体，我们必须将动态范围中较暗的色阶映射到更宽的数值范围内，以扩大动态范围。
Consider what would happen if you took an exposure of a faint nebula that was recorded with only 8 bits of depth, as would be the case with a JPEG image. After several minutes of exposure time, light from a nebula might register in the darkest 15 levels out of the 256 available. 试想一下，如果您对一个暗星云进行曝光，记录的深度只有 8 位，就像 JPEG 图像一样，会发生什么情况。经过几分钟的曝光后，星云发出的光可能会记录在 256 个可用位中最暗的 15 个位上。 Fifteen discrete shades are not enough to smoothly represent the subtle variations in nebulosity we want for our image. We need to distinguish fine differences in brightness, since we are later going to 'stretch' the image to expand the nebula's dynamic range in the final image. 15 种不连续的色调不足以平滑地表现我们想要的图像中星云的细微变化。我们需要分辨出亮度的细微差别，因为我们稍后要对图像进行 "拉伸"，以扩大最终图像中星云的动态范围。 To quantify these differences, we need greater bit depth. The same 15 dimmest levels in 8 -bit would be divided into 240 discrete levels in 12-bit data or 3840 levels with 16 bits, resulting in a more appealing image with smoother gradients. 为了量化这些差异，我们需要更大的比特深度。在 8 位数据中，同样的 15 个最暗色阶在 12 位数据中将被分为 240 个离散色阶，在 16 位数据中将被分为 3840 个色阶，从而使图像的渐变更平滑，更吸引人。
Imagine that after taking a dozen exposures of our hypothetical nebula above, the individual 12-bit values from the camera for one pixel average to 91.52 on the range. If an adjacent pixel had an average value of 92.08 , they would be indistinguishable in 12-bits, as they both round to 92 . 试想一下，在对上述假设的星云进行了十几次曝光后，相机中一个像素的单个 12 位值在 范围内的平均值为 91.52。如果相邻像素的平均值为 92.08，它们的 12 位值将无法区分，因为它们都四舍五入为 92。 A 16-bit file has sixteen times the resolution of a 12-bit file, so it can more accurately express them as the discrete values 1464 and 1473 on a scale of . 16 位文件的分辨率是 12 位文件的 16 倍，因此可以更准确地将它们表示为 标尺上的离散值 1464 和 1473。
Linear data and response curves 线性数据和响应曲线
The eye's response to light is approximately logarithmic. That is, we perceive brightness proportionally. We can detect a tiny increase in photon flux if the overall scene is dim, because the change is noticeable in proportion to the overall level of light. 眼睛对光线的反应近似于对数。也就是说，我们对亮度的感知是成比例的。如果整个场景很暗，我们也能察觉到光子通量的微小增加，因为这种变化与整体光亮度成正比，非常明显。 The same absolute increase would be imperceptible in a brighter scene where it would be a tiny fraction of the overall flux. (This is true for some of our other senses as well-weight, pitch, and loudness are also perceived on an approximately logarithmic basis.) 同样的绝对增加在更亮的场景中是无法察觉的，因为它只是总通量的一小部分（我们的其他一些感官也是如此，重量、音调和响度也是以近似对数的方式感知的）。(我们的一些其他感官也是如此，重量、音调和响度也是以近似对数的方式感知的）。
Combined with the variable aperture of the iris, this compression of sensitivity allows our eyes to perceive an enormous range of brightness that far exceeds that of a printed page or electronic display. 再加上虹膜的可变光圈，这种灵敏度的压缩使我们的眼睛能够感知到远超过印刷页面或电子显示屏的巨大亮度范围。 We don't think of it this way, but the brightness difference between indoors and a sunlit outdoor scene is many thousand-fold. 我们并不这样认为，但室内和室外阳光下的场景亮度相差数千倍。
Electronic sensors are not logarithmically sensitive; they are almost perfectly linear. In order to correctly display linear data from a sensor on a monitor or printed page, adjustments must be made. 电子传感器不具有对数灵敏度；它们几乎是完全线性的。为了在显示器或打印页面上正确显示传感器的线性数据，必须进行调整。
When shooting photos with a consumer camera (or looking at the camera's preview screen), the camera tries to accommodate the nonlinear response of your eyes and the display to reproduce the scene as your eye would have perceived it. 当使用消费类相机拍摄照片时（或观看相机的预览屏幕），相机会尝试适应您眼睛的非线性反应，显示屏会按照您眼睛的感知再现场景。 To do this, it takes the raw linear data from the sensor and applies a non-linear transformation (called a gamma curve) 为此，它从传感器获取原始线性数据，并应用非线性变换（称为伽玛曲线）
that accounts for the display and the human eye's response to light. 它考虑到了显示效果和人眼对光线的反应。
If you are viewing the image in raw format, you are looking at linear data. Because no gamma transformation is applied, the image may look extremely dim. It's easy to be disappointed the first time you see a raw astronomical image on the screen. 如果您查看的是原始格式的图像，您看到的就是线性数据。由于没有应用伽玛变换，图像可能看起来非常暗淡。第一次在屏幕上看到原始天文图像时很容易感到失望。 Perhaps it looks something like Figure 5. This is a reflection of the dynamic range of deep-sky objects, which is revealed in the image's histogram. Histograms will be our guide throughout this book. 也许看起来像图 5。这反映了深空天体的动态范围，图像的直方图揭示了这一点。直方图将是我们在本书中的指南。 They show all possible brightness levels along the horizontal axis, from completely black on the left to the brightest white on the right. The frequency that each of these levels occurs in the image is shown on the vertical axis. 它们沿着横轴显示了所有可能的亮度级别，从左边的全黑到右边最亮的白色。纵轴上显示的是每个亮度等级在图像中出现的频率。 For this image you can see that nearly all of the pixels fall within a very narrow and dim part of the total dynamic range. 在这幅图像中，您可以看到几乎所有的像素都属于总动态范围中非常狭窄和暗淡的部分。
Fortunately, we have tools at our disposal to bring that dim image up to its full potential. By stretching the image in post-processing, we can reveal what's within that spike on the histogram by remapping those few values across a much larger range of brightness. 幸运的是，我们可以利用一些工具来充分发挥暗淡图像的潜力。通过在后期处理中拉伸图像，我们可以在更大的亮度范围内重新映射直方图上的几个值，从而揭示出直方图上尖峰部分的内容。 Figure 6 shows the resulting image and histogram. 图 6 显示了生成的图像和直方图。
Figure 5. Before stretching, the nebula's data are nearly all compressed into a few dim values. 图 5.在拉伸之前，星云的数据几乎都被压缩成了几个暗淡的数值。
Figure 6. After stretching, the image fills the available dynamic range, revealing the nebula 图 6.拉伸后，图像充满了可用的动态范围，显示出星云
Creating color images 创建彩色图像
Sensors are inherently color-blind; they cannot determine the wavelength of the photons they capture. The output of each photosite is a monochrome value representing a level of brightness. 传感器本身是色盲的；它们无法确定所捕捉光子的波长。每个光点的输出是一个单色值，代表一个亮度等级。 Taking images through filters allows us to quantify how much light is from each portion of the spectrum by allowing only a range of wavelengths to pass through to the sensor. 通过滤光片拍摄图像时，我们只允许一定波长的光线通过传感器，从而可以量化光谱中每一部分光线的含量。 There are two primary methods of accomplishing this: putting color filters in front of the sensors and taking separate images through each, or using 'one-shot color' (OSC) sensors, where each photosite has a tiny color filter built onto it. 实现这一目标的主要方法有两种：在传感器前安装彩色滤光片，并通过每个滤光片分别拍摄图像；或者使用 "一次成像彩色"（OSC）传感器，即每个光斑上都内置一个微小的彩色滤光片。
Monochromatic sensors have no color filters built onto the sensor. Color filters can be placed in front of the sensor to capture the red light, green light, and blue light in separate images. These images can then be synthesized into a fullcolor image at the computer. 单色传感器没有内置彩色滤光片。彩色滤光片可以放置在传感器前面，以单独的图像捕捉红光、绿光和蓝光。这些图像可以在计算机上合成为全彩色图像。 In addition, a luminance channel consisting of exposures taken without a color filter can be incorporated into the image. Monochromatic cameras also allow the user to choose filters other than red, green, and blue. 此外，还可以在图像中加入一个亮度通道，该通道由未使用彩色滤光片的曝光组成。单色相机还允许用户选择红、绿、蓝以外的滤光片。 There are narrowband filters that transmit only light from the specific spectral lines that are common to some astronomical objects. As we'll see, these have designations, like H-alpha and OIII, that are based on their atomic source. 有些窄带滤光片只能透过某些天体常见的特定光谱线的光线。正如我们将要看到的，这些滤光片的名称，如 H-α 和 OIII，都是基于它们的原子源。 By blocking all but a small part of the spectrum, these filters can allow you to capture images of some objects through light pollution that would otherwise cause problems. The flexibility of monochrome sensors comes at a cost in terms of money 这些滤光片可以阻挡除一小部分光谱以外的所有光谱，从而使您可以通过光污染捕捉到某些物体的图像，否则就会造成问题。单色传感器的灵活性需要付出代价
and complexity, however. Filters and filter-wheels can be expensive, and there is an additional learning curve involved in properly combining exposures taken through different filters. 但是，滤光片和滤光片轮价格昂贵。滤光镜和滤光片轮可能很昂贵，而且要正确组合通过不同滤光镜拍摄的曝光，还需要额外的学习曲线。
One-shot color systems, like DSLRs and some dedicated astronomy cameras, use an array of tiny colored filters over the individual photosites, called a color filter array. Each pixel thus determines the brightness of either red, green, or blue light. 单镜头彩色系统，如数码单反相机和一些专用的天文相机，在单个像素上使用一个微小的彩色滤光片阵列，称为彩色滤光片阵列。因此，每个像素都能决定红光、绿光或蓝光的亮度。 The true color of each pixel in the final image is then estimated using data from the surrounding pixels. 然后，利用周围像素的数据估算出最终图像中每个像素的真实颜色。
The most common color filter array pattern is called a Bayer matrix, and it consists of an alternating pattern with green-filtered pixels, red, and blue. This bias is reflective of the fact that green is in the middle of the visible spectrum, where the human eye has greatest sensitivity. 最常见的滤色片阵列模式被称为拜耳矩阵，它由 绿色滤波像素、 红色和 蓝色的交替模式组成。这种偏差反映了一个事实，即绿色位于可见光谱的中间，而人眼对绿色的敏感度最高。
So how do we calculate the full color information for each pixel when we only measured one part of the spectrum? Debayering is the mathematical process of interpolating an estimated color for each pixel based on the levels in the surrounding pixels. 那么，当我们只测量了光谱的一部分时，如何计算每个像素的全部色彩信息呢？去色法是根据周围像素的色阶，对每个像素的颜色进行内插估算的数学过程。 There are numerous methods for de-bayering, each varying in calculation speed and accuracy for a given setting. Smooth gradients are generally easy to de-bayer, but sharp edges, like stars on a black background, are more of a challenge. 去分层的方法有很多，每种方法在特定设置下的计算速度和准确性都不尽相同。平滑的渐变一般很容易去分层，但尖锐的边缘（如黑色背景上的星星）就比较困难了。 Modern algorithms create images that are nearly free of artifacts, so this is something that the typical imager rarely has to worry about. 现代算法生成的图像几乎没有伪影，因此一般的相机很少需要担心这个问题。 Note that raw files are not de-bayered, so they may look like a grayscale checkerboard in some imaging programs. The interpolation of color is usually done by the calibration or post-processing software. 请注意，原始文件没有去分层，因此在某些成像程序中可能看起来像灰度棋盘。色彩插值通常由校准或后期处理软件完成。
Figure 7. The Bayer matrix 图 7.拜尔矩阵
Choosing between one-shot color and monochrome image sensors is about trade-offs between flexibility, cost, and simplicity. 在一次拍摄彩色图像传感器和单色图像传感器之间做出选择，需要在灵活性、成本和简便性之间做出权衡。 Dedicated astronomical cameras are available as oneshot color or monochrome, with features like built-in cooling, software control, and low-noise electronics designed for astronomical imaging. 专用天文相机有单色和彩色两种，具有内置冷却、软件控制和专为天文成像设计的低噪音电子设备等功能。 Monochromatic cameras are incredibly efficient, and they lack the infrared filter that is built into most DSLRs, making them more sensitive to this region of the spectrum that is crucial for capturing emission nebulae. 单色相机的效率极高，而且它们没有大多数数码单反相机内置的红外滤光片，因此对光谱的这一区域更加敏感，而这一区域对于捕捉发射星云至关重要。
DSLRs are all one-shot color (with a few very expensive exceptions). They are often cheaper and use larger image sensors than equivalently-priced astronomical cameras. 数码单反相机都是单次拍摄的彩色相机（少数非常昂贵的相机除外）。它们通常比同等价格的天文相机更便宜，使用的图像传感器也更大。 Their built-in preview displays facilitate quick focusing and composition, and they can be used without a separate computer to control them. There are no filter wheels to add, and no additional processing steps to combine color channels. 它们内置的预览显示屏便于快速对焦和构图，使用时无需单独的电脑控制。无需添加滤镜轮，也无需额外的处理步骤来组合色彩通道。
2 SIGNAL AND NOISE 2 信号和噪声
How signal varies 信号如何变化
Signal and noise are inherently mathematical concepts, so this chapter will feature some high school algebra, but we'll explain every step along the way. Understanding signal-tonoise ratios will drive our choice of equipment, exposure duration, and even how we process images. 信号和噪点本质上是数学概念，因此本章将介绍一些高中代数知识，但我们会解释其中的每一个步骤。了解信噪比将有助于我们选择设备、曝光时间，甚至是处理图像的方式。 If you are mathaverse, don't worry too much about the details or formulae; just focus on the big-picture concepts here. 如果你不喜欢数学，就不要太在意细节或公式，只需关注这里的大局概念。
Even if you've never had a class on statistics, you've almost certainly seen the bell curve before, and you probably have an intuitive sense of what it means. 即使你从未上过统计课，你也几乎肯定见过钟形曲线，而且你可能对它的含义有直观的认识。 The concept behind the bell curve, also known as the 'normal' or Gaussian distribution, is that if you create a histogram of nearly any continuous variable, it will always take this specific shape (assuming there are no systematic biases or errors underlying the process that produces the values). 钟形曲线也被称为 "正态分布 "或高斯分布，其背后的概念是，如果你为几乎任何连续变量绘制直方图，它总是会呈现出这种特定的形状（假设产生数值的过程中不存在系统性偏差或误差）。
That statement is a bit technical, so let's break it down: 这种说法有点技术性，让我们来分析一下：
A histogram is a kind of bar chart where the horizontal axis has bars that capture equal ranges of the potential values. The vertical axis counts how many of the values occurred within each range. 直方图是一种条形图，横轴上的条形表示潜在值的相等范围。纵轴统计每个范围内出现的数值数量。 So if we were creating a histogram of the heights of adults in a town, we might choose a horizontal axis that runs from four to seven feet with each bar covering a one-inch part of that range. Shorter people would be on the left side of the histogram, and taller people to right. 因此，如果我们要绘制一个城镇成年人身高的直方图，我们可能会选择一条从 4 英尺到 7 英尺的横轴，每条横轴覆盖该范围内一英寸的部分。矮个子在直方图的左边，高个子在右边。 The tallest bar would represent the most common height in the town. 最高的横杠代表该镇最常见的身高。
Continuous variables are things like height, weight, distance, volume, etc. These are variables where the value can take any fractional amount. 连续变量包括身高、体重、距离、体积等。这些变量的值可以是任何小数。 Weight or height are examples of continuous variables, as the accuracy of our scale or ruler is the only limit to how precise we know the value. 体重或身高就是连续变量的例子，因为体重秤或身高尺的精确度是我们了解数值精确度的唯一限制。 This is as opposed to discrete variables, which are countable things, like how many people live in a town or how many tails occurred in a series of coin flips. Discrete variables can only be integer values. 这与离散变量不同，离散变量是可数的东西，比如一个小镇上住着多少人，或者在一系列掷硬币的过程中出现了多少次反面。离散变量只能是整数值。
Systematic biases or errors are essentially anything in the process of creating the values that would push the shape of the histogram away from the normal distribution. 系统偏差或误差主要是指在创建数值的过程中，会使直方图的形状偏离正态分布的任何因素。 To continue the example of plotting the heights of adults in a town, if we plotted only the men in the town, we would expect to see a normal curve. 继续以绘制镇上成年人的身高为例，如果我们只绘制镇上男性的身高，我们会看到一条正态曲线。 However, if we plotted all of the adults, we would see a bimodal distribution with two humps, one for men and one for women, revealing that there are two separate populations, each normally distributed around a different average height. 但是，如果我们将所有成年人的身高绘制成图，我们会看到一个双峰分布，即男性和女性各有一个驼峰，这表明存在两个不同的群体，每个群体都围绕着不同的平均身高呈正态分布。
Assuming a variable is normally distributed, as we plot a larger and larger sample of values, the shape of the histogram will approach the normal bell curve. The normal distribution is incredibly useful, as nearly every naturally occurring variable is distributed this way. 假设变量呈正态分布，当我们绘制的样本值越来越大时，直方图的形状将接近正态钟形曲线。正态分布非常有用，因为几乎所有自然出现的变量都是这样分布的。 Thus, if we know a variable is normally distributed, we can use the characteristics of the curve to make predictions about a population of values by examining a sample of its members. In our case, taking an exposure is a sample of the light from our deep-sky object. 因此，如果我们知道一个变量是正态分布的，我们就可以利用曲线的特征，通过对其样本的研究，对数值的总体进行预测。在我们的例子中，对深空天体的光线进行曝光就是一个样本。
The normal distribution curve is completely described by two variables: its mean (average value) and its standard deviation, which is a measure of how widely distributed the values are around that mean. 正态分布曲线完全由两个变量来描述：平均值和标准差。 Figure 8 shows an example of three normal curves with the same mean of 100 , but with standard deviations of 5,10, and 25. You can see that the larger the standard deviation, the wider the curve, showing that more values occur further from the mean. 图 8 显示了三条正态曲线的示例，它们的平均值都是 100，但标准差分别为 5、10 和 25。可以看出，标准差越大，曲线越宽，说明离均值越远的值越多。 When the standard deviation is smaller, the values tend to cluster closer to the mean. 当标准偏差较小时，数值往往更接近平均值。
Figure 8. Normal curves with standard deviations of 5,10 , and 25 图 8.标准偏差为 5、10 和 25 的正态曲线
Normal distributions apply to any continuous variable, but you may be surprised to learn that the brightness of light is not a continuous variable. In 1905 Albert Einstein showed that light arrives in discrete packets or 'quanta' that we now call photons. 正态分布适用于任何连续变量，但你可能会惊讶地发现，光的亮度并不是连续变量。1905 年，阿尔伯特-爱因斯坦发现，光是以离散的数据包或 "量子 "形式到达的，我们现在称之为光子。 We don't need to get into the details of quantum physics or the wave-particle duality of light, but the implication for imaging is that measuring light is more like counting marbles in a jar than measuring height or weight. 我们无需深入探讨量子物理学或光的波粒二象性的细节，但这对成像的影响是，测量光更像是数罐子里的弹珠，而不是测量身高或体重。 Light arrives as photons, and we count them as integers; there is no such thing as half a photon. 光以光子的形式到达，我们把它们当作整数来计算；不存在半个光子的说法。
where the outcome or timing of each event is independent of the others-whether coin flips, erroneous jury verdicts in France, or photons arriving at a sensor. 在这种情况下，每个事件的结果或时间都与其他事件无关--无论是掷硬币、法国陪审团的错误判决，还是到达传感器的光子。 While Poisson could have never imagined it, the distribution named after him is what we'll use to describe the statistics of astronomical imaging. 虽然泊松从未想到过这一点，但以他的名字命名的分布就是我们用来描述天文成像统计的。
To quantify discrete events, we need to use a similar distribution curve, known as the Poisson distribution. Figure 9 shows an example of the Poisson distribution. Notice that because it describes a discrete variable, it is not a smooth curve. 要量化离散事件，我们需要使用类似的分布曲线，即所谓的泊松分布。图 9 显示了泊松分布的一个示例。请注意，由于它描述的是离散变量，因此并不是一条平滑的曲线。 This is because there is a specific probability that each integer value occurs, but the probability of any fractional value between them occurring is zero (e.g., you can never get 4.3 heads in a series of 10 coin flips). 这是因为每个整数值出现的概率都是特定的，但它们之间任何一个小数值出现的概率都是零（例如，在一系列 10 次掷硬币的过程中，你永远不可能得到 4.3 个人头）。 Notice that the overall shape, other than the gaps between integer values, resembles the normal curve. 请注意，除了整数值之间的间隙外，整体形状与正态曲线相似。
Figure 9. The Poisson distribution for a mean of 100 图 9.均值为 100 的泊松分布
There is a key difference from the normal curve, however. For discrete events, the mean and the standard deviation are inextricably linked. Poisson's math showed that the standard deviation for a discrete event rate is always the square root of the mean. 但与正态曲线有一个关键区别。对于离散事件，均值和标准差是密不可分的。泊松数学表明，离散事件率的标准差总是均值的平方根。
Figure 10. Poisson histograms for means of 100 and 400 图 10.均值为 100 和 400 的泊松直方图
Whereas the normal distribution required two numbers to describe it (the mean and the standard deviation), Poisson distributions can be completely described by one number: the mean. A mean of 100 automatically determines that the standard deviation will be 10 . 正态分布需要两个数字来描述（均值和标准差），而泊松分布只需要一个数字：均值。平均值为 100 会自动决定标准差为 10。 If the mean is 400 , the standard deviation must be 20. Poisson distributions for these two values are plotted in Figure 10. 如果平均值是 400，标准差一定是 20。这两个值的泊松分布如图 10 所示。
Signal and noise at the pixel level 像素级的信号和噪声
Now that we've covered the basic statistical concepts, let's put them to use on two of the most important concepts in astronomical imaging: signal and noise. Nearly every step of image capture and processing is done with them in mind. 既然我们已经介绍了基本的统计概念，那么就让我们把它们用在天文成像中最重要的两个概念上：信号和噪声。图像捕捉和处理的几乎每一步都要考虑到它们。 In imaging, signal is anything that causes the output of the sensor to increase in a time-dependent manner. This is mostly from photons passing through our optics to the sensor, but heat can be an additional, unwanted source of signal. But what exactly is noise? 在成像中，信号是指任何导致传感器的输出以随时间变化的方式增加的东西。这主要是光子通过光学器件到达传感器，但热量也可能是额外的、不需要的信号源。但噪音到底是什么呢？ Fundamentally, noise can be thought of as uncertainty. Noise is the amount of random variation that a signal exhibits; in other words, how much the signal fluctuates randomly around its true value each time we measure it. 从根本上说，噪声可以被视为不确定性。噪声是信号随机变化的程度，换句话说，就是每次测量信号时，信号围绕其真实值随机波动的程度。 On a histogram, it is the width of our bell curve, and the unit we use for noise is the standard deviation. 在直方图中，它是钟形曲线的宽度，而我们用来表示噪音的单位是标准偏差。
It is important to emphasize that noise is not a distinct portion of the signal nor is it an impurity that we can separate from the signal. It is a value that describes how accurate our estimate of the signal is. 需要强调的是，噪声不是信号的一个独立部分，也不是我们可以从信号中分离出来的杂质。它是一个描述我们对信号估计准确度的值。 It's analogous to the margin of error in a poll, and just as larger polls have smaller margins of error, longer exposure times give us a better estimate of the signal. 这类似于民意调查中的误差范围，就像大型民意调查的误差范围较小一样，较长的曝光时间能让我们更好地估计信号。 Noise isn't something that most daylight photographers think about much because they don't spend hours teasing out faint wisps of signal from a nearly black image. In normal lighting, millions of photons are striking each photosite every second. 大多数白天拍摄的摄影师都不会过多考虑噪点问题，因为他们不会花几个小时从几乎漆黑的图像中找出微弱的信号。在正常照明条件下，每秒钟都有数百万个光子撞击每个光点。 And therein lies the biggest challenge of deepsky imaging: because these objects are often emitting only a few photons per minute, our smaller 'sample size' means that noise is more of a concern. 深空成像的最大挑战就在于此：由于这些天体通常每分钟只发出几个光子，我们的 "样本量 "较小，这意味着噪声是一个更令人担忧的问题。
It is useful to describe the amount of noise in proportion to the signal. The most commonly used expression for this measure is the signal-to-noise ratio, abbreviated SNR, which is the single most important driver of image quality. 描述噪声量与信号的比例非常有用。这种测量方法最常用的表达方式是信噪比，简称 SNR，它是图像质量最重要的驱动因素。 Images with a higher SNR have less visual noise, smoother gradients, and they can be stretched further in post-processing to reveal fainter details. 信噪比越高的图像，视觉噪点越少，梯度越平滑，在后期处理中可以进一步拉伸，以显示更模糊的细节。
The underlying goal of deep-sky imaging is to accurately estimate the rate the photons coming from an incredibly dim object in space are arriving at the sensor. We achieve accuracy through long total exposure times and the use of calibration frames. 深空成像的基本目标是准确估算来自太空中极其暗淡的物体的光子到达传感器的速度。我们通过延长总曝光时间和使用校准帧来实现这一目标。 Long total exposure times, divided across many separate exposures, allow us to capture many photons. Calibration frames allow us to isolate the signal from our deep-sky object by correcting for the attributes of the sensor and optics, and the presence of unwanted signals. 总曝光时间长，分多次单独曝光，使我们能够捕捉到许多光子。通过校正传感器和光学器件的属性以及不需要的信号，校准帧可以将深空天体的信号分离出来。
There are two types of noise we'll encounter: 我们会遇到两种噪音：
Noise that comes from the random fluctuations of a signal. We call this shot noise. Because it is inherent to a signal, shot noise is time-dependent. As shown above, 来自信号随机波动的噪声。我们称之为脉冲噪声。由于它是信号的固有特性，射频噪声与时间有关。如上图所示
one standard deviation of shot noise is the square root of the signal. 射频噪声的一个标准偏差是信号的平方根。
Noise that comes from small errors in the electronic processes used to measure light. We call this read noise. Read noise is not time-dependent; it is a fixed amount for every exposure. 噪声来自用于测量光的电子过程中的微小误差。我们称之为读取噪声。读取噪声与时间无关，每次曝光都是固定的。
Even though we only seek to capture photons from our astronomical object, three signals are detected by the sensor, as shown in Figure 11. First, there are photons from the distant astronomical object that we are interested in. 如图 11 所示，尽管我们只试图捕捉来自天体的光子，但传感器还是检测到了三种信号。首先是来自我们感兴趣的遥远天体的光子。 Second, there are the unwanted photons from the skyglow in our atmosphere. Third, the ambient heat of the sensor contributes an unwanted thermal signal to the image. Each of these signals is a source of shot noise. 其次，大气中的天光会产生不必要的光子。第三，传感器的环境热量会给图像带来不必要的热信号。这些信号都是拍摄噪声的来源。
Thermal Signal 热信号
Figure 11. Three signals are captured in each exposure 图 11.每次曝光采集三个信号
In addition to shot noise, each exposure adds a fixed amount of read noise, which is independent of any signal. Read noise captures all the small uncertainties inherent in each step of the electronic readout processes of the camera. 除了拍摄噪点外，每次曝光都会增加一定量的读取噪点，这些噪点与任何信号无关。读取噪声捕捉了相机电子读取过程中每一步固有的所有微小不确定性。 It does not vary with time-the read noise of a given camera is the same for every exposure, no matter how long. 它不会随时间而变化--无论曝光多长时间，特定相机的读取噪点在每次曝光时都是一样的。
Shot noise 射击噪音
Whatever their source, photons do not arrive at our sensor at a perfectly constant rate. Raindrops are a similar phenomenon. A steady rain falling at a rate of one centimeter per hour does not reach that average rate because the raindrops fall in lockstep at precise intervals. 无论光子的来源如何，它们都不会以完全恒定的速度到达我们的传感器。雨滴也是类似的现象。以每小时一厘米的速度持续落下的雨滴不会达到这个平均速度，因为雨滴是以精确的间隔步调一致地落下的。 Knowing that the long- term rate is a centimeter per hour will not tell you exactly how many drops will splash into your rain gauge over the next minute. 即使知道长期降雨率是每小时一厘米，也无法准确地告诉您在接下来的一分钟内会有多少雨滴溅入雨量计。
To continue the raindrop analogy, imagine your sensor as square tiles on the ground, each tile representing a photosite. Photons rain down at a steady rate, striking randomly all over this sensor floor. After a minute, you go out to count how many have hit a given tile. 继续用雨滴做比喻，将传感器想象成地面上的方形瓷砖，每块瓷砖代表一个光点。光子以稳定的速度落下，随机地打在传感器的地面上。一分钟后，您出去数一数有多少光子击中了某块方砖。 Let's say you count 33 . You then get out your photon squeegee to wipe the sensor clean and open the shutter again another minute. Do you think the count will be 33 again? Not likely. It will probably be a nearby value like 28 or 40 or 34 . 假设您数到 33 。然后您拿出光子刮板把传感器擦干净，再打开快门一分钟。你认为计数还会是 33 吗？不太可能。可能会是 28、40 或 34 等附近的数值。 This is the noise inherent in the rate of photon arrival, which we call shot noise. The light source has constant brightness, but in a short-term measurement we uncover the unavoidable consequence of light arriving in discrete particles. 这就是光子到达速率中固有的噪声，我们称之为 "射击噪声"。光源的亮度是恒定的，但在短期测量中，我们会发现光以离散粒子到达的不可避免的结果。
As we've seen, the arrival rate of photons will follow the Poisson distribution. We've also seen that statistics provides us with a way to quantify noise: the standard deviation (SD). This describes how much variation there is around the average rate. 正如我们所见，光子的到达率将遵循泊松分布。我们还看到，统计学为我们提供了一种量化噪声的方法：标准偏差 (SD)。它描述了围绕平均速率的变化程度。 For a Poisson distribution, the SD is the square root of the rate. 对于泊松分布，SD 是比率的平方根。
What does a standard deviation mean for our measurements? The shape of the Poisson distribution (and normal distribution, for that matter) is such that about of exposures will fall within of the true rate. About will fall within , and more than of exposures should be within SDs. 标准偏差对我们的测量意味着什么？根据泊松分布（以及正态分布）的形状，大约 的测量值将在真实测量值的 范围内。约 将落在 范围内，超过 的暴露应在 SD范围内。
When we talk about the brightness of a point in the sky, we are describing the long-term average rate of photon arrival for that spot. 当我们谈论天空中某一点的亮度时，我们描述的是光子到达该点的长期平均速率。 This is easy for a bright spot, where lots of photons stream toward us, and we can thus confidently estimate the brightness with only a short exposure. But consider a situation where the real long-term rate is 100 photons per minute. Here, the shot noise is , so about of the time you will count between 90 and 110 photons per minute, of the time it will be between 80 and 120 , and only very rarely less than 70 or greater than 130 . The values will cluster around the true rate of 100 , but the standard deviation tells you how tightly they will cluster. This is what we saw in Figure 9. 这对于亮点来说很容易，因为在亮点上有大量光子流向我们，因此我们只需短时间曝光就能很有把握地估计出亮度。但考虑到实际的长期速率为每分钟 100 个光子。在这种情况下，拍摄噪声为 ，因此大约 的情况下，光子计数会在每分钟 90 到 110 个之间， 的情况下，光子计数会在 80 到 120 个之间，只有极少数情况下，光子计数会小于 70 或大于 130。这些值将围绕 100 的真实速率聚集，但标准偏差会告诉您它们聚集的紧密程度。这就是我们在图 9 中看到的情况。
For comparison Figure 12 shows the Poisson distribution for a mean of 1000. As in Figure 9, the horizontal scale ranges from below and above the mean, but you can see the distribution is proportionally narrower. Here the shot noise is . While the actual width of the bell curve is greater than our example where the mean was 100 (31.6 vs 10), as a percentage of the mean (3.16% vs 10%), it is much narrower. This is a critical point. When the mean was 100 , the signal-to-noise ratio was . Now that the mean is 1000 , the SNR is . Shot noise grows at a slower rate than the signal. This leads to a fundamental insight: the more photons we capture, the better our SNR. 为便于比较，图 12 显示了均值为 1000 的泊松分布。与图 9 一样，水平标度范围为均值以下 和均值以上 ，但可以看到分布范围按比例缩小了。这里的拍摄噪声为 。虽然钟形曲线的实际宽度大于平均值为 100 的示例（31.6 vs 10），但从平均值的百分比来看（3.16% vs 10%），它要窄得多。这是一个关键点。当均值为 100 时，信噪比为 。现在，平均值为 1000，信噪比为 。射出噪声的增长速度比信号慢。由此可以得出一个基本结论：捕获的光子越多，信噪比就越高。
7007508008509009501000105011001150120012501300
Figure 12. Poisson distribution with mean of 1000 图 12均值为 1000 的泊松分布
Considering only shot noise, our SNR is: signal/noise object, where is the signal from the deep-sky object. This can be simplified to . This is a trivial expression now, but we'll build out this equation as we add different sources of noise. 只考虑拍摄噪声，我们的信噪比为：信号/噪声 天体，其中 是来自深空天体的信号。这可以简化为 。现在这是一个微不足道的表达式，但我们会在添加不同的噪声源时建立这个等式。
Another way to visualize the concept of noise is to line up many actual samples and plot how they vary. Figure 13 shows this for a mean of 100 and a standard deviation of 10 , just as before. A range of one SD is highlighted in blue. You can see that most of the values stay within one SD of the mean, but there are occasional outliers. Overall, it's a noisy picture, and with only a few samples, it might be hard to guess that the mean was 100 . 另一种将噪声概念形象化的方法是将许多实际样本排成一行，并绘制它们的变化图。图 13 显示了平均值为 100 和标准偏差为 10 的情况。 一个标准差的范围用蓝色标出。可以看到，大部分数值都保持在平均值的一个标准差以内，但偶尔也会出现异常值。总的来说，这是一幅嘈杂的图画，仅凭几个样本，可能很难猜出平均值是 100 。
Figure 13. Shot noise with a mean of 100 (+/- one standard deviation shown in blue) 图 13.平均值为 100 的光斑噪声（蓝色显示 +/- 一个标准偏差）
Compare this to Figure 14, where the mean is 10,000 . The shot noise is 10 times greater here , but the signal is 100 times greater. The SNR is now 100 , or stated another way, our measure of noise, the standard deviation, is now of the total. 对比图 14，这里的平均值是 10,000 。这里的射频噪声是 的 10 倍，但信号是 的 100 倍。信噪比现在是 100 ，或者换一种说法，我们对噪声的衡量标准，即标准偏差，现在是总数的 。
Figure 14. Shot noise example with a mean of 10,000 (+/- one standard deviation shown in blue) 图 14.平均值为 10,000 的光斑噪声示例（蓝色显示 +/- 一个标准偏差）
An example of shot noise 射击噪音示例
Let's look at another illustrative example. We'll again zoom in on one photosite on the sensor. We'll ignore all the others and consider this one pixel gathering light from a small patch of the sky. 让我们来看另一个示例。我们再次放大传感器上的一个光点。我们忽略所有其他像素，只考虑这一个像素从一小片天空中采集光线的情况。 Our hypothetical camera has no read noise-that is, it will perfectly count photons and transfer an appropriate digital value to your computer. Even better, our camera is sitting out in space, so there is no skyglow. It is capturing only photons from a deep-sky object. 我们的假想相机没有读取噪音，也就是说，它可以完美地对光子进行计数，并将相应的数字值传输到你的电脑上。更妙的是，我们的相机位于太空中，因此没有天光。它只能捕捉来自深空天体的光子。
For the spot in the sky we'll examine, the true long-term average arrival rate of photons is 1000 photons per minute. Because of shot noise, sometimes we get a little more than 1000 , sometimes a little fewer. 对于我们要研究的天空中的光点，光子的真正长期平均到达率是每分钟 1000 个光子。由于光子噪声的影响，有时我们得到的光子数会比 1000 多一点，有时会比 1000 少一点。 If we only take one exposure, that will be our best estimate of the true value. Let's say we take a single one-minute exposure, and upon counting up the photons, we find that 985 have arrived. Remember, we don't actually know the true value is 1000 . 如果我们只进行一次曝光，这将是我们对真实值的最佳估计。假设我们只进行了一分钟的曝光，在对光子进行计数时，我们发现有 985 个光子到达。请记住，我们实际上并不知道真实值是 1000 。 For all we know, it is 1050 or 962 or 983 . At this point, our best guess is that it's 985 . And we know that our shot noise is . This is about of the total, or alternately a SNR of 31 . (As you have probably noticed, when we only have shot noise to deal with, the SNR is equal to the shot noise. The situation will get more complex when we add other sources of noise.) 就我们所知，它是 1050 或 962 或 983 .目前，我们的最佳猜测是 985。我们知道我们的拍摄噪声是 。这大约是总数的 ，或者说信噪比为 31 。(您可能已经注意到，当我们只需处理镜头噪声时，信噪比等于镜头噪声。当我们添加其他噪声源时，情况会变得更加复杂）。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
985
985
标清不确定性
985
SD uncertainty
985
(1 SD 不确定性
985
(1 SD uncertainty
Since we know that photons don't arrive regularly, we'd like to be more confident in our estimate, so we take another exposure. Of course, we get a slightly different count this time: 1059 . 由于我们知道光子不会定期到达，我们希望对自己的估计更有把握，因此我们又进行了一次曝光。当然，这次我们得到的计数略有不同：1059 。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
985
1059
2044
(1 SD 不确定性
2044
(1 SD uncertainty
1022
(1 SD 不确定性
1022
(1 SD uncertainty
When we add the two exposures together, we get a total count of 2044 photons over two minutes of exposure time. The square root of 2044 is about 45.2 , so that is our 1 SD uncertainty around that value. 将两次曝光时间相加，两分钟曝光时间内的光子总数为 2044 个。2044 的平方根约为 45.2，因此该值的不确定性为 1 SD。 We divide by two to get a perminute rate of 1022 photons, which is our new estimate of the true rate per minute. We also divide the uncertainty by two, for a new shot noise level of 22.6 in per-minute terms. The SNR is now about 45. 我们除以 2，得到每分钟 1022 个光子的速率，这就是我们对每分钟真实速率的新估计。我们还将不确定性除以二，得出新的每分钟光子噪声水平为 22.6。信噪比现在约为 45。 While our estimate has changed, what's important to notice here is that the noise as a proportion of the total signal went down, meaning our SNR improved. 虽然我们的估计值发生了变化，但值得注意的是，噪声占信号总量的比例下降了，这意味着我们的信噪比提高了。
Capturing more photons improves the signal-to-noise ratio, whether this is done by combining multiple exposures or one long exposure. With our perfect camera, we could have accomplished the same result with a single two-minute exposure if we chose. 无论是多次曝光还是长时间曝光，捕捉更多的光子都能提高信噪比。如果我们选择使用完美的相机，只需一次两分钟的曝光就能达到同样的效果。 This makes sense when you consider that as the signal grows linearly, the shot noise only grows by the square root. Since the noise grows more slowly, it is always falling further behind. 如果考虑到当信号线性增长时，射频噪声只按平方根增长，这就说得通了。由于噪声的增长速度较慢，它总是落后于信号。 Considering only shot noise, the signal-to-noise ratio grows with the square root of the total exposure. In other words, to double your SNR, you'll need four times the total exposure time. To quadruple it, you'll need 16 times as much. 如果只考虑拍摄噪声，信噪比会随着总曝光时间的平方根增长。换句话说，如果要将信噪比提高一倍，则需要四倍的总曝光时间。若要翻两番，则需要 16 倍的曝光时间。
If two one-minute exposures are good, four will be even better, so we take two more. If the math holds, we should expect to get a -fold improvement in our SNR compared with a single exposure. 如果两次一分钟的曝光效果都很好，那么四次曝光效果会更好，因此我们再进行两次曝光。如果计算结果成立，那么与单次曝光相比，我们的信噪比有望提高 倍。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
985
{
4037
(1 SD uncertainty
} {
4037
(1 SD 不确定性
}
{
1009.25
(1 SD uncertainty
} {
1009.25
(1 SD 不确定性
}
1059
991
1002
Based on these four samples, we revise our best estimate of the true per-minute rate to 1009.25 , which is the average of our four values. At this point, we are more confident that the true long-term rate lies somewhere close to this. 根据这四个样本，我们将真实的每分钟费率的最佳估计值修改为 1009.25，即四个值的平均值。至此，我们更加确信真正的长期费率与此相差无几。 And indeed, as our uncertainty gets smaller, our average value is starting to converge toward what we know is the true value. The SNR is now up to about 1009/15.9 = 63. As predicted, that's about twice the value when we had only one minute of exposure time. 事实上，随着我们的不确定性越来越小，我们的平均值开始向我们所知道的真实值靠拢。信噪比现在大约为 1009/15.9 = 63。正如预测的那样，这大约是我们只有一分钟曝光时间时的两倍。
The night is still young, so we decide to double our exposure count again, to eight. (There is nothing special about the exact number of exposures; powers of two were chosen here just to make the math clearer.) It should be apparent by now what sort of result to expect. 夜色尚早，因此我们决定再次将曝光次数增加一倍，达到八次。(曝光的确切次数并没有什么特别之处；这里选择 2 的幂次只是为了让计算更加清晰）。现在我们应该明白会得到什么样的结果了。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
985
1059
991
7972
996.5
1002
(1 SD uncertainty (1 SD 不确定性
(1 SD uncertainty (1 SD 不确定性
958
1020
984
973
Now our average is 996.5 . As we add more exposure time, we grow more confident that our estimate of the rate of photon arrival is more accurate. This reduction in uncertainty is the same as saying that we are reducing noise as a proportion of the signal. 现在我们的平均值是 996.5。随着曝光时间的增加，我们对光子到达率的估计也越来越准确。这种不确定性的降低就等于说，我们正在降低噪声在信号中所占的比例。 Our SNR for eight minutes of exposure time is now 89 . 八分钟曝光时间的信噪比现在为 89 。
The math is all well and good, but what does this reduction in noise mean in the final image? Imagine that our example camera above were pointed at a nebula. Instead of the single pixel we've been considering, let's also look at the three next to it as well. 计算结果固然不错，但在最终图像中，噪点的减少意味着什么呢？想象一下，我们上面的相机对准的是一个星云。我们考虑的不是单个像素，而是它旁边的三个像素。 The tiny area of the nebula where these four photosites are aimed has a subtle gradient from a little darker to a little lighter. Let's say the true flux for each of the four adjacent photosites is exactly , and 1015 photons per minute. We want our final image to show that accurately as a smooth gradient. If we don't have enough exposure time to distinguish between these values due to noise, the final image could have values like 991, 1004, 998, and 1040 instead. 这四个光子所对准的星云的微小区域有一个从稍暗到稍亮的微妙梯度。假设四个相邻光点的真实通量正好是 ，每分钟 1015 个光子。我们希望最终的图像能以平滑的梯度精确显示。如果由于噪点的原因，我们没有足够的曝光时间来区分这些值，那么最终图像的值可能是 991、1004、998 和 1040。 This will look noisy in the image, completely obscuring the gradient. By improving the signal-to-noise ratio, we can capture finer differences in brightness. Noise sets a limit on the smallest change in brightness that can be captured in your image. 这在图像中会显得很嘈杂，完全掩盖了梯度。通过提高信噪比，我们可以捕捉到更细微的亮度差异。噪点为图像中能捕捉到的最小亮度变化设定了限制。
The following two figures show a series of images of the faint nebula LBN331. They are integrations of 5-minute exposures taken through a hydrogen-alpha filter. 下面两幅图是暗星云 LBN331 的一系列图像。它们是通过氢-阿尔法滤光片拍摄的 5 分钟曝光的积分图。 The numbers indicate how many exposures were combined to create each image, so the total integration times run from 5 minutes for the single exposure to 5 hours 20 minutes for the integration of 64 exposures. 数字表示每幅图像是由多少次曝光组合而成的，因此总的积分时间从单次曝光的 5 分钟到 64 次曝光的 5 小时 20 分钟不等。 (Again, any number of exposures could be taken; powers of two were only used for clarity of math.) (同样，可以进行任意次数的曝光；使用 2 的幂次只是为了便于计算）。
Exactly the same processing was done to each image. In the wide view, you can see the nebulosity is gradually revealed as more exposure time is added. This effect is even clearer in the close-up, where you can see the nebulosity appearing as the signal to noise ratio improves. 每张照片都经过了完全相同的处理。在广角镜头中，可以看到随着曝光时间的增加，云雾状物质逐渐显现出来。在特写镜头中，这种效果更加明显，可以看到随着信噪比的提高，云雾状物质也逐渐显现出来。 The SNR is about eight-fold better in the 64-exposure integration vs. the single frame. 64 次曝光整合的信噪比是单帧的八倍。
Figure 15. H-alpha integrations of LBN 331 using progressively more subexposures, all processed exactly the same. 图 15.对 LBN 331 进行的 H-α 积分，使用的子曝光逐渐增加，所有处理过程完全相同。
Figure 16. A detail from the image at left. 图 16.左图中的一个细节。
A dimmer example 调光器示例
Before moving on to other sources of noise, let's look at another example, but with fewer photons arriving each minute. Maybe this is a dimmer part of the object. Or maybe we are taking shorter exposures. Or it could be a different telescope. 在继续讨论其他噪声源之前，让我们来看另一个例子，但每分钟到达的光子数量更少。也许这是物体中较暗的部分。或者我们的曝光时间更短。也可能是使用了不同的望远镜。 In any case, the long-term average brightness we record is now 100 photons per minute instead of 1000 . 无论如何，我们记录的长期平均亮度现在是每分钟 100 个光子，而不是 1000 个。
As before, we have no idea what the real value is, so we take an exposure to try to find out. Our first shot shows 108 photons. Being omniscient in this experiment, we know that the true brightness should be 100, so why is this first shot off? In our previous example, the noise level for even a single exposure was only . Was this an outlier event? Not at all. The shot noise is the square root of the value, and the square root here is 10.108 was a reasonable value to expect. The standard deviation of this dim signal is of its value. When the signal is small, noise is high in proportion to the overall signal. 和之前一样，我们不知道真实值是多少，因此我们进行一次曝光来尝试找出答案。我们的第一次曝光显示了 108 个光子。作为实验中的全知全能者，我们知道真实亮度应该是 100，那么为什么第一次曝光会出现 偏差呢？在我们之前的例子中，即使是单次曝光的噪声水平也只有 。这是异常事件吗？完全不是。拍摄噪声是数值的平方根，而这里的平方根是 10.108，这是一个合理的预期值。这个微弱信号的标准偏差是其值的 。当信号很小时，噪声与整个信号的比例就很高。
As before, we decide to take another shot and average the two. 和以前一样，我们决定再拍一张，然后取两者的平均值。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
101
104.5
不确定性
104.5
uncertainty
Two minutes of exposure increases our SNR from about 10 to 14. As before, let's double our exposure count again. 两分钟的曝光将信噪比从 10 提高到 14。和之前一样，让我们再次将曝光次数增加一倍。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
108
{
415
SD uncertainty
} {
415
SD 不确定性
}
101
118
88
And as before, taking four shots doubles the SNR we got from one exposure, but this combined SNR of 20 is still worse than even a single exposure of the brighter object where the SNR was about 31 . 和以前一样，拍摄四张照片可以将一次曝光得到的信噪比 提高一倍，但 20 的综合信噪比仍然不如对更亮物体的单次曝光，后者的信噪比约为 31。 This is because we are still recording fewer photons in four exposures here than a single exposure in the brighter example gave us. 这是因为我们在这里四次曝光所记录的光子数量仍然少于在更亮的示例中一次曝光所记录的光子数量。
Noise is larger in relation to the total for dim objects. It would take far more exposure time to get the same level accuracy as with our brighter object. 昏暗物体的噪点相对于总噪点更大。要获得与明亮天体相同的精确度，需要花费更多的曝光时间。 Considering only the shot noise, an object one-tenth as bright takes 10 times as much exposure time to achieve the same SNR, and we haven't even brought read noise or skyglow into consideration yet. Astrophotography requires great patience, especially for the fainter objects. 如果只考虑拍摄噪点，十分之一亮度的天体需要十倍的曝光时间才能获得相同的信噪比，我们甚至还没有考虑读数噪点或天光。天体摄影需要极大的耐心，尤其是对较暗的天体。
To overcome shot noise, we need to collect more photons. We have several options to do this: 为了克服光斑噪声，我们需要收集更多的光子。我们有几种方法可以做到这一点：
We can gather more light in each exposure. This means we either take longer exposures or we increase the aperture of our optics while holding the focal length constant (i.e., reducing the focal ratio). 我们可以在每次曝光中收集更多的光线。这意味着我们要么延长曝光时间，要么在焦距不变的情况下增大光学器件的光圈（即减小焦距比）。
We can take more exposures. 我们可以进行更多的曝光。
We can trade resolution for SNR by capturing a larger area of the sky with each pixel (known as our image scale). To do this we either use a sensor with larger pixels, use optics with a shorter focal length, or bin our pixels so that 4 or 9 pixels output as one. 我们可以通过每个像素捕捉更大的天空区域（即图像比例）来换取分辨率和信噪比。为此，我们要么使用像素更大的传感器，要么使用焦距更短的光学器件，要么将像素分门别类，将 4 或 9 个像素作为一个像素输出。
Skyglow 天光
Now let's take a step toward the real world. We still have a perfect camera, but our skies are more realistic. We've come down from orbit, so the sky is not perfectly dark anymore. We have another signal coming in: a faintly glowing sky has replaced pitch-black space. 现在，让我们向现实世界迈出一步。我们仍然拥有完美的相机，但我们的天空更加真实。我们已经从轨道上下来了，所以天空不再是一片漆黑。我们收到了另一个信号：微弱发光的天空取代了漆黑的太空。 Now the photons from our target object aren't the only signal; we have skyglow to deal with too. 现在，来自目标物体的光子并不是唯一的信号，我们还需要处理天光。
Even in the darkest spots on earth, far from human-made light pollution, there is still a small amount of atmospheric glow from ionization in the upper atmosphere, not to mention dust particles, humidity, and the natural light scattering properties of air. 即使在地球上最黑暗的地方，在远离人为光污染的地方，仍然会有少量的大气光辉，这些光辉来自高层大气的电离，更不用说尘埃粒子、湿度和空气的自然光散射特性了。 Though it varies tremendously between locations, skyglow is unavoidable. 虽然不同地点的天光差异很大，但天光是不可避免的。
Since we have powerful image processing tools at our disposal, and our first thought might be, 'we can just subtract that skyglow out!' It should be consistent across the field of view, so we'll measure an empty spot in the image, and subtract that value from every pixel, leaving a nice black background. 由于我们拥有强大的图像处理工具，而我们的第一个想法可能是："我们可以直接将天光减去！"。整个视场中的天光应该是一致的，所以我们要测量图像中的一个空点，然后从每个像素中减去这个值，留下一个漂亮的黑色背景。
Not so fast. What about shot noise? The skyglow is a signal, thus it has its own noise. We can subtract an average value, but each individual exposure will capture a slightly different level of skyglow-this variation (the noise) will remain. 没那么快射击噪音如何？天光是一种信号，因此它有自己的噪点。我们可以减去一个平均值，但每次曝光捕捉到的天光水平都会略有不同，这种变化（噪点）仍会存在。 Noise is an inherent quality of a signal, not a separate entity, so it can't be subtracted away. 噪音是信号的固有质量，而不是一个独立的实体，因此无法将其减去。
We now know that we need to capture a lot of photons to get a decent estimate of a pixel's brightness, so we take four minutes of exposures to start with. 我们现在知道，我们需要捕捉大量的光子，才能对像素的亮度做出正确的估计，因此我们首先要进行四分钟的曝光。 Our hypothetical dim target is still emitting an average of 100 photons per minute, and our camera is still perfectly counting each one. But now we have skyglow, and it is five times brighter than the object. 我们假设的昏暗目标仍在平均每分钟发射 100 个光子，我们的相机仍在完美地计算每个光子。但现在我们看到了天光，它比目标亮五倍。 (Our return from orbit landed us in suburbia.) With each exposure, we are getting around 600 photons: 500 from the skyglow and 100 from the target. (我们从轨道上返回时是在郊区着陆的。）每次曝光，我们都能获得大约 600 个光子：500 个来自天光，100 个来自目标。
Here are our four exposures with skyglow: 以下是我们四次曝光的天光：
个人
Expo-
Sures
Individual
Expo-
sures
总光子数
Count
Total Photon
Count
Average per
minute
573
{
2424
SD uncertainty
} {
2424
SD 不确定性
}
{
606
(1 SD uncertainty
} {
606
(1 SD 不确定性
}
614
630
607
We know that photons are striking the sensor both from our target object many light years away and from light scattered in the atmosphere, but there is no way to tell them apart. 我们知道，光子既来自许多光年之外的目标物体，也来自大气层中的散射光，但却无法将它们区分开来。 Based on four exposures, we estimate the combined flux of the target and the skyglow to be 606 photons per minute. And we know that the noise component in this is about 12.3 , for an SNR of about 49 , which seems pretty good on the surface. But the only signal that we are interested in is that from the target, and those were only about 400 of the total (we don't know exactly how many). That's an SNR of , which is not very good. The larger combined signal of the object and skyglow fluctuates over a larger range than the signal from the object alone. The weaker our target's signal is in relation to the skyglow, the worse the effect. 根据四次曝光，我们估计目标和天光的总通量为每分钟 606 个光子。我们知道，其中的噪声分量约为 12.3 ，信噪比约为 49 ，表面上看似乎很不错。但我们唯一感兴趣的是来自目标的信号，而这些信号只占总数的大约 400（我们不知道具体有多少）。信噪比为 ，这并不是很好。天体和天光的综合信号比天体单独发出的信号波动范围更大。与天光相比，目标信号越弱，效果就越差。 We must shoot longer and longer total exposures to overcome this difference as either the skyglow gets brighter or the targets get dimmer. 随着天光越来越亮或目标越来越暗，我们必须拍摄越来越长的总曝光时间来克服这种差异。
Adding in the effects of skyglow, our image SNR is still total signal divided by total shot noise, which is still the square root of the total signal. But the SNR for our deep-sky object is the object's signal divided by total shot noise: ). 加上天光的影响，我们的图像信噪比仍然是总信号除以总拍摄噪声，也就是总信号的平方根。但深空天体的信噪比是天体信号除以总拍摄噪声： ）。
Now let's briefly consider the same example, but at a darksky location, with less skyglow, a mere 50 photons per minute per pixel through our optical system. As before, we take four exposures. 现在，让我们简要地考虑一下同样的例子，不过是在光线较暗的地方， 天光较少，每个像素每分钟只有 50 个光子通过我们的光学系统。和之前一样，我们进行四次曝光。
个人
Exposures
Individual
Exposures
总光子数
Count
Total Photon
Count
Average per
minute
137
155
591
147.8
146
(1 SD 不确定性
153
(1 SD uncertainty
153
(1 SD 不确定性
(1 SD uncertainty
Because the object's flux is a larger proportion of the total, the skyglow's noise isn't as overwhelming. The SNR for the total signal is 24.3 , which seems lower than the 49.2 we got at our suburban site. 由于天体的通量占总通量的比例较大，因此天光的噪声没有那么大。总信号的信噪比为 24.3，似乎低于我们在郊区观测站获得的 49.2。 But when we consider it relative to the signal we are interested in, the object's, it compares much better: (vs 8 with brighter skyglow). 但是，如果我们将其与我们感兴趣的信号（即天体的信号）相对比，它就会好得多： （与天光更亮的 8 相比）。
Skyglow is the dominant source of noise for urban and suburban imagers. Light pollution filters can help some, as can choosing targets away from the worst pollution. 天光是城市和郊区成像者的主要噪声源。光污染滤镜可以起到一定作用，选择远离污染最严重地区的目标也是如此。 (Join the International Dark-Sky Association to help combat the problem.) Narrowband imaging is an option that avoids most light pollution by filtering out all but the specific wave- lengths emitted by certain objects. (加入国际暗天空协会，帮助解决这一问题。）窄带成像是一种选择，它可以过滤掉除某些天体发出的特定波长以外的所有波长，从而避免大部分光污染。 It works exceptionally well for emission nebulae, but won't help for other targets. For the most part, brighter skies mean that more exposures are required to reach the same signal-to-noise ratios you could achieve under dark skies. 它对发射星云特别有效，但对其他目标却没有帮助。在大多数情况下，较亮的天空意味着需要更多的曝光，才能达到与在黑暗天空下相同的信噪比。 Imaging from a dark location is one of the surest ways to improve your image quality. 在暗处成像是提高图像质量的最可靠方法之一。
Almost as bad as its impact on SNR is the effect skyglow has on dynamic range. As the well fills up with skyglow photons, that leaves less room for target object photons to be counted before the well is full. 天辉对动态范围的影响几乎与它对信噪比的影响一样严重。当天光光子填满光井时，在光井被填满之前，留给目标物光子计数的空间就会减少。 This will make it harder to distinguish different shades within the object, and it forces shorter exposure times. 这样就很难分辨出物体内部的不同色调，同时也会缩短曝光时间。
Why shot noise cannot be subtracted away 为什么不能减去拍摄噪音
It may seem that we can get rid of skyglow by determining the average background value in our image and subtracting that from every pixel. And indeed, that's essentially what we'll do later when we process the image to get a nice, nearly black background. 我们似乎可以通过确定图像中的平均背景值并从每个像素中减去该值来消除天光。事实上，这正是我们稍后处理图像以获得近乎黑色的漂亮背景时要做的事情。 But it's important to realize that the shot noise from the skyglow remains in the image even after we do this. A simple example may help illustrate this. 但重要的是要认识到，即使我们这样做了，天光产生的拍摄噪点仍然会留在图像中。一个简单的例子可以说明这一点。
For simplicity, let's assume we are imaging a square object in the sky, and it is perfectly uniform in brightness such that it generates 1000 electrons in each photosite per exposure. For our first exposure, there is no skyglow. 为简单起见，假设我们对天空中的一个方形物体进行成像，该物体的亮度完全一致，每次曝光都能在每个光斑中产生 1000 个电子。第一次曝光时，没有天光。 If we were to take a single row of pixels and plot their values, we would see something like Figure 17: a nearly perfectly black background with values around 1000 electrons where our object is, with the variations due to shot noise. 如果我们取一列像素并绘制它们的数值，就会看到类似图 17 的情况：背景几乎完全是黑色的，我们的目标所在位置的数值约为 1000 个电子，其变化是由于拍摄噪声造成的。
Figure 17. The values from one row of an exposure with no skyglow. 图 17.无天光曝光的一行数值。
Now, let's add in skyglow with a brightness of 5000 electrons. This exposure would look like Figure 18, with more variation from shot noise. The average background level of 4984 is marked with a red line. 现在，让我们加入亮度为 5000 电子的天光。这样的曝光效果如图 18 所示，但拍摄噪点的变化更大。4984 的平均背景亮度用红线标出。 The pixels pointed at our object now have levels of about 6000, and there is more variance around that value than there was around 1000 . 现在，指向我们对象的像素的级别约为 6000，与 1000 左右相比，该值附近的差异更大。
Figure 18. The values from one row of an exposure with skyglow. 图 18.天光曝光的一行数值。
If we wanted the background in our image to be perfectly black, we'd subtract the skyglow from every pixel. But that value varies at every pixel due to shot noise, so our best estimate is to subtract the average background value (the red line). 如果我们希望图像中的背景是完全黑色的，我们就会从每个像素中减去天光。但由于拍摄噪音的影响，每个像素的天光值都不一样，所以我们最好的估计是减去平均背景值（红线）。 If we do that, we are left with Figure 19. (The negative values shown would be clipped to 0 .) 如果我们这样做，就会得到图 19。(图中的负值将被剪切为 0）。
Figure 19. The values from one row of an exposure with skyglow. 图 19.天光曝光的一行数值。
As you can see, the skyglow is removed, but its shot noise remains in the image. Compared with Figure 17, the pixels from our object and the background are both far noisier. 正如您所看到的，天光已被去除，但其拍摄噪音仍留在图像中。与图 17 相比，物体和背景的像素噪声都要大得多。 This principle is true no matter the source of noise: because it is a variation in the signal, it cannot be subtracted away. Our signal-to-noise ratio can only be improved by collecting more data. 无论噪音的来源是什么，这一原则都是正确的：因为噪音是信号中的一种变化，所以无法将其减去。我们只能通过收集更多的数据来提高信噪比。
Dark current 暗电流
There is a third signal we collect while distant photons hit the sensor, but this one is coming from a much closer source. 当遥远的光子撞击传感器时，我们还会收集到第三个信号，但这个信号来自更近的光源。 The surrounding air and the heat generated by the camera's own electronics can both warm the sensor, causing electrons to be agitated out of the silicon substrate. 周围的空气和相机本身的电子设备产生的热量都会加热传感器，使电子从硅基板中被激发出来。 This thermal signal is referred to as 'dark current.'There is no way to tell whether an electron in the well was dislocated by an extragalactic photon or the heat energy in the sensor itself; the ADC counts them all the same. 这种热信号被称为 "暗电流"。我们无法判断井中的电子是被银河系外的光子还是传感器本身的热能位错的；ADC 对它们的计数都是一样的。 Without some form of cooling, this heat can become a significant source of unwanted signal. 如果没有某种形式的冷却，这些热量就会成为不必要信号的重要来源。
Like any other signal, it is linearly time-dependent. Longer exposures not only generate more electrons due to photons from the sky, they are also getting more electrons from the ambient warmth. 与其他信号一样，它与时间呈线性关系。较长的曝光时间不仅会因来自天空的光子而产生更多电子，还会从环境温度中获得更多电子。 Dark current is also temperature-dependent: for most sensors the thermal signal doubles with every increase in temperature. And just like any other signal, it doesn't arrive perfectly regularly, so it adds its own shot noise to the image. Each photosite also varies slightly in its sensitivity to heat. 暗电流也与温度有关：对于大多数传感器来说，温度每升高 ，热信号就会增加一倍。与其他信号一样，暗电流也不是完全有规律地出现，因此会给图像带来一定的噪点。每个光点对热的敏感度也略有不同。
Cameras with thermoelectric cooling systems can reduce thermal signal and maintain a constant sensor temperature. Cooling the sensor below the ambient temperature reduces the thermal signal for most sensors by about . Deeper cooling can reduce it even more. This makes an enormous difference. Consider the Kodak KAF-8300 CCD sensor as an example. While it is an older sensor, it is still used by many imagers. On a warm summer evening at , the sensor's photosites will each produce around 2.5 electrons per second. For a five-minute exposure, that would be about 750 electrons. Each photosite has a well capacity of about 25,000 electrons, so almost of that capacity would be filled with thermal signal alone. Cooling the chip by drops the 配备热电冷却系统的相机可以减少热信号，并保持传感器温度恒定。将传感器冷却到低于环境温度 时，大多数传感器的热信号会降低约 。更深层次的冷却可以进一步降低热信号。这就是巨大的差别。以柯达 KAF-8300 CCD 传感器为例。虽然这是一款较老的传感器，但许多成像仪仍在使用它。在 温暖的夏日傍晚，传感器的每个感光元件每秒将产生约 2.5 个电子。在五分钟的曝光时间内，大约会产生 750 个电子。每个光敏元件的井容量约为 25,000 个电子，因此仅热信号就能填满几乎 的容量。通过 冷却芯片，可减少 的电子数。
thermal signal to about 25 electrons for the same exposure time, about of the well's capacity. (More recent sensors have improved dark current levels by several orders of magnitude, reducing the need for deep cooling, though it remains important to hold the temperature of the sensor steady.) 在相同的曝光时间内，热信号约为 25 个电子，约为井容量的 。(最新的传感器将暗电流水平提高了几个数量级，从而减少了对深度冷却的需求，但保持传感器温度稳定仍然非常重要）。
The predictability of thermal signal makes its effect a little easier to manage than other sources. By capturing a set of images called dark frames that collect only the thermal signal, we can estimate the total dark signal for each pixel and subtract it from the final image. 与其他信号源相比，热信号的可预测性使其影响更容易控制。通过捕捉一组仅收集热信号的图像（称为暗帧），我们可以估算出每个像素的总暗信号，并将其从最终图像中减去。 While this doesn't remove the shot noise from the thermal signal, it does help correct the variation in thermal signal between pixels. 虽然这并不能消除热信号中的射击噪声，但却有助于校正像素间热信号的变化。
To get an accurate estimate of its value, we must take many dark frames and average them. Dark frames must match the duration and temperature of the exposures used to capture the object (the 'light frames'). 要准确估算其值，我们必须拍摄许多暗帧，然后求取平均值。暗帧的时间和温度必须与拍摄物体（"亮帧"）的曝光时间和温度相匹配。 With thermoelectric cooling, this simply requires taking many dark exposures on a cloudy night or even indoors. 利用热电冷却技术，只需在阴天晚上甚至在室内进行多次黑暗曝光即可。 Without temperature-controlled cooling, as with DSLRs, the most basic method is to take dark frames in the same imaging session as the light frames, alternating taking lights and darks. 在没有温控冷却的情况下，与数码单反相机一样，最基本的方法是在同一次成像过程中拍摄暗部画面和亮部画面，交替拍摄亮部和暗部画面。 While this yields darks that accurately match the temperature of the lights, it is not preferred since it cuts the imaging time in half. Clear sky time is precious, so a better option is to create a library of dark frames taken at known temperatures, gains, and durations. 虽然这样得到的暗像能准确匹配灯光的温度，但并不可取，因为这样会将成像时间缩短一半。晴空时间非常宝贵，因此更好的选择是创建一个在已知温度、增益和持续时间下拍摄的暗色帧库。 It is crucial to be sure that the temperature of the sensor is matched since the ambient air temperature is not always well-correlated with that of the inside of the camera. Later, we'll detail the process for acquiring reliable dark frames. 确保传感器的温度与环境温度相匹配至关重要，因为环境空气的温度并不总是与相机内部的温度密切相关。稍后，我们将详细介绍获取可靠暗帧的过程。
Every photosite is slightly different in how much dark signal it accumulates. We call those at the extremes 'hot' and 'cold' pixels. 每个像素点积累暗信号的程度都略有不同。我们将处于极端的像素称为 "热 "像素和 "冷 "像素。 These can be orders of magnitude more or less sensitive to heat, and they look like specks in an image, especially after it is stretched in normal post-processing. Hot pixels are far more common than cold pixels. 这些像素对热量的敏感度可能会高出或低出几个数量级，它们在图像中看起来就像斑点，尤其是在正常的后期处理中被拉伸之后。热像素比冷像素常见得多。 Every photosite, even those not obviously hot or cold, varies slightly in sensitivity to temperature. We will correct these variations in the calibration process. 每个照相点，即使是没有明显冷热之分的照相点，对温度的敏感度也会略有不同。我们将在校准过程中纠正这些差异。
Figure 20 shows a close up from the same area of two fourminute dark frames from an uncooled DSLR. The one on the top was taken at . The one on the bottom was taken at using the same camera at the same gain and exposure time. Both frames were equally stretched to make the hot pixels more visible. 图 20 显示的是同一区域的两幅四分钟暗景特写，这两幅暗景是用未制冷的数码单反相机拍摄的。上图是在 下拍摄的。下图是在 拍摄的，使用的是同一台相机，增益和曝光时间相同。两幅图像都被拉伸，使热像素更加明显。
Accounting for thermal signal, our object SNR formula is now: . The denominator is growing, but we are still getting the same number of photons from our object. 考虑到热信号，我们现在的目标信噪比公式为 。分母在增大，但我们仍能从物体中获得相同数量的光子。
Figure 20. Comparison of hot pixels at and and ) 图 20. 与 和 处的热像素比较 )
Abstract 摘要
Many DSLRs have a long-exposure mode that automatically takes and subtracts a dark frame from the picture. So why not use this convenient feature? First, only subtracting a single dark frame leaves a lot of noise behind. 许多数码单反相机都具有长曝光模式，可以自动拍摄并从照片中减去暗格。为什么不使用这一便捷功能呢？首先，只减去一个暗格会留下很多噪点。 Thermal signal is very small, therefore noise is a large proportion of it. To effectively reduce the amount of noise added to the final image usually requires averaging dozens or even hundreds of dark frames. 热信号非常小，因此噪声占很大比例。要有效减少最终图像中的噪点，通常需要对几十甚至上百个暗帧进行平均处理。 More importantly, taking dark frames is wasted time when you could be collecting more light from the target. More target signal is almost always better. 更重要的是，拍摄暗帧是在浪费时间，因为您本可以从目标收集更多光线。目标信号越多越好。 Even without any dark frames, your final image will have less noise if you spend the entire night collecting light frames (exposures of the sky) than if you spent half the night with the shutter closed for dark frames. Save dark frame collection for cloudy nights. 即使没有任何暗格，如果整晚都在收集亮格（天空的曝光），最终图像的噪点也会比半晚都在关闭快门收集暗格要少。将暗格收集工作留到阴天晚上进行。
Read noise 阅读噪音
Unlike our hypothetical camera from the examples above, a real sensor's photosites are not perfectly accurate in their ability to count photons. This uncertainty in the process of generating a digital number from the electrons in the well is called read noise. 与上述例子中的假想相机不同，真实传感器的光子计数能力并不完全准确。从井道中的电子生成数字的过程中的这种不确定性被称为读取噪声。 It is unrelated to the exposure time-it is a fixed level of noise that occurs each time the sensor is read The read noise in modern cameras is typically on the order of 1-5 electrons per exposure, depending on the gain level. 它与曝光时间无关，是每次读取传感器时产生的固定水平的噪点。
Given that the full well capacity of most sensors can rangeagain, depending on gain-from 1000 to 100,000 electrons, 考虑到大多数传感器的全井容量都在 1000 到 100000 个电子之间，这取决于增益、
read noise seems like a very small factor. But we care about it because it is a kind of per-exposure penalty that can add up across many exposures. 读取噪声似乎是一个很小的因素。但我们之所以关注它，是因为它是一种每次曝光的惩罚，可以在多次曝光中累加。 Read noise becomes a key factor for setting our exposure times: we want enough signal to ensure that shot noise is the primary source of noise in our exposures, not read noise. 读取噪声成为设置曝光时间的关键因素：我们需要足够的信号，以确保曝光中的主要噪声源是拍摄噪声，而不是读取噪声。
The main source of read noise is simply the imprecision inherent in any measuring device. When measuring the charge created by thousands of electrons, small errors are made by the electronics at each step of the readout process. 读取噪声的主要来源是任何测量设备固有的不精确性。在测量成千上万个电子产生的电荷时，电子元件在读出过程的每一步都会产生微小的误差。 A smaller portion of the read noise is quantization error, a kind of digital rounding error. 读取噪声的一小部分是量化误差，这是一种数字舍入误差。 There are an integer number of electrons in the well, and the ADC outputs an integer value, so one electron in the well can map to a fraction of an ADU (low gain) or several ADU (high gain). In nearly all cases, some rounding is required. 井中的电子数为整数，而 ADC 输出的是整数值，因此井中的一个电子可以映射为一个 ADU 的几分之一（低增益）或几个 ADU（高增益）。几乎在所有情况下，都需要进行四舍五入。
As an example, imagine a sensor with a full well capacity of 10,000 electrons at the current gain setting. The analog voltage output from the sensor could be the result of any number of electrons between 0 and 10,000. 举例来说，假设一个传感器在当前增益设置下的全井容量为 10,000 个电子。传感器输出的模拟电压可能是 0 到 10,000 之间任何电子数的结果。 If this camera has a 12-bit analog-to-digital converter, there are only 4096 different values of output, so it will take about 2.5 electrons to increase the ADU value by one. 如果这台相机有一个 12 位模数转换器，那么只有 4096 种不同的输出值，因此 ADU 值增加一个值大约需要 2.5 个电子。 Because we can't distinguish between 8500 electrons and 8501 electrons, that is a form of uncertainty, and uncertainty is noise. Quantization error is only a small part of read noise-it is typically dwarfed by other sources of imprecision. 因为我们无法区分 8500 个电子和 8501 个电子，这就是一种不确定性，而不确定性就是噪声。量化误差只是读取噪声的一小部分，其他不精确来源通常会让它相形见绌。
It's worth noting here that because of read noise, very dark areas of the image could have a negative count of electrons in the well, since noise is variation above or below the true value. 值得注意的是，由于读取噪声的存在，图像中非常暗的区域可能会出现井中电子计数为负值的情况，因为噪声是高于或低于真实值的变化。 Since the ADC can't output a negative number, it would simply output a zero, and this would be lost information. All such values would be clipped at zero ADUs, making it impossible to distinguish between them. 由于模数转换器无法输出负数，因此只会输出一个零，而这将是丢失的信息。所有这些数值都会在 ADU 为零时被削波，从而无法区分。 In order to fully characterize our data, we need to see the actual values. To avoid this, a small amount, usually 20-100 ADU, is added before readout so the ADC's baseline is actually slightly higher. 为了全面描述数据特征，我们需要看到实际值。为了避免出现这种情况，我们会在读出之前添加少量（通常为 20-100 ADU），这样 ADC 的基线实际上会稍高一些。 This is called the bias or offset value, and it's there so we can accurately capture the values from the dimmest pixels. For most sensors, you can set the bias value in the software. 这就是所谓的偏置或偏移值，有了它，我们才能准确捕捉到最暗像素的值。对于大多数传感器，您可以在软件中设置偏置值。
Knowing the bias/offset value for each pixel becomes important in calibration, where in order to properly divide one frame (e.g., a light) by another (e.g., a flat), we first need to subtract the bias value from both to set the 'zero-point' of the images. 了解每个像素的偏置/偏移值在校准中非常重要，为了正确地将一帧图像（如灯光）除以另一帧图像（如平面图像），我们首先需要从两帧图像中减去偏置值，以设置图像的 "零点"。 We measure the bias for each photosite by taking bias frames, where the sensor is covered completely, and the shortest exposure possible is taken. The idea is to take an exposure that represents the output of the sensor before any photons hit it. 我们通过拍摄偏置帧来测量每个光点的偏置，在偏置帧中，传感器被完全覆盖，并尽可能缩短曝光时间。这样做的目的是在任何光子撞击传感器之前进行曝光，以表示传感器的输出。
Accounting for read noise in our object SNR formula is a little more complicated because read noise is not the square root of some signal; it is a distinct per-exposure value. In order to fit it under the square root sign in our formula, we have to square it: , where R is the read noise. 在我们的物体信噪比公式中，读取噪声的计算要复杂一些，因为读取噪声并不是某个信号的平方根；它是每次曝光的一个独特值。为了使其符合公式中的平方根符号，我们必须对其进行平方处理： ，其中 R 是读取噪声。
Adding signals and noise 添加信号和噪音
Since we've now seen that there are multiple signals and types of noise, it's good time to mention the general method for adding them. Mathematically, we can add and subtract signals normally. 既然我们现在已经看到有多种信号和噪声类型，那么就应该提到将它们相加的一般方法了。在数学上，我们可以对信号进行正常的加减运算。 A dark current of 5 electrons and 10 electrons generated by sky photons are simply 15 electrons in the well. The camera can't tell which is which, but the math is simple: . 5 个电子的暗电流和天空光子产生的 10 个电子就是井中的 15 个电子。照相机无法分辨哪个是哪个，但计算很简单： 。
Noise, however, is a little more complex. Noise is not a measure of a simple countable thing, but a description of variation around a mean. 然而，噪声则要复杂一些。噪声不是对简单可数事物的测量，而是对围绕平均值的变化的描述。 This variation can be positive or negative, so the values have the potential to offset one another, and we need to account for that when we add them. 这种变化可能是正的，也可能是负的，因此这些值有可能相互抵消，我们在相加时需要考虑到这一点。 To add noise values, we use a mathematical method called 'summing in quadrature' (also known as 'root sum of squares' or just 'RSS'). This means that we square all the noise values, sum those squares, then take the square root of the total. 要添加噪声值，我们使用一种称为 "正交求和"（也称为 "平方根和 "或简称 "RSS"）的数学方法。这意味着我们要对所有噪声值进行平方运算，求和这些平方，然后取总和的平方根。
As an example, if we have two sources of noise, one with a standard deviation of 4 electrons, and the other 5 electrons, the sum of these two noise values is . We'll use this method as we add up the sources of noise in our images. 举例来说，如果我们有两个噪声源，一个的标准偏差为 4 个电子，另一个的标准偏差为 5 个电子，那么这两个噪声值的总和就是 。我们将使用这种方法对图像中的噪声源进行累加。
Worked Exercises
If a sensor's dark signal has a doubling temperature, and the ambient temperature is , by what percentage is the dark signal reduced when the sensor is cooled to C? By what percentage is the dark noise reduced? 练习
如果传感器的暗信号具有 倍增温度，而环境温度为 ，那么当传感器冷却到 C 时，暗信号会降低多少百分比？暗噪声降低了百分之几？
This reduction in temperature is times the doubling temperature, thus the dark signal is reduced to of its original value, or a reduction. The dark noise is the square root of the dark signal, so the reduction in noise is smaller than the reduction in signal. In this case, the square root of 0.019 is 0.138 , thus the reduction in noise is about . 温度的 降低幅度是翻倍温度的 倍，因此暗信号降低到原始值的 或 降低幅度。暗噪声是暗信号的平方根，因此噪声的减小要小于信号的减小。在本例中，0.019 的平方根为 0.138 ，因此噪声的减少量约为 。
Consider an example exposure where the dark signal at is 1,000 electrons. In this case the noise contributed by this dark signal is the square root of electrons. At , the dark signal is now only 19 electrons, so the noise is now the square root of electrons. The reduction from 31.62 to 4.36 is an reduction. 考虑一个曝光实例，其中 处的暗信号为 1,000 个电子。在这种情况下，暗信号产生的噪声是 电子的平方根。在 处，暗信号现在只有 19 个电子，因此噪声现在是 电子的平方根。从 31.62 到 4.36 的减少是 的减少。
The sensor's specifications state that it has a thermal signal of no more than electrons per second at , a doubling temperature of , and a full well capacity of electrons. What is the thermal signal at ? At that temperature how long would it take for the well to fill with thermal signal? (Assume a bias signal of zero.) 传感器的规格说明指出，在 处的热信号不超过每秒 个电子，倍增温度为 ，满井容量为 个电子。 时的热信号是多少？假设偏置信号为零）。
This is a drop in temperature, which means that the dark signal is reduced to of the original level, or about 18 electrons per second. , so the well would be full of dark signal electrons in 1392 seconds, or about 23 minutes, at . Obviously, this would make long-exposure imaging difficult at this temperature. 这是 温度的下降，这意味着暗信号降低到原来水平的 ，即大约每秒 18 个电子。 ，因此在 条件下，1392 秒或大约 23 分钟后，井中就会充满暗信号电子。显然，在这种温度下很难进行长时间曝光成像。
Assuming this same sensor has a read noise of 10 electrons, what is the available dynamic range for a 20 -minute exposure at ? And at ? 假设该传感器的读取噪声为 10 个电子，那么在 下曝光 20 分钟的可用动态范围是多少？ 时的动态范围是多少？
At , this is a drop in temperature, thus the dark signal is reduced by a factor of of the original level, or about 1.68 electrons per second. An exposure of 20 minutes would produce - per second electrons. Dark current would still fill 2014/25500 of the full well capacity. The brightest capturable level would be . The noise from the dark current is electrons. The read noise is given in the problem as 10 electrons, thus dynamic range available is , or 54 dB . 在 时，温度会下降 ，因此暗信号会减少原始电平的 倍，即每秒减少约 1.68 个电子。曝光 20 分钟将产生 - 每秒 个电子。暗电流仍将充满 2014/25500 的全井容量。可捕获的最亮电平为 。暗电流的噪声为 个电子。问题中给出的读取噪声为 10 个电子，因此可用的动态范围为 ，即 54 dB。
For the same exposure at , we follow the same steps The dark signal is reduced by a factor of of the original level, or about 0.026 electrons per second. An exposure of 20 minutes at would produce e-per second electrons. Dark current only fills of the full well capacity. The brightest capturable level would be . The noise from the dark current is electrons. The read noise is given in the problem as 10 electrons, thus dynamic range is , or 67 dB . 在 下进行相同的曝光，我们可以按照相同的步骤进行暗信号的减少，减少的倍数为原始电平的 ，即大约每秒 0.026 个电子。在 处曝光 20 分钟，会产生 每秒 个电子。暗电流只能填满 的全井容量。可捕获的最亮电平为 。暗电流的噪声为 个电子。问题中给出的读取噪声为 10 个电子，因此动态范围为 ，或 67 dB。
The calculations of decibels and dynamic range here are not as important as the realization that dark signal is not only a source of noise, but it also reduces the available dynamic range. 在这里，分贝和动态范围的计算并不重要，重要的是要认识到暗信号不仅是噪声源，还会减小可用的动态范围。 Both effects should make clear the importance of cooling for cameras with significant dark current. 这两种效应都说明了冷却对于暗电流较大的相机的重要性。
Variation in two-dimensions 二维变化
Read noise and shot noise vary over time or number of exposures. There is another kind of noise, spatial noise, that varies by location. Photosites vary slightly in their sensitivity, creating spatial variation in your image that isn't in the object you are imaging. 读取噪点和拍摄噪点随时间或曝光次数而变化。还有一种噪点，即空间噪点，会因拍摄地点的不同而变化。照片的感光度会略有不同，从而在图像中产生空间变化，而这些变化并不存在于您所拍摄的物体中。 This variation is called photoresponse non-uniformity (PRNU), and it is proportional to the light received (i.e., it is a multiplicative effect). 这种变化被称为光响应不均匀性（PRNU），它与接收到的光线成正比（即它是一种乘法效应）。 It may be because of a defect in the silicon, a misaligned microlens, coating defects, variations in the amplifier electronics, or any number of other reasons. 这可能是由于硅的缺陷、微透镜的错位、涂层缺陷、放大器电子元件的变化或任何其他原因造成的。 The PRNU is consistent for a given photosite, but it varies between photosites; for most sensors, the variation is less than . 特定光斑的 PRNU 是一致的，但不同光斑之间会有差异；对于大多数传感器来说，差异小于 。
Photosites also vary in thermal signal and their response to it. This is known as fixed-pattern noise, or FPN. Unlike PRNU, it is an additive effect. The combined effect of PRNU and FPN create the pattern noise in an image. 光敏元件的热信号及其对热信号的反应也各不相同。这就是所谓的固定模式噪声（FPN）。与 PRNU 不同，它是一种叠加效应。PRNU 和 FPN 的综合效应会在图像中产生图案噪声。
Except where it manifests as banding artifacts, pattern noise can be hard to spot since the pixel-to-pixel variations just look like other sources of noise. The primary tool to correct the PRNU component is the flat frame. 除了表现为带状伪影外，图案噪声很难被发现，因为像素间的变化看起来就像其他噪声源。校正 PRNU 部分的主要工具是平帧。 This is an exposure of an evenly illuminated field, and in the calibration process we'll divide the value of each pixel in our lights by the value of the corresponding pixel in the flats. We divide because PRNU is a multiplicative effect. 这是对一个均匀照明区域的曝光，在校准过程中，我们将用灯光中每个像素的值除以平 面上相应像素的值。我们进行除法是因为 PRNU 是一种乘法效应。 The primary tool to correct FPN is the dark frame. This is an exposure taken in the dark, but at the same temperature and duration of the light exposure. We subtract darks, since FPN is an additive effect. 校正 FPN 的主要工具是暗格。这是在黑暗中进行的曝光，但温度和持续时间与光照时相同。我们要减去暗部，因为 FPN 是一种叠加效应。
Even after our light frames have been corrected with flats and darks, there may also be a small amount of residual pattern noise. 即使我们的亮框经过平暗校正，也可能会有少量残留图案噪点。 This can be mitigated by shifting the aim of our telescope a tiny bit between exposures, known as dithering, so that when the images are aligned to the stars, the remaining pattern noise is no longer aligned between exposures. 这可以通过在两次曝光之间稍微移动望远镜的瞄准点来缓解，也就是所谓的抖动，这样当图像对准恒星时，剩余的图案噪声就不会再在两次曝光之间对准了。
Bringing it all together 将一切融为一体
Let's take a moment to recap the different signal and noise components in an image. There are three signals contributing to the total number of electrons in each photosite: 让我们花点时间来回顾一下图像中不同的信号和噪声成分。每个光斑中的电子总数由三个信号组成：
The electrons generated by thermal agitation of the silicon during the exposure. 硅在曝光过程中受热膨胀产生的电子。
The electrons generated by skyglow photons striking the sensor. 天光光子撞击传感器产生的电子。
The electrons generated by target photons striking the sensor. 目标光子撞击传感器产生的电子。
We are only interested in the third signal. The others are nuisances that we'll try to remove from our image later. 我们只对第三个信号感兴趣。其他信号都是干扰信号，我们稍后将设法从图像中去除。
There are five potential sources of noise: 噪音有五个潜在来源：
Dark current shot noise 暗电流冲击噪声
Figure 21. The electronic imaging paradigm with noise sources 图 21.带有噪声源的电子成像范例
Read noise, which is inherent to the electronics in the readout process and is independent of signal. 读取噪声，是读取过程中电子设备固有的噪声，与信号无关。
Shot noise associated with the thermal signal. 与热信号相关的射频噪声。
Shot noise associated with the skyglow signal. 与天光信号相关的光斑噪声。
Shot noise associated with the target signal. 与目标信号相关的射击噪声。
Spatial pattern noise due to variation in the sensitivity of each photosite to light and dark signal. 由于每个光点对光和暗信号的敏感度不同而产生的空间模式噪声。
Figure 21 builds on Figure 2, adding the sources of noise at each stage of the electronic imaging process. As you can see, read noise is actually the sum of several smaller noise sources that happen at the different stages of readout. 图 21 以图 2 为基础，增加了电子成像过程每个阶段的噪声源。如图所示，读取噪声实际上是在读取的不同阶段产生的几个较小噪声源的总和。 We don't need to worry about each of those contributing elements, as the sensor manufacturers roll it all into one read noise value. 我们不需要担心这些因素的影响，因为传感器制造商会将所有这些因素整合到一个读取噪声值中。
Now that we have all of our signals and noises identified, let's bring it together into a formula for signal-to-noise ratio (SNR). Recall that noise must be added using the summing in quadrature method: 现在，我们已经确定了所有的信号和噪声，让我们把它们整合到一个信噪比（SNR）公式中。回想一下，必须使用正交求和法来添加噪声：
Since shot noise is the square root of its corresponding signal, for the four sources of noise in an image, it looks like this: 由于镜头噪声是其相应信号的平方根，因此对于图像中的四种噪声源来说，它看起来是这样的：
where R is read noise. (Pattern noise is excluded here, as that represents variation between pixels, not within a single pixel.) 其中 R 为读取噪声。(这里不包括图案噪声，因为图案噪声代表的是像素之间的变化，而不是单个像素内部的变化）。
The square roots and the squares cancel out for the three shot noise terms, leaving us with 三个射频噪声项的平方根和平方抵消后，我们得出
This is the total noise for one exposure. For multiple exposures, we simply multiply everything under the radical by the number of exposures, n . 这是一次曝光的总噪声。对于多次曝光，我们只需将基数下的所有噪声乘以曝光次数 n 即可。
The signal is a very simple calculation: the number of exposures times the object's signal for each exposure. Putting the total signal over the total noise gives us our pixel-level SNR formula for a stack of n images: 信号的计算非常简单：曝光次数乘以每次曝光的物体信号。将总信号除以总噪声，就得到了由 n 张图像组成的像素级信噪比公式：
Consider the example of the data from a single hypothetical exposure in Figure 22. In this case we have an exposure of a dim target taken under skyglow. At the end of an exposure, we don't know the source of each electron, we only know that 以图 22 中的一次假设曝光数据为例。在这种情况下，我们在天光下对昏暗的目标进行曝光。在曝光结束时，我们不知道每个电子的来源，我们只知道
Figure 22. Four sources of electrons that compose a hypothetical exposure 图 22.构成假想曝光的四个电子源
The normal distribution was first described in the early 19th century by Carl Friedrich Gauss, and his equations form the basis for much of modern statistics. A few decades after Gauss, another brilliant mathematician solved the problem of how to deal with discrete variables. 卡尔-弗里德里希-高斯在 19 世纪初首次描述了正态分布，他的方程构成了现代统计学的基础。高斯之后几十年，另一位杰出的数学家解决了如何处理离散变量的问题。 Siméon Denis Poisson was actually interested in a matter of law: how do the requirements for the number of jurors required to vote guilty affect that chance of false conviction or acquittal? Siméon Denis Poisson 实际上对一个法律问题很感兴趣：投票表决有罪所需的陪审员人数要求如何影响误判或无罪释放的几率？ His book, Research on the Probability of Judgments in Criminal and Civil Matters, lays out most of the math describing the statistics of discrete events like the outcomes of jury trials. 他的著作《刑事和民事案件判决概率研究》（Research on the Probability of Judgments in Criminal and Civil Matter）阐述了描述离散事件（如陪审团审判结果）统计的大部分数学知识。 Within a few decades, others showed that Poisson's approach applied to discrete events generally. This includes any situation 几十年后，其他人发现泊松方法一般适用于离散事件。这包括任何情况
