1.Signals and Noise in Images
You now have enough background to examine the signals and noise that you will encounter in real images from your CCD or digital camera. Before beginning that examination, we need to get certain units of measurement squared away.
We introduced signals and noise in terms of detected photons, electrons, and ADUs; that is, in different units. To understand digital images, it is necessary to know how these different units relate to one another.
• When photons strike a detector, not all of them generate a signal. In a typical CCD, roughly 40% to 80% of the photons are detected—meaning that the photon has liberated an electron. Therefore, the detected photon count, x, translates directly into electrons.
• The statistical uncertainty in the photon count, a, often called shot noise, has units of root-mean-square electrons.
• Dark current electrons, xd, are already in units of electrons.
• The dark current noise, od, has units of root-mean-square electrons.
• Readout noise, Gron, is almost always given in units of root-mean-square electrons to make it easier to compare readout noise to other sources of noise.
• In CCD and CMOS devices, electrons are converted to a voltage that is digitized and sent to your computer as an integer value. For lack of a more mellifluous term, the integer value is called an analog-to-digital unit (ADU) or digital number (DN).
• The gain or conversion factor relates electrons to ADUs, and is denoted by the symbol g. The units of the gain are electrons per ADU. In most CCD cameras, the gain is reasonably close to 1, but the gain may be as large as 500 e~/ADU in webcams, or as small of 0.1 e /ADU in some CCDs.
As a general rule, astronomers use fundamental physical units (electrons) when they talk about properties of the detector and amplifier; and by necessity, they use the arbitrary derived units (ADUs) that the camera generates when they are discussing the images made by cameras.
Let’s look at a few examples to see how these conversions work. Suppose 100 photons fall on a pixel of the detector in your CCD, digital camera, webcam, or whatever detector you happen to be using (and remember, the math is the same for all such devices). Typically 60 of those photons will generate an electron, and therefore be detected as a signal x in units of electrons. A device such as a charge detection node (in a CCD) senses the electrons and generates a voltage proportional to the number of electrons, and passes that voltage to an analog-to-digital converter. Suppose that the amplifier and A/D converter together have a gain of 2.5. In our example, the A/D converter adds a bias of 100.
The output signal from the camera will be:
5= – + b= -60 electrons-+ 100 ADU= 124 ADU . (Equ. 2.11)
g 2.5 electrons/ADU
To convert the signal electrons to ADUs, we’ve divided the signal in electrons by the gain in electrons per ADU, which gives us ADUs. The bias is already in units of ADUs, so we can add the terms.
In the example, we neglected dark current and did not even consider noise, but you can see the need to pay close attention to the units of measurement.
Let’s now look at some realistic examples.
2.4.1 Signal and Noise in a Raw Image
You decide to make a raw image. What signals and what sources of noise do you expect to find? The signals are:
Figure 2.4 The raw image is the sum of a photon signal (with Poisson noise), an unwanted dark-current signal (with Poisson noise), and a bias constant (with readout noise). Althought the dark current and the bias can be subtracted, the random noise that they introduce remains.
• The detected photon count, x, in electrons;
The total signal in the raw image, ,S’raw , converted into units of ADUs, is:
Digital Cameras For Beginners
Although we usually tend to think of the digital camera as the best thing since sliced bread, there are both pros and cons with its use. Nothing is available on the market that does not have both a good and a bad side, but the key is to weigh the good against the bad in order to come up with the best of both worlds.
2.CCD Noise Sources and Signal-to-Noise Ratio
2.1 What is the CCD noise
Charge-coupled device (CCD) sensors have numerous advantages over photographic film in scientific imaging applications such as astronomy and optical microscopy. By directly producing images in digital format, suitable for immediate computer processing, CCD-based image capture systems are ideally suited to a wide range of current microscopy and image analysis methods. In particular, the much greater sensitivity of such sensors compared to film is invaluable in low-light techniques, for which every available signal photon may be significant. Noise, arising from a variety of sources, is inherent to all electronic image sensors, and careful control of noise components, both in the design and operation of the CCD system, is necessary to ensure that the signal level relative to noise is adequate to allow capture of accurate image information. For any electronic measuring system, the signal-to-noise ratio (SNR) characterizes the quality of a measurement and determines the ultimate performance of the system.
Figure 1:The effects of decreasing signal-to-noise ratio in fluorescence microscopy is illustrated by the series of digital images presented in Figure 1
In a well designed digital camera, the noise performance is limited by the CCD rather than by associated system electronic components. The signal-to-noise ratio for a CCD image sensor specifically represents the ratio of the measured light signal to the combined noise, which consists of undesirable signal components arising in the device, and inherent natural variation of the incident photon flux. Because a CCD sensor collects charge over an array of discrete physical locations, the signal-to-noise ratio may be thought of as the relative signal magnitude, compared to the measurement uncertainty, on a per-pixel basis. A detailed engineering consideration of noise contributions in charge-coupled devices includes many sources that are normally handled by combining them into more general categories, or which are not significant except at much lower signal levels than are typically encountered in microscopy. The three primary broad components of noise in a CCD imaging system are photon noise, dark noise, and read noise, all of which must be considered in a calculation of signal-to-noise ratio.
A further useful classification distinguishes noise sources on the basis of whether they are temporal or spatial.Temporal noise, by definition, varies with time, and can be reduced by frame averaging, whereas spatial noise cannot. Spatial noise is subject to at least partial removal by various frame subtraction algorithms, or by gain and offset correction techniques. The temporal noise category includes photon noise and dark (current) noise, which are both forms of shot noise, read noise (primarily from the output amplifier), and reset noise. Among potential spatial noise sources are factors that produce non-uniformity(不均匀性) in pixel output, including photo response non-uniformity and dark current non-uniformity.
The effects of decreasing signal-to-noise ratio in fluorescence microscopy is illustrated by the series of digital images presented in Figure 1. The specimen is an adherent culture of opossum kidney proximal tubule epithelial cells (OK cell line) stained with SYTOX Green to image the nuclei. At high signal-to-noise ratios, a pair of interphase nuclei (Figure 1(a)) is imaged with sharp contrast and good definition of fine detail on a black background. As the signal-to-noise ratio decreases (Figures 1(b) and 1(c)), the definition and contrast of the nuclei also decrease until they almost completely blend into the noisy background (Figure 1(d)) as the SNR approaches unity.
During image acquisition with electronic sensors, including CCDs, noise superimposed on the signal is manifested(明显的) as apparently random fluctuations in signal intensity, and as the magnitude of noise increases, uncertainty in the measured signal becomes greater (as illustrated in Figure 1). Signal-to noise ratio is typically evaluated in terms of the broad noise categories stated above, although each category may encompass(包含) several contributing noise components (discussed in following sections). The relative significance of each potential source depends upon the specific device and the type of application in which it is utilized. As stated, a large signal-to-noise ratio is important in the acquisition of high-quality digital images, and is particularly critical in applications requiring precise light measurements. Changes made to the factors that directly affect signal level, and to those variables primarily contributing noise to the system, obviously have an inverse effect on signal-to-noise ratio.
The measured signal from a CCD imaging system, utilized in calculating the signal-to-noise ratio, depends upon the photon flux incident on the CCD photodiodes (expressed as photons per pixel per second), the quantum efficiency of the device (where 1 represents 100 percent efficiency), and the integration time (exposure time) over which the signal is collected. The product of these three variables determines the signal portion (numerator) of the signal-to-noise ratio value, which is weighed against all noise sources that contribute to the denominator(分母) term of the ratio, and which degrade the performance of a CCD imaging device. Three primary undesirable signal components (noise) are typically considered in calculating overall signal-to-noise ratios:
Photon noise results from the inherent statistical variation in the arrival rate of photons incident on the CCD. Photoelectrons generated within the semiconductor device constitute the signal, the magnitude of which fluctuates randomly with photon incidence at each measuring location (pixel) on the CCD. The interval between photon arrivals is governed by Poisson statistics(泊松分布), and therefore, the photon noise is equivalent to the square-root of the signal. In general, the term shot noise is applied to any noise component reflecting a similar statistical variation, or uncertainty, in measurements of the number of photons collected during a given time interval, and some references use that term in place of photon noise in discussions of CCD noise sources.
Dark noise arises from statistical variation in the number of electrons thermally generated within the silicon structure of the CCD, which is independent of photon-induced signal, but highly dependent on device temperature. The generation rate of thermal electrons at a given CCD temperature is referred to as dark current. In similarity to photon noise, dark noise follows a Poisson relationship to dark current, and is equivalent to the square-root of the number of thermal electrons generated within the image exposure time. Cooling the CCD reduces the dark current dramatically, and in practice, high-performance cameras are usually cooled to a temperature at which dark current is negligible over a typical exposure interval.
Read noise is a combination of system noise components inherent to the process of converting CCD charge carriers into a voltage signal for quantification, and the subsequent processing and analog-to-digital (A/D) conversion. The major contribution to read noise usually originates with the on-chip preamplifier, and this noise is added uniformly to every image pixel. Certain types of noise in the CCD’s output amplifier are frequency dependent (and consequently the application for which the camera is intended) and the required read-out rate or frame rate partially determine the read noise specification and its practical effect on overall signal-to-noise level. High-performance camera systems utilize design enhancements that dramatically reduce the significance of read noise.
The following equation is commonly used to calculate CCD camera system signal-to-noise ratio:
where P is the incident photon flux (photons/pixel/second), Q(e) represents the CCD quantum efficiency, t is the integration time (seconds), D is the dark current value (electrons/pixel/second), and N(r) represents read noise (electrons rms/pixel).
Careful examination indicates that the equation above is simply structured as a ratio of total signal generated during the exposure time divided by the combined noise attributable to the three primary noise components. The noise terms are not correlated, and the denominator incorporates appropriate values for each noise component: the square-root of the signal accounts for the photon noise, dark noise is equivalent to the square-root of the product of dark current and integration time, and the square-root of N(r)-squared corresponds to the read noise component.
The calculation of signal-to-noise ratios using the previous equation assumes that the signal is the only source of light. In the optical microscope, various sources of unwanted background light, such as scatter and reflections in the imaging system, may contribute noise, and if significant, this background photon flux (B) must be added to the photon noise component as follows:
An additional factor to be considered is that the values of incident and background photon flux, as well as quantum efficiency, are functions of wavelength, and when broadband illumination sources are employed, the calculation of signal-to-noise ratio requires these variables to be integrated over all wavelengths utilized for imaging.
2.2 reduce noise
Various approaches are used to increase signal-to-noise ratio in high-performance CCD imaging systems. To reduce thermal charge generation within the semiconductor layers of the CCD, which is manifested as dark current, special device fabrication techniques and operation modes are sometimes employed. It is common to cool the CCD to reduce dark current to a negligible level using thermoelectric or cryogenic refrigeration(冷藏), or if necessary, the extreme approach of liquid nitrogen cooling may be taken. In general, high-performance CCD sensors exhibit a one-half reduction in dark current for every 5 to 9 degrees Celsius as they are cooled below room temperature, a specification referred to as the doubling temperature. This rate of improvement typically continues to a temperature of approximately 5 to 10 degrees below zero, beyond which the reduction in dark current diminishes quickly (see Figure 2). In addition to specialized circuit and electronics design, filtration techniques utilizing advanced integrators and double sampling methods are sometimes undertaken to remove certain components of read noise.
Several manufacturers of high-performance CCD cameras provide a specification for “signal to noise” or “SNR”, often expressed in decibels (dB). This value is equivalent to the ratio of the sensor’s maximum pixel well capacity divided by the number of noise electrons resulting from on-chip thermal and electrical sources, neglecting photon noise, and should not be confused with the signal-to-noise ratio calculation described previously. It does not represent a determination of signal-to-noise ratio under specific operating conditions, but is a useful representation of a camera’s dynamic range that is independent of how the camera is used. Under low-signal conditions, where read noise is the dominant noise source, the full SNR equation stated previously can be reduced to a simple ratio equal to the total signal collected during the integration time divided by the read noise value, a similar form to the dynamic range (“SNR”) specification referred to here. The dynamic range value, however, corresponds to the limiting situation in which the full well capacity of a sensor element is reached, and is defined as follows:
The full well capacity of a CCD represents the maximum charge (number of electrons) that can be stored in each pixel, and therefore determines the maximum signal available for a single read-out event. The ratio of the full well value (sometimes referred to as well depth or linear full well) to the number of per-pixel read noise electrons characterizes the ability of the device to capture both low and high signal levels in one image.
The dynamic range of a CCD and the true maximum bit depth of the camera’s analog-to-digital converter are closely interrelated in that the total available signal relative to noise governs the maximum number of gray-level steps into which the signal can be divided.In order to represent subtle intensity differences in a digital image, it is necessary to discriminate as many gray-level steps as possible, and therefore a typical approach is to match analog-to-digital conversion bit depth to CCD dynamic range. The dynamic range relative to bit depth determines the number of electrons that comprise each gray level in the final image. Note that an analog-to-digital converter with a bit depth specification that exceeds the dynamic range of the CCD image sensor cannot attain its full theoretical range of grayscale discrimination (bit depth) because each gray-level step must correspond to a minimum difference of one signal electron.
As an example of appropriate strategy, a CCD with a full well capacity of 18000 electrons, and a read noise of 4 electrons per pixel at the specified read-out rate, has a dynamic range of 18000/4, or 4500. In order to utilize the full dynamic range of the CCD, a camera incorporating 12-bit analog-to-digital conversion is required, having the ability to detect 4096 (2 to the 12th power) grayscale levels (or 1.1 electrons per gray-level step). If 10-bit A/D conversion is used, only 1024 (2 to the 10th power) gray levels can be displayed, corresponding to 4.4 electrons per grayscale step. On the other hand, a camera having 14-bit A/D conversion, which has the capability of discriminating 16,384 gray levels, will be limited by the dynamic range (4500 electrons per pixel) of the CCD, and will not attain a satisfactory performance level.
A primary goal in the manufacture of scientific-grade CCD cameras is to maximize the signal available and minimize the noise, resulting in maximum dynamic range. By cooling the CCD to minimize thermal noise, as well as optimizing clocking, sampling, and other read-out electronics, the noise associated with each read-out cycle has been reduced in some high-performance cameras to as little as 3-5 electrons per pixel at typical read-out rates of approximately 1 megahertz. With the read noise of current CCDs nearing a likely lower limit, the remaining practical mechanism for improving dynamic range is to increase the available signal level. Although this can be accomplished by a CCD design incorporating larger pixels with very large full well capacity, there is an accompanying trade-off of lower spatial resolution in exchange for the improved effective sensitivity.
As previously discussed, the general category referred to as read noise actually comprises many sources, and dark current has not only an average component, but also exhibits a statistical fluctuation that contributes to shot noise. Although noise originates from different sources, its effect, in every instance, is to produce variations in image intensity. The level of detail required in modeling CCD noise depends upon the application, and generalizations adequate for evaluating the performance of camera systems are common. It is useful to describe, and to have an awareness of, most of the noise sources even though many may be reduced in practice to negligible levels. For signal-to-noise analysis, it is sometimes sufficient to consider only the on-chip amplifier noise, and most manufacturers provide this specification, referring to it as read noise, noise equivalent electrons, or the noise floor.
While read noise can be considered a noise floor with regard to electronics sources, under typical illumination conditions, the photon shot noise constitutes a natural fundamental limit on noise performance of a CCD camera (or any light detection system). Uncertainty in the number of photons collected during a specific time period is governed by Poisson statistics, and therefore the photon shot noise can be expressed as follows, in terms of equivalent electrons at the detector output:
1.therefore, the photon noise is equivalent to the square-root of the signal
2.Dynamic Range = Full Well Capacity (electrons) / Read Noise (electrons)
量子效益(Quantum Efficiency) ：
1.Signals and Noise in Images
2.CCD Noise Sources and Signal-to-Noise Ratio