Noise, Noise, Noise
M. Colleen Gino
The charge coupled device (CCD), which was introduced in the 1970s, has virtually replaced film and photographic plates for professional astronomical imaging. This is due largely to the fact that the CCD is more efficient at collecting light than photographic film, an astronomical image can be produced in a matter of seconds to minutes rather than hours, and because the digital nature of the resulting data enables it to be easily processed. However convenient and efficient CCDs are, they arent perfect. Various sources of noise inherent in the use of CCDs and other external effects such as space radiation (cosmic rays) can have negative effects on the obtained data.
The purpose of this paper is to explore CCDs and understand the limitations on their use to obtain astronomical data. The paper begins with a brief overview on the construction and operation of a CCD detector. The various sources of noise that exist in CCD imagers will be discussed, along with an explanation of the causes of each type of noise and a description of the methods used to correct for each example. There are a number of aspects to using CCDs including efficiency, signal to noise and manufacturing yields that will be discussed throughout the paper, along with the specific problems associated with professional-grade CCDs versus those pertaining specifically to amateur-grade CCDs.
The CCD Detector
The CCD was developed in the early 1970s at Bell Labs as a memory storage device. Due to the light-sensitive nature of the CCD, its application to astronomical imaging was soon realized, with the first CCD used for astronomical imaging in 1975 by the Jet Propulsion Laboratory. The resulting images of Uranus obtained using a CCD imager on a 61-inch telescope heralded the beginning of NASAs use of CCD imagers in Earth-orbiting and interplanetary spacecraft. By the mid-1980s, the CCD imager had all but replaced photographic plates and film in professional observatories. Advancements in the manufacturing of CCD chips and the associated electronic circuitry has made possible the introduction of CCD imagers into the amateur astronomy community as well. With a modest 8-inch telescope outfitted with a relatively inexpensive CCD imager, the amateur astronomer of today is able to produce astronomical images rivaling the quality of those produced by the professional astronomers of the 1960s (1).
A CCD is most simply described as an electronic photon detector. The typical CCD camera used for astronomical applications consists of a two-dimensional array of photon detectors in a layer of semi-conducting material, in this case silicon, which is placed at the focal plane of a telescope in order to collect an image. Each individual detector in the array is referred to as a pixel (the abbreviated form of picture element) and can vary in size from a few to several tens of microns. The smaller the size of the pixels, the higher the resolution of the image produced for a given focal length telescope and ignoring astronomical seeing. The total number of pixels in an array varies as well, with typical values ranging from thousands to millions of pixels. When describing the size of a CCD it is common to refer either to the number of pixels in rows and columns in the matrix (e.g. 512 x 512 or 5122) or the total number of pixels in the array. The more pixels in the array, the larger the imaging field of view of the CCD. Each individual pixel is capable of collecting photons and storing the produced electrons, which can be read out from the CCD array to a computer to produce a digital image of the varying intensities of light detected by the CCD. In this way, digital storage, reproduction and processing is possible, with the digital representation of the image field containing information that is extremely accurate and easily reproduced (2).
CCD imagers utilize the photoelectric effect. When photons hit the detector surface of the CCD sensor, electrons are liberated and stored in the detector elements, or pixels. Each pixel in the CCD is thus an electron well, and accumulates electrons in proportion to the number of photons received.
The electrons in the atoms that make up the silicon crystal exist in discreet energy bands. The lower energy band is referred to as the valence band, while the higher energy band is called the conductive band. The electrons, typically occupying the valence band, can be raised into the higher energy conductive band (excited) either by heat or by absorbing a photon. Electrons that have been excited into the conductive band are able to move freely in the silicon crystal lattice. When this occurs, a "hole" is left in the valence band, which then behaves as a positively charged carrier. The CCD introduces an electric field in order to keep the electrons from dropping back into the valance band and filling the hole, a process known as recombination. Recombination will occur if there is no electric field present (3).
Unfortunately, electrons can be excited into the conduction band by the heat produced by the system (thermal noise) and these electrons cannot be distinguished from those generated by photons (the signal). The problems associated with this form of noise will be discussed in the section dealing with CCD noise.
CCDs are created on silicon wafers in a similar manner as computer chips. The quality of the silicon wafer has a direct impact on the efficiency of the resulting detector, and creating large wafers of high quality is prohibitively expensive. For this reason, one major difference between amateur and professional CCDs are their size, with amateur grade detectors built upon smaller, more easily producible chips. In the professional realm, the largest CCD produced to date occupies a 6-inch wafer of silicon (4).
As photons come in contact with the CCD surface and electrons build up in the wells (pixels) over the period of its exposure to light (the integration), a digital image is built consisting of the pattern of the electrical charge present in each pixel. At the end of the integration period when light is no longer allowed to reach the CCD detector, the accumulated charge in each pixel is transferred to the on-chip amplifier, pixel by pixel.
Each pixel in the array acts as a well capable of storing the electrons that build up during the period of the integration. The number of electrons, also referred to as the charge, is in direct proportion to the number of photons detected by the pixel. The total amount of charge that can be stored is dependent upon the physical size of the pixel, referred to as the well depth. Well depths typically range from 20,000 electrons to more than 350,000 electrons, with the larger wells capable of holding more electrons.
During the read out process of the array, charge must be moved out of the imaging region of the array to a location where the amount of charge can be measured. There are several different schemes by which this is done. In the simplest scheme, rows of pixels are moved in parallel down to a single row (the serial register) which is read out sequentially to Analog to Digital (A/D) converter where it is measured and then recorded. The measuring device is emptied and and once again the rows of pixels are moved in parallel to the serial register, then each pixel is read out sequentially. This process continues until all of the pixels have been measured (read out).
The silicon used for CCD detectors is sensitive to light ranging in wavelengths from 330 nm to 1000 nm. However, front-illuminated or "thick" CCDs, typically used in amateur grade CCD detectors and video or digital cameras, have a very poor blue response. In addition, silicon is highly reflective and approximately 1/3 of the incident photons are reflected off the surface of the detector. In spite of such inefficiencies, these detectors are still more sensitive than photographic film, and as such are a viable and affordable option for amateur astronomical imaging purposes.
Professional grade CCD detectors used for astronomical imaging employ techniques to improve their quantum efficiency and spectral response.
Improved spectral response in the blue end of the spectrum is achieved by thinning the silicon wafer to about 15 micrometers. An overall improvement in the QE is achieved as well, with nearly 100% of the photons being transformed into useable output. Because light enters from the back side, these thinned chips are also referred to as back-illuminated CCDs. Since the process of thinning the silicon wafer reduces the manufacturing yield of CCD chips, they are more costly than the standard thick chips used in amateur grade CCDs. Back-illuminated CCDs are used exclusively at professional observatories.
To counteract the silicons reflective properties, a thin layer of a transparent dielectric material is applied to the CCD surface to make an anti-reflective coating. Since anti-reflective coatings can be created to enhance the effeciency at specific spectral bands, different coatings can be chosen to enhance the response of the chip in the desired spectral region. Thick chips, typically used in CCDs in amateur grade and digital cameras, are not usually be coated.
Primary Sources of Noise
Read or readout noise is a form of electronic noise added to the final signal upon readout of the device. This additive type of noise, described in the number of electrons per pixel, is independent of exposure time. This noise is produced during the conversion from an analog to a digital number. In addition, the electronics of the system will introduce spurious electrons during the readout process, adding to the fluctuations in output.
Read noise can be isolated and removed from a CCD image via the subtraction of a bias frame. A bias frame is an image of zero exposure time where the CCD is read out without having been exposed to light. In this manner, thermal noise produced by the heat generated by the devices electronics and contributions of light to the exposure are at a minimum, thereby isolating the effect of read noise. Since the read noise varies from pixel to pixel and readout to readout, a number of such bias images (nine or more) are recorded then averaged together. This is accomplished using the technique of median combining to produce a master bias frame.
As described previously, in the photoelectric effect electrons generated by the heat produced by the system (thermal noise) cannot be distinguished from electrons generated by photons (signal). Therefore, there is always some number of electrons stored in the pixels that are not the result of photons hitting the detector. The electrons generated by thermal noise exists even when light does not hit the detector surface, and is referred to as dark current. Dark current is a multiplicative form of noise, the level of which is proportional to the length of the exposure. Given a long enough exposure time, the detector could be fully saturated with electrons due in large part to thermal noise (5).
The first line of defense from the generation of thermal noise is to cool the detector to extremely low temperatures. This is accomplished by two primary methods. Professional instruments are cooled with liquid nitrogen (LN2). In this case the CCD sits in an evacuated environment and the dewar acts very much like a thermos, with the cooling to the chip provided by a cold finger, a metal contact between the chip and the LN2. Because of the extremely low temperature that the camera operates under, a professional grade CCD camera is virtually thermal noise free. The second method is thermoelectric cooling, which in professional applications is used only in those circumstances where dark current is not important, such as short exposure instruments.
Amateur grade instruments employ the technique of thermoelectric cooling. In this method an electric current is applied to two metal plates, in between which exists a semi-conducting material. Due to the Peltier effect, this device acts as a heat pump, pulling heat from the CCD detector onto the Peltier cooling device, then dissipating the heat via radiating fins (a fan). Some cameras employ a two-stage Peltier cooler to improve the effectiveness of the device. Peltier coolers incorporate a regulating system in an effort to keep the CCD detector at the desired constant temperature. In reality, however, these devices do not function precisely, and the temperature may vary slightly with time.
In spite of the cooling of the chip and the resulting reduction of thermal noise, some noise is still generated, particularly in the case of amateur grade systems. Luckily, this dark noise can be easily characterized and removed via the use of a dark frame. In a dark frame, no light is allowed to come in contact with the CCD detector. Since dark current noise is created in proportion to the length of the exposure, dark frames are exposed for the same length of time that the source images will be exposed. As with the bias frame, a number of dark frames are taken and averaged together to create a master dark frame. This dark frame will be subtracted from the source image during the image calibration process.
Example of a typical dark frame. (ESO)
Since professional CCD imagers are cooled with LN2 to temperatures where dark current is essentially zero, many such systems may not require the use of darks in the data calibration process. Amateur grade thermoelectrically cooled instruments definitely require the use of dark frames. In addition, the temperature of the CCD may not remain stable due to the imprecision of the Peltier cooler, resulting in a fluctuating dark current over time.
Not all of the pixels in a CCD have the same sensitivity to light. Even small variations in the thickness of the silicon wafer will effect the sensitivity. In addition the chip may not be uniformly illuminated due to the vignetting that occurs in telescope optics. While these slight variations may not be readily detected in an image due to the variations of brightness of the objects in the images itself, the unwanted pixel or illumination variation can be from 5 10%. The varying sensitivity of the pixels and the uneven illumination pattern on the CCD can be determined by taking an image of a uniformly lit screen placed in front of the telescope. In this way, each pixels response to the same level of brightness can be measured. This type of image, a flat field frame, allows for the correction of not only pixel sensitivity variations and chip illumination variations, but the presence of dust or other foreign objects on the CCD window which could be responsible for blocking light from reaching certain pixels.
Flat field frames can be made in several different ways. A typical flat field frame is a short exposure of an illuminated screen. Any source of even illumination that can be imaged such as the sky or the inside of the dome works as well. As with the other calibration frames discussed previously, a number of frames are taken and averaged together to produce a master flat field. Before combining the flats, the master bias and master dark frames are subtracted from each flat field image, with the exposure time of the dark frame matching that of the flat filed frame. The corrected flat field frames are then median combined to create a master flat field, which is divided into the source image. It is important to note that flat fields must be taken with the telescope at the same focus as it will be when imaging the source. In addition, if creating tri-color images or science images calling for the use of filters, a master flat field frame must be produced with each different filter in place.
While the precise technique of calibrating images may vary from astronomer to astronomer, the basic process is the same. The mathematical description (6) of calibrating the source image frame through the removal of the above noise sources is as follows:
FI = RI MBF MDF
FI = final image
RI = Raw image
MBF = master bias frame
MDF = master dark frame
MFFF = master flat field frame
The three types of calibration frames bias, dark and flat field can be effective at correcting for other sources of noise as well as those described above.
Other Sources of Image Degradation
There are a number of other sources of noise that can affect the image quality. For example, hot spots are pixels whose dark current is higher than average. Like dark current, the brightness increases linearly with increased integration time. Other problems can occur due to defects in the silicon used for the chip or damage caused to the CCD during the manufacturing process. Electrons can sometimes be caught in traps, and the vertical transfer of charge that occurs during the readout process is blocked. Dark columns, long vertical dark streaks, indicate that electrons are being blocked during the readout process. Bright columns, appearing as bright vertical streaks, are also caused by traps. In this case, the electrons that have been captured leak out into adjacent pixels during the readout process. In all of these cases, the location of the defect will be revealed in a dark frame.
Example of dark columns. (C. Gino)
Space radiation can cause defects in an image as well. Cosmic rays are charged particles from space bombard the Earth continuously and are unavoidable. When this form of radiation strikes the surface of the detector, electrons are produced which cannot be distinguished from those generated by photons. On average about two cosmic rays per square centimeter per minute will be detected (7).
Signal to Noise Ratio
One of the most important equations in astronomical imaging is that which allows one to calculate the ratio of the photons being collected by the CCD, the signal, compared to the amount of noise or other spurious signal in the image. Commonly called the CCD Equation, it is as follows:
N* = total number of photons collected from object of interest (may be one or more pixels)
Npix = number of pixels considered in S/N ratio
NS = total number of photons per pixel from background or sky
ND = total number of dark current electrons per pixel
NR2 = total number of electrons per pixel resulting from read noise
As illustrated by the equation, the signal to noise ratio of a CCD source image is simply the signal divided by the sum of a number of noise terms defined above. With the exception of the term describing the noise from read noise, the noise terms including the signal itself behave as Poisson terms, with the square root of the term giving the associated one sigma error. The term for read noise is shot noise rather than Poisson noise, so the term is squared in the equation so as to retain its original value. This equation adequately determines the signal to noise ratio of an image in most situations, unless one is dealing with a particularly faint source. An excellent example on the use of this equation is given in Howells book, "Handbook of CCD Astronomy" on page 56 (8).
CCD detectors are not able to convert all of the photons that strike the surface into electrons for a variety of reasons. Quantum efficiency (QE), which describes the ability of the CCD to turn photons into a useful form of output, is basically the ratio of incoming photons to those photons actually detected by the CCD. The typical range of efficiency is from a few percent up to 90%. Efficiency will also vary with the frequency of light (color) observed. Front-illuminated thick chips are not as sensitive to blue light as they are to light with longer wavelengths. This is one of the many difficulties faced by the amateur astronomer using the less-expensive thick chips typically found in consumer-grade CCD imagers. The more expensive back-illuminated thinned chips, used in professional astronomy settings, are much more sensitive to blue light. Thinned chips are increasingly being used in consumer-grade CCDs (9) which are much less expensive than professional CCDs, but they remain higher in cost relative to CCDs employing thick chips, and as such are still not a viable option for many amateurs.
A graph showing quantum efficiency across the spectrum for different chips used in Apogee CCDs. (Apogee)
System gain refers to how many electrons of charge are represented by each digital unit or count (ADU) produced by the cameras Analog to Digital Converter (ADC). The gain of the CCD is set by the output electronics and determines how the amount of charge collected in each pixel will be assigned to a digital number in the output image. For example, if the gain of a particular system is two electrons per ADU (written 2e-/ADU), then each count or level of gray represents two electrons. If the total well depth was 60,000 electrons, then the pixel could be represented in 60000/2=30,000 counts. Many astronomers feel it is preferable to use a lower gain in an effort to minimize the noise contribution from the electronics. However, if the gain is too low then the total well depth of the pixel may not be represented (10).
Charge transfer efficiency (CTE) is the term describing the level of accuracy that the charge stored in each pixel can be transferred from one pixel to another in the readout process. As the charge is transferred, not all of the electrons are moved efficiently; some may remain trapped in a pixel. Modern CCDs have CTEs in the range of 99.999%, meaning that only one out of 100,000 electrons will get left behind (11).
Well depth refers to the total amount of charge (number of electrons) that can be stored in the pixels before the charge overflows into adjoining pixels. The well depth is dependent upon the physical size of the pixel and the depth of the depletion zone. A larger well is capable of holding more charge than a smaller one. Full well capacity is a term describing the capacity of a CCD pixel to hold a certain number of electrons and is dependent upon the physical size of the pixel. When a pixels full well capacity is exceeded, any additional electrons (charge) will leak into adjoining pixels, a process called blooming.
Blooming causes vertical streaks of light to appear in the final images, which is cosmetically unattractive and difficult to correct. Blooming is not generally considered to be problematic for most professional astronomy imaging (12). However, for those whose primary goal is to create attractive images, blooming can be extremely problematic. To counteract this problem, many amateur grade CCDs build onto the chip anti-blooming gates to bleed off some of the overflow from a saturated. However, these can take up as much as 30% of the pixel area, resulting in a reduction of the overall sensitivity of the CCD. Because of this loss of well depth and efficiency, anti-blooming features are not usually employed by professional astronomers or those amateurs conducting scientific observations.
Analog to digital conversion is the process of converting a continuous analog signal (such as one obtained with photographic film) to a series of discreet digits. In this process, the image filed is divided into a large number of squares (pixels on the CCD chip) and the varying levels of brightness in the individual squares are represented by a series of digits. The number of levels of light intensity that can be represented (dynamic range) is dependent upon the number of bits used in the analog to digital converter. The higher the number of bits, the greater the range of charge in each pixel according to the following: 2(number of bits). Thus, a 16-bit A/D converter produces a range of 216 or 65,536 discreet levels of quantization. In this instance, 0 represents black while 65,535 represents white, with the varying levels of gray represented by the digits between. With the level of dynamic range, the resulting digital representation of the image is so smooth that it is nearly indistinguishable from a continuous analog image.
The cost of CCDs have fallen dramatically thanks to their use in consumer video cameras and digital cameras. However, the cost is still significant. One reason is that the manufacturing process isnt perfect. In a manufacturing run, many dozens of CCDs can be built on a single wafer. However, in the process of going from the wafer to individual cameras, not every array will work. In addition, there will be defects of varying types from individual pixels that dont work or are hot, to entire columns or large regions on the chip that do not function. For this reason there are several different classes of CCD arrays based on the number of defects they exhibit. These various grades of varying quality and even the dead devices cost as much to make as the working devices, and yet their full value cant be recovered. For this reason, CCDs remain expensive.
As illustrated throughout this paper, CCDs are not perfect devices. Defects in the silicon chips, system electronics or other problems ocurring at some step in the manufacturing process can reduce the quality and efficiency of the device. CCDs have other limitations as well; they are subject to various kinds of internally and externally generated sources of noise and other spurious signals, which can negatively effect the quality of the data that is obtained. In most cases, however, the noise sources can be characterized and removed, and once the data has been properly calibrated it is of high quality. In spite of the limitations of CCDs, they are far superior to photographic plates and film for astronomical imaging, especially in the professional realm where imaging is done for scientific purposes. This view is clearly supported by the ubiquitous use of CCDs at professional observatories. CCDs are able to produce digital images using much shorter exposure times than would be necessary for film, and the resulting image is available almost immediately for processing and analysis. It is widely acknowledged that the Charge Coupled Device has revolutionized the field of astronomical imaging (13).
(1) (3) (4) (7) (12) Swinburne Astronomy Online, "An Introduction to Astrophotography and CCD Imaging", CD, 2002
(2) (6) (11) Teare, S.W. and Kenyon, D.A., "Practical Astronomical Photometry", 2001, IAPPP Western Wing, Inc.
(5) Meade Website, www.meade.com
(8) (10) (13) Howell, Steve B., "Handbook of CCD Astronomy", 2000, Cambridge University Press
(9) Apogee Website, www.ccd.com