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Introduction to CCD Imaging
 CCD detectors caused revolution in observational astronomy comparable to invention of the telescope. They provide very high sensitivity, linear response to light, mechanical stability and mainly astronomical images in the digital form, which can be immediately processed by computers.

This article focuses to general principles of CCD detectors, their physical characteristics influencing CCD imaging (like thermal noise) and basic procedures dealing with unlovely effects (like elimination or at last reduction of thermal noise). Those with some experience with CCD cameras—observers who understands why the raw CCD images must be calibrated (at last “dark frame” should be subtracted, ideally also “flat field” should be applied)—need not to read it.

However, this article is not intended for thorough explanation of all CCD solid state detector operation principles. This topic is well described in number of books and also some companies publish PDF document covering this topic (e.g. ccdPrimer1 and ccdPrimer2 application notes published on Kodak web site).

Charge-Coupled Devices (CCDs)

CCDs originated its life as experimental computer memories, but their capability to convert incoming light into electrical charge made them the best solid state light detectors. The basic operation principle is rather simple—incoming light creates electrical charge (electron particles) in the silicon chip. Free electrons cannot travel through the chip freely, because the chip is designed so the grid of negative potential walls (stripes on the chip with negative charge, which repel electrons) and electrodes (conductors also polarized with negative voltage and thus repelling electrons) keep them in areas called potential wells. Each potential well represents one pixel (“pixel” is an abbreviation for “picture element”—the smallest “square” in image). Number of pixel in horizontal and vertical direction as well as physical dimensions of one pixel comprise basic CCD characteristics. Pixels more exposed to light contains more electrons and vice versa. Here comes the big advantage of CCD over human's eye: charge can be accumulated in pixels, thus CCDs can detect light from very dim sources simply by accumulating light-generated electrons over a long time.

As was already said, CCD silicon chip is covered by a structure of electrodes, which keep light-generated electrons in pixels. But the electrode structure is somewhat more complex. By applying various voltages to various electrodes, electrons can be poured from one well to the neighboring well. So it is possible to shift the charge over a chip area. This process is used when it is necessary to read the image from CCD. Chunks of electrons, representing individual pixels, are shifted to the CCD output node, where the electrical charge is converted into electrical voltage. This voltage appears on the CCD output pin. The camera electronics then measures the voltage (converts the voltage to number using ADC—Analog to Digital Converter) of each pixel. Information about charge accumulated in each pixel (number representing number of electrons and thus number of detected photons) then creates image data file.

Pixels can be organized several ways:

  • A single row of pixels comprise linear CCD. Linear CCDs can be used when only one-dimensional image is needed (e.g. while obtaining the spectra, which are one-dimensional in principle). However, full two-dimensional image can be created with linear CCD during a period of time—it is enough when the detector and the target object moves relative to each other and image is scanned line by line. This principle is used e.g. in document scanner, which scan line by line while the detector and its optics moves under the document. Also cameras used in orbiting spacecrafts often use linear detectors, read in time intervals—the orbital motion of the spacecraft is used to accumulate planetary surface image line by line.

  • Pixels arranged into a matrix on a silicon chip comprise array CCD. Array CCD detects an image at once. They are used in video and still cameras and also in astronomical CCD cameras.

    Pixels accumulating light are organized into columns in area CCDs. Applying appropriate voltage to vertical electrodes shifts whole image (all pixels) along columns one row down. This means all image rows move to the next row, only the bottom-most row moves to so-called horizontal register. Horizontal register can be then shifted by horizontal electrodes to the output node pixel by pixel. Reading of array CCD means vertical shifts interlaced with horizontal register shifts and pixel digitization.

Even array CCDs can have various design:

Full Frame (FF)

devices expose all its area to light. It is necessary to use mechanical shutter to cover the chip from incoming light during readout process else the incoming light can smear the image. FF devices are best suited for astronomy tasks, because they use maximum area to collect light. Devices with really high QE are always FF devices.

Full Frame sensor (number of horizontal and vertical clock pins differ depending on CCD architecture)

Full Frame sensor (number of horizontal and vertical clock pins differ depending on CCD architecture)

Kodak Full Frame CCDs: KAF-0402ME, KAF-1603ME, KAF-3200ME and KAF-6303E

Kodak Full Frame CCDs: KAF-0402ME, KAF-1603ME, KAF-3200ME and KAF-6303E

Remark:

CCD quantum efficiency (QE for short) determines how many photons reaching the detector is converted into signal. QE around 30% means approximately every third photon generates electron in the CCD.

Frame Transfer (FT)

devices comprise two areas, one exposed to light (Imaging Area—IA) and second covered by opaque coating (Storage Area—SA). When the exposition finishes, image is very quickly transferred from IA to SA. The SA then can be relatively slowly digitized without smearing the image by incoming light. This feature is sometimes called electronic shuttering. But such kind of shuttering also have some limitations. First it does not allow to expose dark frames—camera must be equipped with mechanical shutter either way to automatically obtain dark frames without bothering the observer to manually cover the telescope. Second, although the SA is shielded from the incoming light, charge can leak to SA from IA during slow digitization when imaging bright objects (e.g. Moon).

Important negative side of FT is its price. Manufacturing large silicon chips without faulty pixels is an expensive task and FT chips must be two times the size of the IA. This is why companies are abandoning production of FT chips.

Interline Transfer (IT)

devices work similarly to FT devices (they are also equipped with electronic shutter), but their storage area is interlaced with image area. Only odd columns accumulate light, even columns are covered by opaque shields. Odd columns are quickly transferred to even columns on the end of exposition, even columns are then shifted down to horizontal register and digitized.

Progressive Interline Transfer sensor

Progressive Interline Transfer sensor

Interlacing of image and storage columns limits the light-collecting area of the chip. This negative effect can be partially eliminated by advanced manufacturing technologies (like microlensing) described later.

The television signal does not contain simple sequence of individual frames from historical reasons. It rather consists of interlacing images containing only half rows, so called half-frames. The odd half-frame contains rows 1, 3, 5 etc., the even half-frame contains rows 2, 4, 6, etc. Companies producing CCD sensors followed this convention and created CCD chips for usage in TV cameras, which also read only half-frames.

But if only half of rows is read and the second half is dumped, the CCD sensitivity would decrease by 50%. This is why the classical “TV” CCD sensors electronically sums (see Pixel binning) neighboring rows so that the odd half-frame begins with single 1st row, followed by sum of 2nd and 3rd rows, then by sum of 4th and 5th rows etc. The even half-frame contains sum of 1st and 2nd row, followed by sum of 3rd a 4th rows etc.

Interlaced Interline Transfer sensor (even half-frame read)

Interlaced Interline Transfer sensor (even half-frame read)

CCDs using this architecture are called interlaced read sensors, as opposite to sensors capable to read all pixels at once, called progressive read sensors.

Despite the implementation of micro-lenses, the opaque columns reduces the quantum efficiency of IT CCDs compared to FF ones. If the sensor dynamics range should not be limited, the opaque columns must be of the same width as the active ones. There is a combination of both interlaced and progressive architectures, which allows narrowing of opaque columns and thus boosting of the chip sensitivity. Such CCDs are called frame read CCDs—each two pixels in adjacent rows shares one pixel in opaque column, which then can be only half as wide, because each pixel is two times high. The pixel area and also its dynamic range remains the same. Individual rows are not summed during frame read, but odd and even half-frames are read sequentially.

Let us note that this way of CCD read requires using of mechanical shutter—pixels of the even half-frame ere exposed during odd half-frame read. Frame readout CCDs are often used in digital still cameras.

Remark:

Some affordable, low-resolution astronomical cameras use interlaced CCD detectors, because they are relatively sensitive and cheap. But it is impossible to read only one half frame after a long exposure, typical when imaging deep space objects. The whole frame (containing all pixels) must be read. Usually interlaced CCDs also allow reading similar to frame read mode—two independent half-frames can be read without adding of adjacent lines. But images from such cameras can be usually easily identified by contours showing traces of interlacing, because odd and even half-frames often slightly differ.

Chip QE is influenced by number of manufacturing technologies:

  • The negative shielding effect of electrodes on the chip surface can be reduced by using more transparent material.

  • Manufacturers can create a small lenses above every pixel. Such lens focus light from insensitive chip areas (e.g. covered by electrodes) to sensitive areas, where light is not wasted. Especially Interline Transfer devices use microlenses to eliminate the effect of opaque columns in the imaging area. But also FF devices can benefit from microlenses applied above pixels to increase overall QE.

  • The best possible QE is achieved by thinned, back-illuminated chips. The chip is packaged “upside-down”, so electrodes and all shielding armature appears on the bottom side of the chip. The chip is then thinned to be very slim. All chip area then collects light. But production of back-illuminated chips is expensive and such chips can also introduce some negative effects, like occurrence of interference figures caused by atmospheric IR radiation etc.

Quantum efficiency of some popular CCDs

Quantum efficiency of some popular CCDs

But the image quality is determined by the resulting signal to noise ratio, not only by the pure quantum efficiency. For instance two times better QE and four times bigger noise results to two times worse S/N ratio. That means a slightly less sensitive chip with low thermal noise can deliver better results than comparatively cooled high-sensitive chip with bigger thermal noise.

Typical dark current (in e-/s/pixel) for back-illuminated Marconi CCD47-10 and front-illuminated Kodak KAF-3200ME and KAF-1603ME

Typical dark current (in e-/s/pixel) for back-illuminated Marconi CCD47-10 and front-illuminated Kodak KAF-3200ME and KAF-1603ME

Although the KAF-3200ME front-illuminated CCD has slightly lower integral quantum efficiency than back-illuminated Marconi CCD47-10, it has about 1/12 dark current at -25 °C. Even if the KAF-3200ME is used in 2 × 2 binned mode to achieve similar pixel size (13.6 μm vs. 13 μm), the dark signal remains 3× lower compared to back illuminated chip at this temperature. It is necessary to cool down the CCDs to about -45 °C to achieve similar dark noise.

Pixel binning

Let us note one feature of CCD chips often used in astronomy—individual pixels can be electronically binned. It is possible to pour charge from one pixel into another before the target pixel is emptied. The charge in the target pixel then represents illumination of two pixels. It is possible to bin pixels vertically by shifting of two image rows into horizontal register without reading it after the first shift. It is also possible to bin pixels horizontally by shifting horizontal register two times into output node without resetting it after the first shift. Combining of both vertical and horizontal binning leads to square (or rectangular) image binning. For example 2 × 2 binning is a combination of 2× vertical and 2× horizontal binning. Then number of binned pixels is usually limited by the camera electronics and firmware. Some cameras allow for only a few predefined binnings, e.g. 2 × 2 and 3 × 3. Some cameras are capable to bin image in a predefined ranges, e.g. any combination of 1–4 in horizontal and 1–16 in vertical direction.

What is the reason for reading binned images? The resolution of image (number of pixels) is lowered and the sensitivity is increased. Binning is very useful e.g. if the camera pixels are much smaller than the smallest detail the telescope can create, be it due to bad seeing, long focal length etc. Binning then increases the pixel size and enhances sensitivity without loosing angular resolution—unbinned image would be unnecessary oversampled. Modern high resolution, multi-megapixel CCD chips make binning even more important.

CCD in astronomy

CCD detectors took the astronomy imaging in storm and turned photography films into obsolete light detectors. Not only in astronomy, but also in overall photography films become outdated within several years.

First CCD detectors suffered from small imaging area, high noise, high price and low resolution compared to classical film. All these disadvantages were eliminated today—CCDs offer better resolution, image areas comparable to films used in SLR cameras and their price is dropping systematically. Only numerous advantages over film persisted:

  • CCDs are much more sensitive than film. The quantum efficiency of CCDs used in still cameras can be around 20 or 30 %. But QE of CCDs used in astronomical cameras can be 60 or 80 % and thinned, back-illuminated CCD chips can reach even 90 % QE in some wavelengths. Very good and sensitive film reaches approx. 3 or 5 % QE. Every astronomer, who spent nights of long exposures to collect rare photons incoming from some distant galaxy, really appreciates if only 20 % of photons reaching his or her telescope are wasted instead of loosing of 95 photons from every 100.

  • CCDs have linear response to light. At last CCDs without anti-blooming gates are linear—as opposite to films, which are very non-linear. Why is this important? Linear detector response is a key for precise photometric applications. If we compare the signal (pixel values) of two stars on CCD image, we can rely that they star flux (amount of light) is in the same relation. The relation will not be the same in the case of non-linear detector and the photometric measurement is affected by serious uncertainty.

    Remark:

    What is “anti-blooming gate” and why it harms linearity? The so-called “blooming” effect occurs when a pixel receives so much light that the generated charge cannot be stored in its potential well and electrons start to flow to surrounding pixels. Typical strokes around a saturated pixels occur in the images.

    CCD blooming effect on saturated star

    CCD blooming effect on saturated star

    Some CCDs have special electrodes designed to drain away the charge when it approaches pixel saturation level. Such electrode is called anti-blooming gate. The problem is the anti blooming gate does not influence pixel charge only if it reaches certain saturation level, but it curves pixel response to light even from very low charges. This is why CCDs with anti-blooming gate are less sensitive (have lower QE) and are less suitable for photometric applications.

    Serious astronomers prefer CCDs without anti-blooming gate. A few bloomed stars are either not important, because astronomer is interested in object whose image is not bloomed, or (if the aesthetic appearance is important) the image can be created from numerous exposures with shorter exposure time, which does not cause blooming yet.

    Let's also note that modern astronomical software packages have filters eliminating blooming effects on the image. However, applying such filter is acceptable only for images taken for aesthetic reasons, reliable science data can be obtained only from unaltered images.

  • CCD silicon chip have very stable dimensions. Precisely defined physical dimensions enable precise astrometry applications. It is possible to measure stars (or asteroids, comets, supernovae, etc.) positions up to approx. 1/10 of pixel angular size by mathematical techniques like weighted average. Every amateur astronomer can perform astrometry of observed objects with sub-arcsecond precision. Only professionals could reach such precision several decades ago.

    Only photographs taken on glass plates have similar mechanical stability. Photographic films is much less stable and positions measured on films are less precise. When comparing CCD images to photographs, even taken on glass plates, the question of instruments needed for both photometric and astrometric measurement arise. Photographs should be digitized to enable image processing using computers either way. So the last and extremely important CCD advantage becomes obvious:

  • CCD images are digital data files, immediately available for processing by computers. This is really huge advantage. Astronomers appreciate digital nature of CCD images from the moment of downloading of image from the camera to the final processing and archiving. It is possible to inspect images just seconds after the camera shutter is closed. Making sure object is right centered in the image field and the telescope is properly focused is easy. New important discovery appears on the image? Alert your colleagues immediately, not a day or a week later, when you develop your films.

    Digital processing enables e.g. stretching of intensity ranges for viewing of images, which virtually eliminates the sky background glow and enhances fine details.

    The same image of M81 galaxy displayed as is (left) and with stretched luminance range (right)

    Single exposure can be easily divided into number of shorter exposures and individual images can be electronically added. This enables usage of less stable mounts—short exposures are less demanding for tracking accuracy. One unpleasant event, like flashing a light into a telescope or shaking a mount, does not hurt whole exposition, only one distorted image will not be included into resulting image.

    Stacking of multiple images also improves image dynamic range. Added brightness can easily exceed the saturation range of single CCD image. Thus brightness of bright star can reach hundreds of thousands or millions of counts, while subtle details of galaxy structure contain only tens or hundreds counts per pixel on the same image.

    As we already said, digital image is immediately available for image processing, be it photometry, astrometry, blink comparison etc. Very important attribute of digital image is that the only tool we need to do anything with the image is a computer (and appropriate software), which everybody needs either way to be able to perform even basic operation of CCD camera. No specialized and expensive equipment like photometers, blink comparators and micrometric microscopes are necessary.

    Digital images can also be easily archived, duplicated, sent to colleagues by e-mail, published on the WWW sites, etc.

A few words about colors

People used to see only color images, black and white prints disappeared together with black and white newspapers and TV sets. Black and white digital still cameras never appeared on the market—they offered color images from the early 1 Mpx models.

We need to measure intensity of light in three separate colors to get color image, usually red, green and blue. But CCD pixels are sensitive to all wavelengths of visible light, even including some invisible portions of the spectrum. It is necessary to use color filters to pass only the requested color.

Basically there are two methods of applying filters to get color image:

  • It is possible to perform separate exposures with monochrome chip over red, green and blue filters. It takes some time to expose color image this way (it is necessary to perform three exposures and it is also necessary to exchange filters between exposures), so this method cannot be used to image fast moving objects (e.g. kids, except sleeping ones :-).

  • The manufacturer can also apply filters directly on CCD pixels. It is then possible to perform one exposure and to obtain complete color information. The disadvantage is the actual resolution and QE of CCD chip with color filters are lower compared to monochrome chip.

Both solutions have their advantages and disadvantages and both solutions are used in different situations. All applications in video cameras, still cameras, web cameras etc. use color detectors. First color CCD detectors used whole columns covered by respective color filters—first column was red, second green, third blue, fourth again red etc. One pixel with full color information was created by three horizontally adjacent pixels. Although such chips were designed with prolonged shape, the horizontal resolution of such chip was limited.

Current CCD chips use so-called Bayer mask. This mask covers individual pixels with color filters in chessboard-like pattern:

Bayer mask image processing relies on the fact, that human eye is much more sensitive to the image luminance than to the image color (also ordinary TV signal relies on this fact and transmits color information with 1/4 of bandwidth compared to luminance information). Bayer mask almost keeps the chip resolution in luminance—it is possible to calculate luminance for each pixel from color information of surrounding pixels with only a small error. Color information is calculated with less resolution, but it not as important.

Remark:

Every red, green and blue filter passes approximately 1/3 of the visible spectrum. But it is possible to use different color scheme with complementary colors—cyan, magenta and yellow—and to restore the same color information from them. The plus side of CMY filter set is that each complementary color covers 2/3 of the visible spectrum. Every pixel covered with C, M or Y filter grabs almost two-times light compared to RGB filters. So CMY chips can be almost two-times more sensitive than RGB chips.

Things are not so easy. Making filter passing R, G and B or C and Y light is relatively easy. But magenta is complement to green, so filter passing magenta should pass red light, block green light and pass blue light. Manufacturing such filter as a combination of glasses (in e.g. 1.25 ” threated ring) still can be done. But manufacturing M filer on each pixel is really tough work.

This is why some manufacturers are combining CMY filters with green filters (chip is then covered by a chessboard-like pattern interlacing M, G, M, G, ... and C, Y, C, Y, ... lines). Color reconstruction is still not perfect and CMYG chips are intended for sensitive video cameras with rather low resolution.

Although perfectly suitable for still and video cameras, astronomers use color chips only exceptionally. Mainly amateurs focused to obtaining nice images of deep-sky objects with less effort prefer one-shot-color CCD cameras. But majority of amateurs as well as all professionals, including cameras on spacecrafts and satellites, use monochrome CCD chips with color filters. They are generally more suitable for astronomy for number of reasons:

  • First of all, monochrome CCD is perfectly capable to take color image of astronomical objects using color filters. But color CCD can create monochrome image only at the price of much lower QE and lower resolution.

  • Color CCD chips have one fixed set of filters without the possibility to exchange them or to completely remove them. Number of applications require unfiltered images taken with maximum QE and color information is not important. Also number of applications require images in precisely defined spectral range. Monochrome chip is perfectly capable to take images with narrow-band filters like Hα, OIII, etc. Professionals prefer standard photometric (U)BVRI filter set to (L)RGB filters, aimed at color imaging, for precision photometry etc.

  • Color chips have less QE then monochrome ones. Limiting QE from around 80 % to around 25 % by color filters only wastes light in number of applications.

  • Lenses used in still cameras are usually mated with CCD chips with better resolution than is the resolution of the lens itself. This means single pixel is not very important in the image—even smallest details usually cover several pixels. This is not so true in astronomy. The best fit between the telescope focal length and the CCD pixel size results in star images covering only a few pixels. Thus interpolation of pixel value from surrounding pixels introduces significant error and prohibits precise measurement of position and brightness.

  • Color CCD chips do not allow reading of binned images. Binning would mix the colors from individual pixels and the color information would be lost.

  • Color CCD chips do not allow so-called Time Delay Integration (or Drift-Scan Integration). Image drifts over CCD vertical lines in this kind of integration. But the image drift is synchronized with image vertical shift. This means image is always exposed on the same pixels—when the image moves to another row, accumulated charge in pixels are also shifted into another row. Image is then read line by line in precisely defined time intervals.

    TDI mode can create possibly long strip with the width defined of CCD width and length defined only by exposure time. This mode is very important for large-area surveys. The big plus of TDI is the possibility to use Earth rotation as the source of the image drift. Stationary telescope can take images as stars pass over the chip due to daily motion.

Monochrome chips can take color images not only by exposing through three filters (say RGB), but it is possible to take hight quality luminance exposure in white light and to use shorter R, G and B exposures only to get color information (such technique is designated as LRGB). Because the color information is less important than luminance information, it is possible to use binning to enhance chip sensitivity at the price of lower resolution for color images and to take only luminance exposure at the full chip resolution.

Remark:

Monochrome CCD chip combined with color filters advantage somewhat disappears, when the filters have to be exchanged manually. Filter wheel integrated into the camera allows software-controlled filter exchange. It is a necessity for automated, robotic setups.

Still, using of modern color chips with relatively high QE and low noise can be perfectly suitable for taking beautiful images of deep-sky wonders, so everybody should decide himself or herself.

Dark current, CCD read noise and A/D units

The disadvantage of CCD technology is the fact, that electrons in pixels are generated not only by incoming light, but also randomly, depending on the chip temperature and also on pixels size, chip architecture and production technology. This temperature-generated charge is called dark current (it generates signal even if the chip is completely in the dark). Dark current is usually expresses in electrons per second per pixel at the defined temperature. For instance Kodak KAF-0400 CCD chip generates 1e/s per pixel at 0 °C.

One positive thing on dark current is that it is always the same (or very similar) at the same temperature. If we take picture of some astronomical object, the signal we read from CCD contains both signal generated by incoming light and signal generated by dark current. It is possible to perform the same exposition again, but with shutter closed. Such image will contain the signal generated by dark current but not the signal generated by light. Such image is called dark frame. It is then possible to simply subtract dark frame from original image to eliminate it. We will discuss this procedure in the sub-chapter about Image calibration.

Remark:

Dark frame subtraction is performed not only by astronomical software, but also by some still cameras. If the camera allows for longer exposure times (e.g. up to 15 s or more), you can notice the “Busy” or similar message on the camera display after long exposures for the same time like the original exposition. The camera is taking dark frame to subtract if from the exposed image to reduce noise.

But dark current is not the only source of unwanted noise in the CCD image. We already described mechanism of reading of CCD image—charge is shifted through the chip and then it is converted to voltage in the output node. The conversion electronics cannot work without noise, too. This noise is also characteristic for certain chip and is often expressed in electrons. For example the read noise of the said Kodak KAF-0400 CCD chip is 15 e RMS. Simply put, it is not possible to read image with better precision than 15 e RMS, no matter what is the chip temperature. It must be also emphasized, that the output voltage is digitized by external electronics, which also introduces some noise to the image. Very good electronics introduces very little noise so the combined read noise can be as low as the CCD read noise (or a few electrons higher).

You can note that we mentioned the electronic read noise expressed in electrons. But electronic noise is usually expressed in RMS volts. The relation is very simple: every CCD chip (or its output node) is characterized by the “volts per electron” ratio. For example the Kodak KAF-0400 CCD has output node converting 1 electron to 10 μV.

But the result of CCD image download is an image—an array on numbers, each one number representing brightness of one image pixel. Numbers are generated by the A/D converter used in the camera electronics. Here comes the camera parameter expressed in electrons per ADU (ADU means Analog to Digital converter Unit, also referred as count). Every CCD output node converts electrons to voltage at some ratio and every camera electronics converts voltage to ADU counts. It is then possible to simply calculate resulting e/ADU ratio.

Let's determine the e/ADU parameter for some example camera:

  • Assume we have 16-bit A/D converter with 2 V input range. That means 2 V signal is divided to 65,536 counts. 1 count represents 2 V / 65,536 = 30.5 μV.

  • Assume we have a CCD with 10 μV per electron output node.

  • The resulting ratio is (30.5 μV / ADU) / (10 μV / e) = 3 e / ADU. This means every 3 electrons in each pixel charge well causes one count increment in the resulting image.

It is important to keep on mind that such calculations are valid only statistically, in average for many electrons on many pixels. We can often meet cameras with 2.3 e / ADU or 1.5 e / ADU. This does not mean we have to divide elementary particles, of course :-).

Some interesting facts can be calculated from these ratio. For instance 15 electrons RMS of read noise and 3 electrons per ADU means that it is not possible to read image with smaller RMS noise than 5 counts. So if our hypothetical camera produces bias frame with 5 ADU RMS, then it is “ideal and perfect”.

Remark:

Bias frame is often used by some software packages as the basic level of pixel values determined by camera electronics. It is nothing more than dark frame with zero exposure time. But keep on mind that image digitization time is always non-zero. It takes seconds to digitize image on modern cameras and even minutes on old cameras with serial interface. Reading zero exposition dark frame is then impossible either way—the last portion of chip represents dark frame with the exposure time equivalent to readout time.

Bias frames are used to interpolate dark frames of different exposure times. As already stated, dark current is linearly proportional to chip temperature and exposure time. If we know the exposure time and chip temperature of some dark frame, we know one point on the line. Bias frame represents origin of this line. So we can calculate dark frame for different temperatures and/or exposure times.

But line is determined by any two points, it is not necessary that one point must be the origin. Instead of using a bias frame and dark frame to interpolate another dark frame, it is enough to use any two dark frames. The term bias frame becomes superfluous.

The electrons per ADU ratio is important also in relation to CCD well capacity. Every potential well representing CCD pixel has some capacity, usually depending on pixel size. Small pixels (around 6 μm square) can typically hold around 50,000 e. Medium-sized pixels (around 10 μm square) can hold approx. 100,000 e and large pixels (around 25 μm square) can hold up to 300,000 e.

CCD cameras usually utilize 16-bit AD converter, which results in resolution 65,536 ADUs. It is clear that converting 50,000 e into 65,536 levels does not take any sense and 15 or even 14-bit converter should be sufficient for such chip. On the other side converting 300,000 e into 65,536 levels leads to 4 or 5 e/ADU, which is quite appropriate.

Not only image pixels, but also horizontal register pixels and output node have limited capacity. This fact must be taken into account especially when using binning. Let's take the Kodak KAF-0400 as example: the pixel capacity is 100,000 e, horizontal register pixel capacity is 200,000 e and the output node capacity is 220,000 e. It is possible to use 2 × 2 binning if there are no more than 50,000 e in each pixel. But if there are pixels with almost full capacity filled, vertical binning would create pixels with almost 200,000 e, which the horizontal register should handle well, but subsequent horizontal binning would try to sum two pixels into output node and the output note would be saturated. The workaround of this problem can be combination of software and hardware binning. Image is binned 1 × 2 in hardware and then 2 × 1 in software. The result image is 2 × 2 binned but without saturated pixels, but with 2-times image download time. Maximal pixel value in such case exceeds 16-bit range.

Pixels and image size

Physics teaches us that telescope angular resolution depends on the wavelength of the detected light and telescope aperture. Resolution increases as the wavelength shrinks and the aperture enlarges. This is why the angular resolution of small 5 cm (2 inch) refractor is 1,000 times better than angular resolution of radio dish 100 m across receiving 1 m radio waves (receiving aperture is 2,000× bigger, but wavelength is 2,000,000× bigger). Wavelength of visible light is between 400 and 700 nm. Telescope aperture is not so strictly defined and depends mainly on the astronomer's budget.

But resolution is in practice affected by another factor—air turbulence. Hotter air has less density and also less refraction index than cooler air, so the air convention in our atmosphere distorts star image. The quality of star image is called “seeing” and is usually expressed as angular size of star image. Typical star image is blurred by seeing to 3 ” or 4 ” disk. If the star image has 2 ” or less angular diameter, the seeing is very good. On the other side very bad seeing distorts star image to disks 6 ” or even 8 ” across. When taking seeing into account, we find that a typical backyard telescope with 25 cm (10 inch) aperture reaches seeing-limited angular resolution, so increasing aperture does not enhance resolution, only allows shorter exposures.

“Ideal” star image has two pixels across. Star image covering just one pixel lowers the position precision (it is impossible to determine image centroid) and image is under sampled. Star image covering too many pixels wastes light, dividing star flux among too many pieces—such image is oversampled.

Pixel size [μm] Focal length for 2" per pixel [cm] Focal length for 1" per pixel [cm]
4.7 48 96
6.8 70 140
9 93 186
13 134 268
20 206 412
24 247 494

“Ideal” focal length for 2" and 1" per pixel for typical pixel sizes

If the telescope focal length is too long for pixel size (e.g. the pixel angular resolution is less than 2 ”), it is possible to either use binning for increasing the pixel size or to use focal reducer to shorten the telescope focal length. Binning was a bit of problem when CCD chips had only tens or hundreds of thousands pixels. With today's chips counting millions of pixels, binning and reducing of image resolution does not cause any problems. So multi-megapixel cameras with relatively small pixels becomes very popular, even if their pixel angular resolution is often under 1 ” per pixel on typical Schmidt-Cassegrain or Ritchey-Chretien telescope.

Hint:

Although over-sampled images, with star images covering many pixels, does not bring any significant information compared to well sampled images (star position and brightness cannot be determined with better precision), they are obviously more aesthetically appealing. Really nice–looking images are often acquired with multi-magapixel cameras with small pixels, coupled with long focal length telescopes.

Even when cameras with giant 24 × 36 mm CCD chips with 10+ MPx resolution are available today, typical astronomical CCD camera has smaller chip and lower resolution. Just keep in mind that there are tremendously more small objects in the sky than big ones. If the big object is to be imaged, techniques like image mosaic or time delay integration can help cover bigger portion of the sky than single exposure of the particular CCD camera and telescope allows.

Image calibration

Image immediately downloaded from the camera is called raw image. It is often surprising how aesthetically unpleasant raw images are, especially when compared to fully processed images, which appear in magazines and on web sites. Image processing can eliminate hot or dark pixels, remove unwanted gradients, reduce noise, sharpen image, enhance details etc.

Such image processing can make images more beautiful, but it changes information contained in the image. It can be performed with images intended for publication, but it eliminates the possibility to gather reliable scientific data from the image (measure brightness, position, etc.). Still there are some image processing, which together with enhancing the image appearance also enhances the scientific value of raw images instead of decreasing it—image calibration. It is almost necessary to perform calibration with every raw CCD image.

Depending on the CCD camera, telescope (or objective lens) and object imaged, the calibration can be more or less complex. Some setups even do not require the calibration at all.

Image calibration basically consists of two steps:

  1. dark frame subtraction.

  2. applying flat field

Raw image is affected by thermal noise and uneven field illumination

Raw image is affected by thermal noise and uneven field illumination

The purpose of dark frame subtraction was already explained—elimination (or at last reduction) of thermal noise. CCD dark current is proportional to temperature. Thermal noise doubles every 6 or 7 °C, depending on the chip architecture. For instance the Kodak KAF-0400 has dark current doubling temperature 6.3 °C. The charge accumulated in pixels is also proportional to exposure time (dark current is expressed in electrons per pixel per second at the defined temperature). To reduce image thermal noise, the dark frame subtracted from image should be obtained at the same temperature for the same time as is the image itself.

Dark frame corresponding to the raw image above (left) and the result after its subtraction (right)

If the dark current depends linearly on temperature and exposure time, it is possible to calculate dark frame from other dark frames taken at different temperature and/or exposed for different time. Some software packages require one dark frame exposed for zero time (and call it bias frame), other software does not require any special exposure times. Just take two dark frames at different temperatures and the software interpolates dark frame for required temperature. The same is true for the dark frame exposition time.

Remark:

Dependency of dark current on temperature is the reason, why cooled cameras need regulated cooling. If the camera electronics is able to keep the chip temperature within 0.1 °C, the necessity for multiple dark frames taken at different temperatures and their interpolation is eliminated. The calculated dark frame is always less precise than dark frame physically taken at the required temperature either way.

Let's also note that taking dark frames requires closing of the mechanical shutter (so-called electronic shutter, a property of FT and IT CCDs, does not work for dark frames). It is necessary to cover the telescope aperture (if the telescope has a truss tube, covering it can be a challenging task) by the observer every time dark frame is to be obtained. So the unattended robotic observation is no option for cameras without mechanical shutter.

This remark only explains why the regulated cooling and mechanical shutter should be in the “must have” portion of the camera features list.

Telescope field of view is often illuminated non-uniformly—image intensity on the borders can be lower than in the center, e.g. thanks to the smaller telescope secondary mirror. Also dust particles on filter or CCD camera window creates ring-like shades. All these effects alter image brightness and cause not only aesthetics artifacts, but also reduces measurement precision. It is possible to eliminate these effects by applying flat field image.

Flat field corresponding to the raw image above (left) and the result after flat field correction (right)

Flat field image is an image of uniformly illuminated area. Thus all image brightness variations on flat field are caused by telescope or camera, not by the object we image. Ideal flat field values are around one half of the image scale (average pixel count should be around 32,000 for 16-bit cameras). Applying flat field means dividing every image pixel with the appropriate pixel of the flat field. Image pixels brighter due to telescope or camera non uniformity are divided by bigger flat field value, also brighter due to same reasons. But such division changes image scale so we also multiple each pixel by flat field average pixel value. If the operation is performed on integer values, multiplication must precede division of course, else the precision lost during integer division would destroy the image.

 
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