Astronomy ccd handbook
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Use of overscan regions to provide a calibration of the zero level generally consists of determining the mean value within the overscan pixels and then subtracting this single number from each pixel within the CCD object image. This process removes the bias level pedestal or zero level from the object image and produces a bias-corrected image. Bias frames provide more information than overscan regions, as they represent any two-dimensional structure that may exist in the CCD bias level.
Two-dimensional 2-D patterns are not uncommon for the bias structure of a CCD, but these are usually of low level and stable with time. Upon examination of a bias frame, the user may decide that the 2-D structure is nonexistent or of very low importance and may therefore elect to perform a simple subtraction of the mean bias level value from every object frame pixel.
Another possibility is to remove the complete 2-D bias pattern from the object frame using a pixelby-pixel subtraction i. When using bias frames for calibration, it is usually best to work with an average or median frame composed of many 10 or more individual bias images Gilliland, This averaging eliminates cosmic rays,1 read noise variations, and random fluctuations, which will be a part of any single bias frame. Variations in the mean zero level of a CCD are known to occur over time and are usually slow drifts over many months or longer, not noticeable changes from night to night or image to image.
These latter types of changes 1 Cosmic rays are not always cosmic! Producing a histogram of a typical averaged bias frame will reveal a Gaussian distribution with the mean level of this distribution being the bias level offset for the CCD.
We show an example of such a bias frame histogram in Figure 3. The width of the distribution shown in Figure 3. For example, in Figure 3. Histogram of a typical bias frame showing the number of pixels vs.
One of the major advantages of a CCD is that it is linear in its response over a large range of data values. Linearity means that there is a simple linear relation between the input value charge collected within each pixel and the output value digital number stored in the output image.
The linearity curve shown in Figure 3. Note that the CCD response has the typical small bias offset i. As we have mentioned a few times already in this book, modern CCDs and their associated electronics provide high-quality, low-noise output.
Early CCD systems had read noise values of times or more of those today and even five years ago, a read noise of 15 electrons was respectable. For these systems, deviations from linearity that were smaller than the read noise were rarely noticed, measurable, or of concern. However, improvements that have lowered the CCD read noise provide an open door to allow other subtleties to creep in.
One of these is device nonlinearities. These are integral nonlinearity and differential nonlinearity. The slope of the linearity curve is equal to the gain of the device. The linearity curve for a CCD is determined at various locations and then drawn as a smooth line approximation of this discrete process.
The two types of CCD nonlinearity are shown here in cartoon form. Integral nonlinearity right is more complex and the true linearity curve solid line may have a simple or complex shape compared with the measured curve dashed line. Both plots have exaggerated the deviation from linearity for illustration purposes.
Astronomers call this type of nonlinearity digitization noise and we discuss it in more detail below. If one uses the top 12 bits, then bits 4—7 are affected.
How the INL comes into play for an observer is as follows. This is a very unacceptable result for astronomy, but fine for digital 58 Characterization of charge-coupled devices cameras or photocopiers that usually have even higher values of INL caused by their very fast readout conversion speeds. The lesson here is to use a large dynamic range as many bits as possible to keep the nonlinearity as small as possible.
So for a given modern CCD, nonlinearity is usually a small but nonzero effect. For the CCD in the example shown in Figure 3. This particular example, however, illustrates the most dangerous type of situation that can occur in a CCD image. The nonlinear region, which starts at 26 ADU, is entered into before either type of saturation can occur. Thus, the user could have a number of nonlinear pixels for example the peaks of bright stars and be completely unaware of it.
No warning bells will go off and no flags will be set in the output image to alert the user to this problem. The output image will be happy to contain and the display will be happy to show these nonlinear pixel values and the user, if unaware, may try to use such values in the scientific analysis.
Thus it is very important to know the linear range of your CCD and to be aware of the fact that some pixel values, even though they are not saturated, may indeed be within the nonlinear range and therefore unusable. Luckily, most professional grade CCDs reach one of the two types of saturation before they enter their nonlinear regime.
Most observatories have linearity curves available for each of their CCDs and some manufacturers include them with your purchase. Obtain exposures of say 1, 2, 4, 8, 16, etc. Since you have obtained a sequence that doubles the exposure time for each frame, you should also double the number of incident photons collected per star in each observation.
Plots of the output ADU values for each star versus the exposure time will provide you with a linearity curve for your CCD. This CCD has micron pixels and is operated as a back-side illuminated device with a full well capacity of 90 electrons per pixel. This example results in a very reasonable gain setting, thereby allowing the CCD to produce images that will provide good quality output results.
This gain value certainly made use of the entire dynamic range of the CCD, allowing images of scenes with both shadow and bright light to be recorded without saturation. The brief nature of this book does not allow the many more subtle effects, such as deferred charge, cosmic rays, or pixel traps, to be discussed further nor does it permit any discussion of the finer points of each of the above items.
The reader seeking a deeper understanding of the details of CCD terminology a. Above all, the reader is encouraged to find some CCD images and a workstation capable of image processing and image manipulation and to spend a few hours of time exploring the details of CCDs for themselves. As a closing thought for this chapter, Table 3. The sample shown tries to present the reader with an indication of the typical properties exhibited by CCDs.
Included are those of different dimension, of different pixel size, having front and back illumination, cooled by LN2 or thermoelectrically, and those available from different manufacturers. Information such as that shown in Table 3. Most have readily available data sheets for the entire line of CCDs they produce. Each example for a given CCD in Table 3. Most manufacturers produce a wide variety of device types.
Appendix B provides a listing of useful CCD websites. Using only the data presented in Figures 3. Why might real QE curves be different? Discuss two major reasons why CCDs are better detectors than the human eye. Are there instances in which the eye is a better detector?
Design a detailed observing plan or laboratory experiment that would allow you to measure the quantum efficiency of a CCD. Discuss the specific light sources astronomical or laboratory you might use and over what band-passes you can work. How accurate a result would you expect? Why is charge diffusion important to consider in a deep depletion CCD?
Using the standard physics equation for diffusion, can you estimate the area over which electrons from one pixel will spread in a CCD as a function of time? You will have to look up the properties of bulk silicon and keep in mind the operating temperatures and voltages. For each, discuss a method for mitigation. When does read noise get introduced into each pixel of a CCD during the readout process?
How could you design a CCD to have zero read noise? An image is obtained that contains only read noise. What range of values would one expect to find in any pixel on the array? How would these values be distributed around the ADU value? Using the data presented in Figure 3. Given your answer, how do video or digital cameras record scenes that are not saturated by thermal noise?
Estimate the dark current for the CCD illustrated in Figure 3. What level of dark current is acceptable? Do the numbers discussed in Section 3. What limits the practical use of CCD binning on any given chip? Detail the difference between overscan and bias. Why do CCDs have a bias level at all? What is so important about a device being linear in its response to light?
How might your choice change if the CCD became nonlinear at 65 electrons? Design a detailed observing plan or laboratory experiment that would allow you to measure the linearity of a CCD.
Discuss the specific light sources astronomical or laboratory you might use and the sequence of integrations you would take. What measurements would you make from the collected images? Over what band-passes would you work and how accurate a result would you expect? Which type of nonlinearity is more acceptable in a CCD for spectroscopic observations?
For photometric observations? What if the INL was 32? Using Table 3. What is the best CCD to use if you were attempting to measure very weak stellar absorption lines? Compare the dynamic range of a CCD to that of a typical sub-woofer speaker. Compare it to a police-car siren.
We will discuss a few more preliminaries such as flat fields, the calculation of gain and read noise for a CCD, and how the signal-to-noise value for a measurement is determined. The chapter then continues by providing a brief primer on the use of calibration frames in standard two-dimensional CCD data image reduction.
Clearly the conversion from one to the other is simple. This image scale is usually quite a good value for direct imaging applications for which the seeing is near 1 or so arcseconds. There are times, however, when the above expression for the plate scale of a CCD may not provide an accurate value. This could occur if there are additional optics within the instrument that change the final f-ratio in some unknown manner.
Under these conditions, or simply as an exercise to check the above calculation, one can determine the CCD plate scale observationally. Using a few CCD images of close optical double stars with known separations e. This same procedure also allows one to measure the rotation of the CCD with respect to the cardinal directions using known binary star position angles. For the novice, it is just another term to add to the lexicon of CCD jargon.
The idea of a flat field image is simple. Within the CCD, each pixel has a slightly different gain or QE value when compared with its neighbors. In order to flatten the relative response for each pixel to the incoming radiation, a flat field image is obtained and used to perform this calibration. Ideally, a flat field image would consist of uniform illumination of every pixel by a light source of identical spectral response to that of your object frames.
That is, you want the flat field image to be spectrally and spatially flat. All of these methods involve a light source that is brighter than any astronomical image one would observe. This light source provides a CCD calibration image of high signal-to-noise ratio. For imaging applications, one very common procedure used to obtain a flat field image is to illuminate the inside of the telescope dome or a screen mounted on the inside of the dome with a light source, point the telescope at the bright spot on the dome, and take a number of relatively short exposures so as not to saturate the CCD.
Since the pixels within the array have different responses to different colors of light, flat field images need to be obtained through each filter that is to be used for your object observations.
As with bias frames discussed in the last chapter, five to ten or more flats exposed in each filter should be obtained and averaged together to form a final or master flat field, which can then be used for calibration of the CCD.
In addition, most instrument user manuals distributed by observatories discuss the various methods of obtaining flat field exposures that seem to work best for their CCD systems. Flat fields obtained by observation of an illuminated dome or dome screen are referred to as dome flats, while observations of the twilight or night sky are called sky flats. To achieve large-scale, uniform flat fields Zhou et al.
Shi and Wang discuss flat fielding for a wide field multi-fiber spectroscopic telescope. They use 4. CCD imaging and photometric applications use dome or sky flats as a means of calibrating out pixel-to-pixel variations. For spectroscopic applications, flat fields are obtained via illumination of the spectrograph slit with a quartz or other high intensity projector lamp housed in an integrating sphere Wagner, The output light from the sphere attempts to illuminate the slit, and thus the grating of the spectrograph, in a similar manner to that of the astronomical object of interest.
This type of flat field image is called a projector flat. Well, so far so good. So what is the big deal about flat field exposures? The problems associated with flat field images and why they are a topic discussed in hushed tones in back rooms may still not be obvious to the reader.
There are two major concerns. One is that uniform illumination of every CCD pixel spatially flat to one part in a thousand is often needed but in practice is very hard to achieve.
This wavelength dependence means that your flat field image should have the exact wavelength distribution over the band-pass of interest spectrally flat as that of each and every object frame you wish to calibrate. Quartz lamps and twilight skies are not very similar at all in color temperature i. In addition, the time needed to obtain nighttime sky flats is likely not available to the observer who generally receives only a limited stay at the telescope.
Thus, whereas very good calibration data lead to very good final results, the fact is that current policies of telescope scheduling often mean that we must somehow compromise the time used for calibration images with that used to collect the astronomical data of interest. Often the calibration frames desired are not what is obtained. Laboratory flat fields taken prior to launch are often used as defaults for science observations taken in orbit.
Defocused or scanned observations of the bright Earth or Moon are often used for these. Dithered observations of a star field can be used as well in a slightly different way. Multiple observations of the same assumed constant stars as they fall on different pixels are used to determine the relative changes in brightness and thus map out low frequency variations in the CCD.
An example of such a program is discussed in Mack et al. Within the above detailed constraints on a flat field image, it is probably the case that obtaining a perfect, color-corrected flat field is an impossibility.
But all is not lost. Many observational projects do not require total perfection of a flat field over all wavelengths or over the entire two-dimensional array. However, a project with end results of absolute photometric calibration over large spatial extents e. For such demanding observational programs, some observers have found that near-perfect flats can be obtained through the use of a combination of dome and sky flats.
This procedure combines the better color match and low-spatial frequency information from the dark night sky with the higher signal-to-noise, high spatial frequency information of a dome flat. Experimentation to find the best method of flat fielding for a particular telescope, CCD, and filter combination, as well as for the scientific goals of a specific project, is highly recommended.
A summary of the current best wisdom on flat fields depends on who you talk to and what you are trying to accomplish with your observations. An answer to that question is: a good flat field allows a measurement to be transformed from its instrumental values into numeric results in a standard system that results in an answer that agrees with other measurements made by other observers.
Without them, near perfect agreement of final results is unlikely. While the ideal flat field would uniformly illuminate the CCD such that every pixel would receive equal amounts of light in each color of interest, this perfect image is generally not produced with dome screens, the twilight sky, or projector lamps within spectrographs. This is because good flat field images are all about color terms.
That is, the twilight sky is not the same color as the nighttime sky, neither of which are the same color as a dome flat. If you are observing red objects, you need to worry more about matching the red color in your flats; for blue objects you worry about the blue nature of your flats. Issues to consider include the fact that if the Moon is present, the sky is bluer then when the Moon is absent, dome flats are generally reddish due to their illumination by a quartz lamp of relatively low filament temperature, and so on.
Thus, just as in photometric color transformations, the color terms in flat fields are all important. One needs to have a flat field that is good, as described above, plus one that also matches the colors of interest to the observations at hand. Proper techniques for using flat fields as calibration images will be discussed in Section 4. Modern CCDs generally have pixels that are very uniform, especially the new generation of thick, front-side devices.
Modern thinning processes result in more even thickness across a CCD reaching tolerances of microns in some cases. Thus, at some level flat fielding appears to be less critical today but the advances resulting in lower overall noise performance provide a circular argument placing more emphasis on high quality flats.
Appendix A offers further reading on this subject and the material presented in Djorgovski , Gudehus , Tyson , and Sterken is of particular interest concerning flat fielding techniques. Noted above, when we discussed bias frames, was the fact that a histogram of such an image see Figure 3. Furthermore, a similar relation exists for the histogram of a typical flat field image see Figure 4.
The mean level in the flat field shown in Figure 4. Histogram of a typical flat field image. Note the fairly Gaussian shape of the histrogram and the slight tail extending to lower values. This is not unreasonable at all given the low values of read noise in present day CCDs. Let us now look at how bias frames and flat field images can be used to determine the important CCD properties of read noise and gain.
Using two bias frames and two equal flat field images, designated 1 and 2, we can proceed as follows. Determine the mean pixel value within each image.
Also, do not include overscan regions in the determination of the mean values. Various formulations of this equation have been produced e. In optical observations, every photon that is collected within a pixel produces a photoelectron; thus they are indeed equivalent. When talking about observations, it seems logical to talk about star or sky photons, but for dark current or read noise discussions, the number of electrons measured seems more useful.
In our short treatise, we will remark on some of the highlights of that paper and present an improved version of the CCD Equation. For some CCD observations, particularly those that have high background levels, faint sources of interest, poor spatial sampling, or large gain values, a more complete version of the error analysis is required.
The term nB is the total number of background pixels used to estimate the mean background sky level. One can see that small values of nB will introduce the largest error as they will provide a poor estimate of the mean level of the background distribution.
Thus, very large values of nB are to be preferred but clearly some trade-off must be made between providing a good estimate of the mean background level and the use of pixels from areas on the CCD image that are far from the source of interest or possibly of a different character. From our discussion of the digitization noise in Chapter 3, we noted that the error introduced by this process can be considerable if the CCD gain has a large value.
In the instances for which they become important — for example, cases in which the CCD gain has a high value e. A second observation is made of an astronomical source with a CCD detector attached to a 1-m telescope.
We will further assume here for simplicity that the CCD image scale is such that our source of interest falls completely within 1 pixel good seeing! Most instrument guides available at major observatories provide tables that list the count rate expected for an ideal star usually 10th magnitude and of 0 color index within each filter and CCD combination in use at each telescope.
Similar tables provide the same type of information for the observatory spectrographs as well. The types of images used are essentially the same although possibly generated by different means in imaging, photometric, and spectroscopic applications.
This basic set of images consists of three calibration frames — bias, dark, and flat field — and the data frames of the object s of interest. Table 4. The shutter remains closed and the CCD is simply read out. The purpose of a bias or zero frame is to allow the user to determine the underlying noise level within each data frame. The bias value in a CCD image is usually a low spatial frequency variation throughout the array, caused by the CCD on-chip amplifiers.
This variation should remain constant with time. The rms value of the bias level is the CCD read noise. A bias frame contains both the DC offset level overscan and the variations on that level. The nature of the bias variations for a given CCD are usually column-wise variations, but may also have small row-wise components as well. Thus, a 2-D, pixel-by-pixel subtraction is often required. A single bias frame will not sample these variations well in a statistical fashion, so an average bias image of 10 or more single bias frames is recommended.
CCD dark frames are images taken with the shutter closed but for some time period, usually equal to that of your object frames. That is, if one is planning to dark correct a 45 second exposure, a 45 second dark frame would be obtained.
Longer dark frames can often be avoided using the assumption that the dark current increases linearly with time and a simple scaling can be applied. However, this is not always true. Dark frames are a method by which the thermal noise dark current in a CCD can be measured.
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