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Dark Frame — 60-Second Integration

Figure 6.11 This cross-histogram plots pixel values in a 60-second dark frame against the pixel value for the same pixel in a 300-second integration. Although not made at the same temperature, the points lie close to a straight line; therefore scaling even compensates for small changes in CCD temperature.

'Tip: AIP4Win features automatic dark-frame matching. Dark-frame matching enables observers to make one set of dark frames with long integration times and then use a master dark frame made from them to dark-subtract images with differing integration times made during the night.

6.2.2.5 Changing CCD Temperature

Dark current depends quite sensitively on the temperature of the silicon substrate of the CCD. If its temperature varies by a fraction of a degree Celsius during the interval between taking an image and taking a dark frame, the number of thermal electrons in the dark current will not match the number in the image; and you will see "hot" pixels or "dark" pixels in the calibrated image.

If you observe with a CCD camera that does not actively control the CCD temperature, use the advanced calibration protocol with automatic dark-frame-matching. Even if the CCD temperature changes by a few degrees, a dark-frame-matching algorithm such as that described above can find the best fit between the master dark frame and the dark current generated during the image integration.

• Tip: In its Advanced Calibration tool, AIP4Win allows you to automatically scale (or "match") a dark frame to the image. In addition to allowing you to use dark frames with integration times that differ from those used for images, automatic dark-frame matching allows you to calibrate images using dark frames taken at somewhat different temperatures.

6.2.2.6 When to Use a Single Dark Value

Throughout the preceding discussion, we have assumed there will be a significant accumulation of thermal electrons during image integrations, and also that different photosites have significantly differing dark current. However, if you observe with a CCD that has extremely low, uniform levels of dark current, you can subtract the average value of the dark frame from all pixels in the image. When thinned and back-illuminated scientific-grade CCDs are cooled below -80° Celsius, the dark current becomes vanishingly small (i.e., in the range of 1 to 3 electrons per photosite per hour). If the variation in the accumulated thermal electrons from one photosite to the next is random, and if the accumulation of thermal electrons drops below about half the readout noise of the CCD, then it is best to determine the average value of dark current for the whole CCD and subtract this single dark value from the entire raw image.

6.2.2.7 Cosmic Ray Events

When cosmic rays strike the Earth's upper atmosphere, they trigger a shower of high-energy particles, some of which reach the ground. When a high-energy subatomic particle crashes through the silicon matrix of your CCD, it leaves a track of several thousand free electrons. Cosmic ray events may appear as an intensely bright point of light or as a track several pixels in length. When a dark frame with a cosmic ray is used for calibration, the resulting images have a dark spot where the cosmic ray signal was subtracted.

Even when you average multiple dark frames to create a master dark frame, a single cosmic ray hit can mar all images calibrated with it. Instead of averaging, it is often good practice to take the median of multiple dark frames. Although the median combination does not reduce the statistical variation in the number of thermal electrons as effectively as averaging, it rejects extreme pixel values such as those arising from a cosmic ray hit.

• Tip: AIP4Win supports both dark-frame averaging and determining the dark-frame median. If you average dark frames, it is a good idea to inspect the individual frames for cosmic ray hits before averaging them. Do not include frames with obvious cosmic ray hits in an averaged master dark frame.

6.2.2.8 Electroluminescence

Electronic circuit elements on the CCD may act as light-emitting diodes, giving off light whenever voltage is applied to them. This effect is called electroluminescence. In the earliest amateur CCD cameras, based on the Texas Instruments TC211 chip, the bright spot in the corner was the most prominent feature in the

Figure 6.12 Here is a typical cosmic ray hit. Whenever you shoot images or dark frames, your images accumulate cosmic rays. Although the rate of accumulation depends on your altitude and the size of the CCD, you should expect around ten cosmic rays to hit each square centimeter of your CCD each hour.

Figure 6.12 Here is a typical cosmic ray hit. Whenever you shoot images or dark frames, your images accumulate cosmic rays. Although the rate of accumulation depends on your altitude and the size of the CCD, you should expect around ten cosmic rays to hit each square centimeter of your CCD each hour.

dark frame as seen in Figure 6.13. Fortunately, electroluminescence acts just like dark current and can be subtracted exactly as if it were.

6.2.2.9 How to Make Master Dark Frames

How you take the dark frames needed to create a master dark frame depends on how you plan to calibrate your images. If you plan to use the standard calibration protocol, the integration time of individual dark frames should be the same as that used in your images. For the advanced calibration protocol, ideally you should use integration times that are at least five times longer than the integrations used for your images.

To collect data for making a master dark frame, close any shutter in the CCD camera and cap the telescope. It is essential that no light reach the CCD when you are making dark frames. The camera should be cooled to normal operating temperature. Often the best strategy is to make dark frames midway through an imaging session, but that depends on your observing program. If you plan to use the advanced calibration protocol, shoot your bias frames at the same time you shoot your dark frames. This insures that you will have scalable thermal frames.

Figure 6.13 Electroluminescence brightens the upper left corner of this dark frame, a 60-second integration with a TC211-based camera. The glow occurs because the on-chip amplifier remained energized during integration, and glowed like an LED. Turning off the amplifier during integration eliminates the glow.

Figure 6.13 Electroluminescence brightens the upper left corner of this dark frame, a 60-second integration with a TC211-based camera. The glow occurs because the on-chip amplifier remained energized during integration, and glowed like an LED. Turning off the amplifier during integration eliminates the glow.

• Tip: For the basic and standard calibration protocols, your CCD cam era must be fully cooled before you make dark frames. For best results, make dark frames well into an observing session. Cap the telescope and close the camera's shutter. Use the same integration time that you use for images. Make at least 10 dark frames.

• Tip: For the advanced calibration protocol, make at least 10 dark frame integrations using an integration time five times the normal integration time that you use for images. For the best results, make bias frames at the same time you make dark frames.

6.2.3 Flat Frames

CCD sensitivity variations and vignetting are deeply buried layers of the raw-image onion, so deeply buried, in fact, that they cannot be removed until the overlying dark current and bias layers have been peeled away. Although CCD sensitivity variations and vignetting can be corrected in two separate steps, they are almost always treated as one "layer" and removed by dividing the image by a master flat-field frame.

The flat-field frame records the response of the entire optical system—the telescope, filters, window, cover glass, and CCD itself—to a uniform, or "flat," field of light. The resulting flat-field images cannot distinguish whether optical vignetting, quantum efficiency, or some combination of the two produced a particular pixel value in the frame, but it does not matter. So long as the optical system and CCD do not change, a good master flat-field allows the observer to correct both effects as if they were one.

Figure 6.14 The image above is a master flat-field frame made by taking the average of 16 flat-field frames and subtracting the average of 16 flat-dark frames. In the version above, 1900 displays as black and 2300 as white; so the rather bland-looking flat is actually seen at five times normal contrast.

Figure 6.14 The image above is a master flat-field frame made by taking the average of 16 flat-field frames and subtracting the average of 16 flat-dark frames. In the version above, 1900 displays as black and 2300 as white; so the rather bland-looking flat is actually seen at five times normal contrast.

Recall from Equ. 6.4 that the number of electrons generated at photosite

When we illuminate the CCD with a "flat" (uniform) field of light, the resulting data can serve as a map of the CCD's efficiency in converting photons into electrons. Since both t and Ix ,, are constant, the pixel values in the image are proportional to Vx vQx . Given this information, we can allow for and correct both effects in raw images taken with the CCD camera on this particular telescope. This is the role of the master flat-field frame.

Like all images, a flat-field frame contains not only the signal that we want, but also bias and thermal electrons:

(FLATRAW)^ = ~(tVx yQx ylx y) + <BIAS>,.r+ (DARK),,,. (Equ. 6.15)

To remove the bias and dark contributions from the raw flats, we must therefore shoot flat-field dark frames:

( FLATDARK)x> v = (BIAS), ,, + ( DARK), v. (Equ. 6.16)

Figure 6.15 This is just one of the images used to make the flat shown in Figure 6.16, shown with a 10x stretch in contrast (black = 2000, white = 2200). Even though the image has been optimally exposed to half the full-well capacity of the CCD, it nonetheless appears slightly noisy.

Although it does not appear explicitly, it is important to remember that the integration time for a flat-field dark frame (a.k.a. "flat dark") must be the same as the integration time for the raw flats. It is also desirable to shoot a special set of flat darks to insure that the flat dark is an independent sample of the dark current.

Ideally, the raw flat-field exposure should fill the charge wells in the CCD photosites to roughly one-half their full depth, enough to produce a strong signal but not so close to saturation that the CCD's response to light becomes nonlinear. If you are using an artificial light source to make flat-field frames, set its brightness so the integration times are between 2 and 10 seconds. In the CCDs used by amateur astronomers, the signal will be at least 40,000 photoelectrons, which implies a random variation of roughly 200 electrons. The flat-field frame is, therefore, photon-noise limited rather than limited by any of the internal noise sources of the CCD.

To make a master flat-field frame of extremely high quality, shoot at least 16 raw flat-field frames and 16 flat darks. To make the master, average the flats and average the flat darks, then subtract the averaged flat dark from the average flat field. With a signal of 640,000 total electrons, even allowing for the readout noise from 32 image readouts, the signal-to-noise ratio of the master flat-field frame should be around 600, sufficiently good that no loss of image quality will result

Figure 6.16 By averaging flat-fields, you can beat down random noise. Compare this flat, made by averaging 16 raw flats, with Figure 6.15, made from just one frame. Both are shown with black = 2000 and white = 2200. The averaged image has a signal-to-noise ratio of -400:1, giving excellent flat-field correction.

Figure 6.16 By averaging flat-fields, you can beat down random noise. Compare this flat, made by averaging 16 raw flats, with Figure 6.15, made from just one frame. Both are shown with black = 2000 and white = 2200. The averaged image has a signal-to-noise ratio of -400:1, giving excellent flat-field correction.

from flat-fielding during calibration.

Several factors bedevil the making of flat-field frames. First is that the optical configuration must be the same as that used for images. Removing or rotating the CCD camera, or even changing the focus, can invalidate a carefully prepared master flat-field frame. In some telescopes, movement of optical components in their cells when the telescope pointing changes can alter the optical configuration. Dust can fall on windows and filters, filter slides may position the filter differently with every insertion, and internal reflections can mimic the appearance—but not the behavior—of vignetting. Scattered light is another factor that can lead to poor flat-fielding. If flat-fielding light reaches the CCD by paths that sky light does not normally take, the resulting master flat will give poor results. Finally, because the quantum efficiency of CCDs is wavelength dependent, the spectral energy distribution of the light used for making flat-field frames should match that of the night sky, and should ideally be the light of the night sky. However, at good observing locations, the night sky is not bright enough to allow a deep exposure in a reasonable length of time.

Because of these factors, producing good flat fields is something of an art, and in some people's jaundiced view, akin to black magic. Techniques that work well for one observer may fail in the hands of another, for reasons that remain ob scure. In preparing a telescope for CCD imaging, all internal surfaces should be meticulously blackened, all optics mounted securely, and the motions of all mechanical components (such as the focuser, filter slides, and auxiliary lens mounts) made tight and reproducible. Eliminating these common problems will greatly increase your chances of getting excellent flat-field frames.

6.2.3.1 Four Types of Flat-Field Frames

There are four generally accepted methods of making flat-field frames: light-box flats, dome flats, twilight flats, and sky flats. Light-box flats are made by placing a back-lit diffusing screen immediately in front of the telescope; dome flats by turning on lights in the dome and shooting a white screen mounted on the dome. Twilight flats are made by shooting the twilight sky, either dusk or dawn; and sky flats are made by taking the median of large numbers of images of the night sky. Each technique has its merits and demerits, but all of them are capable of producing good flat fields.

Light-box flats and dome flats offer the advantage of being under the control of the observer. With small instruments, the light box can be placed directly over the front of the telescope, and the box can be designed to produce any desired level of brightness. Dome flats make sense for large telescopes, where illuminating a screen attached to the inside of the dome or roll-off roof is more practical than a gigantic light box. However, it is very difficult to construct a light-box or dome illumination system whose spectrum matches that of the night sky.

Twilight flats demand quick work on the part of the observer, not only to determine when the sky has reached the right brightness, but also to take enough flat-fields to make a master flat with a good signal-to-noise ratio. Operationally, evening twilight flats are tricky because they may be taken before the telescope has been focused for the night, and dawn twilight flats require observers to stay awake until dawn. Twilight flats also record star images, so that in calibration, you must take a median to eliminate them.

Sky flats require huge amounts of observing time, or an observing program in which the images serve as their own flat-field frames. Sky flats do, of course, match the spectrum of the night sky, so in that respect they are ideal. However, because the sky is dark and full of stars, it is necessary to take the median of hundreds of sky flats not only to eliminate star images, but also to obtain an acceptable signal-to-noise ratio. Another consideration is that the imaging targets must be randomly positioned in the images, lest you end up with a hot spot in the center of the master flat. For an observing program that generates hundreds of images of small, faint, randomly placed objects, sky flats are ideal.

6.2.3.2 How to Shoot Light-Box and Dome Flats

Light-box flats and dome flats are easy to shoot. At a convenient time in the observing session, the light box is attached to the telescope or the dome rotated so that the telescope is pointed at the screen. If you are using the camera in a mode

Figure 6.17 Above you can see low-contrast structure in the master flat-field revealed by local adaptive sharpening, a detail-extraction algorithm. The CCD shows small-scale and large-scale variations of about 0.2% in the sensitivity of columns. Flat-fielding removes artifacts like these from your images.

Figure 6.17 Above you can see low-contrast structure in the master flat-field revealed by local adaptive sharpening, a detail-extraction algorithm. The CCD shows small-scale and large-scale variations of about 0.2% in the sensitivity of columns. Flat-fielding removes artifacts like these from your images.

that reduces the well capacity, disable it and set the camera to make integrations of between two and 10 seconds. No other settings are changed. Make the flat-field frames as follows:

1. Switch on the lamps illuminating the dome screen or the light-box.

2. Adjust the lamp brightness and integration time to fill the charge wells in the photosites to half of their full capacity.

3. Shoot enough flat-fields to guarantee a high signal-to-noise ratio. With the CCD cameras used by amateur astronomers, 16 flats are ample.

4. Without changing anything else, turn off the lamps.

5. Shoot an equal number of flat darks.

The entire sequence can be completed in about 10 minutes. Despite the disadvantage of spectral mismatch between the night sky and the lamps in your light-box or dome screen, with amateur telescopes and CCD cameras. light-box flats or dome flats produce excellent and consistent master flat-fiela frames.

6.2.3.3 How to Shoot Twilight Flats

Twilight flats require careful planning. At the end of the previous observing session, leave the CCD camera on the telescope, and do not change the focus setting. Be sure the camera is fully cooled and operating normally. Then take test integrations of five seconds' duration. During evening twilight, the sky brightness halves every minute. As soon as the sky is dark enough to produce unsaturated images, begin taking and saving five-second integrations as fast as you can. At the end of three minutes, the sky will be too dark to continue. Cap the telescope and shoot as many flat darks as you shot twilight flats. If you plan to use the advanced calibration protocol, shoot your bias frames.

One little wrinkle has foiled many observers: when you're shooting twilight flats, shut off the telescope's drive motor so that stars form trails. If you have the drive running, the star images will become part of your master flat! If you let them trail, you can eliminate them by using a median combination.

To shoot dawn flats, reverse the process. Begin to integrate and save flats when the sky background reaches 5% of full-well capacity, and continue shooting and saving flats until the camera saturates. Cap the telescope and shoot as many flat darks as you shot twilight flats. If you observe all night, be sure to compare the dusk and dawn flats to see if the telescope and camera remained the same all night long.

Because the brightness of the sky changes, you cannot simply average sky flats. Instead, you must subtract an average dark frame from each image, measure the average brightness of a small region near the center of each frame, and then multiply the images so that all have the same average pixel value near the center. This process is called "normalizing" the images. Once the flats have been normalized, you can take the median pixel value (to eliminate the star images) from the set of dark frames as you create the master flat.

6.2.3.4 How to Shoot Sky Flats

Making sky flats is tricky because the telescope and CCD camera must remain the same, except for minor changes in focus, long enough to build a "flat library" of at least one hundred images. To be used as flats, images must not have bright objects near the center; and in all other respects they should be as similar as possible, using the same camera settings and integration times. Avoid using images shot near the horizon or on nights with strong Moonlight. Otherwise, a sky-flat library is just a large collection of normal images of small, faint objects that are not centered in the frame. In the course of making the images, shoot lots of dark frames and bias frames.

An observer who expects to use sky flats should be aware that the final calibration of an image may not be possible for days or weeks after it is made, because the raw images can be flat-fielded only when you have accumulated enough images to form a normalized median master flat with an acceptable signal-to-noise ratio. The sky background in sky flats is usually not bright, so the individual frames are fairly noisy—and not all the same brightness. Later, when we compute the signal-to-noise ratio of a single short-exposure image of the night sky, you will see it's around 15:1. To reach the 600:1 signal-to-noise ratio you would expect in a master flat-frame made with a light box, you will need to take roughly 1,600 sky flats—too many to be practical for most amateur astronomers.

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