Calibration Frames

As astronomers, we want to know the photon flux—that is, the rate at which photons fall on our CCD. Yet a raw CCD image contains the signal we want mingled with a bias voltage, a dark current, and nonuniform photosite sensitivity. To recover the photon flux, we take additional images that allow us to subtract the additive values and divide out the multiplicative factors. These additional images— support frames—include dark frames, flat-field frames, and bias frames.

Support frames provide a record of the CCD's peculiarities, allowing us to peel off layers of the onion one by one. For best results they should be taken at the telescope immediately before, during, or immediately after a set of astronomical images. This insures that the image frames and support frames match.

Although it is possible to use "ordinary" bias, dark, or flat-field frames in calibration, it is better to use "master" frames made by combining multiple bias, dark, or flat-field frames into a support frame that has less random noise than a single one. Although making master frames takes more observing time, the resulting calibrated images are significantly better.

In this section, we explore each type of support frame, the specific types of information that they capture, and how we can use that information to recover a celestial image that is corrected for bias, dark current, and nonuniformities.

6.2.1 Bias Frames

Astronomers make bias frames to capture the bias level. Because the CCD is in total darkness and the integration time is zero, the bias level, Bx , should be exactly the same for every pixel on the CCD since (in theory) neither photoelectrons nor thermal electrons were generated.

However, the bias level may fluctuate because of things that happen every time the CCD is read out or because extraneous signals are added to the bias level. Repetitive events during readout form a fixed pattern in the bias, (BFP)x , while extraneous events such as interference from a nearby computer monitor are unpat-

Figure 6.3 In this bias frame, a pixel value of 99 appears black and a pixel value of 102 appears white. The average pixel value is 100.00 ADU, and the standard deviation is 0.56 ADU. Fixed-pattern bias is visible at the lower left, and low-level horizontal and vertical pattern noise are also apparent.

Figure 6.3 In this bias frame, a pixel value of 99 appears black and a pixel value of 102 appears white. The average pixel value is 100.00 ADU, and the standard deviation is 0.56 ADU. Fixed-pattern bias is visible at the lower left, and low-level horizontal and vertical pattern noise are also apparent.

terned, (CTup)^ , and are considered noise because they appear randomly at a given photosite.

Fixed-pattern bias may result from light-emitting circuit elements on the CCD or the clocking circuits in its control electronics. (In this context, the word "fixed" means unchanging.) A fixed pattern in the bias frame is not a problem because it is the same in every bias frame, and can therefore be subtracted out.

Unpatterned events originate in power supplies, nearby electronics, motors, and radio-frequency interference from computers and monitors. These unwanted contributions are usually very small. Nonetheless, you should take and examine bias frames at every observing session simply to check that the bias frames are indeed free of spurious signals. If such signals are present, the condition causing them should be diagnosed and corrected.

In addition, the charge detection node on the CCD that converts electrons into an output voltage adds a random component to the bias called readout noise, oRO. Because readout noise has a Gaussian distribution, the pixel values in the bias frame will display a Gaussian distribution around the bias value.

Finally, even when the integration time is zero, it takes several seconds to read out the CCD, and a small amount of dark current accumulates in that time. The readout time, tRO, short near the CCD's serial register, is relatively long on

Figure 6.4 This image is the median of 64 bias frames, displayed with black = 99.8 and white = 101.4. With the exception of the artifact at lower left, every pixel value is either 100 or 101. "Hot" photosites generate a few thermal electrons during the time it takes to read out the CCD, producing the vertical streaks.

Figure 6.4 This image is the median of 64 bias frames, displayed with black = 99.8 and white = 101.4. With the exception of the artifact at lower left, every pixel value is either 100 or 101. "Hot" photosites generate a few thermal electrons during the time it takes to read out the CCD, producing the vertical streaks.

the side of the CCD farthest from the serial register; so there is a gradient in the number of thermal electrons, dx y, from the bottom to the top of the image, plus a random variation, oTE, in the electron count.

Thus, the bias frame, the simplest type of image, with no light on the CCD and zero integration time, contains the following elements:

Recall that the conversion factor g has units of electrons per ADU; so when the bias, fixed-pattern bias, unpatterned interference, readout noise, and dark current are measured in electrons, the bias frame is expressed in ADUs.

6.2.1.1 Using a Single Bias Value

In a healthy CCD camera, the bias value Bx y is by far the most important element of the bias frame. The bias is important because it displaces the zero-point of the pixel-value scale away from the zero signal of the CCD. Because of this offset, pixel values in the image are not proportional to the signal. When the bias is removed, the zero points of the CCD output and pixel-value scales coincide, and pixel values are proportional to the signal from the CCD.

Figure 6.5 This is the average of the same 64 bias frames shown in Figure 6.4, shown using the same black and white display values. Note that the overwhelming majority of pixels have a value of 100 (between 99.50 and 100.49 ADU), showing that for this CCD camera, a single bias value is justified.

The amplitudes of the fixed-pattern bias, interference, and readout noise are usually quite small, sometimes less than one ADU in a master bias frame. When this is the case, it is best to treat the bias frame as if it had only one value, Bt j, obtained by taking the average value of the bias frame.

For example, if your CCD camera has a measured readout noise of 20 electrons r.m.s., and the conversion factor is 30 electrons per ADU, averaging bias frames will produce a master bias frame with most pixels having the average bias value, plus a scattering of pixels with values one ADU lower or higher than the rest. The low and high pixels are probably no different from the average pixels; they are simply statistical accidents. In this case, it is best to use a single bias value.

6.2.1.2 Bias with Drift-Subtraction

Some CCD cameras, the Cookbook camera among them, feature a drift subtract mode designed to eliminate changes in the bias level caused by temperature-sensitive components in the camera. When this mode is active, the acquisition software continues to clock the CCD after the image storage area has been emptied, and several hundred readings of Bx ,, are averaged to obtain the system bias. This value is subtracted from every pixel in the image, and a fixed bias (usually 100) is added to prevent negative values from appearing in the image data. This technique

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