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from the raw image, where Q (read as "Q-bar") is the average quantum efficiency of the CCD array. Preparation for calibration consists of the following steps:

1. Averaging or taking the median of the dark frames to create a master dark frame. Note that the integration time used for the dark frames must be the same as the integration used for the raw images.

2. Averaging or taking the median of the raw flat-field frames to create a combined raw flat-field frame.

3. Averaging or taking the median of the flat-field darks to create a combined flat-dark frame.

4. Subtracting the combined flat dark from the combined raw flat to produce a master flat-field frame.

Once the master dark and master flat have been made, they can be used for all of the raw images made using the same integration time and optical setup. Calibration itself consists of the following steps:

1. Subtracting the master dark from the raw image.

2. Computing the average pixel value of the master flat-field frame.

3. Dividing, on a pixel-by-pixel basis, the dark-subtracted image by the ratio of the master flat-field pixel value over the average pixel value of the central region of the master flat-field frame.

4. Saving the resulting calibrated image.

Although flat-fielding is sometimes called "division," the actual operation is more complex. We assume that a region near the center of the master flat-field is free of vignetting and has a quantum efficiency typical of the entire CCD, and find the average pixel value of this region. The size of the averaged region can be as small as 100 pixels on a side, or the central 50% of the frame; as long as the flat-field is reasonably uniform, it doesn't matter. This average value,

Raw Image Dark Subtracted Image Calibrated Image

Raw Image Dark Subtracted Image Calibrated Image

Flat Darks

Standard Calibration

Dark frames should have the same integration time as the raw images.

Flat darks should have the same integration time as the raw flats.

Figure 6.19 Although standard calibration requires multiple darks, flats, and flat darks, it produces an image corrected for bias, dark current, and vignetting. Dark frames must have the same integration time as that of your images. Standard calibration does an excellent job for most types of CCD imaging.

Flat Darks

Standard Calibration

Dark frames should have the same integration time as the raw images.

Flat darks should have the same integration time as the raw flats.

Figure 6.19 Although standard calibration requires multiple darks, flats, and flat darks, it produces an image corrected for bias, dark current, and vignetting. Dark frames must have the same integration time as that of your images. Standard calibration does an excellent job for most types of CCD imaging.

forms a standard for the rest of the master flat:

If the flat were perfectly uniform, the ratio of the average value to the value of the individual pixel would always be one. If a particular photosite has low sensitivity or is shaded by a speck of dust, then the pixel value in the master flat will be low. When the ratio is computed, its value will be greater than one and the value of the corresponding pixel in the raw image will be raised, correcting its value to what it should have been.

• Tip: AIP4Win takes care of the details of flat-fielding for you. All you have to do is select the raw flats and flat darks to make the master flat-field frame.

6.3.3 Advanced Image Calibration

The aim of the advanced calibration protocol is the same as standard calibration: to extract the quantity from the raw image. However, this procedure seeks to give the observer greater flexibility by removing the constraint of equal integration time for images and darks. To an observer contemplating using the advanced calibration protocol, the raw image looks like this:

(RAW)t v = -{{tVx,yQx yIxJ + (tdx>, + GTE) + (BIAS)V , } (Equ. $.20)

o where g is the conversion factor, t is the integration time, I is the photon flux, Q is the quantum efficiency, Vx^y is the vignetting factor, dx y is the dark current, and cTE is the thermal noise. The crucial change in thinking is that the bias is now seen as separate from the accumulated dark current instead of being lumped together as part of a dark frame.

Now consider a dark frame in which the integration is ¿DK instead of t:

(DARK)^ = ~{{tDYidXty + GTE) + <BIAS>x?7} . (Equ. 6.21)

By subtracting a bias frame, the accumulated dark current during the time /DK can be converted to the dark current that would have accumulated during the raw image integration time, t. Follow it step-by-step. First, subtract the bias frame:

(DARK) ( BI AS) y = ~{(tDKdx,y + 0TE)}. (Equ. 6.22)

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