## Calibration frames

Calibration frames are recordings of the camera's errors, made so that the errors can be corrected (Table 12.1, p. 147). One form of calibration, dark-frame subtraction, was introduced in the previous chapter; here we deal with the rest.

### 14.2.1 Dark-frame subtraction

As you already know, a dark frame is an image taken with the lens cap on, so that no light reaches the sensor. Its purpose is to match the hot pixels (and partly hot pixels) of an image of a celestial object, so that they can be subtracted out. The two must match in exposure time, ISO setting, and camera temperature.

### 14.2.2 Bias frames and scaling the dark frame

A bias frame is a zero-length exposure, or, with a DSLR, a dark frame with the shortest possible exposure time (1/1000 second or less). Its purpose is to record the pixel value for minimum black, even without leakage. Many pixels have small errors that cause them to start at a value higher than 0.

If you are going to subtract a matching dark frame from an image, you do not need a bias frame because the dark frame contains the bias information.

Bias frames are needed if your software is going to scale the dark frame to match a different exposure time. Suppose, for example, you have a 2-minute exposure of a celestial object but only a 1-minute dark frame. You might think you could use the dark frame by doubling all the pixel values in it. But that wouldn't be quite right, because the dark frame is the sum of two things - dark

(b)

Figure 14.5. Detecting an asteroid by its movement. (a) 3-minute exposure of asteroid Iris with Canon XTi (400D) and 300-mm lens at f /5.6. (b) Identical exposure 90 minutes later, converted to negative image. (c) Result of pasting (b) onto (a) with 30% opacity.

current and bias - and the bias doesn't need to be doubled. That's why additional information from the bias frame is needed.

### 14.2.3 Flat-fielding The concept

A flat field is an image taken with a plain white light source in front of the camera and lens. Its purpose is to record any variations of light intensity across the field -especially vignetting and the effect of dust specks. Figure 14.6 shows what flat-field correction accomplishes.

Acquiring flat-field frames

There are many ways to take flat fields. What you need is a uniform light source in front of the telescope or lens. Some possibilities include:

• Hand-holding a light box in front of the camera. That's what I do, with a 10-cm-square battery-powered fluorescent panel originally made for viewing 35-mm slides.

• Putting wax paper across the front of the telescope and then holding the light box about an arm's length in front of it. That's what I do when the telescope is larger in diameter than the light box.

• Illuminating the inside of the observatory dome (if you have one) and taking a picture of it through the telescope.

• Photographing the sky in twilight.

• Photographing several sparse star fields, then median-filtering them to remove the stars and retouching to remove any star images that are left.

What is important is that the telescope or lens must be set up exactly the same as for the celestial images, down to the setting of the focus and the positions of any dust specks that may be on the optics or the sensor.

The flat field should match the ISO setting of the celestial images, and the camera should be at the same temperature. However, the exposure time obviously will not match.

Fortunately, if you have a relatively bright light source, exposing a flat field is easy. Just set the camera to auto exposure (A or Av) and take a picture. Better yet, take several so they can be averaged for more accurate corrections. The flat field will automatically be placed right in the middle of the camera's brightness range.

Making the correction successfully

Actually performing flat-field correction can be tricky. Each pixel is corrected as follows:

New pixel value = Old pixel value x

Flat-field pixel value in this position

Figure 14.6. The effect of flat-fielding on a wide-field view of Orion with a Canon EOS 20Da and Ha filter. (a) Image calibrated with dark frames but not flat fields. (b) A flat field taken through the same lens on the same evening. Note the slight vignetting and prominent dust spot. (c) Image calibrated with dark frames and flat fields. (Slightly undercorrected; see text.)

Figure 14.6. The effect of flat-fielding on a wide-field view of Orion with a Canon EOS 20Da and Ha filter. (a) Image calibrated with dark frames but not flat fields. (b) A flat field taken through the same lens on the same evening. Note the slight vignetting and prominent dust spot. (c) Image calibrated with dark frames and flat fields. (Slightly undercorrected; see text.)

Figure 14.7. Flat-field and dark-frame calibration can be done in a single step in MaxDSLR.

The computation is very sensitive to errors. That's why it's so important to match the original ISO setting and optical conditions.

Better yet, make a calibrated flat field. That is, along with your flat fields, take some dark frames that match them. Subtract the dark frames from the flat fields, then average the flat fields (without aligning or de-Bayerizing them). Save the calibrated flat field and use it to calibrate your astronomical images.

Another reason for making a calibrated flat field is that you can adjust it. If your images come out undercorrected (with vignetting and dust spots still visible), scale up the contrast of the corrected flat field just a bit, and try again. If they are overcorrected, with reverse vignetting (edges brighter than the center), do the opposite.

Figure 14.7 shows the Set Calibration window in MaxDSLR when both darks and flats are to be applied. Don't make the mistake of subtracting, from your flats, the dark frames that go with the images; the exposure times are very different and you'll end up brightening the hot pixels instead of removing them. If MaxDSLR knew the exposure times, it could keep track of which dark frames go with which images and flats - but if you're working from DSLR raw files, it doesn't know. That's why I recommend keeping things simple.

The results of flat-fielding are often less accurate than we might like. Perfect correction would require infinite bit depth in both the images and the calibration frames, as well as a perfect match between the flat-fielding light source and the effects of collimated starlight. Besides, the vignetted edges of the image, and also the areas blocked by dust specks, really are underexposed and will not look exactly like normal exposures no matter what you do. I generally prefer slight undercorrection, as in Figure 14.6, rather than overcorrection.

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