Info

/.Ai iVi'".-, " Lj¡ ' . •

Bias#1

Bias#2

'À ' * ¿"¿J - "

Figure 6.6 These enlarged sections of five bias frames were taken a few seconds apart, yet no two are the same. When many bias frames are averaged—the case for the frame in the lower right—the root-mean-square noise decreases with the square root of the number of bias frames.

removes the effects of a drifting analog bias value, and locks the value of (BIAS).,. y at the fixed bias value. If you use drift subtract mode, use it for all of your images and for all of your calibration frames.

'Tip: AIP4Win allows you to use a single bias value in the advanced calibration protocol. The Cookbook camera and several commercial CCD models make drift subtraction an option in their image acquisition software.

6.2.1.3 When to Make a Master Bias Frame

To calibrate a scientific-grade CCD camera with a 16-bit analog-to-digital converter, it is desirable to create a master bias frame by calculating the average of many bias frames (or, alternatively, by finding the median value of many bias frames). Assuming normal statistics, the readout noise and the unpatterned bias decrease with the square root of the number of frames averaged.

Consider a high-quality CCD with measured readout noise of five electrons r.m.s. and a conversion factor of one electron per ADU. The pixels in a single bias frame display a random variation of five ADUs about some central value. Averaging 50 bias frames will reduce statistical uncertainty in the bias to less than one ADU, thereby improving the quality of the calibration. In so sensitive a camera, a high-quality master bias frame will help define low-level bias patterns that may exist.

There are two basic methods of combining multiple bias frames: averaging and taking the median. If you operate your CCD in an electrically noisy environment, individual bias frames sometimes show large noise spikes. Averaging bias frames makes these abnormal events part of the master bias frame, whereas determining the median of the bias frames excludes the abnormal values, but does not reduce random noise as effectively. The bottom line is: use the median if you operate in an electrically noisy environment; use the average if you do not.

• Tip: To take bias frames, your CCD camera should be fully cooled and operating normally. Cap the telescope or close the camera's shutter. Set the integration time to the minimum allowed by the operating software, and then make at least as many bias frames as you make dark frames.

6.2.2 Dark Frames

The dark frame captures a sample of the dark current to be used in peeling away the dark-current layer from an image. During the integration time of a dark frame, no light is allowed to strike the CCD. Depending on the calibration protocol, the integration time is chosen to be equal to or greater than the integration time for the images to be calibrated. For amateur CCD cameras, taking good dark frames is the single most important step in the calibration process.

The dark frame contains the thermal electrons that accumulate during integration, of course, but it also contains thermal noise, a random variation in the number of thermal electrons that accumulate, plus all of the elements that make up a bias frame:

Recall that the factor 1/g converts the number of electrons to ADUs. The accumulation of thermal electrons is tdx y , the product of the dark current and the integration time. Thermal noise, oTE, is the random variation in the number of thermal electrons. It obeys a simple law that governs many random processes involving unlikely events over long intervals: the standard deviation in the number of thermal electrons is the square root of the number of electrons:

Figure 6.7 Above is an average of 16 dark frames with a 60-second integration time, displayed with black = 100 and white = 102. At this stretch, the dark frame clearly shows the underlying fixed-pattern bias. Pixels with high dark current, including a few scattered pixel values as high as 627, display as white.

Figure 6.7 Above is an average of 16 dark frames with a 60-second integration time, displayed with black = 100 and white = 102. At this stretch, the dark frame clearly shows the underlying fixed-pattern bias. Pixels with high dark current, including a few scattered pixel values as high as 627, display as white.

Other phenomena, such as the number of raindrops that fall on a patch of ground in a given interval, or the number of clicks from a Geiger counter in a given time, obey the same statistical law.

Consider an example: if the average rate at which thermal electrons accumulate is 100 electrons per second, then in one average second, 100 electrons will accumulate. However, in any particular 1-second interval, the number of electrons will be 100 ± 10 electrons. The "plus or minus" symbol means that 68% of the time, some number between 90 and 110 electrons will accumulate. This statistical property has important consequences for CCD imaging: it means that a dark frame is merely a sample of the dark current, not a precise measure.

6.2.2.1 "Image-Times-Five" Rule for Dark Frames

The purpose of taking dark frames is to determine the dark current accurately, so that you can peel away another layer of the "onion." To accomplish this, it is necessary to acquire a large sample of thermal electrons. To see why this is so, look at the numbers: for 100 electrons, the uncertainty is 10%. Take a bigger sample of 1,000 electrons and the uncertainty is 1000 ± 31.6, or 3%. Take an even bigger sample of 10,000 and the uncertainty drops to 1%. The goal in calibration is to create a dark frame that is sufficiently accurate that subtracting it from a raw image will not significantly increase the noise in the calibrated image.

Figure 6.8 Above you see the same dark frame shown in Figure 6.7, but displayed with black = 100 and white = 120. The dark frame is the sum of the bias plus the dark current, but the principal effect of the bias is to add an average of 100 ADUs to the dark current that accumulates during the 60-second integration.

Figure 6.8 Above you see the same dark frame shown in Figure 6.7, but displayed with black = 100 and white = 120. The dark frame is the sum of the bias plus the dark current, but the principal effect of the bias is to add an average of 100 ADUs to the dark current that accumulates during the 60-second integration.

This goal is met when the total integration time of the dark frames (whether the information is collected in a long integration or is the average of many short ones) is at least five times longer than the image integrations. This number is somewhat arbitrarily chosen because it reduces the noise contribution caused by dark subtraction to an addition of 10%, which is generally acceptable.

Here is the detailed thinking behind the "image-times-five" rule: suppose that a raw image accumulates some number of thermal electrons, tdx ,,. The thermal noise is

Jtd^y, or cTF. Single dark frames with T thermal electrons will also have noise oTE. When the images are subtracted, the total number of thermal electrons will be zero, but because noise adds in quadrature, the noise will be

a 41% increase in thermal noise in the dark-subtracted image over that in a raw image. However, if the dark-frame integration is increased from t to 51, so that 5 id thermal electrons accumulate, the thermal noise increases to

Figure 6.9 This is a scalable dark frame (thermal frame) displayed with black = 0 and white = 100. It is the average of ten dark frames of 300 seconds' integration each minus the average of 64 bias frames. Subtracting bias from a dark frame creates an image with pixel values proportional to the dark current.

Figure 6.9 This is a scalable dark frame (thermal frame) displayed with black = 0 and white = 100. It is the average of ten dark frames of 300 seconds' integration each minus the average of 64 bias frames. Subtracting bias from a dark frame creates an image with pixel values proportional to the dark current.

If we now divide the pixel values in the dark frame by 5, the amplitude of the thermal noise becomes

When the thermal electrons in the dark frame are subtracted from those in the raw image, the total noise becomes v°te + (0.447cte)2 = 1.095ote, an increase in thermal noise just under 10%, which is usually acceptable. Obviously, the longer the dark integration time, the less the noise added during calibration.

6.2.2.2 Thermal Frames

Dark frames cannot be scaled because they contain a bias offset in addition to the accumulation of thermal electrons. Imagine how nice it would be if you had a "thermal frame" consisting only of thermal electrons:

(IDEAL-THERMAL) x>, = ~{tdxy + aTE} . (Equ.6.10)

Was this article helpful?

0 0
Telescopes Mastery

Telescopes Mastery

Through this ebook, you are going to learn what you will need to know all about the telescopes that can provide a fun and rewarding hobby for you and your family!

Get My Free Ebook


Post a comment