In June 1995, Willmann-Bell released an upgrade package for the Cookbook CCD cameras with new software (211PLUS and 245PLUS) plus directions for improving the performance of the Cookbook CCD cameras (adding Low-Dark-Current mode, etc.) with fairly simple hardware modifications. This article explores the implications of two changes -- LDC mode and Drift Subtract -- and shows you how they help you make better and more efficient use of your Cookbook camera.
Of course, 211PLUS and 245PLUS have a lot more to offer. Some features of the new software simply make life easier. The camera configuration is stored in a file. Display mode shows an on-screen histogram. The new input routine means you are more likely to enter data correctly. However, Low Dark Current mode and Drift Subtract are by far the most important. Together, these changes make the Cookbook CCD cameras significantly more sensitive.
Low-Dark-Current mode changes the electrical bias on the CCD during integration, dramatically lowering the average dark-current. However, the average does not tell the whole story. There are at least three different groups of pixels and they behave differently. In the largest group of pixels, those we'll call group 1 pixels, the dark current drops by a factor of about 30. The reduction in dark current adds at least one magnitude to the lower limit of the Cookbook CCD camera, and makes the higher resolution of 378-wide mode preferable to any of the 252-wide modes.
But other groups of pixels behave differently. The cross-histogram is particularly valuable for exploring the effect of LDC mode on the dark current. The cross-histogram shown here was made from two dark frames taken in 378-wide mode, with 10-minute integrations. One of the images has LDC turned OFF and the other has LDC turned ON. The cross histogram is a graph of pixel value versus pixel value for the same pixel in each of two different images. The cross-histogram shows how each of the 91,476 pixels behaves under two different conditions.
If dark current of each pixel simply fell by a constant factor when LDC was ON, then the cross-histogram would show a straight line with a slope was equal to that factor. Instead, the graph shows that the overwhelming majority of the pixels drop from 1,800 PV to a value between 100 and 250 PV. (Since the images have a zero-point bias of 100 PV, the actual dark current values are 1,700 and 0 to 150, respectively.) When group 1 pixels drop from 1,700 PV to ~60 PV, the dark-current reduction is a factor of 30.
A second group of pixels -- group 2 pixels -- extends along the horizontal axis: these are pixels that were "hot" with LDC OFF but are "cool" with LDC ON. In longer integrations with LDC OFF, this population appears to saturate at 3,970 PV.
Yet another group of pixels occupies a comet-like tail that rises from 300 to 1,950 PV; this small population of pixels were originally "hot" and although their intensity is reduced, they have remained relatively "hot" even with LDC turned ON. These are the group 3 pixels. This tail reaches a ceiling at 1,950 PV because the changed bias conditions on the chip reduce the well depth of the CCD. The highest 20 or so pixels in this group are saturated and bloom with longer integration times.
In summary, then, group 1 pixels are normal pixels in which the dark current drops by a factor of 30 when LDC is turned ON. Group 1 pixels account for the overwhelming majority of pixels in the image. Group 2 is composed of hot pixels that become normal when LDC is turned ON. Group 3 pixels are troublemakers: they are hot pixels that remain hot even with LDC turned ON.
The drastic reduction in the dark current suggests that much longer integrations are possible with LDC turned ON, but there is a price to pay. Because the well-capacity of the photosites is less with LDC turned ON, group 3 pixels begin to bloom when integrations exceed 20 minutes. In an integration time of 10,000 seconds, some of the blooming trails grow to five or six pixels long. Because the trails vary in length from one integration to the next, when a long-integration dark frame is subtracted from a long-integration raw image, streaks generated by blooming trails that did not subtract properly remain in the image. There are usually a few dozen, and they can be edited out. That's the bad news.
The good news is that with integration times of 10 minutes, Cookbook LDC cameras appear to work perfectly. If you shoot 100 dark frames of 600 seconds each and compare each of these dark frames to the average of all 100 dark frames, the dark-frame pixel values match up. This means that images made with 10-minute integrations will be streak-free. In view of the tracking performance of most telescopes, however, integration times under 10 minutes place no restraints on most Cookbook CCD camera users.
The reduced well capacity of the CCD with LDC turned ON creates another more subtle problem. Because the pixel values in flat-field frames approach the LDC ON saturation level of 1,900, group 3 pixels may bloom. This produces artifacts that look like little rivets in the flat-field. To avoid this effect, set LDC to OFF when you shoot flats and flat darks.
Preliminary testing shows that flats made with LDC turned OFF are valid for flat-fielding images taken with LDC turned ON. However, the possibility remains remains that flats made with LDC turned OFF may not map CCD variations at the single-pixel level if changing the bias on the CCD also changes the sensitivity of the pixel. These flats, however, faithfully map variations in the light intensity on the CCD, so they have considerable value. Considering that flat fields with rivet-like artifacts are totally useless, shooting your flats and flat-darks with LDC turned OFF appears to be the best strategy.
Every Cookbook builder has noticed that the Ref and Reset values drift during a night of observation. When the air temperature is constant, the Ref and Reset values jump around a bit, but they are stable over, say, an hour or maybe two. Extend this three or four hours, however, and Ref and Reset drift. The drift occurs because the voltage drop across transistor Q7 varies with temperature. Just what does this mean for the observer?
Ref measures the voltage output of the amplifier when the detector node is switched to an internal reference source on the CCD. Turning potentiometer P1 allows you to set to Ref so there is no danger it will drift below zero; the Cookbook specifcally recommends setting Ref to 50 to 100 PV, an small arbitary distance above zero.
Reset measures the voltage left in the charge detection node of the CCD when it is fully discharged, the zero-point of the CCD's output. It's what you get in the absence of dark current and any signal due to light. In an ideal CCD, the Reset value would be zero, but in the real world, the Reset is offset from zero. You can make an image of the bias from the CCD -- a bias frame -- just shoot a dark frame with an integration time of 1 millisecond. The pixels in the bias frame have pixel values equal to the Reset level plus a bit of random noise plus a small amount of dark current that accumulates during the CCD readout.
Since the Cookbook recommends that the Ref value be set to about 75, the Reset value is usually somewhere between 500 to 800. However, the only time the acquisition software uses the Ref value is in 252-wide double sample mode, when the software measures the Ref, then measures the CCD output, and then subtracts Ref from the CCD output. Double sampling removes common-mode signals such as 60Hz line noise that you get with poor grounding.
However, because experience with hundreds of Cookbook CCD cameras has shown that common-mode noise is rare, we have changed this recommendation. For all exposure modes except 252-wide double sample mode, set Reset to a value around 100. This pegs the Ref value at zero so double sample mode will not work, but it places your images in a range from 100 to 4095 instead of 650 to 4095.
(To fully capitalize on this, however, you must also increase the value of the amplifier feedback resistor R43 from 39k-ohms to 51k-ohms, 68k-ohms, or 82k-ohms, the next standard resistor values. This increases the gain from the nominal 17.7 to 23, 31, or 37, raising the saturation level of the pixels when LDC is ON from whatever it was originally to a new value larger than 4,095. Make this change only after you have determined the actual saturation level in your LDC-modified Cookbook CCD camera.)
In an ideal universe, the Ref and Reset values would be constant. You
would shoot images and dark frames and the following relationships would
be true for each pixel in the image:
RawImage = Light + Thermal + Bias
DarkFrame = Thermal + Bias
Therefore, when you calibrate:
Image = Light
Now consider what happens when you actually make images. You shoot some
images now and shoot some dark frames a couple hours later. During the
interval, the Reset level drifts a bit. Here's is what happens for each
pixel in the image:
RawImage = Light + Thermal + Bias1
DarkFrame = Thermal + Bias2
In the interval between taking the images, Reset has drifted and Bias1 has become Bias2. When you calibrate:
Image = Light + Bias1 - Bias2
Gadzooks! The PV for the light now has a bias equal to the difference between the bias levels in the two frames. If the Reset drifted down, everything still works: when you subtract the dark frame, the difference is positive and all the PVs in the image are slightly too high. No big deal -- except that zero PV no longer represents zero light.
If the Reset has drifted down, it's trouble. The difference is negative, so PVs are set to zero if the software truncates negative pixel values. Your sky background might go black, and the faintest parts of your image go to zero with it. With good technique and by taking lots of dark frames, you can keep the difference between Bias1 and Bias2 small. It remains a concern, however, because sooner or later you will take some potentially great images and neglect to shoot a good set of dark frames.
(All is not lost when this happens. Iinstead of the subtract command, use the merge command in CB245; this allows you to add a constant when you compute the algebraic sum of the frames.)
Drift subtraction eliminates this concern. When you shoot an image with
Drift Subtract ON, 245PLUS measures the bias level of the image, automatically
subtracts it from every pixel, and adds a constant of 100 PV. (The constant
prevents loss of information to negative pixel values.) The equation for
each pixel is:
RwImage = Light + Thermal + Bias1 - Bias1 + 100
DarkFrame = Thermal + Bias2 - Bias2 + 100
Thus when you subtract the dark frame:
Image = Light + Thermal + Bias1 - Bias1 +100
-(Thermal + Bias2 - Bias2 + 100
Image = Light
Drift subtraction therefore allows you to shoot "ideal" images -- linear images for which the zero point is known precisely -- in a non-ideal world. This has two important consequences: dark frames can be scaled for different integration times and dark-subtracted images become linear records of the light detected by the CCD, allowing exact flat-fielding of images.
In the following sections, we will examine why each of these properties is important.
Why the fuss about scalable dark frames? Well, since the drift in Reset no longer matters, you can shoot dark frames at any convenient time of the night and use them for images taken at any time during the night. This produces a huge improvement in observing efficiency
It also means that you can use dark frames taken a few nights ago for
images taken tonight. And because you also know the true zero point for
each PV in a dark frame, you can multiply the pixel values in a dark frame
by a scaling coefficient, coeff, to calibrate an image taken with a different
integration time or at a (slightly) different temperature:
ScaledDark = (coeff x (Thermal - 100)) + 100
An important caviat is that over long spans of time and over large differences in temperature, dark frames do not scale. The only quibble is how long is "long" and how large is "large". Although dark frames taken a few days apart usually appear identical, those taken a month or two apart may show changes in the group 3 hot pixels. It is a good policy to shoot some number (for example, 10) dark frames at the beginning and at the end of each observing session, and to average these to produce a scalable master dark frame for each night.
It also is good policy to ensure that the scaling coefficient is equal to or smaller than unity; that is, make the dark integration the same or longer than the image integrations. It is okay to scale a 60-second dark for use with a 15-second image (that is, coeff = 0.25) but not the other way around.
Using Drift Subtract preserves the linearity of dark-subtracted images; this is important because unless the pixel values in the dark-subtracted images are proportional to the amount of light from the sky, flat fielding will not work properly (nor will photometry or any other process that relies on the linearity of the image).
Consider an example: you take images with vignetting such that only 90% as much light from the sky reaches the left side of the frame; that is, when the sky at the frame center is 50 PV, the sky in the left side of the image is 45 PV. If a dark frame is taken with Drift Subtract OFF, and during the interval between image and dark the bias drifts upward 20 PV, then after dark subtraction, the image center is 70 PV and the left side is 65 PV.
When you flat-field the image, the center of the frame remains at 70 PV and the left side becomes 65/0.90, or a pixel value of 72 rather than the value that it should have, which is 70 PV. As a result of the drift in the Reset value, the left is edge of the image appears too bright.
Similar difficulties occur when scattered light contaminate the image; for example, a uniform field flooding of 20 PV produces the same effect as a Reset drift of 20 PV. To get images with uniform backgrounds, set Drift Subtract to ON and make sure that your images are free of scattered light.
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