Dithering is a technique that consists of slightly moving the telescope between exposures to reduce some types of CCD sensor noise such as pattern noise, hot and cold pixels. The benefits were discussed previously.
A relatively standard method of dithering, practiced by nearly all programs that offer this capability, is to move the telescope by an amount determined by a random number generator. While this is an easy and straightforward approach, it leads to a kind of statistical clumping, in spite of using a random number generator. An example of this phenomenon can be demonstrated by tossing a coin 10 times. Probability statistics say that there is a 50-50 chance of either heads or tails. More often than not, you will get more of one than another. This is because the statistic is true only for an infinite number of trials. Since we use a non-infinite number of sub-exposures, we can expect to be impacted by the same clumping if we depend on a random number alone. By using a newly developed proprietary algorithm, it is possible to eliminate this clumping and insure a more uniform spacing of dithered locations.
Fig. 1: Random Number Generated Fig. 2: Algorithm Generated
Figure 1 shows a dither pattern generated by a random number generator, even with a randomized seed. Note that the distribution of points is not very uniform. Indeed, there are some points that could result in sensor noise not being eliminated but in fact being reinforced due to insufficient difference in positions.
Figure 2 shows the dither pattern that results from the use of this algorithm. It achieves maximize separation from one frame to another with a minimum overall movement of the guide star.
This algorithm is incorporated in CCDAutoPilot2, version 2.06 and later.
Choosing a Dither Factor
With most other dithering programs, there is no way to predict to proper setting of the maximum dither movement. This is due to the statistical clumping discussed above. CCDAutoPilot2 version 2.06 solves this problem.
In CCDAutoPilot2, there is a slider to set the maximum movement that is adjustable from 0 to 10 in arc-sec. for unguided imaging and 0 to 10 in guider pixels for guided imaging. In order to set the maximum movement most effectively, you need to know some values:
G = Guider image scale in arc-sec./pixel (asp)
I = Imager image scale in arc-sec./pixel (asp)
A good starting point is to dither at least 4 pixels on the imager. Even though a hot pixel is only one pixel, currently available alignment and combining techniques will smear out that hot pixel over as many as 4 pixels. In order to effectively eliminate the hot pixel, the dither must at least be that much.
Unguided Example: Assume you are taking LRGB images with the RGB binned at 2x2 and your unbinned image scale, I, is 0.5 asp. Your 2x2 binned sub-exposures will be 1 asp. Therefore, you should set your maximum dither at 5 arc-sec., when using version 2.06.
Guided example: Now, let's assume you are using an ST10XME with a built-in TC-237 autoguider. In the above example, assume the ST10's 6.8 micron pixel correspond to 0.5 asp. The guider's image scale can be calculated by:
G = I * Guider pixel size/Imager pixel size = 0.5 * 7.4 / 6.8 = .54 asp
Most bin the guider at 2x2 so the equivalent image scale is 1.08 asp. Again using current align and combine techniques, you want to move at least 5 pixels on the imager. For 2x2 binned pixels, you need to move the telescope 5 arc-sec. So, the number of pixels you need to move the guider is given by:
Movement = 5 * (Imager binning * I) / (guider binning * G)
Assuming the above image scales, your guider is binned at 2x2 and you are taking binned color images, then your movement should be set at:
Movement = 5 * ( 2 * 0.5) / (2 * 0.54) = 4.63. So use a dither of 5 here as well.
Now, assume you are taking a run that consists solely of unbinned sub-exposures. Then your movement should be set at:
Movement = 5 * (0.5) / (2 * 0.54) = 2.32. Here, a dither of 3 could be used.
Since you will be moving the guider for dithering, you need to allow time for your guider to achieve the center position. This is accomplished by an appropriate guider delay setting, Light Exposure Delay Factor in CCDAutoPilot2. The delay depends on a number of factors including your aggressiveness factors. When dithering is enabled in CCDAutoPilot2, the first sub-exposure is undithered and the second and third are dithered to the maximum move specified. So as a test, run a series of three 5-second exposures and watch the guider error in your camera control program. Adjust the Light Exposure Delay Factor so that your guider has enough time to recover to the error you will allow. Then you can run your desired run with an appropriately set delay.
For unguided dithering, it may we worth allowing a second of two for the mount to settle.
This recent innovation in CCDAutoPilot2 allows more predictive dithering and better sensor artifact rejection.