WT5L Blog

In any astronomical image there are three noise regimes that figure into the image’s signal-to-noise ratio (SNR). These regimes are the uncertainty associated with the signal itself (shot noise), the uncertainty associated with the readout electronics of the camera (read noise), and the uncertainty associated with the dark current that builds up within the sensor due to thermal effects (dark noise). All CCDs experience a certain amount of dark current during an exposure. Dark current is expressed as electrons per second per pixel and these electrons add to the electrons that build up in pixel wells as a result of exposure to the light from astronomical objects (stars, planets, galaxies, etc.). Dark current can be reduced by cooling the sensor and this is why astronomical CCD cameras usually have an ability to be cooled.

As an example, the Kodak sensor in the SBIG ST-8 camera specifies a dark current of 1 electron per second per pixel at a sensor temperature of 0.0^o Celsius. This means that over the course of a ten-minute exposure, each pixel will accumulate approximately 600 extra electrons over and above that provided by the light from the object being imaged. The specifications for the ST-8 sensor also say that the dark current doubling temperature is 6.3^o Celsius. This means that if the sensor is cooled to -6.3^o Celsius the dark current will then be 0.5 electrons per second per pixel and for each additional cooling by 6.3^o Celsius, the dark current will be cut in half again.

To combat dark current, calibration dark frames are created by taking an exposure of the same length of time and at the same sensor temperature as the light frame but with the shutter closed. This dark frame records only the dark current that builds up over the course of the exposure for each pixel. The dark frame can then be subtracted pixel-by-pixel from the light frame to completely remove the dark current effects from the light frame. However, this subtraction operation is not without consequences because by performing the subtraction, extra noise is injected into the light frame. This noise can be mitigated by taking multiple dark frames and combining them into one “master dark”. The usual way to create the master is to find the average or median value for each pixel across all dark frames. As more dark frames are added, the noise contribution to the light image becomes less. The question becomes: How many dark frames is enough?

In an effort to figure out how many dark frames is enough, I captured 100 dark frames (600 second exposure @ -20^o Celsius) and combined different number of dark frames into master dark frames. For each master dark frame, I measured the noise in the frame by finding the Standard Deviation of a small patch of the frame not affected by hot pixels. The table below summarizes the results of this effort:

¹ Method “Clip Min/Max Mean” first removes or “clips” the specified number of max values and min values then calculates the mean of all the remaining values for each pixel in the image.

The graph of the Standard Deviation versus the number of dark frames combined is shown below.

Summary: As is apparent from the table and the graph, the point of diminishing returns in reached somewhere around the area where 40 dark frames is reached. At this point, the master dark frame has a Standard Deviation of around 1.65 ADU or about 4.3 electrons (assuming a gain of 2.6 electrons per ADU). Since the dark current noise is very much less than the read noise (20 electrons), 40 dark frames seems sufficient.