Hot pixel


The individual pixels of a CCD chips have some different characteristics. Not only can you have different light sensitivities (which by flats can be corrected), but also the various dark current. Dark current is defined as the creation of thermal electrons (measured in ADU / s) that are formed without any incidence of photons, so in the dark. These electrons formation is strongly temperature dependent: By cooling the CCD dark current is minimized.

However the CCD includes isolated pixels, which produce compared to the average of the whole chip significantly increased dark current. These pixels are called hot pixels.

To remove the dark current of individual pixels from different spectrums shots, you basically create dark images, where no light can fall on the CCD. Possible number of such "darks", with the same exposure time and CCD temperature as the spectra images are then averaged (formation of an average or better-mostly the median of the darks). Then this "Masterdark" is subtracted of all spectra recorded before they are processed further.That way it is eliminated the excess intensity of the hot pixels and we have the dark corrected spectra frames.

This method has the disadvantage that each recording of spectra of each exposure time series (and CCD temperature) has a corresponding dark series, which takes a lot of time. To avoid this, it is also possible to scale a masterdark too. This refers to the conversion to other exposure times. This is achieved in the following manner:

Man macht eine möglichst große Serie von Darks bei der längsten Belichtungszeit, die man normalerweise verwendet. Jedes dieser Darks wird vom Bias befreit (Masterbias = Median von kurzzeitig belichteten Darks, die wegen der kurzen Belichtungszeit <1 s keinen Dunkelstrom enthalten). Übrig bleibt der reine Dunkelstrom der Darkaufnahmen. Diese Dunkelstromaufnahmen werden wieder gemittelt (Median) und man erhält das Masterdunkelstrom-Image für die gewählte Belichtungszeit (und CCD-Temperatur). Dieses kann dann auf andere Belichtungszeiten umgerechnet ("skaliert") werden. Wurde beispielsweise das Masterdunkelstrom-Image aus 20 min belichteten Dunkelaufnahmen gewonnen, dann können Spektrenaufnahmen, die nur 10 min belichtet wurden, folgendermaßen darkkorrigiert werden:

You make a great number of darks at the longest exposure time, which is normally used. Each of these darks will be freed from the bias (median = Masterbias made of briefly exposed darks, because of the short exposure time <1 s contain no dark current). That leaves the pure darkcurrent . This darkcurrents be averaged (median) and we obtain the masterdarkcurrent image for the selected shutter speed (and CCD) temperature. This can then be converted to other exposure times ("scaled"). For example, if winning the mastedarkcurrent from 20 min exposed darks, then spectra recorded were exposed to only 10 min be darkcorected as follows:

corrigated [10min-exposure] = [10min-exposure] - [Masterbias] - (10/20)*[masterdarkcurrent]

The scaling method assumes, however, that develop into the dark current of each pixel linearly with the exposure time, this is therefore considered first time. Such a test I conducted with my Sigma 1603ME CCD at a temperature of -20 C as follows. Inclusion of 10 bias (0.5 s), darks of 5 min, 10 min and 20 min. Calculation of the medians of the 10 pictures series. Examination of the median image.

The graph shows the mean pixel intensity of the median and the mean of the darks, depending on the exposure time. Both rise only slightly above the value of the bias (0.5 s) exposure time. The mean dark current seems to be quite low over the first 20 min exposure time.



Nachfolgend wurden jeweils 3 Pixel mit etwa gleicher Dunkelstromrate ausgewählt und hinsichtlich des Zusammenhangs zwischen ADU und Belichtungszeit ausgewertet.

Here are the histograms of the four medians (0, 5, 10 and 20 min exposure time) are shown from left to right in a double logarithmic plot. In the long-exposure photographs, many pixels exist, which are significantly higher than 2000 ADU. For example, in the 20-min median show 222 pixels > 3000 ADU intensity.

Below are each 3 pixels selected with approximately the same rate of dark current and evaluated regarding the relationship between ADU and exposure time.

Hier sind die Zeitkurven der Intensität dreier Pixel dargestellt, die nur wenig Dunkelstrom produzieren. Ihre Dunkelstromrate ist etwa linear mit der Belichtungszeit.

Here the intensity curves are shown of three pixels, which produce only a little dark current. Their rate of dark current production is approximately linearly with the exposure time, but with different slopes.

Here are 3 pixels are shown, have developed in the 20 min exposure time, an intensity of about 9000 ADU. Also, they are linear in the exposure time.

3 pixels with an intensity of about 20000 ADU: One behaves linearly, a second shows the influence of higher terms, the third behaves as if it were saturated with 22000 ADU.
Pixels that have developed 30,000 ADU in 20 minutes, are obviously not linearly dependent on time but exhibit polynomial terms.
The 3 randomly selected pixels with intensities around 50,000 ADU are significantly non-linear.
These evaluations show that many hot pixels, especially the hottest, do not develop their dark current linearly with time. So they can not be represented by linear scaling of darks ! The behavior of each individual CCD chip must be separately verified before scaling of dark currents.

















































































































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