The evidence of Bad Pixels in the Coldrick Observatory Coldrick ST-7E CCD Camera soon became apparent, following dark current Calibration.
Dark current follows a Poisson distribution. Therefore, since pixel counts received during dark current calibration are sufficiently large, the Poisson distribution from these measurements should theoretically take the form of a Gaussian-shaped distribution.
However, as can be seen from the histograms in Fig. 1 below, this evidently not the case.
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| Figure 1: Poisson distribution, for the Coldrick Observatory CCD Camera Dark Current. It can be seen that the distribution tails off to the right-hand side as opposed to following a (theoretically correct) Gaussian curve. This implies that there is an abundance of excessively "hot" pixels on the CCD camera, which are defined as "bad pixels". |
These curves deviate from a traditional Gaussian distribution due to the ’tail’ at the upper end of the distribution. This "tail" is as a result of excessively hot, or "bad" pixels. Bad pixels are defined as pixels which do not behave in the same manner as an average CCD pixel. This investigation focuses on three types of bad pixel:
1) Hot pixels: Hot pixels accumulate charge faster then the the average CCD pixel, producing pixel values significantly higher than an average CCD pixel.
2) Warm pixels: Warm pixels behave in the same way as hot pixels, however their charge accumulation is less dramatic and therefore the final pixel values are marginally higher than an average CCD pixel.
3) Cool pixels: Cool pixels behave in exactly the opposite way as warm pixels: the pixel values they produce are marginally lower than that of an average CCD pixel.
The effect of hot pixels causes the most dramatic effect on a CCD histogram pilot - therefore this was the first class of bad pixel which was investigated.
Fig. iteration depicts a 30 min dark frame with a log x & y axes to highlight a significant secondary peak in the distribution.
Note that this peak is not present in Fig. 9 due to the x-axis range.
The secondary peak present in Fig. iteration is as a result of hot pixels. The pixels contained within this peak give significantly greater pixel counts than the average pixel distribution in the frame, which constitutes the first peak in the figure. It was concluded that the pixels constituting the secondary peak
had to be corrected for in some way.
In order to do this, the co-ordinates of the hot pixels themselves had to be identified by IDL. To identify a ”hot” pixel a cut-off value had to be determined. The Rose criterion, named after Albert Rose states that a signal-to-noise ratio of 5 is necessary to identify an object with 100% certainty 16. It was therefore concluded that the standard deviation, of the primary peak would be identified and any pixels above a value 5 would be identified as ”hot” pixels. In order to perform this procedure, an iterative IDL program was written which used FIG. 10. 5 cut-off limit to eliminate hot pixels, which cause the
secondary peak in this plot.
an initial guess of the cut-off point and calculated the corresponding value to the left of this point. The output 5 value would then be used as the next cut-off assumption and so until the procedure converged at a constant cut-off value. The full IDL code for this procedure is given in Appendix C.
The above process is also known as ”sigma-filtering”. The filter chosen in this case is a 5 filter which is applied to the image. IDL can define the ”hot” pixels as arraywhere(array gt 5*). Once the coordinates of these hot pixels had been identified, a masking technique was able to be applied to account for their statistically anomalous values.
”Masking” implies generating a pixel mask which is an array of the same dimensions as the original array with values of 1 and 0. The co-ordinates of the hot pixels as identified by IDL dictate which pixels in the mask are given a value of ”0”.
Since the remaining ”good” pixels maintain a value of 1 in the mask, the mask is then able to be multiplied by the original image. This process is called ”masking” the original image. In this case, the original image is ”5 masked”, which simply sets the value of every identified hot pixel to 0, whilst leaving
every good pixel value unchanged. Fig. 11 demonstrates the resulting histogram after a 5 mask has been applied.
As can be seen in Fig. 11, a tail still exists on the histogram which distorts its shape away from a theoretical Gaussian distribution.
This smaller ’tail’ is a result of warm pixels; these are addressed further in section 3.1.2.
