In-flight monitoring of the Random Telegraph Signal behavior

Introduction

The detectors employed in OMI are two charge coupled devices (CCD), one for the ultra-violet (UV) and one for the visual (VIS) wavelength range respectively. These detectors are so-called frame transfer CCD’s because they contain two sections each. One section is used to detect the incoming signal and is referred to as the image section. After illuminating the image section for a certain pixel exposure time the acquired charge is clocked into the other section referred to as the storage section. This information is onwards clocked out through the read out register (ROR) and converted into a digital signal by the analogue to digital converter (ADC). It is an established fact that the CCD pixels are slowly degrading since launch. The degradation is due to radiation damage to the detector material due to the impact of charged particles encountered in the space environment. A typical result of this degradation is that pixels can suffer from quickly changing dark current also known as RTS. These pixels have to be identified because they can not be corrected for this effect and can lead to errors in the level 1b data and the derived level 2 products. The flagging of RTS pixels has to be done dynamically because an increasing number of pixels will develop RTS behaviour during the mission. The approach chosen for OMI detects RTS pixels on a daily basis, based on the analysis of dark current data over a certain time span. The algorithm runs in the Trend Monitoring and Calibration Facility (TMCF) as a Product Generation Executive (PGE). The output of the PGE will be used by the OPF manipulator to update the RTS warning flag in the dead and bad pixel map for the time dependent OPF.

Dark Current

The dark current of the OMI CCD detectors is caused by (thermal) electrons moving into the conduction band under influence of the electrical field due to the applied bias voltage. This dark current causes a background signal that is linearly proportional to the exposure time, and which is added to the observed signal due to detected photons. This dark current background signal has to be subtracted from the measurement to yield the true observed signal. Because the dark current scales with the exposure time it can be measured by subtracting two non-illuminated measurements that have been taken with different pixel exposure times. Dividing this difference by the difference in exposure time yields the dark current of the pixel in electrons per second. The nominal dark current of the OMI instrument is very low, it amounts to approximately 50 electrons per second for the UV channel, and 90 electrons per second for the VIS channel.

Random Telegraph Signal

Random Telegraph Signal (RTS) is a detector specific effect in which the dark current of the detector device randomly changes between two or more discrete levels; the distance between these levels can easily exceed the device’s intrinsic noise. The time scale of these changes varies between seconds to days; discrete changes with very short intervals will result in enhanced noise, while changes on long intervals will look like jumps in the background signal. RTS behaviour is associated with lattice damage to the detector material. This damage is due to singular radiation events from energetic charged particles encountered in space. RTS behaviour due to radiation damage is permanent feature, even though some mild annealing is expected. This means that a pixel that has been damaged will continue to show degraded performance. Moreover, consecutive particle hits will further degrade the performance and aggravate the RTS behaviour, leading to either more discrete levels, shorter time scales between jumps, higher maximum dark current levels, or any combination of these effects.

Moments of a distribution

The OMI method is based on the calculation of the so-called moments of the distribution function of a time series of dark current measurements. The moments of a distribution are the sums of integer powers of the values. Best known is the first moment, which gives an estimate of the central value of the distribution; commonly, the mean is taken for this purpose. The spread around the central value is described by the second moment, the variance. The third moment describes the amount of asymmetry of the distribution around its central value. Negative values of this so-called skewness indicate distributions with an asymmetrical tail extending to the lower values, while positive values indicate asymmetrical tails extending to higher values of the distribution. The fourth moment is known as the kurtosis of the distribution and describes the amount of flatness or peakedness of the distribution function. This definition is chosen to be relative to a normal Gaussian distribution function.

Robust estimators

As mentioned in the previous section, moments give an estimate of the certain properties of a distribution function. These estimates however all depend heavily on the specific distribution function for which commonly the normal distribution or Gaussian distribution is assumed. Real-life problems often show behaviour which is not well described with Gaussian statistics, due to the relatively large number of outliers in the measured distribution. These will strongly affect the moments of the distribution, yielding wrong estimates for its values. Therefore more robust estimators are needed. A very good estimator of the central value of a distribution which contains many outliers is the median. The median is defined as the value of the distribution such that there are an equal number of measurements above and below the central value. For a sorted data set, the median is thus the middle value. This median is highly insensitive to outliers and therefore a very good measure of the central tendency of real-life data sets. A robust estimation of the spread around the central value is the so-called mean absolute deviation which is significantly less sensitive to outliers than the standard deviation.

Detection of RTS behaviour

A time series of dark current measurements can be readily characterized by calculation of its moments and the observed to expected noise ratio. The moments and noise are thus parameters that describe the underlying distribution function in a condensed manner. Now the task remains to use the parameters to distinguish between pixels that have RTS and those that have not. This is not straight-forward for two reasons. Firstly, a pixel can have enhanced dark current due to radiation damage, i.e., a so-called dark current spike, and not show RTS. If the time series includes this jump, its distribution function will be highly asymmetrical which suggest strong RTS, while it has not. Secondly, RTS may present itself as increased noise. There is no unambiguous definition as to how much noise a pixel may have; this depends heavily on the required precision dictated by the specific application. In this case the specific applications are the level 2 data processing algorithms, which all have different requirements as it comes to signal to noise ratio (SNR).

RTS levels

The issue concerning the different levels of RTS behaviour that is acceptable by level 2 data reduction algorithms cannot be solved. However, by variation of the thresholds used in the RTS detection function, different RTS maps can be created that are either more stringent or more relaxed as it comes to allow a certain amount of RTS. The current approach is to create 8 different RTS maps that are increasingly stringent in their RTS flagging. These 8 maps are coded in a single byte per pixel; the least significant bit (LSB) allows more RTS than the most significant bit (MSB). The task to select the appropriate mask for each application now remains with the level 2 data reduction algorithm developers.

Examples of RTS pixels

The RTS masks are determined per channel and section, and for each level. The effectiveness of the algorithm is demonstrated by showing the dark current time series over the measured period as a function of orbit number. Because many pixels are flagged, we only display the time series for eight pixels that have been randomly picked. The figure display RTS pixels with level 1. This level flags the least number of pixels, thus only the worst RTS pixels are flagged. As can be seen from the figures many pixels show multiple dark current levels, and jumps at irregular intervals. In all cases the jumps exceed the intrinsic noise many times.

RTS evolution in the UV Image section for all levels

RTS evolution in the UV Storage section for all levels

RTS evolution in the VIS Image section for all levels

RTS evolution in the VIS Storage section for all levels

Conclusion

The graphs indicate that approximately 20 % of the individual pixels have a certain amount of RTS after 5 years or 30.000 orbits. Both the UV and VIS channel show approximately the same behavior, as well as the image and storage section.

For more information contact Quintus Kleipool or Marcel Dobber

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In-flight monitoring of the Random Telegraph Signal behavior

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