Residual Dark Distribution (RDD)
Last update: 2000 July 16
1. What is RDD?
RDD (Residual Dark Distribution) was originally defined as
a distribution of the pixel levels calculated after the
DFE (Dark Frame Error) correction.
However, it may be simply regarded as the distribution of the
dark current (including a readout noise), because the DFE
correction does not change the RDD shape largely.
It is known that radiation damage increases the dark current of a ccd.
This means that excess charge is accumulated in a pixel even if it
gets neither X-ray photons nor charged particles.
However, such excess charge might not have any impact on the
X-ray data if it were same for all the pixels.
Such uniform charge will be subtracted in the course of
on-board data processing, because the amount of charge accumulated
in a pixel is measured from the local mean,
which is defined in 16x16 pixels in the case of ASCA.
However, increase of the dark current due to the radiation
damage is not uniform.
In fact, it varies largely from pixel to pixel.
Analysis of the frame mode data showed that most of pixels show
moderate increase of the dark current, but some show large increase.
Thus, the distribution of the dark current shows a tail toward
higher pulse height.
The distribution becomes gradually wider with the accumulation of
the radiation damage.
Because the distribution is remained even after the correction of
the DFE error in the ground data analysis, it is called residual
dark distribution (RDD).
Note that, when there is no dark current, RDD coincides the distribution
of the readout noise.
2. What determines RDD?
I list below the parameters on which RDD depends.
However, among the parameters, we ignore the position dependence and
light leak dependence of RDD in the SIS calibration.
Dependence on these parameters is small.
We ignore the temperature dependence of RDD in some degree.
When we model the RDD, we use data obtained when the CCD temperature
was close to the nominal value (-61.7°C).
However, current model of RDD does not reproduce
the temperature dependence.
This may introduce excess systematic error for 4 ccd mode data, which
have large dark current, but we believe that the systematic error
is not very large in most case.
- RDD depends on the elapsed time since the launch of
- Because RDD results from the dark current, it is a strong
function of the exposure time. But it is not proportional to the
- Because it takes about 4 sec to read an image data
from the ccd, the last-read pixel stays on the ccd about 4 sec longer
than the first-read pixel. This produce the position (V-address)
dependence of the dark current, i.e. RDD.
- Temperature of SIS ccds is usually controlled to -61.7°C,
but sometimes increases up to about -58°C. Because the dark current
depends on the ccd temperature, RDD also depends on the ccd temperature.
- Light leak
- Smoothly varying component (over the ccd position) of the
light leak is subtracted as a part of the dark frame during the on-board
processing and also by the DFE correction on ground. However, Poisson
fluctuation of the number of electrons due to the light leak
contributes to RDD.
3. Effects of RDD on the SIS Performance
RDD can affect the SIS performance in various way.
Some effects are very complicated and are not fully investigated yet.
I summarize below the effects briefly.
- Shift of zero in energy scale
- Definition of zero in energy scale (hereafter, zero level) is
very simple and straightforward when the dark current is negligible.
Readout noise has a gaussian distribution, and we can take the center
of the gaussian distribution as zero. However, when the RDD becomes
significant, the distribution shows a tail toward higher pulse height.
This means that we need to define the zero level appropriately.
We have introduced three definitions of zero level: (1) peak,
(2) truncated mean, and (3) mean. "Peak" is for backward compatibility.
"Truncated mean" is used for the analysis of the bright mode data,
and "mean" is for the faint mode data.
These definitions are shown in the above figure schematically.
- Line profile
- When the RDD effect is negligible (i.e. RDD is well
approximated by a gaussian), a line for monochromatic X-ray has a
profile approximated by two gaussians, i.e. main peak and sub peak.
(There are several other features, such as constant component,
escape, and fluorescence lines, which are not discussed here.)
The line center energy is defined as the center of the main gaussian.
When the RDD effect become significant, the two gaussians need to be
replaced with the RDD profile. This is schematically explained in
the right-hand-side figure. When the RDD effect is moderate,
the line profile becomes almost symmetric. The line profile tends
to have a hard tail, when the RDD effect become strong.
"Mean" of the main RDD profile is taken as the center of the line.
- Degradation of the energy resolution
- As explained above, RDD makes the line profile broad. This
causes the degradation of the energy resolution. Because this is
equivalent to larger readout noise, the effect is most significant in
the lower energy bands.
- Loss of the detection efficiency
- RDD can change the grade branching ratio, which results in
the loss of the detection efficiency. ASCA SIS uses a grade to
distinguish X-ray events from the particle events. Basically,
single-pixel events and two-pixel events (grade 0234) are regarded as
X-ray events, while others (3 or more pixel events) are discarded as
particle events. RDD changes the grade branching ratio. RDD makes
the zero distribution wider and asymmetric; zero distribution tends to
have a tail toward higher pulse height. This makes the probability
higher for a pixel to exceed the split threshold (40 adu in most cases).
This means that a single-pixel event tends to become a two-pixel
event, and a two-pixel event to a 3-pixel event, and so on, under the
effect of RDD. Once the grade becomes larger than 4, it will be discarded
as a particle event. This leads the reduction of the detection efficiency.
As expected from the explanation above, loss of the detection
efficiency due to RDD is basically energy independent.
Among these effects, loss of the detection efficiency may be reduced
if we use higher split threshold. But we did not adopt this method,
because, once the split threshold is changed, we need to re-calibrate
the ccd almost completely. Split threshold affect the line profile,
energy resolution, grade branching ratio, and quantum detection
efficiency. Because it is practically impossible to redo all these
calibration, we decided not to change the split threshold.
4. Decrease of the detection efficiency: Simulation based on 3C273
To estimate the decrease of the detection efficiency, we performed
a Monte-Carlo simulation. The method of simulation is described
- Take the real 3C273 data obtained in 1 ccd faint mode
- Add random excess dark current which obey RDD to each pixel.
We assumed RDD of 1/2/4 ccd mode expected on 1999/1/1.
- Calculate the energy spectrum from the RDD added
event data following the standard data analysis method.
- Compare the energy spectra thus obtained with the
original one for 1 ccd faint mode on 1993/12/20.
The RDD parameters we used are those expected on 1999/1/1 and have
the following values:
RDD parameters used for the simulation
|| 1 ccd
|| 2 ccd
|| 4 ccd
|| 1 ccd
|| 2 ccd
|| 4 ccd
Results of the simulation are shown in the graphs below.
Because of the degradation of the energy resolution due to RDD,
the detection efficiency varies rapidly around 2 keV and 0.5 keV.
Except for these energy ranges, the reduction of the detection
efficiency is almost energy independent.
- Sensor-0, Chip-1, 1 ccd mode
- Sensor-0, Chip-1, 2 ccd mode
- Sensor-0, Chip-1, 4 ccd mode
- Sensor-1, Chip-3, 1 ccd mode
- Sensor-1, Chip-3, 2 ccd mode
- Sensor-1, Chip-3, 4 ccd mode
Detection efficiency obtained from the simulation may be tabulated
as follows. Reduction of the efficiency is slightly energy dependent,
which is ignored in the table below.
Relative detection efficiency as of 1999/1/1 compared
to the 1 ccd mode data on 1993/12/20
|| 1 ccd mode
|| 2 ccd mode
|| 4 ccd mode
5. Decrease of the detection efficiency: Observed data
To check the long-term change of the detection efficiency in the real
ASCA data, we need to use observations of stable X-ray sources.
Rotation powered pulsars and their synchrotron nebula, like the Crab, are
the best. However, the Crab is too bright for SIS, and other sources,
such as 3C58 and PSR0540-69, were not observed with enough intervals.
Next best targets may be SNRs of small diameter (small enough to fit in
the SIS fov). However, unfortunately, most of the SNRs are located on the
galactic plane and suffer from large absorption. This is not good to see
the long-term change of the lower energy part. In spite of this problem,
we used SNRs to see the effects of RDD on the detection efficiencies,
because there is no other choice.
Comparison of the energy spectra of the SNR observed twice
with long interval is shown below.
- G11.2-0.3, 1994/4/10 and 1998/3/30, 1 ccd mode,
Angular size of about 4 arcmin. Energy spectra are
calculated by integrating whole chip.
Please ignore the energy bin at 0.4 keV, because the
event threshold is included in the energy bin.
So far, only 1 ccd mode data have been analyzed. The results are
basically consistent with the simulation. No change of the detection
efficiency is seen in 1 ccd mode data. Although there is a hint of the
slight decrease of detection efficiency in SIS-1 data (especially lower
energy part), we need more analysis to confirm whether or not this result
is really due to the RDD.