CCD dark calibration (cont'd) : 2018 -- 2019

21-Jan-2020 : initial version.
4-Feb-2020 : added horizontal profiles.
21-Feb-2020 : added horizontal CTE.
23-Apr-2021 : added a coronal image with CTI effect.

link to the 2017 data analysis page.
link to the CCD basics page.

Summary of the Analysis (2017-2019)

To evaluate the degree of the CCD degradation over 10 years of operation, the calibration images were obtained in a few CCD bakeout operations in 2017-2019, and analyzed with the support of R. Kano at NAOJ. The main results are as follows.

Although some signs of degradation is observed after 10+ years of operation, they are not at a significant level and XRT's CCD is working OK. The degradation is of this level is not surprising.
As reported well in recent years, the current dark images show the patterns which were not existed in 2007 (white blob + horizontal extension, on which the dark current is ~10% higher).
The dark current accumulated during the period of charge transfer (8 sec for the full CCD area) at 30C was 369 DN/sec in 2017, while it was 200 DN/sec in 2007 at the same temperature.
The charge transfer efficiencies (CTEs) in the vertical direction (for parallel transfer) measured at 20C from 2018 and 2019 data are around 0.999988. These values are lower than the values in 2007 (0.999995).
The charge transfer efficiencies in the horizontal direction (for serial register transfer) measured in 2019 at 20C are around 0.999980. These values are lower than the values in 2007 (0.999997 at 30C).

Analysis of the data in 2018 and 2019

Motivation : deriving charge transfer efficiency (CTE) of the CCD.
Additional data set (calibration mode images) was taken at the begining of two CCD bakeouts:

2018/05/26 05:03 -- 09:50 (with XOB #1BFC)
2019/10/16 18:30 -- 22:30 (with XOB #1BFC)

Obtained cal-mode images

list of calibration mode images .

(sample images. click image to enlarge)

26-MAY-2018, 08:11:48
1.04800(sec), 17.2966(C)
with reference lines. 16-OCT-2019, 21:39:41
full-CCD 2176x2112(pix),
1.04800(sec), 21.3437(C) 24-JUL-2007, 07:04:27
full-CCD 2176x2112(pix),
1.04800(sec), 30.0359(C)

Vertical slope analysis

2018 (click image to enlarge)

2019 (click image to enlarge)

2007 (click image to enlarge)

CTE derivation (in the vertical direction)

CTE of a CCD can differ pixel by pixel, but it is hard to calculate CTE for a single pixel because of low S/N. Here we calcuate the CTE averaged by ~200 pix around 3 different positions along x-axis (x=512, 1070, and 1700 pix).

------------------------------------------------------
 I(y) - I(2111) = ( I(yo) - I(2111) ) * (yo*p)^(y-yo)
------------------------------------------------------

  I(y) : Vertical intensity slope of a cal-mode image.
         (averaged over 201 pix)
    yo : Pix number of the edge of CCD from the bottom.
         (yo = 2051 in our case)
  I(2111) : Converged I(y) value at the over clocking area (y>2052).
            (calculated by mean(I(2060:2111)))
  p : Charge Transfer Inefficiency    
      (CTE = 1 - p)

For y=yo+1=2052, the above formula is reduced to the following.
------------------------------------------------------------------------
2051 * p = [I(2052) - mean(I(2060:2111)] / [I(2051) - mean(I(2060:2111)]
------------------------------------------------------------------------

measured and calculated values (averaged over 201 pix). (averaged over 101 pix) .

Calculated CTE values and errors at each position.
(a) : 201 pix average around x=512
(b) : 201 pix average around x=1070 (region with the bright blob)
(c) : 201 pix average around x=1700
Errors were estimated from the standard deviation of the averaged pixels propagated through the reduced equation in the above.

date CCD temp. (a) (b) (c)

16-OCT-2019, 21:39:41 21.3437(C) 0.99998780 ±
0.000033 0.99998739 ±
0.000062 0.99998863 ±
0.000031

26-MAY-2018, 08:11:48 17.2966(C) 0.99998735 ±
0.000037 0.99998770 ±
0.000069 0.99998843 ±
0.000036

24-JUL-2007, 07:04:27 30.0359(C) 0.99999575 ±
0.000016 0.99999538 ±
0.000018 0.99999615 ±
0.000016

23-JUL-2007, 10:39:04 8.0682(C) 0.99999776 ±
0.000064 0.99998966 ±
0.000080 0.99999387 ±
0.000061

ratio :
(16-OCT-2019)/(24-JUL-2007) --- 0.99999201 0.99999166 0.99999475

plot with error bars case of 101 pix average

Horizontal profile analysis

(click image to enlarge)

16-OCT-2019, 21:39:41 full-CCD 2176x2112(pix), 1.04800(sec), 21.3437(C) with reference lines	24-JUL-2007, 07:04:27 full-CCD 2176x2112(pix), 1.04800(sec), 30.0359(C)

Plots of the horizontal profile averaged over the following region.
(d) : 201 pix average around y=200
(e) : 201 pix average around y=800
(f) : 201 pix average around y=1800

(click image to enlarge)

The counts at the over clocking area of the horizontal profile are bi-modal (see the right-most plots in the above). This reflects the characteristics of our serial register, i.e., because of the electrical noise created by the system (DC-DC converter), even- and odd-numbered pixels have slightly different base of the signals. It affects the whole area of CCD, but becomes obvious only when the signal level is low (like in the over-clocking area).

We therefore subtracted different base values from even and odd pixels separately, and got the following plots (left plots: DN in linear scale, right plots: DN in log scale).
(click image to enlarge)

For simplicity, the CTE in the horizontal direction was calculated by the same method as the case of vertical CTE using I(0) and I(1) values of the above plots.

Calculated CTE values and errors at each position.
(d) : 201 pix average around y= 200
(e) : 201 pix average around y= 800
(f) : 201 pix average around y=1800

measured and calculated values

date CCD temp. (d) (e) (f)

16-OCT-2019, 21:39:41 21.3437(C) 0.99996869 0.99998135 0.99998765

24-JUL-2007, 07:04:27 30.0359(C) 0.99999589 0.99999749 0.99999834

Use of Poisson distribution approx. formula

In theory, the counts of the over-clocking area are created by the remained charge failed to be transferred to the neighboring pixel. The k-th pixel of the over-clocking area is considered to collect the remained charge for k times. This leads the following expression of I(k) with binomial distribution.


 I(k) = I(0) * nCk * p^k * (1-p)^(n-k)

Under the condition, p<<1 and n>>1, the above expression is approximated by the Poisson distribution as follows.

--------------------------------------
 I(k) = I(0) * (np)^k * exp(-np) / k!
--------------------------------------
   k : number of pixel from the right most edge of the image area 
       (i.e., k=0 is x=2111 in a cal-mode image).
   n : total number of transfer to the readout = 2111+k-14
   p : Charge Transfer Inefficitncy (p=1-CTE)

Here we estimate the value of p using the value the above equation at k=7.

---------------------------------------------
 I(7)/I(0) = (2104*p)^7 * exp(-2104*p) / 7!
---------------------------------------------

From the horizontal plot of 2019 and 2007, we have the following values at the lines y=200, 800 and 1800. Derived p and CTE are also shown in the table below.

date line I(0) I(7) I(7)/I(0) p CTE (=1-p)

16-OCT-2019 200 353.866 8.2278 0.02325 1.4525e-3 0.99854

16-OCT-2019 800 742.553 10.102 0.01360 1.2758e-3 0.99872

16-OCT-2019 1800 1356.47 12.196 0.00899 1.1622e-3 0.99883

24-JUL-2007 200 392.978 0.80497 0.002048 8.588e-4 0.99914

24-JUL-2007 800 871.807 1.1204 0.001285 7.861e-4 0.99921

24-JUL-2007 1800 1617.25 1.3422 0.000829 7.250e-4 0.99927

Charge Transfer Inefficiency seen in coronal images

Thin_Be 16.4 sec image by K. Ishibashi in his DV reports ([xrt_co:43685], [xrt_co:43702]).

26-MAY-2018, 08:11:48 1.04800(sec), 17.2966(C) with reference lines.	16-OCT-2019, 21:39:41 full-CCD 2176x2112(pix), 1.04800(sec), 21.3437(C)	24-JUL-2007, 07:04:27 full-CCD 2176x2112(pix), 1.04800(sec), 30.0359(C)

date	CCD temp.	(a)	(b)	(c)
16-OCT-2019, 21:39:41	21.3437(C)	0.99998780 ± 0.000033	0.99998739 ± 0.000062	0.99998863 ± 0.000031
26-MAY-2018, 08:11:48	17.2966(C)	0.99998735 ± 0.000037	0.99998770 ± 0.000069	0.99998843 ± 0.000036
24-JUL-2007, 07:04:27	30.0359(C)	0.99999575 ± 0.000016	0.99999538 ± 0.000018	0.99999615 ± 0.000016
23-JUL-2007, 10:39:04	8.0682(C)	0.99999776 ± 0.000064	0.99998966 ± 0.000080	0.99999387 ± 0.000061
ratio : (16-OCT-2019)/(24-JUL-2007)	---	0.99999201	0.99999166	0.99999475

date	line	I(0)	I(7)	I(7)/I(0)	p	CTE (=1-p)
16-OCT-2019	200	353.866	8.2278	0.02325	1.4525e-3	0.99854
16-OCT-2019	800	742.553	10.102	0.01360	1.2758e-3	0.99872
16-OCT-2019	1800	1356.47	12.196	0.00899	1.1622e-3	0.99883
24-JUL-2007	200	392.978	0.80497	0.002048	8.588e-4	0.99914
24-JUL-2007	800	871.807	1.1204	0.001285	7.861e-4	0.99921
24-JUL-2007	1800	1617.25	1.3422	0.000829	7.250e-4	0.99927