Background Brightness and Dark Current Calibration

The dark current calibration data gathered on July 10, 2005 showed a significant shift in the peak of the histogram of the dark current on the CCD.

See the calibration information here: Calibration Data: July 10, 2005

We examined the apparent deviation here: Evaluation of Dark Current Shift

Further discussion prompted the hypothesis that the apparent shift is actually due to the use of a new dark current calibration attitude; one that might have a much brighter background. This hypothesis is supported by the data that we've since gathered about the expected background brightness.

Zodiacal Brightness should be the most significant source of background brightness, and thus we've evaluated the expected zodiacal background brightness for all dark current calibration data sets and compared those brightness values to the information from the dark current histograms.

Estimated Zodiacal Brightness and Observed Dark Current

The following is a table that includes the calibration attitude and sun position during all of the dark current calibrations, with the estimated zodiacal brightness calculated for that attitude and the peak of the resultant dark current.

Table 1

Date	Year	RA	Dec	EL	EB	SUN EL	L-L0	Β	ZodiB	PeakDC
19-Aug-1999	0.05								0	9.7
20-Nov-2000	1.33	30	-40	8.21	-47.91	238.9	129.28	47.9	88	11.5
01-Mar-2001	1.6	30	-40	8.21	-47.91	340.9	27.27	47.9	205	12.5
26-Feb-2002	2.59	30.86	-38.25	10.37	-46.74	337.9	32.42	46.7	192	12.5
17-May-2002	2.81	30.86	-38.25	10.37	-46.74	56.6	46.27	46.7	157	12.2
25-Aug-2002	3.08	30.86	-38.25	10.37	-46.74	152.2	141.86	46.7	91	11.9
04-Dec-2002	3.36	30.86	-38.25	10.37	-46.74	251	119.37	46.7	89	11.9
26-Apr-2003	3.75	30.86	-38.25	10.37	-46.74	36.2	25.88	46.7	208	12.8
14-Jul-2003	3.97	30.86	-38.25	10.37	-46.74	111.7	101.38	46.7	96	7.6
02-Jan-2004	4.44	30.86	-38.25	10.37	-46.74	281.4	88.98	46.7	102	7.8
24-Mar-2004	4.66	30.86	-38.25	10.37	-46.74	3.7	6.69	46.7	252	8.5
19-Jun-2004	4.9	30.86	-38.25	10.37	-46.74	88.6	78.28	46.7	111	7.7
09-Sep-2004	5.13	30.86	-38.25	10.37	-46.74	167.2	156.83	46.7	97	7.6
24-Dec-2004	5.42	111.03	23.98	109.15	1.93	273	163.8	1.9	193	9
11-Mar-2005	5.63	182.52	7.49	179.31	7.87	350.5	171.23	7.9	191	8.4
10-Jul-2005	5.96	162.37	24.46	154.29	15.68	108.5	45.75	15.7	415	12.2

Year = Years since launch
RA,Dec = Target Coordinates (Equatorial)
El,Eb = Target Coordinates (Ecliptic)
Sun El = Sun position (Ecliptic, Sun Eb defined as 0)
L - L0 = Target EL - Sun EL
B = Abs(Target Eb)
ZodiB = Zodiacal Brightness from Table 17 of Leinert et al. (1998), A&AS, 127, 1 (included below)

Estimating Zodiacal Brightness

As mentioned, the values of zodiacal brightness used above were taken from Table 17 of Leinert et al. (1998), A&AS, 127, 1 which we include here in its entirety.

Table 2

Zodiacal light brightness observed from the Earth (in SI units). Values are given in 10^-8 W m^-2 sr^-1 µm ^-1, for a wavelength of 0.50 µm.
	0	5	10	15	20	25	30	45	60	75

0				3140	1610	985	640	275	150	100
5				2940	1540	945	625	271	150	100
10			4740	2470	1370	865	590	264	148	100
15	11500	6780	3440	1860	1110	755	525	251	146	100
20	6400	4480	2410	1410	910	635	454	237	141	99
25	3840	2830	1730	1100	749	545	410	223	136	97
30	2480	1870	1220	845	615	467	365	207	131	95
35	1650	1270	910	680	510	397	320	193	125	93
40	1180	940	700	530	416	338	282	179	120	92
45	910	730	555	442	356	292	250	166	116	90
60	505	442	352	292	243	209	183	134	104	86
75	338	317	269	227	196	172	151	116	93	82
90	259	251	225	193	166	147	132	104	86	79
105	212	210	197	170	150	133	119	96	82	77
120	188	186	177	154	138	125	113	90	77	74
135	179	178	166	147	134	122	110	90	77	73
150	179	178	165	148	137	127	116	96	79	72
165	196	192	179	165	151	141	131	104	82	72
180	230	212	195	178	163	148	134	105	83	72

Global Fit of Dark Current Data with a Simple CCD Model

We attempted to fit all of the available dark current data from OAC through to the present with a simple time-dependent model of the ACA CCD. Constants for our model include a temperature multiplier, a value for the true dark current, CCD responsivity, and CCD degredation over time. The temperature multiplier is built in to our simple model to acknowledges the fact that the first 8 dark current calibrations were recorded with the CCD at -10C and to directly compare peak values from these calibrations and the later ones requires adjustment via a multiplicative constant.

Thus, we minimized the sum of the squares of the differences of the observed peak dark current, peak_obs, and the predicted peak dark current, peak_pred, over the dark current observations, with peak_pred defined as:

peak_pred = m ( d0 + g*T ) + r*Z

m = temperature multiplier, defined as 1 for all calibrations done at -15C
(peak at -10C)/m = (peak at -15C)
d0 = OAC dark current (e-/sec)
g = degradation (e-/sec/year)
T = time (years)
r = responsivity (e-/sec/SI unit flux)
Z = zodiacal brightness (SI unit flux)

Minimization was performed using the AMOEBA procedure.
We minimized chi² for 4 cases:
1: All: All calibrations included
2: NI First: All except first
3: NI Last: All except most recent
4: NI First,Last: All except first and most recent

Table 3

	All	NI First	NI Last	NI First,Last	Definition
m	1.71	1.70	1.70	1.65	Temperature Multiplier
d0	5.71	5.81	5.89	6.46	OAC Dark Current (e-/sec)
g	0.150	0.130	0.202	0.116	Degradation (e-/sec/year)
r	0.0118	0.0117	0.0081	0.0071	Responsivity (e-/sec/SI unit flux)
chi²	2.02	2.00	0.77	0.45

Figure 1

Case 1: All Calibrations Top: Points = peak_obs, Line = peak_pred Bottom: Points =peak_obs-Zr, Line =peak_pred-Zr	Case 4: Without First and Most Recent Top: Points = peak_obs, Line = peak_pred Bottom: Points =peak_obs-Zr, Line =peak_pred-Zr

However, based on OAC calibrations, we calculate that:
1 S10 produces a measured dark current per pixel of 7220 e-/sec / 518400 pixels = 0.0139 e-/sec/pixel
1 S10 = 1.28 "SI" units
And thus we predict r = 0.0108 e-/sec / SI

As we have high confidence in this value of r, we performed the above minimization again, this time fixing r.
Table 4

	All	NI First	NI Last	NI First,Last	Definition
m	1.70	1.69	1.72	1.69	Temperature Multiplier
d0	5.76	5.88	5.77	6.06	OAC Dark Current (e-/sec)
g	0.175	0.150	0.146	0.085	Degradation (e-/sec/year)
r	0.0108	0.0108	0.0108	0.0108	Responsivity (e-/sec/SI unit flux)
chi²	2.11	2.09	1.12	1.01

Figure 2

Case 1: All Calibrations Top: Points = peak_obs, Line = peak_pred Bottom: Points =peak_obs-Zr, Line =peak_pred-Zr	Case 4: Without First and Most Recent Top: Points = peak_obs, Line = peak_pred Bottom: Points =peak_obs-Zr, Line =peak_pred-Zr

Reexamination of Zodiacal Brightness vs Peak

Our initial evalution of the zodiacal brightness data was in the form of a plot of zodiacal brightness vs peak dark current. Here is that plot again with the new constants, m and g taken from the the Table 4 "NI First,Last" fit above.

Figure 3

In this plot, the dark current peak values gathered before the CCD was cooled to -15C are represented as red diamonds; the newer values are blue diamonds. The peak values for the pre-cool era have all been scaled by 1/1.69 (m from Table 4 "NI First,Last" fit) to be comparable to the post-cool data points. All peak values have also been adjusted by subtracting a degradation constant of .085 (e-/sec/year) with "year" being years since launch. The most recent data point (at (415, 11.7)) is 1.15 (e-/sec) or 1.8*sigma from the fit line.

Conclusions

The zodiacal brightness seems to be strongly related to the measured dark current.

Solving for constants for a simple model of the CCD built around the zodiacal brightness data returns values that are close to the estimates that were used previously.

Our consideration of the zodiacal brightness appears to explain some of the variability in the dark current measurements that have been made. However, the last dark current measurement still appears to be an outlier. Our assumption in our simple model that degredation is a linear phenomenon that is uniform from launch may not be a good assumption. The next table and figure examine that.

Below is a table that includes information from Table 1 and adds ZB_part and Int_peak. ZB_part is the expected contribution of the Zodiacal Brightness to the Peak, and Int_peak is the "intrisic" Peak dark current, Peak-ZB_part.

Table 5

Day	Year	ZodiB	Peak	ZB_part	Int_peak
19-Aug-1999	0.05	0	9.7	0	9.7
20-Nov-2000	1.33	88	11.5	0.95	10.55
01-Mar-2001	1.6	205	12.5	2.21	10.29
26-Feb-2002	2.59	192	12.5	2.07	10.43
17-May-2002	2.81	157	12.2	1.7	10.5
25-Aug-2002	3.08	91	11.9	0.98	10.92
04-Dec-2002	3.36	89	11.9	0.96	10.94
26-Apr-2003	3.75	208	12.8	2.25	10.55
14-Jul-2003	3.97	96	7.6	1.04	6.56
02-Jan-2004	4.44	102	7.8	1.1	6.7
24-Mar-2004	4.66	252	8.5	2.72	5.78
19-Jun-2004	4.9	111	7.7	1.2	6.5
09-Sep-2004	5.13	97	7.6	1.05	6.55
24-Dec-2004	5.42	193	9	2.08	6.92
11-Mar-2005	5.63	191	8.4	2.06	6.34
10-Jul-2005	5.96	415	12.2	4.48	7.72

ZB_part = Zodiacal brightness contribution to peak, ZodiB*r where r = 0.0108.
Int_peak = Intrinsic peak dark current, Peak-ZB_part, not adjusted for degredation

Here we have plotted the intrinsic dark current over time without removing our estimate of linear degredation.
Figure 4

At this point, we need more data (more calibrations) to better characterize the degredation and to determine if the information from the 10-July-2005 calibration accurately reflects the current state of the CCD.

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Last modified:12/27/13