Continued: Measuring ACA CTI by dithering a star across quadrant boundaries

Introduction

Process

Analysis

Analysis: Best Example

Analysis: Parallel Data

Analysis: Serial Data

Analysis: Averages

Analysis: Outlier

Conclusions

Introduction

Previously, projects were undertaken to evaluate and quantify ACA CCD CTI. This was done first by evaluating the trailing charge of "warm" pixels in dark current calibration data. See that work at:

Measuring ACA CTI from dark current calibration data

That work suggested that better results might be obtained by dithering stars over quadrant boundaries and measuring the resulting centroid shifts. See that work here:

Measuring ACA CTI by dithering a star across quadrant boundaries.

The primary conclusion of that CTI dither investigation was that further evaluation with more data was required and that the data sets involved in a future project should include stars of a range of magnitudes with dither patterns centered on quadrant boundaries. The following is an analysis following those data selection guidelines.

Process

We collected a set of observations that met our revised selection criteria. In each, a single guide star was positioned to allow the star to dither across a CCD quadrant boundary. The observations were done using 8x8 raw pixel images to collect Header 3 diagnostic telemetry.

We then did a rough examination by evaluting the centroid offsets of the border star from an aspect solution calculated from the average of the positions of the OBC first moment centroids of the non-border stars. That rough analysis showed some of the residual patterns for which we looked, but made it clear that we'd need the cleaner aspect solution produced by the ground processing pipeline to have an accurate evalution.

Therefore, we processed the observations with the aspect pipeline. Actually, we ran each obsid twice: once to get centroids for all stars and once to generate an aspect solution that didn't include the border star centroids. As we expected the CTI to cause a shift in the centroids of the border star (and it was this shift that we wanted to measure), we didn't want the border star to contaminate our aspect final solution.

To see a complete HOWTO of the steps involved, follow this link:
Pipeline CTI
After pipeline processing the data, we recomputed the residuals of the border star centroids with respect to the aspect solution and used these differences for the tables and analysis that follows. We omitted observations that turned out to not dither across the boundary sufficiently (i.e. small dither amplitude and not centered on -.5 row or column) and those for which warm pixel problems were much larger than any potiential CTI centroid shifts. See examples on this page:
Omitted Observations

Analysis

Of the remaining observations, 8 involved border stars that dithered across the border defined by row=-.5 and 9 of the observation involved border stars that dithered across the border defined by column=-.5. The first 8 cases were used to get an estimate of the parallel CTI and the remaining 9 were used to obtain an estimate of the serial CTI. Here is a diagram that shows where these border stars occurred on the CCD. The legend in the lower left contains the parallel cases; the legend in the lower right contains the serial cases. The numbers after the OBSIDs are star magnitudes.

Figure 1

For the parallel cases, we expect to see the CTI induced centroid shift in Row direction and we expect no shifts in the Column direction. We expect the inverse for the serial cases. Here is the best example of the phenomenon.

Best Case

OBSID 60223 present one of the cleanest signals and demonstrated the expected CTI induced centroid shifts in column. (Fig. 3)

Figure 2	Figure 3

We then compared the centroid shift to the distance the border star should have been from the CCD boundary, based on the aspect solution.

Figure 4	Figure 5

For the remainder of our analysis, I've used the distance Y1-Y0 as the maximum centroid offset caused by CTI and labeled this either Delta R or Delta C.

Because we should expect no shift in the column direction for a parallel case, we have used the Column data as a Control for our Row data for the parallel cases. We have done the inverse for for the serial cases. Here are some data tables summarizing the findings from this process. The OBSIDs in the tables are links to pages with more plots for each obsid.

Table Key

OBSID=	observation ID
MAG=	magnitude of border star
RMSMAG=	rms of the magnitude over the duration of the observation
Δr=	Delta row; approximate signed range (in pixels) of the difference between the border star centroid position and its projected position based on the aspect solution. See Figure 4. Delta R is Y1-Y0
&sigma Δr=	sigma of delta row; sigma of the line fit to the slope of the "projected distance from border vs deviation from projected position" plot. See Figure 4 to see an example fit line and sigma
Δc=	Delta column; approximate signed range (in pixels) of the difference between the border star centroid position and its projected position based on the aspect solution. See Figure 5. Delta C is Y1-Y0
&sigma Δc=	sigma of delta column; sigma of the line fit to the slope of the "projected distance from border vs deviation from projected position" plot. See Figure 5 to see an example fit line and sigma
Mean Row=	average pixel row coordinate of border star
Mean Col=	average pixel column coordinate of border star

Table 1: Parallel Cases

OBSID	MAG	RMSMAG	Δr (Case)	σ Δr	Δc (Control)	σ Δc	Mean Row	Mean Col
60259	7.2122	0.0146	-0.0044	0.0071	0.0085	0.0074	-0.6	148.4
60328	9.1249	0.0115	-0.0158	0.0125	0.0111	0.0111	-0.5	366.5
60250	9.1540	0.0155	-0.0383	0.0139	-0.0182	0.0167	-0.5	379.0
60231	9.4253	0.0117	-0.0611	0.0134	-0.0643	0.0143	-0.5	213.1
60230	9.6972	0.0214	0.0085	0.0117	0.0683	0.0159	-0.5	-284.3
60271	10.2442	0.0302	-0.0151	0.0222	0.0055	0.0306	-0.7	-476.8
60216	10.5442	0.0435	-0.0736	0.0391	-0.0320	0.0406	-0.5	59.0
60208	10.6213	0.0231	0.0045	0.0213	-0.1342	0.0288	0.0	67.0

Averages			-0.0244	0.0176	-0.0194	0.0207

Figure 6	Figure 7

Table 2: Serial Cases

OBSID	MAG	RMSMAG	Δr (Control)	σ Δr	Δc (Case)	σ Δc	Mean Row	Mean Col
60243	7.9508	0.0154	-0.0047	0.0091	-0.0627	0.0104	-272.0	-0.4
60239	8.8348	0.0141	-0.0066	0.0098	-0.0705	0.0115	398.6	-0.3
60261	9.2411	0.0137	-0.0057	0.0105	-0.0583	0.0118	-202.4	-0.5
60223	9.3161	0.0155	0.0054	0.0126	-0.0743	0.0125	-410.0	-0.4
60245	9.3363	0.0161	-0.0019	0.0138	-0.0612	0.0175	368.4	-0.6
60222	9.5988	0.0156	0.0093	0.0142	-0.0840	0.0132	-378.4	-0.3
60241	9.6370	0.0245	-0.0008	0.0150	-0.0621	0.0178	305.8	-0.5
60270	10.4673	0.0325	0.0249	0.0285	-0.1502	0.0393	-204.6	-0.5
60235	10.4788	0.0299	0.0241	0.0349	-0.0740	0.0341	-413.8	-0.6

Averages			0.0049	0.0165	-0.0775	0.0187

Figure 8	Figure 9

The colors on the plots are solely to represent the magnitude of the uncertainty on each point (more clearly represented by the error bars).
Green : sigma = 0-0.5
Yellow : sigma = 0.5-1
Red : sigma > 1

To look at both sets of plots simultaneously, use this link:
Both Sets of Plots

Here is a small table of just those averages that are included in the above tables:

Table 3: Averages

	Δr	σΔr	Δc	σΔc
Parallel	-0.0244	0.0176	-0.0194	0.0207
Serial	0.0049	0.0165	-0.0775	0.0187

Odd Case: Outlier

OBSID 60208, which should have shown centroid shifts in Row due to parallel CTI, instead showed CTI-like centroid shifts in Column. For this, I have no explanation.

Figure 10	Figure 11

Conclusions

Parallel Conclusions:
While, on average, there does seem to be a constant deviation of the border star from the aspect solution, there is very little difference between the parallel row (case) and column (control) deltas. Thus, we see no clear CTI effect in this direction.

Serial Conclusions:
There is, however, a marked difference between the serial row (control) and column (case) deltas. The row average is close to the expected value of zero and the column value is 0.0775 pixels. As you may have seen on the Serial Plots page, there does not appear to be a particularly magnitude dependent relationship in our data (though we might be able to see more there was less variation in the centroiding of the >10 mag stars). The next step will be to determine the value of the CCD CTI from the centroid shifts that have been measured.

Serial CTI:

Here we've used the simple model for a 4x4 pixel box where the total charge is located in the center of the box, and a very small displaced charge is located at the outer edge of the box. We then solved for the percent charge needed at the outer edge of the box to account for the centroid shift that we saw in the data above.

Total charge = ∑ y(r,c)

Displaced charge = (Total charge) * CTI * #transfers

Simple Centroid: <r> = ∑ r * y(r,c) / ∑ y(r,c)

Using centroid formula:

Max displacement <R> = ∑ ( r1 * (Total Charge) + r2 *(Displaced charge)) / ∑ y(r,c)

This reduces to

<R> = <r1> + <r2> * CTI * #transfers

For the 4x4 pixel box, r1 = 0 and r2 = 2 pix. As these dither experiments were done at the ccd boundary, we'll use 512 as the number of transfers.

<R> = 2 * CTI * 512

<R> in the Serial Case is equal to Δc/2 .

.0775/2 = 1024 * CTI

CTI = 3.78 * 10^-5

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Last modified:12/27/13