Latency @ MIPS 24 um array

Kate Su

Abstract:

This document gives a summary analysis for the latent behaviors on MIPS 24 um array. The
analysis intends to characterize the latency due to a bright stim at different background levels.
In general, the latents decay quickly after the stim turn off. The residual count rate at the
first time sample (~5 sec) is about 1~2% of the stim flash. The decay curve is best fitted with
a two-exponential function (fast decay + slow decay) with fast decay constant tau1 and slow
decay constant tau2. Tau1 is in the range of 1.0+/-0.2 seconds and tau2 is 12+/-5 seconds.
The decay constants and the amplitude of the fast decay are also a function of backgrounds.
The higher the background, the lower the amplitude of the fast decay and the longer tau1
(increasing with background), but shorter tau2 (decreasing with background). The results
also show that the more number of resets does lower the slow decay constant so that the
array suffers less from latency, while the fast decay constant seems to be independent
of the number of resets. There is a huge pixel-to-pixel variation in the time constants
(10~30% in tau1 and 20~50% in tau2) across the array. The amplitude of the fast decay is
pretty steady across the whole array (varys only a few %), while the amplitude of the slow
decay varies greatly. The latent contribution is significant for shorter exposures since
the latency is an very function of time. The latent contribution for each following DCEs
compared with the background variation is briefly discussed in order to help setting the
threshold value for latent correction.


Introduction:

This is a data analysis report on the latency@mips 24 um array based on test experiments,
done in Oct. 2001. The previous test results (experiments done in April 2001) show that the
latent is a strong function of bias boosts as illustrated in Figure 1a and 1b. Those experiments
were done with exposing the array to a bright stim flash (first image in each sequce of images),
then taking more data after shut-off the stim to monitor the latency. Figure 1a and 1b show
two data sets taken with bias boost only at the 1st following DCE, and with bias boosts for
each following DCE respectively.

Figure 1a: Bias boost only at the 1st following DCE

Figure 1b: Bias boost at all the following DCEs

The test experiments done in Oct. 2001 were concentrated on the latent behavior when
there is no bias boosts in the following DCEs and at exposing at different level of background.
Figure 1c and 1d display an example of the new test. Similiar to Figure 1a and 1b, the first
image of each sequence of images is when stim was on. The array was exposure to another
stim (as background), then take the rest of following DCEs. To demonstrate the latent, the last
DCE taken was subtracted off from the rest of DCEs to take out the background pattern
contribution (see Figure 1d).

Figure 1c: An example of new data set. Bright stim was on at the first image, then shut off,
move array to exposure to anther stim as background for the rest of DCEs.

Figure 1d: Same as 1c, but the following DCEs have been subtracted the last DCE (background).

Experiments and Data Reduction:

The new experiments were done for different background and both 4 and 10 sec exposures
to test the influence of number of resets. The array was exposed to bright stim flash (1 DCE),
then shut off to measure the residual counts for other 11 DCEs for 10 sec exposure and other 20
DCEs for 4 sec exposure, with constant exposing to different background levels.  Note that
these experiments were done when preparing for Brutus testing, and the photon shutter was
open, which means the external stims are not in function (The external stims all bounce off the
photon shutter, so with the shutter open, there is no bounce). As for internal stims, the
commanding is set up so that we can only use one at a time. Therefore, the bright stim DCE
does not include the background that was used later for the rest of the following DCEs. There
is one mips sec delay between the data with stim on and the data with stim shut-off for turning
off the stim and turning on the background. In each background level, the experiment was run
through seven cycles, and each cycle has a pair of files with the first one for the stim flash and
the other for the rest of following DCEs. All the data were taken in the RAW mode. The data
used in this report were listed in Table 1. Data were reduced with mips_sloper with droop and
linearity corrections. The output data are in both slop (DN/sec) and ramp (DN) format. To
increase the signal-to-noise ratio, the final data used to analysize the latent were averaged
over the seven cycles for each background level.

Table 1: data numbers used with stim level + background level
Day 284
Day 285/286
Day 289
10s DCEs 10s DCEs 4s DCEs
Stim 0x2A + 0x1E: 04.49-05.08 Stim 0x2E + 0x21: 01.35-01.53 Stim 0x2C + 0x21: 01.41-01.55
Stim 0x2A + 0x20: 05.09-05.27 Stim 0x2E + 0x23: 03.21-03.39 Stim 0x2C + 0x23: 01.58-02.12
Stim 0x2A + 0x22: 05.33-05.52 Stim 0x2E + 0x25: 03.40-0.359 Stim 0x2C + 0x25: 02.15-02.30
Stim 0x2A + 0x24: 05.53-06.11 Stim 0x2E + 0x28: 03.01-03.20 Stim 0x2C + 0x28: 02.31-02.46
  4s DCEs  
  Stim 0x2E + 0x21: 04.06-04.20  
  Stim 0x2E + 0x23: 04.21-04.36  
  Stim 0x2E + 0x25: 04.41-04.55  
  Stim 0x2E + 0x28: 04.57-05.11  

Analysis Method:

There are four different background levels (bak1, 2, 3, and 4 with intensity in an increase
order), and two stim flash levels: low ~4950 DN/s (Day 284), ~9200 DN/s (Day 289) and
high ~14600 DN/s (Day 285). The latent at 24um is known to follow two decay curves:
fast decay (less equal than a sec) and slow decay (a few sec), from previous CTA tests.
In order to better characterize the fast decay for the 10s DCEs, the first following DCE
is splited into 4 sub-DECs using the output ramp files from mips_sloper. Including the
stim flash (t=0) and the rest of 10 DCEs, each cycle has 15 time sample points to monitor
the decay curve for 10s DCEs.

In order to compensate the illumination pattern of the stim flash, each pixel value was
normalized to the asscociated stim flash value. The high stim flash in the 10s DCEs
(20 reads) was saturated after 10 reads, however, the final counts rate can be determined
by the non-saturated reads by mips_sloper since the data are in RAW mode. In order to
see the deviation caused by the illumination pattern, two statistical areas were used to
get average normalized response values: using a box (30x30) near the center and using
the whole array (128x128). The average values are listed in Table 2.
 

Fitting Function:

The fitting function is given as:

y = p(0) + p(1).exp(-t/tau1) + p(3).[ 1 - exp(-t/tau2) ]

y: normalized response
t: time elapse in unit of sec
tau1: fast decay time constant in unit of sec
tau2: slow decay time constant in unit of sec
p(0): fitted background level
p(1): fitted amplitude of the fast decay
p(3): fitted amplitude of the slow decay

The IDL fitting package MPFIT was used to do the latency fitting.

The quality of the fit is shown in the Figure 2 where the data points and associated fitted lines are plotted.

Results:
 


Table 2a: Normalized Response for Day 284 10s DECs. (The 3rd and the last line are in DN/s unit given the
information of the stim and bacground levels before normailzation.)
Time (sec)
Bak 1
  
Bak 2
  
Bak 3
  
Bak 4
  
 
box
whole
box
whole
box
whole
box
whole
0.000 4914.05 3474.25 4938.31 3491.16 4957.63 3504.93 4927.35 3483.85
0.000 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
5.243 1.488e-02 1.605e-02 3.041e-02 3.168e-02 6.399e-02 6.532e-02 1.369e-01 1.388e-01
6.816 1.364e-02 1.458e-02 2.867e-02 2.977e-02 6.194e-02 6.323e-02 1.342e-01 1.360e-01
8.389 1.263e-02 1.346e-02 2.750e-02 2.845e-02 6.077e-02 6.187e-02 1.319e-01 1.340e-01
9.961 1.120e-02 1.280e-02 2.670e-02 2.763e-02 5.992e-02 6.098e-02 1.323e-01 1.335e-01
22.544 1.049e-02 1.119e-02 2.515e-02 2.593e-02 5.834e-02 5.935e-02 1.303e-01 1.318e-01
33.554 9.751e-03 1.039e-02 2.437e-02 2.511e-02 5.761e-02 5.855e-02 1.297e-01 1.310e-01
44.564 9.405e-03 1.000e-02 2.402e-02 2.473e-02 5.727e-02 5.818e-02 1.293e-01 1.307e-01
55.575 9.184e-03 9.769e-03 2.380e-02 2.449e-02 5.707e-02 5.759e-02 1.292e-01 1.305e-01
66.585 9.054e-03 9.622e-03 2.367e-02 2.434e-02 5.695e-02 5.781e-02 1.291e-01 1.304e-01
77.595 8.949e-03 9.517e-03 2.356e-02 2.422e-02 5.685e-02 5.771e-02 1.290e-01 1.303e-01
88.605 8.885e-03 9.444e-03 2.351e-02 2.415e-02 5.678e-02 5.762e-02 1.289e-01 1.302e-01
99.615 8.836e-03 9.391e-03 2.345e-02 2.407e-02 5.673e-02 5.756e-02 1.289e-01 1.302e-01
110.625 8.794e-03 9.338e-03 2.341e-02 2.403e-02 5.667e-02 5.751e-02 1.288e-01 1.301e-01
121.635 8.746e-03 9.283e-03 2.337e-02 2.339e-02 5.665e-02 5.748e-02 1.288e-01 1.301e-01
121.635 42.9616  32.2384 115.074 83.5091 279.231  200.295 637.707 455.332

Fig 2a: Decay curves for Day 284 10s DCEs. Black dots are the average values over a box with green
fitting line, and red diamonds are the average values over the whole array with blue fitting line.
The fitted decay constants are given inside the box of each plot.

 

Table 2b: Normalized Response for Day 285 10s DECs. (The 3rd and the last line are in DN/s unit.)
Time (sec)
Bak 1
  
Bak 2
  
Bak 3
  
Bak 4
  
 
box
whole
box
whole
box
whole
box
whole
0.000 14201.3 10045.3 14338.2 10138.7 14399.5 10181.9 14423.7 10199.9
0.000 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00 1.000e+00
5.243 1.764e-02 1.858e-02 3.543e-02 3.645e-02 7.014e-02 7.124e-02 1.919e-01 1.938e-01
6.816 1.648e-02 1.728e-02 3.381e-02 3.470e-02 6.763e-02 6.910e-02 1.896e-01 1.912e-01
8.389 1.573e-02 1.644e-02 3.280e-02 3.361e-02 6.736e-02 6.817e-02 1.884e-01 1.898e-01
9.961 1.519e-02 1.584e-02 3.183e-02 3.279e-02 6.632e-02 6.741e-02 1.876e-01 1.887e-01
22.544 1.389e-02 1.442e-02 3.063e-02 3.130e-02 6.522e-02 6.612e-02 1.864e-01 1.876e-01
33.554 1.332e-02 1.376e-02 3.005e-02 3.065e-02 6.463e-02 6.545e-02 1.860e-01 1.871e-01
44.564 1.303e-02 1.344e-02 2.977e-02 3.032e-02 6.441e-02 6.517e-02 1.858e-01 1.869e-01
55.575 1.288e-02 1.325e-02 2.961e-02 3.013e-02 6.430e-02 6.505e-02 1.858e-01 1.868e-01
66.585 1.278e-02 1.314e-02 2.951e-02 3.001e-02 6.421e-02 6.494e-02 1.857e-01 1.868e-01
77.595 1.272e-02 1.307e-02 2.944e-02 2.993e-02 6.415e-02 6.486e-02 1.857e-01 1.867e-01
88.605 1.267e-02 1.301e-02 2.940e-02 2.987e-02 6.411e-02 6.481e-02 1.857e-01 1.867e-01
99.615 1.263e-02 1.296e-02 2.936e-02 2.983e-02 6.408e-02 6.477e-02 1.857e-01 1.867e-01
110.625 1.260e-02 1.293e-02 2.933e-02 2.979e-02 6.407e-02 6.475e-02 1.857e-01 1.867e-01
121.635 1.258e-02 1.290e-02 2.932e-02 2.977e-02 6.404e-02 6.472e-02 1.857e-01 1.867e-01
121.635 178.662 129.575 420.405 301.832 922.177 658.993 2678.97 1904.62

Fig 2b: Decay curves for Day 285 10s DCEs. Black dots are the average values over a box with green fitting line,
and red diamonds are the average values over the whole array with blue fitting line. The fitted decay constants
are given inside the box of each plot.

Table 2c: Normalized Response for Day 285 4s DECs. (The 3rd and the last line are in DN/s unit.)
Time (sec)
Bak 1
  
Bak 2
  
Bak 3
  
Bak 4
  
 
box
whole
box
whole
box
whole
box
whole
0.00 14678.4  10361.7 14652.6 10343.8  14837.9 10470.9  14930.2  10538.0
0.00 1.000e+00 9.998e-01  1.000e+00  9.998e-01 1.000e+00 9.998e-01 1.000e+00 9.998e-01
5.243 1.761e-02 1.934e-02  3.447e-02  3.639e-02 6.948e-02 7.186e-02 1.875e-01 1.915e-01
9.961 1.477e-02 1.596e-02 3.140e-02  3.277e-02 6.509e-02 6.710e-02 1.827e-01 1.862e-01
14.680 1.380e-02 1.477e-02  3.042e-02  3.158e-02 6.400e-02 6.578e-02 1.817e-01 1.850e-01
19.400 1.334e-02 1.418e-02  2.998e-02  3.101e-02  6.355e-02 6.520e-02 1.814e-01 1.845e-01
24.117 1.308e-02 1.384e-02  2.972e-02  3.068e-02 6.329e-02 6.487e-02 1.811e-01 1.842e-01
28.836 1.290e-02 1.360e-02  2.955e-02  3.046e-02 6.314e-02 6.465e-02 1.810e-01 1.840e-01
33.554 1.279e-02 1.345e-02  2.944e-02  3.030e-02 6.304e-02 6.451e-02 1.810e-01 1.839e-01
38.273 1.269e-02 1.332e-02  2.935e-02  3.019e-02 6.294e-02 6.439e-02  1.809e-01 1.838e-01
42.992 1.263e-02 1.324e-02  2.929e-02  3.010e-02 6.289e-02 6.430e-02 1.809e-01 1.838e-01
47.710 1.257e-02 1.316e-02  2.925e-02  3.003e-02 6.284e-02 6.424e-02 1.808e-01 1.837e-01
52.429 1.253e-02 1.311e-02  2.920e-02  2.997e-02 6.279e-02 6.418e-02 1.808e-01 1.837e-01
57.147 1.248e-02 1.305e-02  2.916e-02  2.992e-02  6.277e-02 6.414e-02 1.808e-01 1.837e-01
61.886 1.246e-02 1.302e-02  2.912e-02  2.987e-02  6.274e-02 6.411e-02 1.808e-01 1.836e-01
66.584 1.244e-02 1.298e-02  2.911e-02  2.983e-02 6.273e-02 6.408e-02 1.808e-01 1.836e-01
71.303 1.241e-02 1.294e-02  2.908e-02  2.981e-02 6.271e-02  6.405e-02 1.808e-01 1.836e-01
76.022 1.239e-02 1.291e-02  2.906e-02  2.978e-02 6.270e-02 6.403e-02 1.807e-01 1.836e-01
80.740 1.238e-02 1.290e-02  2.904e-02 2.976e-02 6.268e-02 6.401e-02 1.807e-01 1.836e-01
85.459 1.237e-02 1.288e-02  2.903e-02  2.974e-02 6.266e-02 6.399e-02 1.807e-01 1.836e-01
90.178 1.236e-02 1.286e-02  2.901e-02  2.972e-02  6.266e-02 6.397e-02 1.807e-01 1.836e-01
94.896 1.235e-02 1.285e-02  2.901e-02  2.970e-02 6.267e-02 6.396e-02 1.807e-01 1.836e-01
94.896 181.184 131.13 8 425.038 304.271 929.624 663.798 2697.88 1920.95

Fig 2c: Decay curves for Day 285 4s DCEs. Black dots are the average values over a box with green fitting line,
and red diamonds are the average values over the whole array with blue fitting line. The fitted decay constants
are given inside the box of each plot.

Table 2d: Normalized Response for Day 289 4s DECs. (The 3rd and the last line are in DN/s unit.)
Time (sec)
Bak 1
  
Bak 2
  
Bak 3
  
Bak 4
  
 
box
whole
box
whole
box
whole
box
whole
0.000 9222.18 6112.23 9257.12 6134.12 9307.77 6166.42 9406.66 6231.63
0.000  1.000e+00  1.000e+00  1.000e+00  1.000e+00 9.998e-01 9.998e-01 9.998e-01 9.998e-01
5.243  2.660e-02  5.503e-02  1.125e-01  3.119e-01  2.832e-02  5.699e-02  1.150e-01  3.160e-01
9.961 2.339e-02  5.122e-02  1.082e-01  3.067e-01  2.460e-02  5.268e-02  1.104e-01  3.102e-01
14.680 2.236e-02  5.012e-02  1.071e-01  3.057e-01  2.340e-02  5.141e-02  1.092e-01  3.092e-01
19.400 2.184e-02  4.963e-02  1.067e-01  3.053e-01  2.283e-02  5.084e-02  1.087e-01  3.088e-01
24.117 2.155e-02  4.932e-02  1.064e-01 3.052e-01  2.245e-02  5.049e-02  1.083e-01  3.086e-01
28.836 2.135e-02  4.916e-02 1.062e-01  3.051e-01 2.221e-02 5.027e-02  1.081e-01  3.084e-01
33.554 2.122e-02  4.901e-02  1.061e-01  3.050e-01  2.205e-02  5.008e-02  1.080e-01  3.083e-01
38.273 2.114e-02  4.893e-02  1.060e-01  3.050e-01  2.194e-02  4.999e-02  1.079e-01  3.083e-01
42.992 2.105e-02  4.886e-02  1.059e-01  3.049e-01  2.184e-02  4.991e-02  1.078e-01  3.082e-01
47.710 2.099e-02  4.878e-02  1.059e-01  3.049e-01  2.177e-02  4.981e-02  1.077e-01  3.082e-01
52.429 2.094e-02  4.876e-02  1.059e-01  3.049e-01  2.171e-02  4.976e-02  1.077e-01  3.082e-01
57.147 2.091e-02  4.872e-02  1.058e-01  3.048e-01  2.165e-02  4.973e-02  1.077e-01  3.082e-01
61.866 2.086e-02  4.866e-02  1.058e-01  3.049e-01  2.161e-02  4.967e-02  1.076e-01  3.081e-01
66.585 2.084e-02  4.865e-02  1.058e-01  3.048e-01  2.156e-02  4.964e-02  1.076e-01  3.081e-01
71.303 2.081e-02  4.862e-02  1.058e-01  3.048e-01  2.153e-02  4.959e-02  1.076e-01  3.081e-01
76.022 2.081e-02  4.860e-02  1.057e-01  3.048e-01  2.151e-02  4.956e-02  1.075e-01  3.081e-01
80.740 2.078e-02  4.858e-02  1.058e-01  3.048e-01  2.150e-02  4.956e-02  1.075e-01  3.081e-01
85.459 2.076e-02  4.857e-02  1.057e-01  3.048e-01  2.147e-02  4.953e-02  1.075e-01  3.081e-01
90.178 2.073e-02  4.856e-02  1.057e-01  3.048e-01  2.143e-02  4.952e-02  1.075e-01  3.081e-01
94.896 2.073e-02  4.857e-02  1.057e-01  3.048e-01  2.142e-02  4.951e-02  1.074e-01  3.081e-01
94.896 191.062 129.417 449.497 301.337 983.597 658.102 2867.16 1910.94

Fig 2d: Decay curves for Day 289 4s DCEs. Black dots are the average values over a box with green fitting line,
and red diamonds are the average values over the whole array with blue fitting line. The fitted decay constants
are given inside the box of each plot.

For this averaging whole array analysis, the latent drops quickly after the stim turn off.
The count rate of the  first time sample (~5 sec) is about 1~2% of the stim flash.
The tau1 is ~ 1+/- 0.1 sec, and the tau2 is ~ 10 +/- 2 sec for this analysis. Both the
tau1 and tau2 seem to be a function of background levels. The higher the background,
the less latent contribution and the short slow decay constant.
 

The fit was also applied to each individual pixel (128x128=16,384 pixels, that will
take a LONG time! ) An acceptable fit was defined by: 0 < tau1 < 2 and 0 < tau2 < 100.
Within these good fits, statistics (median, average and standard deviation values) is
calculated for each fitting parameter. Table 3 lists all the median, average values with
associated standard deviations over the whole array. Histograms are also plotted in
Figure 3 for each fitted parameters. In order to see the distribution of the decay
constants over the array, tau1 and tau2 images (Figure 4) are also displayed using
blackbody color table (the darker the lower value and the brighter the higher value).

Table 3a: Statistics of the fitting parameter for Day 284 - 10s DCEs
Bak #
 good pixels median of p(0) average of p(0) sigma of p(0)
1 99.95% 0.015793 0.024006 0.270996  (big)
2 99.95% 0.031667 0.039284 0.121742 (big)
3 99.97% 0.066300 0.072510 0.060157 (big)
4 99.96% 0.139193 0.149617 0.214249 (big)
    median of p(1) average of p(1) sigma of p(1)
1   0.984205 0.976170 0.270672 (27%)
2   0.968333 0.960896 0.121047 (12%)
3   0.933703 0.927669 0.058841 (6%)
4   0.860808 0.850578 0.214388 (25%)
    median of p(3) average of p(3) sigma of p(3)
1   -0.006582 -0.013947 0.267467 (big)
2   -0.007460 -0.014397 0.117654 (big)
3   -0.007834 -0.014003 0.057553 (big)
4   -0.007889 -0.018101 0.213220 (big)
    median of tau1 average of tau1 sigma of tau1
1   0.826384 0.740214 0.264198 (32%)
2   0.858841 0.756456 0.276896 (32%)
3   0.864532 0.729355 0.309062 (36%)
4   0.929491 0.764076 0.343972 (37%)
    median of tau2 average of tau2 sigma of tau2
1   18.3066 17.5625 7.51056 (41%)
2   16.9192 16.3308 7.63495 (45%)
3   16.0424 15.8477 9.15577 (57%)
4   14.9267 15.7193 10.8409 (72%)

Figure 3a: Histograms for the fitting parameters in Day 284-10s DCEs

Figure 4a: Decay time images for Day 284-10s DCEs. First four images are for fast decay and the
last four are for slow decay.

Summary remarks:


Table 3b: Statistics of the fitting parameter for Day 285 - 10s DCEs
Bak # good pixels median of p(0) average of p(0) sigma of p(0)
1 99.99% 0.018377 0.020002 0.016593  (big)
2 99.99% 0.036205 0.037913 0.016378 (big)
3 99.99% 0.070338 0.073164 0.081765 (big)
4 99.98% 0.199049 0.204236 0.019566 (9.8%)
    median of p(1) average of p(1) sigma of p(1)
1   0.981623 0.980180 0.009971 (1%)
2   0.963796 0.962267 0.009948 (1%)
3   0.929664 0.927018 0.080803 (8%)
4   0.800968 0.795946 0.016568 (2%)
    median of p(3) average of p(3) sigma of p(3)
1   -0.005593 -0.006268 0.0197404 (big)
2   -0.006516 -0.007230 0.0163932 (big)
3   -0.005704 -0.007252 0.0798609 (big)
4   -0.008898 -0.015808 0.0204555 (big)
    median of tau1 average of tau1 sigma of tau1
1   0.808061 0.812415 0.070245 (8%)
2   0.855063 0.855840 0.072593 (8%)
3   0.884799 0.864545 0.133980 (15%)
4   0.909255 0.767274 0.334563 (36%)
    median of tau2 average of tau2 sigma of tau2
1   16.7539 17.1294 2.16576 (13%)
2   15.3634 15.7481 2.75268 (18%)
3   15.6839 15.8531 3.52784 (22%)
4   10.0612 10.1756 6.15205 (61%)

Figure 3b: Histograms for the fitting parameters in Day 285-10s DCEs

Figure 4b: Decay time images for Day 285-10s DCEs. First four images are for fast decay and the
last four are for slow decay.

Summary remarks:


Table 3c: Statistics of the fitting parameter for Day 285 - 4s DCEs
Bak # good pixels median of p(0) average of p(0) sigma of p(0)
1 99.99% 0.018377 0.019644 0.016009 (87%)
2 99.99% 0.035410 0.036534 0.013901 (39%)
3 99.99% 0.070681 0.071915 0.013824 (19%)
4 99.99% 0.191022 0.193184 0.014317 (7%)
    median of p(1) average of p(1) sigma of p(1)
1   0.981624 0.980601 0.004656 (1%)
2   0.964591 0.963651 0.004845 (1%)
3   0.929324 0.928269 0.005855 (1%)
4   0.808979 0.807001 0.009622 (1%)
    median of p(3) average of p(3) sigma of p(3)
1   -0.005763 -0.006232 0.015890 (big)
2   -0.005899 -0.006383 0.013849 (big)
3   -0.006808 -0.007515 0.014082 (big)
4   -0.007087 -0.009278 0.015635 (big)
    median of tau1 average of tau1 sigma of tau1
1   0.847177 0.851158 0.064767 (7%)
2   0.864019 0.862588 0.079260 (9%)
3   0.923563 0.912409 0.099213 (10%)
4   0.961009 0.900537 0.209569 (21%)
    median of tau2 average of tau2 sigma of tau2
1   12.3638 12.6558 2.24748 (18%)
2   12.1971 12.6375 2.98247 (24%)
3   10.9767 11.5202 3.53750 (32%)
4   9.4716 10.5350 5.39418 (57%)

Figure 3c: Histograms for the fitting parameters in Day 285-4s DCEs

Figure 4c: Decay time images for Day 285-4s DCEs. First four images are for fast decay and the
last four are for slow decay.

Summary remarks:

  • The background values vary diversely across the array, whick reflects the faint background levels.
  • The amplitude of the fast decay is a function of background while the amplitude of the slow decay is not.
  • Both tau1 and tau2 have two peaks in the histrograms, and seem to be a function of background levels.
  • The deviation of tau2 across the array gets larger as the background increases.


    • Table 3d: Statistics of the fitting parameter for Day 289 - 4s DCEs
    Bak # good pixels median of p(0) average of p(0) sigma of p(0)
    1 99.99% 0.027300 0.028533 0.014642 (53%)
    2 99.99% 0.055867 0.057274 0.014405 (26%)
    3 99.99% 0.113899 0.115689 0.015844 (14%)
    4 99.99% 0.314515 0.317923 0.022804 (7%)
        median of p(1) average of p(1) sigma of p(1)
    1   0.972702 0.971650 0.006393 (0.65%)
    2   0.944135 0.942912 0.006731 (0.71%)
    3   0.886103 0.884494 0.010500 (1.2%)
    4   0.685488 0.682258 0.021291 (3.1%)
        median of p(3) average of p(3) sigma of p(3)
    1   -0.006114 -0.006703 0.014064 (big)
    2   -0.006518 -0.007401 0.014453 (big)
    3   -0.006444 -0.007943 0.016438 (big)
    4   -0.006067 -0.009662 0.024938 (big)
        median of tau1 average of tau1 sigma of tau1
    1   0.866123 0.856375 0.112025 (13%)
    2   0.899684 0.875255 0.143850 (16%)
    3   0.925513 0.871542 0.195289 (21%)
    4   1.020920 0.918012 0.282719 ((28%)
        median of tau2 average of tau2 sigma of tau2
    1   12.6101 13.1142  3.61906 (28%)
    2   12.0453 12.6701  4.37224 (36%)
    3   11.6221 12.3950  5.45756 (47%)
    4   9.5892 10.3338  6.60788 (69%)

    Figure 3d: Histograms for the fitting parameters in Day 289-4s DCEs

    Figure 4d: Decay time images for Day 289-4s DCEs. First four images are for fast decay and the
    last four are for slow decay.

       Summary remarks: (Similar to Day 285-4s DCEs)

    Discussion:
     

    In order to generalize the latent behavior over the whole array, median values of the fitted parameters
    (p(0), tau1 and tau2) are better representations than average values. These median values are listed
    in Table 4 with each associated deviation over the whole array, and plotted in Figure 5.

    Table 4: Summary of the decay constants with deviation over the array v.s. different stim and background levels.
    Bak/Stim [p(0)]
    deviation
    tau1 (sec)
    deviation
    tau2 (sec) 
    deviation
    Day284-10sDCEs
     
     
     
     
     
    0.015689
    0.156309
    0.831599
    0.268446
    18.9518
    7.47123
    0.031382
    0.098394
    0.865427
    0.284105
    17.7348
    7.73296
    0.066300
    0.060157
    0.871933
    0.321650
    17.1758
    9.27240
    0.138516
    0.103279
    0.929491
    0.343972
    14.9267
    10.8409
    Day285-10sDCEs
     
     
     
     
     
    0.018377
    0.0165925
    0.808061
    0.070245
    16.7539
    2.16576
    0.036205
    0.0163779
    0.855063
    0.072593
    15.3634
    2.75268
    0.070338
    0.0817649
    0.884799
    0.133980
    15.6839
    3.54784
    0.199049
    0.0195663
    0.909255
    0.334563
    10.0612
    6.15205
    Day285-4sDCEs
     
     
     
     
     
    0.018377
    0.0160093
    0.847177
    0.064767
    12.3638
    2.24748
    0.035410
    0.0139013
    0.864019
    0.064767
    12.1971
    2.98247
    0.07081
    0.0138235
    0.923563
    0.099213
    10.9767
    3.53750
    0.191022
    0.0138235
    0.961009
    0.209569
    9.47155
    5.39418
    Day289-4sDCEs
    		          
    0.027300
    0.0146142
    0.866123
    0.112025
    12.6101
    3.61906
    0.055867
    0.0144045
    0.899684
    0.143850
    12.0453
    4.37224
    0.113899
    0.0158440
    0.925513
    0.195289
    11.6221
    5.45756
    0.314515
    0.0228037
    1.02092
    0.282719
    9.58922
    6.60788

    Within the error bars (deviation over the whole array, represents the variation from pixel to pixel)
    in Figure 5, both fast and slow decay constants are not related to the stim levels (low or high) for
    both 4s and 10s DCEs. (Different color represents different stim level.) Over all, the fast decay
    constant increases as background increases, while the slow decay constant decreases as
    background increases for all 4s and 10s DCEs. However, detailed repeatability for one single pixel
    is needed to confirm that the big variation is really caused by the various behavior from pixel to pixel,
    or something else.  (ps. repeatability study is currently under going)

    Figure 5: Decay constants v.s. different Stim/Background settings. The data points are the median values
    of the fitted parameters and the error bars are the standard deviation over the whole array. The error bars
    on the y-axis represent a difference in latent behavior from pixel to pixel. The plot on the left are for 4s
    DCEs and the plot on the right are for 10s DCEs.
    4s DCEs: black dots are day 285 (higher stim ~14,600 DN/s) and red dots are day289 (lower stim ~9,000 DN/s) 10s DCEs: black dots are day 284 (lower stim ~5,000 DN/s) and red dots are day 285 (higher stim ~14,600 DN/s)

    In terms of the effect of the number of resets, the decay constants from Day 285 both 4s (more
    number of resets) and 10s DCEs (less number of resets) at the same stim and background levels
    are plotted in Figure 6. It appears that the fast decay constant is indepent of the number of resets,
    whille the slow decay constant is a function of the number of resets. The more number of resets
    (like 4s DCEs), the smaller slow decay constant, which is consitent with what James found for
    the pin-hole data.

    Figure 6: Decay constants v.s. number of resets. Under the same stim flash and backround level,
    black dots represent the 10s DCEs and red diamonds represent the 4s DCEs.

     

    Note that the first following DCE taken was delayed for 1 mips sec to wait for the bright stim
    shut-off and background turn-on. The real observation won't have this delay. Nevertheless,
    we still would like to know the latent contribution in the following DCEs (Latent#) (# means
    the #th following DCE) compared with the background. We define this latent in unit of the
    sigma above the background as:

                Latent1 =[CR(1st) - CR(last)] / sqrt(CR(last))
               Latent2 =[CR(2nd) - CR(last)] / sqrt(CR(last))
               Latent3 =[CR(3rd) - CR(last)] / sqrt(CR(last))
               Latent4 =[CR(4th) - CR(last)] / sqrt(CR(last))
               Latent5 =[CR(5th) - CR(last)] / sqrt(CR(last))

    with
        CR(1st) : counts rate for the 1st following DCE .....
        CR(last): counts rate for the last following DCE (background)

    Latent# was calculated over the whole array for each background. The median , average and deviation
    values of Latent# are listed in Table 5. In general, among these four different backgrounds, Latent1
    is larger  for the lower background, but smaller than the higher background. The following Latent2,
    Latent3, Latent4, Latent#5 are getting smaller and smaller.

    Table 5: Latent contribution at following DCEs in unit of sigma above background
    10s DCEs
     
     
     
     
     
     
    Bak # 1
     
    Day 284
     
     
    Day 285
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    2.989592
    2.895470
    0.378282
    3.551846
    3.509561
    0.246245
    Latent2
    1.236061
    1.190238
    0.229281
    1.385829
    1.387835
    0.125636
    Latent3
    0.726486
    0.699324
    0.178492
    0.802028
    0.802931
    0.157860
    Latent4
    0.466103
    0.457774
    0.134402
    0.505715
    0.507341
    0.139636
    Latent5
    0.315923
    0.314134
    0.114858
    0.334825
    0.336465
    0.138021
    bak # 2
     
    Day 284
     
     
    Day 285
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    1.991961
    1.947177
    0.238273
    2.581309
    2.563217
    0.165761
    Latent2
    0.783640
    0.762095
    0.167298
    0.931095
    0.932840
    0.108051
    Latent3
    0.453681
    0.443112
    0.131831
    0.531853
    0.534353
    0.142671
    Latent4
    0.293951
    0.288434
    0.114592
    0.337361
    0.339436
    0.125846
    Latent5
    0.196872
    0.196242
    0.102794
    0.222182
    0.222617
    0.105625
    bak # 3
     
    Day 284
     
     
    Day 285
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    1.254431
    1.236391
    0.170801
    1.603664
    1.600269
    0.117065
    Latent2
    0.473999
    0.464549
    0.140663
    0.582946
    0.584341
    0.105725
    Latent3
    0.267846
    0.266007
    0.122296
    0.307845
    0.309601
    0.100392
    Latent4
    0.178533
    0.176516
    0.097719
    0.191998
    0.192487
    0.095799
    Latent5
    0.119179
    0.119331
    0.094436
    0.138012
    0.138904
    0.092201
    bak # 4
     
    Day 284
     
     
    Day 285
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    0.846847
    0.840045
    0.143853
    0.905945
    0.905693
    0.108379
    Latent2
    0.289437
    0.286171
    0.125561
    0.223211
    0.226248
    0.108038
    Latent3
    0.159911
    0.159885
    0.121626
    0.102065
    0.102703
    0.100613
    Latent4
    0.100143
    0.101671
    0.099402
    0.051172
    0.052226
    0.096944
    Latent5
    0.069600
    0.069361
    0.107307
    0.024884
    0.025271
    0.092732
                 
    4s DCEs
     
     
     
     
     
     
    Bak # 1
     
    Day 285
     
     
    Day 289
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    5.351721
    5.284613
    0.688553
    3.445401
    3.398005
    0.616202
    Latent2
    2.502441
    2.486189
    0.272347
    1.572576
    1.547692
    0.280853
    Latent3
    1.524258
    1.520277
    0.234000
    0.968083
    0.957080
    0.234571
    Latent4
    1.050261
    1.049686
    0.221696
    0.681898
    0.674503
    0.219552
    Latent5
    0.775666
    0.776835
    0.214976
    0.495822
    0.494144
    0.212389
    bak # 2
     
    Day 285
     
     
    Day 289
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    3.615166
    3.582954
    0.489683
    2.460192
    2.434586
    0.471592
    Latent2
    1.623623
    1.616745
    0.207951
    1.032030
    1.017980
    0.221362
    Latent2
    0.981232
    0.980763
    0.188211
    0.612886
    0.606674
    0.196869
    Latent3
    0.681737
    0.681017
    0.185207
    0.425737
    0.421986
    0.185430
    Latent5
    0.502044
    0.504715
    0.182101
    0.310867
    0.309653
    0.181672
    bak # 3
     
    Day 285
     
     
    Day 289
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    2.993857
    2.934183
    0.478669
    1.721208
    1.678255
    0.366956
    Latent2
    1.134692
    1.129488
    0.184671
    0.649664
    0.643393
    0.184715
    Latent3
    0.645164
    0.645708
    0.171283
    0.379177
    0.377847
    0.168894
    Latent4
    0.437461
    0.438001
    0.168789
    0.260226
    0.260579
    0.163731
    Latent5
    0.317404
    0.319114
    0.167101
    0.191395
    0.190611
    0.163525
    bak # 4
     
    Day 285
     
     
    Day 289
     
    DCE
    median 
    average
    deviation
    median
    average
    deviation
    Latent1
    1.741875
    1.723316
    0.278518
    1.053827
    1.039335
    0.244690
    Latent2
    0.555441
    0.555490
    0.161089
    0.284984
    0.283736
    0.161906
    Latent3
    0.293956
    0.293079
    0.159875
    0.147324
    0.145638
    0.156995
    Latent4
    0.189027
    0.189122
    0.156546
    0.090514
    0.091468
    0.154658
    Latent5
    0.131132
    0.130951
    0.155516
    0.061415
    0.061616
    0.155191

    Since the latent is a function of decay times, the latent is more server in short exposures (4s DCEs)
    than in long exposures (10s DCEs). For the 4s DCEs at the lowest background, latent contribution is
    still around 2 sigma above the background after four DCEs taken.

    The Latent1 v.s. its associated bak/stim for each pixel is plotted in Figure 8. Colors represent different
    background levels using the same color table as before (red the lowest, pink the highest). Similar
    bacground level (same color) is tested at two stim levels (higher on the left, and lower on the right).

    Figure 8: Latent1 v.s. bak/stim.

    Assuming that the latent contribution below 2 sigma above the background is acceptable and no
    need for correction. For 10s DCEs, when the ratio of background over stim is larger than ~0.05,
    the Latent1 is less than 2 sigma above the background, which means the threshold (bak/stim)
    for latent correction is 0.05.  For 4s DCEs, when the ratio of background over stim is larger than
    ~0.3, the Latent1 is less than 2 sigma above the background, which means the threshold (bak/stim)
    for latent correction is 0.3. The latent at the second following DCE (Latent2) and the third
    following DCE (Latent3) is also needed to be corrected. Similar plots for Latent2 and Latent3
    are shown in Figure 9. Therefore, the threshold is ~0.05 for Latent2, and ~0.02 for Latent3.

    Figure 9: Latent2 and Latent3 at 4s DCEs v.s. bak/stim.