Hi,
I have tried to repeat some of the experiments from Craig Stark's paper for my Canon EOS40D. For this purpose, I took 10 darks each at different exposure times from 1/8000s (effectively a bias) to 960 seconds, all at room temperature 19 degree Celsius, with 30-60 seconds between them to give the sensor some time for cooling. The raw statistical data is attached to the end of this post.
The data suggests that the bias is 1024.6. The dark current appears reasonably linear with exposure time, see screenshot 1 (note log scale on both axis). The wiggles at exposure times <1sec may be due to the jumps of +-1 that I reported in my previous post, but their absolute values are irrelevant to dark calibration. The remaining wiggles may well be due to changes in the environment, such as changes in room temperature (18.9-19.7 degrees C), sensor heating (see below) and the change of batteries at 120 seconds. I do not see the apparent change of bias that Craig observed in Fig. 1 of his paper for other Canon cameras.
Looking at the variance (noise) in screenshot 2, it grows stronger than expected for exposures<15 seconds. The variance (=stdDev*stDev)should be roughly linear with exposure or dark current. Clearly something is reducing noise for <15 seconds images. If we plot variance against elapsed time in screenshot 3, we can also see a certain heating effect for the long exposure images - one minute apparently is not enough for cooling the sensor. This can also be seen in a plot of mean vs. elapsed time (not shown).
Looking at the histograms of masterBias (10 shots at 1/8000s, screenshot 4, note log scale on y) , we see the clear peak at 1024 that actually shows a nice normal distribution (=read noise?), a long tail going to 1200 (=warm pixels?), and occasional pixels with values >1200 (defects).
For masterDark (10 shots at 30s, screenshot 5, note log scale on y), we again can see the 3 sections again. The warm pixel section of course goes up to 7000 now. Screenshot 6 shows the histogram of the masterDark for all pixels<1100. We clearly see the two peaks.
MasterDark-MasterBias has a histogram as show in screenshot 6, limited to x=+-100, and the statistics shown below. To avoid negative values, I apparently need a pedestal.
> summary(as.numeric(masterDark-masterBias))
Min. 1st Qu. Median Mean 3rd Qu. Max.
-105.100 -3.473 -0.593 7.565 2.407 15370.000
Here is what I seemingly can lean:
- I need not worry about a changing bias for my DSLR.
- Darks are roughly linear for exposure times>15 seconds
- Noise is also linear, but for exposures<15 seconds some kind of noise reduction kicks in.
- I need more than 60 seconds between shots to avoid heating effects, or I need more than 10 shots to reach an equlibrium for heat.
- I need a small pedestal of maybe 120 to avoid negative values during calibration.
Georg
exposure mean median sd
1 0.000122 1024.170 1024 12.90816
2 0.000122 1024.859 1025 12.89027
3 0.000122 1024.872 1025 12.91453
4 0.000122 1024.564 1025 12.88926
5 0.000122 1024.591 1025 12.89589
6 0.000122 1024.611 1025 12.90209
7 0.000122 1024.900 1025 12.89584
8 0.000122 1024.840 1025 12.89873
9 0.000122 1024.889 1025 12.91116
10 0.000122 1024.893 1025 12.89672
11 0.010132 1024.644 1025 13.95698
12 0.010132 1024.212 1024 13.96718
13 0.010132 1024.898 1025 13.95350
14 0.010132 1024.896 1025 13.96014
15 0.010132 1024.183 1024 13.94923
16 0.010132 1024.197 1024 13.92837
17 0.010132 1024.895 1025 13.95674
18 0.010132 1024.725 1025 13.94495
19 0.010132 1024.595 1025 13.95277
20 0.010132 1024.651 1025 13.96647
21 0.040526 1024.788 1025 14.01994
22 0.040526 1024.963 1025 14.01980
23 0.040526 1024.947 1025 14.03727
24 0.040526 1025.006 1025 14.02093
25 0.040526 1024.961 1025 14.03190
26 0.040526 1024.141 1024 14.01569
27 0.096388 1025.099 1025 14.16422
28 0.096388 1025.041 1025 14.20052
29 0.096388 1025.052 1025 14.19465
30 0.096388 1024.768 1025 14.18104
31 0.096388 1024.269 1024 14.20591
32 0.096388 1024.769 1025 14.20028
33 0.096388 1025.035 1025 14.17686
34 0.096388 1025.027 1025 14.19935
35 0.096388 1024.318 1024 14.18619
36 0.096388 1024.581 1025 14.18765
37 0.324210 1024.721 1025 15.18252
38 0.324210 1025.038 1025 15.08274
39 0.324210 1024.741 1025 15.14556
40 0.324210 1024.720 1025 15.18813
41 0.324210 1025.097 1025 15.13278
42 0.324210 1024.452 1025 15.18279
43 1.000000 1025.280 1025 20.68702
44 1.000000 1025.204 1025 20.67807
45 1.000000 1025.273 1025 20.75284
46 1.000000 1025.308 1025 20.71311
47 1.000000 1025.229 1025 20.87962
48 1.000000 1025.212 1025 20.71697
49 1.000000 1025.320 1025 20.73751
50 1.000000 1025.268 1025 20.76022
51 1.000000 1025.289 1025 20.77404
52 1.000000 1025.238 1025 20.77030
53 5.187358 1025.980 1025 62.42621
54 5.187358 1026.380 1025 62.40257
55 5.187358 1026.350 1025 62.42279
56 5.187358 1026.366 1025 62.66998
57 5.187358 1026.256 1025 62.73121
58 5.187358 1026.357 1025 62.84192
59 5.187358 1026.418 1025 62.95821
60 5.187358 1026.383 1025 63.12903
61 5.187358 1026.309 1025 62.98107
62 5.187358 1026.307 1025 63.09342
63 16.000000 1028.759 1025 176.12136
64 16.000000 1028.771 1025 176.36056
65 16.000000 1028.735 1025 176.69793
66 16.000000 1028.827 1025 177.13879
67 16.000000 1028.881 1025 177.49895
68 16.000000 1028.941 1025 177.90368
69 16.000000 1028.868 1025 178.35236
70 16.000000 1028.831 1025 178.69796
71 16.000000 1028.893 1025 178.97281
72 16.000000 1028.935 1025 179.34006
73 30.000000 1030.907 1025 262.09529
74 31.000000 1030.659 1025 263.51427
75 31.000000 1030.635 1025 263.65746
76 31.000000 1030.904 1025 263.94066
77 31.000000 1031.047 1025 264.08750
78 31.000000 1030.643 1025 264.22004
79 31.000000 1030.682 1025 264.41856
80 31.000000 1030.886 1025 264.53648
81 31.000000 1030.891 1025 264.62104
82 31.000000 1030.754 1025 264.78100
83 59.000000 1031.774 1023 304.21146
84 60.000000 1031.547 1023 304.40356
85 60.000000 1031.782 1023 304.58206
86 60.000000 1031.862 1023 304.76579
87 60.000000 1032.400 1024 304.87072
88 60.000000 1031.939 1023 305.01412
89 60.000000 1031.767 1023 305.13291
90 60.000000 1031.742 1023 305.20812
91 60.000000 1032.561 1023 305.32153
92 60.000000 1032.590 1023 305.39698
93 120.000000 1034.068 1021 318.78778
94 120.000000 1034.336 1021 319.28860
95 120.000000 1034.982 1021 319.57189
96 120.000000 1034.874 1021 319.82557
97 120.000000 1034.989 1020 320.06215
98 120.000000 1035.478 1021 320.31031
99 120.000000 1034.975 1020 320.44354
100 120.000000 1035.632 1021 320.62560
101 120.000000 1035.541 1020 320.76830
102 120.000000 1035.705 1020 320.92059
103 240.000000 1045.834 1021 364.27368
104 240.000000 1047.338 1021 366.80720
105 240.000000 1048.437 1021 368.85005
106 240.000000 1049.630 1022 370.28304
107 240.000000 1050.043 1022 371.67265
108 240.000000 1050.536 1021 373.03865
109 240.000000 1050.837 1021 373.88219
110 240.000000 1051.077 1021 374.42117
111 240.000000 1051.733 1022 375.14148
112 240.000000 1052.089 1022 375.59733
113 480.000000 1073.041 1021 474.20141
114 480.000000 1073.743 1019 480.56519
115 480.000000 1076.079 1020 484.70915
116 480.000000 1076.910 1020 488.05670
117 480.000000 1077.300 1019 490.87133
118 480.000000 1077.994 1019 493.06115
119 480.000000 1078.469 1019 495.12496
120 480.000000 1079.176 1019 496.71547
121 480.000000 1079.226 1019 499.48021
122 480.000000 1080.426 1019 503.63972
123 960.000000 1119.885 1007 711.80435
124 960.000000 1119.289 1006 716.64172
125 338.000000 1065.605 1020 437.09502