freak k001.fex 14.0
resulted in extraction counts for point sources brighter than 14th mag.
Most pixels are 0 or 1 in low density scans. Therefore
the images were thresdholded above 1.
Next the *.fex.fits images were transformed into (X,Y) plots with numerical symbols representing the extraction count. This allows much more convenient visualization of the extraction count at each pixel than is possible by looking at the direct "freak" images. Movies of scans 001-005 fex results for bands J, H and K were also produced to conviently search for scan-to-scan persistence. See Figure 1.
The hot or "warm" pixel events are minimal at J and H, and the results are summarized below. The situation at K is more complex, so additional software was written to automate the comparison of the extraction counts on scans k001-k005 and to perform statistical comparisons and summaries.
2) J-array: There appear to be no significant hot pixels in the J array. The two 3-fex events (yellow "3" in Figure 1) at pixels (57,139) and (57,181) only appear in S003 (j003.fex.fits).
3) H-array: There is only one definite hot pixel persistent in all 5 scans: (8,117). The number of H<14 mag extractions at pixel (8,117) is 15,9,7,4,28 in scans S001-S005 respectively. A hot pixel mask (used to construct a simple image mask) for the H array in the format prescribed by John Fowler (2-May-97) would thus be simply (H, X, Y):
2 8 117
Following is a tally of the number of "warm" pixels (3-5 counts in randomly distributed pixels) in each H-band scan:
Table 1--- Potential "Warm" pixels in the H Array
| Scan | Number of "warm" pixels | Pixel(s) |
|---|---|---|
| H001 | 1 | (254,7) |
| H002 | 0 | --- |
| H003 | 5 | (31,63);(58,18);(59,101);(60,184);(231,75) |
| H004 | 4 | (38,245);(126,34);(127,117);(254,78) |
| H005 | 4 | (41,38);(42,121);(43,204);(79,32) |
Figure 1 and Table 1 show that none of these "warm" pixel candidates are persistent in different scans. They occur in 14 different pixels in the 5 scans examined. Further analysis is desirable to learn if their frequency is consistent with random sources that happen to fall in the same array pixel for different frames [different sky positions], or whether they may be due to a weak "persistence" effect after the pixels are illuminated by a very bright source (or cosmic ray?). As discussed below, such analysis will likely be necessary for K array anyway, since the majority of hot pixels (FEX > 5) are not seen in all K scans.
4) K-array: There are 7 pixels with >=4 frame extractions which are present in all 5 scans examined here. The number of source extractions (frames effected) for each of the 5 scans for these pixels are tabulated here:
Table 2--- Hot Pixels (FEX >= 4) Present in all 5 Scans at K
| Pixel | Number of Frames in which the Pixel is "Hot" | ||||
|---|---|---|---|---|---|
| K001 | K002 | K003 | K004 | K005 | |
| (66,225) | 9 | 9 | 5 | 11 | 6 |
| (87,242) | 57 | 71 | 63 | 67 | 62 |
| (91,229) | 66 | 39 | 55 | 21 | 48 |
| (141,254) | 53 | 15 | 43 | 8 | 16 |
| (177,209) | 60 | 67 | 69 | 54 | 36 |
| (186,194) | 28 | 54 | 11 | 30 | 38 |
| (231,206) | 5 | 12 | 6 | 6 | 21 |
The K array mask (in the format requested by John Fowler) for these 7 pixels which occur in all 5 scans is referred to here as the "AND mask". Although this is certainly not a complete list of problem pixels, these are the only pixels which are consistently hot across scans.
Examination of the data in Figure 1 shows many intermitent hot pixel candidates (FEX >= 4) in addition to those discussed above which are present in all 5 scans. They range from pixels which appear hot in the majority (3-5) of the scans, to a few pixels which are very "hot" (>10 frame extractions) in only 1 or 2 of the 5 scans, but lack even a moderate number of extactions in the remaining majority of scans. Examples:
There is a total of 55 pixels in the K array in which more than 3 frame extractions (FEX >= 4) occur in at least one scan (K001 or K002 or K003 or K004 or K005). This complete list of mostly intermittent hot pixels is referred to here as the "OR mask". Of course, the "AND mask" discussed above in which FEX >= 4 in all 5 scans (K001 and K002 and K003 and K004 and K005) is a small pixel subset (13%) of the "OR mask". Figure 2 is a plot of the K array mask, with the 7 AND pixels plotted in red and the remaining 48 OR pixels plotted in yellow.
Figure 2--- K Array "OR mask"
A statistical comparison was made between the distributions of the FEX data for scans K001-K005, after thresholding the data at FEX >2. Basic summary statistics are tabulated below. Comparisons of the distributions in a pair-wise fashion shows no evidence for significantly different means (Student's t test) or variances (F test) in the extraction counts for scans K001-005. Likewise, the non-parametric K-S statistic, which measures the significance of the maximum value of the absolute difference between two observed cumulative distribution functions (CDFs), independent of their intrinsic underlying distribution functions, shows no differences between the CDFs at a significance level of 0.05 or better (smaller).
Table 3--- Statistical Comparison of FEX Distributions for >2 Extractions with K<14 mag
| Scan | No. Pixels with FEX>2 | Min. Extactions (Frames) | Max. Extractions (Frames) | Mean | Sigma | Median |
|---|---|---|---|---|---|---|
| K001 | 33 | 3 | 66 | 17.5 | 19.0 | 10 |
| K002 | 36 | 3 | 71 | 15.9 | 19.4 | 8 |
| K003 | 31 | 3 | 86 | 16.9 | 23.2 | 7 |
| K004 | 32 | 3 | 106 | 18.8 | 24.6 | 7 |
| K005 | 29 | 3 | 90 | 17.3 | 22.0 | 5 |
For these 5 K-band scans, we conclude that the number of candidate hot pixels is about 30, and a "typical" median hot pixel is on for 8 frames (17 in the mean, skewed by a few pixels with many frame extractions). A zeroth-order pixel mask of hot pixels which occur on all 5 scans examined here accounts for only 7 out of ~30 pixels that are likely to appear hot (FEX > 5), or at least "warm" (FEX > 3), during any particular K scan. The intermittent nature of most hot pixel events (the fact that they occur on different pixels in different scans) indicates that more detailed study is warrented. The next step might be a trend analysis to determine if intermittent (or "transient") hot pixels occur on frames which follow illumination by an extremely bright source or cosmic ray on a previous frame. Also, the possibility of computing dynamic "hot pixel masks" using on-the-fly analysis of the FEX data such as that performed here might be considered. However, any such process would be complicated (foiled?) by varying source density in different regions of the sky.