Analysis of an effect of the fcompress program on photometry of g0483977.fts and g0493955.fts images.

Jure Skvarc

I analyzed two of the images (g0483977.fts and g0493955.fts) that Michael R. kindly uploaded to his ftp server. First I used fitsblink to make star lists and match them to the GSC catalog. The two images happen to be partially overlapped so here is an opportunity to compare the same stars on the two images. I made a small awk program to join the records from the two lists which corresponded to the same GSC stars. For beginning I made a graph which compares the measured magnitudes with the magnitudes of the GSC stars.

The trasformation between the two magnitude values was

20 + 0.8 * (-2.5 log10(v)),

where v is the instrumental star intensity and log10 is the base 10 logarithm. At the moment I do not know why the transformation between the intensities is not linear. Below are the numbers of detected catalog stars which are present in both images for each magnitude. Note that fitsblink did not detect stars close to the left and right edges.

mag. no. of stars
6 2
7 0
8 3
9 8
10 20
11 41
12 70
13 54
14 11
15 2

In the next step I compared star magnitudes of the GSC stars in the two images, as shown here:

The average magnitude differences and standard deviations are shown in the table below:
mag. n dif. std.
6 2 0.0802 0.0044
8 3 0.0575 0.0090
9 8 -0.0056 0.0100
10 21 0.0481 0.0167
11 41 -0.0112 0.0092
12 71 0.0091 0.0398
13 55 -0.0360 0.0648
14 11 -0.0620 0.0931
15 2 0.2554 0.0022

Here mag. means the magnitude, n is the number of stars in that magnitude range, dif. is the average distance and std. is the standard deviation.

Now everybody wonders what has the whole story to do with data compression. This: I made a similar procedure as before, only that this time I compared results of magnitude measurements for the same image.

In the first experiment, I used a value 60 for the -s (scale) fcompress switch, what gave compression factor of 4.9 and 4.8 for g0483977.fts and g0493955.fts, respectively. The following tables show average differences of star magnitudes in non-compressed and compressed images for different magnitude values. Only stars matched with the GSC were taken into account.
g0483977.fts
mag. n dif. std.
6 1 -0.0075 0.0000
7 2 -0.0013 0.0000
8 7 -0.0040 0.0000
9 13 -0.0016 0.0002
10 40 -0.0080 0.0001
11 81 -0.0026 0.0010
12 138 -0.0102 0.0057
13 159 -0.0329 0.0120
14 31 -0.0216 0.0145
15 5 -0.0019 0.0046
g0493955.fts
mag. n dif. std.
6 1 -0.0007 0.0000
7 1 -0.0023 0.0000
8 7 0.0065 0.0005
9 16 -0.0067 0.0000
10 44 -0.0079 0.0001
11 85 -0.0136 0.0008
12 168 -0.0191 0.0023
13 171 -0.0199 0.0046
14 76 -0.0229 0.0072
15 6 -0.0211 0.0094
In the second experiment, I used fcompress -s 200, what gave compression factors of 10.0 and 9.6.
g0483977.fts
mag. n dif. std.
6 2 0.0189 0.0004
7 1 -0.0047 0.0000
8 6 -0.0015 0.0000
9 13 -0.0065 0.0001
10 40 -0.0101 0.0005
11 80 -0.0166 0.0052
12 125 -0.0301 0.0119
13 122 -0.0832 0.0353
14 21 -0.0905 0.0588
15 2 -0.0742 0.0003
g0493955.fts
mag. n dif. std.
6 1 -0.0024 0.0000
7 1 -0.0053 0.0000
8 7 0.0284 0.0065
9 16 -0.0080 0.0002
10 44 -0.0138 0.0004
11 82 -0.0087 0.0017
12 160 -0.0192 0.0070
13 132 -0.0320 0.0237
14 56 -0.0632 0.0319
15 3 0.0330 0.0297
We can see that image compression with fcompress lowers star intensities and that compression factor of 10 gives 2-3 times larger magnitude scatter than compression factor of 5. However, even higher compression factor has lower scatter than one found in comparison of two different images. The fdecompress program has an option (-s) which enables image smoothing. Let's check (for compression factor of 10) what happens if we use it:
g0483977.fts
mag. n dif. std.
6 2 -0.1881 0.0001
7 1 -0.2159 0.0000
8 6 -0.1620 0.0002
9 13 -0.1596 0.0005
10 40 -0.1423 0.0011
11 79 -0.1173 0.0054
12 124 -0.0939 0.0139
13 122 -0.0903 0.0330
14 20 -0.0472 0.0373
15 2 -0.0812 0.0001
g0493955.fts
mag. n dif. std.
6 2 -0.1346 0.0008
7 1 -0.1734 0.0000
8 7 -0.1492 0.0019
9 15 -0.1646 0.0004
10 44 -0.1500 0.0006
11 84 -0.1161 0.0017
12 159 -0.0751 0.0095
13 134 -0.0560 0.0292
14 48 -0.0762 0.0353
15 4 0.1059 0.0165

It seems that no significant change in magnitude scatter is achieved, but we can see that few faint stars are missing in the statistic and, more apparent, that star magnitudes decrease for 0.1 to 0.2 magnitudes what leads to loss of some stars.

Conclusion: it seems to me that no significant loss in information would happen if Mark 3 images were compressed by a factor of 5 or even 10 using lossy compression with the fcompress program. Certainly, this conclusion can not be simply extrapolated and a similar analysis should be performed for every specific telescope/CCD/observatory combination.

Links

The Amateur Sky Survey

Fitsblink

Crni Vrh Observatory