Introduction
Analysis Procedure
Results
Limits To Additional Noise
Implications For The Presence Of Additional Noise At J Band
The 2MASS J Band Cameras have different noise problems in the north and the south. For example, the south camera has a "noise pickup" which can create a periodic noise variation in the Atlas Images that causes the background level to be constant at +0.20 DN, changing rapidly to -0.20 DN, at maximum. This "noise pickup" can cause J band photometric errors of an additional 20% for sources that should have photometric errors of 10%. The average value for the "noise pickup" is significantly smaller. This extra noise might be discernible as extra noise in the noise vs. background relationship.
Therefore, I have carefully analyzed the noise, measured by the GALWORKS background_sigma, in the Atlas Images for both the North and South data, to see if it is possible to detect differences between the North and South data, and if it is possible to detect Atlas Images that are affected by the presence of additional noise.
I obtained the J noise and background for every processed Image that was not affected by high source densities. There were 25,704 Images in the North and 7,449 in the South. The Northern data spans most of a year, whereas the Southern data was taken only in March and April. Hence it is possible that seasonal effects as well as infrequent effects may be present in the Northern data that are not yet present in the Southern data.
The J noise I analyze is the background_sigma, which is measured using the histogram of Image Atlas pixels after bright sources and their artifacts are masked, and a four parameter fit to the background is removed. See Analysis of Noise In The 2MASS Atlas Images for previous work and exact definitions of the background_sigma parameter. The background_sigma is reported to only 2 decimal places, which is barely enough to not limit the analysis below. The banding seen on some of the plots below is due to this limitation.
For each hemisphere separately, I fit the following relationship to the noise and the background:
Noise^2 = a^2 + b^2 * Background.
If there were no sources of additional noise, a would be proportional to the read noise of the J array divided by the electronic gain, and b would be inversely proportional to the gain:
Noise^2 = { 0.585^2 / (4^2 * 6) } * { (rn/G)^2 + (4*B/G) },
where:
0.585 comes from the Weinberg coadd kernel used to make the Images,
4^2 comes from the division of the frame fluxes by 4 to create the Images,
6 comes from the combination of 6 frames in the Image,
G is the gain in electrons per DN,
rn is the read noise in electrons, and
B is the Image Atlas Background, which is 1/4 of the frame background.
See Analysis of Coadd Noise: Gain and Read Noise Derived From Coadd Noise Versus Background for further explanation.
For a gain of 7 electrons / DN, and a read noise of 50-60 electrons, a should be 0.43 - 0.51 and b should equal 0.045.
To determine the fit parameters, I minimized the sum of the squares of the residuals about the fit. This is the same as the chi-square if the error in the determinations of the noise and background is constant. The best-fit parameters were identical whether or not larger residuals were excluded.
The best-fit parameters and the resulting mean residuals are given in the following table:
| Hemisphere | a | b | Mean Square Residual (DN) | |
|---|---|---|---|---|
| Using All residuals | Excluding |residuals| > 0.05 DN | |||
| North | 0.305 | 0.0410 | 0.0192 | 0.0182 |
| South | 0.337 | 0.0430 | 0.0088 | 0.0082 |
The formal uncertainties are very small, as calculated by setting the chi-squared equal to the minimum value plus one, after normalizing the chi-squared minimum to the number of degrees of freedom. The error for the southern parameters is 0.004 for a and 0.0002 for b. However, as always, it is likely that other systematics cause the actual uncertainties to be somewhat larger.
Plots of the data, fits to the data and histograms of the residuals are given in the following table:
| Hemisphere | Data With Fit | All Residuals Vs. Background | Mean Binned Residual Vs. Background | Histogram of Residuals |
|---|---|---|---|---|
| North | plot | plot | plot | plot |
| South | plot | plot | plot | plot |
Note that even though there is a definite trend of the mean binned residual vs. background in the north, the absolute values of the mean residual are very small.
If there were no other sources of noise, the derived value of the gain would be 8.5 in the North and 7.7 in the South, with a formal error of 0.1, and the read noise would be 43 in both the North and South, with a formal error of 1. All of these are reasonable values.
The most noticeable difference between North and South is the residuals, which are about twice as large in the North as in the South. It is possible that seasonal effects will cause the South residuals to become as large as the North residuals once more Southern data are processed.
There are several ways additional noise might be present in the data:
For case 1 above, suppose that the fit parameters for the south should actually be the same as the north. Then the constant term a has been inflated by:
sqrt{ 0.337^2 - 0.305^2 } = 0.14 DN.
Hence it is possible that on average the Southern data has an additional noise source with a mean sigma of 0.14 DN.
For case 2 above, suppose that the Northern residuals are inflated by airglow, compared to the south, and hence consider only the Southern residuals themselves of 0.009 DN. Using an average J noise of 0.6 DN, the extra noise needed to create a residual of 0.009 DN is:
sqrt{ 0.609^2 - 0.600^2 } = 0.10 DN.
The largest residual in the South is 0.15 DN when the predicted noise was 0.52 DN. Hence the extra noise in that coadd is:
sqrt( 0.67^2 - 0.52^2 } = 0.42 DN.
In fact, the three largest residuals all come from the scan 65 from 980402s in coadds 198, 209 and 267, with residuals 0.15, 0.12 and 0.11 DN. The Q.A. report notes that coadd 209 has "U Hya, carbon star, VERY bright", which probably affects the neighboring coadd 198 as well, and that coadd 267 has a "bright star". Hence these largest residuals are due to bright stars, and hence the applicable limit for noise other than that caused by bright stars is probably closer to 0.10 DN.
For case 3 above, suppose that the fit parameters correctly model the noise, and the observed residuals are determined by the accuracy of our measurement of the background and background_sigma. Using an average J noise of 0.6 DN, an error of 0.009 DN in its determination with an accuracy of 0.001 DN in the measurement of the error, implies that it would be impossible to detect any noise below:
sqrt{ 0.610^2 - 0.609^2 } = 0.03 DN.
The most striking characteristic of the J Band Residual Noise is the absence of a tail to large residual values in the histogram of residuals. The few large residual values in the South are due to bright stars, not electronic pickup. Hence there clearly are no intermittent sources of noise with sigmas of ~0.3 DN.
Other sources of noise characterized by mean sigmas of ~0.15 DN are clearly permitted by what is known now, and the residuals themselves allow for a source of noise with mean sigma ~0.10 DN.
Unfortunately, therefore, it is not possible to identify the electronic pickup noise through analysis of the parameters currently in the database. Other techniques, such as the Fourier analysis of the coadds just added to GALWORKS, are needed to identify the presence of such noise.
