Conclusions
Introduction
Analysis of Noise For All Source Densities
Analysis of Noise In Unconfused Areas
Coadd Noise And Background Sigma Versus Each Other And Date
Histograms Of Coadd Noise, Background Sigma And Their Ratio
Comparison Of Observed Image Atlas Noise To Expected Noise And Identification Of Images Affected By Airglow
Analysis Of Observed Minus Expected Noise
J and K vs. the H background
Observed Scan Noises
Scans With Unacceptable Severe Airglow
Scans With Unacceptable Severe Airglow and the Jump Counter
Acknowledgments
Conclusions
The 2MASS system - telescope, camera, electronics, operations and data processing software - usually produces Atlas Images that have nearly the minimum noise set by the NICMOS chips and the backgrounds of the telescope and atmosphere. A detailed analysis of the noise at J and K shows no excess noise contributed by, for example, non-optimal flat-fielding, extra electronic noise, or poor coaddition algorithms. In addition, the background-removal algorithm used by GALWORKS successfully removes any background variation across the Images at J and K that is present to the extent that the residual noise in the Images is usually consistent with the measurement error. That error is 0.020 DN, equivalent to a K surface brightness of 24.3 mag per square arcsecond.
Because additional noise combines in quadrature with the baseline noise to produce the observed noise, these results show that there are no intermittent sources of noise with sigmas of ~0.3 DN. However, other sources of noise characterized by mean sigmas of ~0.2 DN are not excluded by this analysis, and the residuals themselves allow for an additional source of noise with mean sigma ~0.1 DN.
The mean background-removed noises for J, H and K are 0.51, 0.95 and 1.11 DN, with 90% of the observed noises falling in the ranges 0.45 - 0.61, 0.78 - 1.20, and 0.81 - 1.27 DN. The K numbers will change slightly until we accumulate a full year's worth of data, due to the K variation with season.
At first glance, the background-removal algorithm used by GALWORKS appears to also successfully remove any background variation across the Images at H except in the most severe cases of airglow. However, careful analysis of the noise shows that nearly all background-removed H Atlas Images are still affected by airglow variation. That residual airglow variation is probably a combination of the "frame edges" caused by airglow emission variations on scales of less than a frame length (8.5') that cannot be removed by our present coaddition algorithm and smaller scale airglow spatial variations that cannot be removed by our present background-subtraction algorithm.
The residual airglow variation has a sigma of 0.20 DN, and probably represents a coherent background error that affects the H fluxes of galaxies. This one sigma value of 0.20 DN would cause a flux error at H of 4-13% for a source with H = 13.8 mag, which alone flirts with violating the Level 1 Specification for galaxy photometry of 10%. (Recall that Poisson errors themselves are already close to a 10% error, leaving little margin for additional error sources.) If the distribution of residual airglow background variation is uniform, as might be expected from a "frame-edge" effect, the maximum and minimum values of the uniform distribution correspond to 0.39 DN, creating an H flux error of 8-26% for a source with H = 13.8 mag.
The sources found in the 16% of all coadds in the tail of the distribution beyond one sigma will of course have a much larger H flux error. A subsequent analysis will report the actual observed effect on galaxy photometry.
It clearly is not desirable to toss all scans with residual H airglow variation, since we would never finish the survey if we tossed so many scans and better algorithms may allow improved removal of airglow. However, there is a clear small non-Gaussian tail in the distribution consisting of about 5% of all scans. Those scans should probably be marked for reobservation with the appropriate priority, since those H observations are tantamount to non-photometric observations for extended sources, and there are significant airglow effects on the simultaneous K observations as well.
In all other respects, the noise in the 2MASS Atlas Images behaves as expected. In confused areas, the noise correlates directly to source density. In unconfused areas, the noise is tightly proportional to the square root of the background, except for those ~5% of H scans with severe airglow variation.
As the H background increases due to airglow, the J background increases as 0.13 - 0.20 of the H background (both in DN), and the slope can vary from one extreme to another in a single night, and include rare periods where the H background increases and the J background remains unchanged. The K background increases as 0.35 of the H background, and can also rarely be unchanged when the H background increases.
Curiously, the excess noise in the Atlas Images has a different dependence between bands - the slope of J vs. H is much lower, 0.05 (25-38% of the background slope), and the K slope is cut in half to 0.18, which may imply that the emission of the airglow on scales smaller than ~4' has a different spectral distribution than the emission of the airglow on larger scales.
The measure of the noise used to extract sources is however affected by airglow most of the time, resulting in a value too high for optimum source extraction. On average for all low-density coadds, the measure is 6% too high, for 30% of the coadds the measure is 10% too high, and for 10% of the coadds the measure is 43% too high. One accepted coadd has a measure which is a factor of 10 too large, raising the H completeness level by 2.5 magnitudes! A change should be made to the data processing software as soon as possible to better calculate the point source noise in the Images.
Introduction
The analysis was motivated by the need to understand the effect of airglow on the 2MASS processing. In order to analyze the effects of airglow, it is necessary to understand the noise in the Atlas Images. This analysis therefore characterizes the overall noise in the Images, including a theoretical discussion of the effect on extended source photometry. A subsequent analysis will characterize the observed effects of airglow on the point and extended sources. For general information on airglow, and some scary movies, see J. Adams and M. Skrutskie's Wide-Field Airglow Experiment.
The organization of this memo is as follows. First, the noise in the Images is shown to be strongly correlated with source density, as expected. Subsequent analysis concentrates on low source density areas to analyze the true noise properties of the Images, both before and after background-removal in the Images. These noise measures are analyzed versus date and each other. Histograms of the noise distribution are presented. The noise is then compared to the expected noise from the background measurement, and scans with excess noise are shown to be due to airglow variations on the spatial scale of the Images. The properties of the excess noise are presented. The residual noise variations are then analyzed to show that airglow contaminates most H Images at some level. The scan-average properties of noise are presented and compared with the scan "jump" counter. Finally, scans with unacceptable severe airglow are identified.
The data set used for this analysis consisted of all scans in the database as of 26 August 1998. It included all northern nights through 10 October 1997, plus the RTB nights, and the 6-25 January 1998 nights.
Analysis of Noise For All Source Densities
There are two fundamental parameters that measure the noise in each 512" x 1024" Atlas Image: the coadd noise and the background-removed noise. The coadd noise determines the sensitivity of the point source processing and the background-removed noise determines the photometric accuracy of the extended source processing. In detail, the parameters are:
Both noises will increase whenever there is background structure that is not removed, such as airglow, and in confused areas of high source densities. In addition, only the coadd noise will increase whenever there is low-frequency background structure that is effectively removed by the GALWORKS background fit.
To separate these effects, I will first examine the increase of the noise with source density. Unfortunately, the density measurement made by GALWORKS for every Atlas Image is not currently in the database. However, a good proxy for density is the magnitude threshold (mag_thresh) used by GALWORKS. In areas of high source density (above ~1200 sources per square degree with K < 14 mag per sq. deg.), all flux thresholds are raised to avoid working deeper than allowed by source confusion. The magnitude thresholds for unconfused areas are 15.50, 14.75 and 14.25 mag for J, H and K, respectively.
To discover whether large bkgnd_sigmas are primarily due to high source densities, airglow, or some other source of noise, I examined all processed coadds that have bkgnd_sigma > 0.7, 1.3 and 1.3 for J, H and K, respectively. These thresholds were picked to be in the high-end tail of the distribution of the values of that parameters, but the values picked were somewhat arbitrary, since it is unwieldy to work with the entire dataset. About 2, 3 and 7% of the coadds at J, H and K have bkgnd_sigmas larger than these values.
Plots of coadd sigma and background sigma versus each other and magnitude threshold from this database show the following:
Both of these effects are due to source confusion. In low source density areas, where the pixel histogram is not dominated by sources, the bkgnd_sigma must be smaller than the coadd noise, since the coadd noise calculation includes the background excursions removed to calculate the bkgnd_sigma. However, in high source density areas, the positive part of the pixel histogram is dominated by sources. Since the bkgnd_sigma calculation uses the positive part of the pixel histogram, the bkgnd_sigma will be increasingly larger than the coadd sigma as the source density increases. As will be seen later, in low source density areas the coadd noise is indeed always higher than the bkgnd_sigma.
The rest of this analysis is confined to scans not affected by high source density by selecting only coadds that have the magnitude thresholds for unconfused areas given above. There are 25,706; 25,705 and 25,710 such coadds at J, H and K, respectively, representing 1,484 scans. All the H coadds are also J and K coadds; most of the analysis below will consider just the 25,705 coadds in common, with the other 5 coadds neglected. The additional 5 coadds probably come from areas where the thresholds are increased by less than the 0.01 mag I added to the thresholds for my database query for safety.
Coadd Noise And Background Sigma Versus Each Other And Date
Plots of coadd noise and background sigma versus each other and date for low source density areas show the following:
Due to the large number of points and the wide distribution, the most informative way to present the overall histogram of points is to compute percentile values. The mean background-removed noises for J, H and K are 0.51, 0.95 and 1.11 DN, with 90% of the observed noises falling in the ranges 0.45 - 0.61, 0.78 - 1.20, and 0.81 - 1.27 DN.
See plots and table for the rest of the histogram.
The K histogram is quite different from the other bands due to the significant seasonal variation, and hence its histogram will change as we process more data from different time periods.
The noise reduction caused by removing a 4-parameter background fit across the coadd is very similar at J and K, as measured by the ratio of background sigma to coadd noise. Both J and K have a mean reduction in noise of only 2%, with 10% of the coadds having a noise reduction of over 7% for J and K. However, the noise reduction is quite different at H, due again to background variations across the coadds caused by airglow. The mean reduction in noise is 6%, about 30% of the coadds have noise reduction of more than 10%, and 1% of the coadds have a noise reduction of 62%!
Comparison Of Observed Image Atlas Noise To Expected Noise And Identification Of Images Affected By Airglow
With few exceptions, there is little excess noise in the coadds after background subtraction. If we are fully background-limited, the noise in the Atlas Images as measured by the background sigma should be directly proportional to the sqrt of the background counts. Indeed, plots of noise versus sqrt(background) shows that these two quantities are tightly related, with only a handful of coadds showing background sigmas higher than expected from the sky background. Thus for nearly all coadds, any residual background variation in the background-removed coadds is significantly less than one sigma.
Most of the points that fall above the mean relationship are due to airglow. D. Kirkpatrick, R. Hurt, and R. Cutri have identified a number of scans as having noticeable to severe airglow effects as detected either by the H jump counter or by jumps in the background plots. Plots of noise versus sqrt(background) for scans with identified airglow clearly show that most of the points above the mean relationship are due to airglow.
It is possible that some of the deviant coadd noise values at J that fall well above the mean relationship at low background levels are due to bright star artifacts dominating the coadd.
These plots imply the following:
There are no noise points that scatter below the mean relationship. This implies that, at least in low source density areas, the points which scatter low in the plots for all source densities vs. mag threshold are probably not due to problems in the determination of the noise, since that should show up in these plots as well.
The above conclusions are consistent with angular scales of ~17° and time scales of 11 minutes for the major periodic emission variation of airglow due to gravity waves (Ramsay et al. 1992, MNRAS, 259, 751). However, 2MASS is clearly observing and characterizing emission variation of airglow on much finer spatial scales than Ramsey et al were able to measure. The source of this emission variation must be something other than gravity waves in the atmosphere.
A two-parameter fit to these distributions can derive the "background-independent" coadd noise and the slope of the sqrt(background) term. A constant slope can fit the data in all bands. The best-fit values by eye are constant noise terms of 0.25 - 0.41 DN, with a slope of 0.045 times the sqrt(background). See the plot of this fit and the table of the fit parameters.
The values for the slopes are exactly that expected for a gain of 7 electrons / DN (see Analysis of Coadd Noise: Gain and Read Noise Derived From Coadd Noise Versus Background). The constant noise term should vary from 0.33 to 0.51 DN for a read noise of 50-60 electrons and gains from 7 to 9 electrons / DN. The errors on the values derived above are probably large enough to encompass that range.
Analysis Of Observed Minus Expected Noise
A slightly better two-parameter fit to the above distributions has been subtracted from the measured noise for each coadd, which was optimized to eliminate any trends of the residuals with background. The fits have constant noise terms of 0.28, 0.25 and 0.36 at J, H and K, respectively, and slopes of 0.042, 0.043 and 0.045 times the sqrt(background). The plots show histograms of those residuals.
Note that the absolute zero of the fit is somewhat arbitrary, especially at H and K, and I have not spent much effort to make the residuals either symmetric about zero or to have a mean of zero. The fit is used solely to understand the distribution of the residual points, and hence the zero level is arbitrary. The highest bin contains all the points with higher values.
The standard deviation of the residual background sigma is 0.019, 0.029, 0.020 DN at J, H and K, respectively, about means of 0.00, 0.02, and -0.01 DN, including all points in the distribution. The standard deviation of the residual coadd noise is 0.063, 0.419, 0.079 DN at J, H and K, respectively, about means of 0.03, 0.20, 0.02 DN, again including all points in the distribution. (Recall the means have little meaning, but are quoted so that the reader can know the average of the distribution.)
If points with residuals greater than 0.10 are tossed, the standard deviation of the residual background sigma is still 0.019, 0.025, 0.020 DN at J, H and K, respectively, about nearly the same means of 0.00, 0.01, and -0.01 DN, with 25, 302 and 2 points excluded. The standard deviation of the residual coadd noise decreases markedly to 0.022, 0.029, 0.029 DN at J, H and K, respectively, about means of 0.02, 0.04, 0.01 DN, but 974; 11,169; and 1,386 points are tossed. These standard deviations for the residual coadd noise are therefore severely truncated, with about 40% of the H points being tossed, and thus are not accurate measurements of the distribution.
The histograms and the values above show the following:
R. Hurt has noted that the observed variation in backgrounds for rapid airglow changes scales roughly as 0.2 : 1.0 : 0.4 DN for J : H : K. I have plotted the J and K vs. the H background separately by date to refine these numbers. At high H backgrounds caused by airglow, the J background scales as 0.13 - 0.20 of the H background, and the K background scales as 0.35 of the H background.
If the residual unremoved mean background variations across the coadd at J and K scales vs. H in the same way, the expected sigma of those mean background variations would be ~0.002 - 0.004 DN at J and ~0.005 - 0.008 DN at K. These variations are well under the measurement error and observed sigma of 0.020 DN. These expected residual unremoved airglow background variations are in fact consistent with the increase from 0.019 at J to 0.020 at K, but I am not claiming that this is proof for their existence!
Note that this discussion is for the vast majority of the scans that are in the Gaussian distribution of residual noise. Those scans severely affected by airglow, which are found in the extreme tails of the residual noise distribution, have much higher background variations detectable in all bands (see below).
Because additional noise combines in quadrature with the baseline noise to produce the observed noise, these results show that there are no intermittent sources of noise with sigmas of ~0.3 DN. However, other sources of noise characterized by mean sigmas of ~0.2 DN are not excluded by this analysis, and the residuals themselves allow for an additional source of noise with mean sigma ~0.1 DN. See also Analysis Of J Coadd Noise Vs. Background For North And South.
Large H residual noise is always accompanied by large J and K residual noise. Plots of J and K residual noise vs. H residual noise for all coadds with H residual coadd noise above 2 DN and for all values for the scans identified as having significant airglow show that:
Since the same coadd algorithms are used for every band, I know of no reason why the residual coadd noise would be more attenuated by our processing at J and K than at H. This may imply that the emission of the airglow on scales smaller than ~4' has a different spectral distribution than the emission of the airglow on larger scales. If the different spatial scales of airglow had the same spectral distribution, a residual background variation of 5 DN at H would imply a variation of 0.6-1.0 DN at J and 1.7 at K. Such large variations would have no problems being observed, as evidenced by the clear detection of residual background variations of 0.25 DN at J and 0.9 at K, and the observation that there is no deviation from the linear trend with the size of H background variation.
For smaller values of residual noise, the residual coadd noise at H scales directly with the expected noise from the background - see Residual Noise Versus Background, but there is no such correlation for J and K nor for the background sigma at any band. The median residual coadd noise scales as 0.6 times the expected noise above an expected noise of about 0.9 DN. The 90% percentile point for the residual coadd noise scales as 2.5 times the expected noise above an expected noise of about 0.9 DN for the entire range of observed noises.
Observed Scan Noises
Because the basic unit of 2MASS data is a scan, not an Atlas Image, it is of interest to know how much the noise can vary within a scan. Fortunately, the minimum and maximum values of the background sigma from the Atlas Images within a scan are highly correlated. This implies that the amplitude of the airglow variation varies slowly with time and that the percentage of scans affected by severe airglow is close to the percentage of Images that are affected.
The minimum and maximum values of the coadd noise within a scan are not so highly correlated presumably due to the change of amplitude of the coadd-scale airglow emission versus time and the presence of bright stars pushing up the maximum values of the coadd noise. There are 1,484 scans analyzed in all bands.
The mean minimum background-removed noises for J, H and K are 0.50, 0.93 and 1.09 DN, with 90% of the observed noises falling in the ranges 0.44 - 0.60, 0.77 - 1.16, and 0.80 - 1.26 DN. These values differ only in the hundredths place from the similar quantities computed for all coadds.
See plots and table for the rest of the histogram.
Again, the K histogram is quite different from the other bands due to the significant seasonal variation, and hence its histogram will change as we process more data from different time periods.
Scans With Unacceptable Severe Airglow
Airglow is a fact of life at H band. Recall that the distribution of H background sigma residuals shows clearly that there are mean background variations present in the H coadds equivalent to a Gaussian distribution with a sigma of ~0.02 DN. Although this value sounds small, it actually corresponds to unremoved mean background variations (one sigma) over a coadd of ~0.20 DN, which is very much larger than the normal one sigma error in the calculation of the background of 0.02 DN. (This is a different 0.02 DN than the earlier number in this paragraph, but the same number as the one sigma values of the J and K residual background sigmas. See also Analysis of Photometric Noises for 2MASS Galaxies.)
For example, using the mean H background sigma value of 0.95 DN, an H background sigma residual value of 0.02 makes the actual background sigma value to be 0.97. This actual background sigma value consists of the noise distribution, with sigma of 0.95 DN, and another "noise" term resulting from mean background variations over the coadd. The derived sigma of those mean background variations over the coadd is sqrt(0.97^2 - 0.95^2) = 0.20 DN.
This one sigma value of 0.20 DN would cause a flux error at H of 4-13% for a source with H = 13.8 mag (see Analysis of Photometric Noises for 2MASS Galaxies), which is flirting with violating the Level 1 Specification for galaxy photometry of 10%.
Since this is the normal H residual background variation due to airglow, we clearly cannot toss all the scans with residual H background sigmas greater than 0.02, since this would correspond to ~16% of all coadds and a higher percentage of all scans.
There are two thresholds that can be used that will toss only those scans that have quite severe airglow that wildly violates the Level 1 specification and are quite non-uniform compared to the other scans.
The first threshold is objectively determined solely from the H distribution of residual background sigma values itself. That value is determined by fitting a Gaussian to the observed distribution, and determining where there should be no observed points if the distribution is actually Gaussian.
Recall that the H residual background sigma histogram has a mean of 0.01 with a sigma of 0.025, after tossing points greater than 0.10. A value of 0.10 corresponds to 3.6 times that sigma, after removing the mean. For a Gaussian distribution, only 0.00016 of the distribution should be found at larger values. Only 4 coadds out of 25,705 should be found by chance from this distribution. In actuality, 302 coadds exceed this value, coming from 73 scans on 19 nights. 49 of those scans come from only 6 nights, including 6 scans from the night of the sampler data release of 971116n.
Hence the first clear threshold is the value of 0.10, which would toss 5% of all scans in unconfused areas. (Fewer scans would be tossed in confused areas since the confusion noise makes us more tolerant of higher observed noises.)
A threshold of 0.10 for an H background residual is clearly the highest threshold value that should be used, since the scans which fail that threshold are few in number, and badly violate the Level 1 specification. An H background sigma residual value of 0.10 implies mean background variations (one sigma) over a coadd of ~0.45 DN. This one sigma value would cause a flux error at H of 10-30% for a source with H = 13.8 mag (see Analysis of Photometric Noises for 2MASS Galaxies), and significantly violate the Level 1 Specification for galaxy photometry for all size galaxies. (Recall that the Poisson noise of nearly 10% must be combined with this flux error as well.)
See Scans Which Violate A 0.10 Threshold for a list of the scans, plots of their distribution versus time and versus number of coadds which violate that threshold. Note the quality job done by R. Hurt, D. Kirkpatrick and R. Cutri - they have picked out nearly every single scan with a maximum residual H background sigma above 0.20 past 970913n. Scans with a threshold of 0.20 are the ones that make your stomach sick when you look at them, with such reactions as this:
R. Cutri (maximum residual background sigma values of 0.35, 0.23, 0.22, 0.14 and 0.09 DN in these scans):
On the night of 971004n, there are apparently severe background variations in H and to a lesser extent in J due to airglow in scans 053-057. It is hard to believe GALWORKS won't be affected by this. Is there any way we can quantify the impact of these relatively high frequency BG variations on extended source id? I'm worried that we're giving these scans high scores on the basis of everything else, but missing real deficiencies in the extended source processing.
R. Hurt (the maximum residual background sigma values of these scans are 0.14, 0.08, 0.21, and 0.15 DN):
In the worst scans of 980113n (14, 31, 34, 37), the H airglow variations introduce significant structure to the backgrounds including banding artifacts from one tile to the next. These background structures can also be seen at much reduced levels at K. ***Is this bad enough to DEGRADE these scans???***
T. Jarrett looked at scans 53-57 of 971004n (maximum residual background sigma values of 0.35, 0.23, 0.22, 0.14 and 0.09 DN), and reported:
Yes this is some of the worst airglow I have ever seen. Absolutely hideous. Roc, are you telling me that these are Q=10 scans??? This is impossible. There is no way we are getting the H mags correct for these scans.
T. Jarrett has posted the H coadds for scans 68, 162 and 266 of 971005n, which have residual background sigma values of 0.27, 0.30 and 0.48. R. Hurt has posted images of various H and K coadds from scan 40 of 971128n, but I haven't been able to get the residual background sigma values for those scans since they haven't made it to the database yet.
The second threshold is subjectively determined from a balance of the pain of discarding scans with the pain of violating the Level 1 specification for galaxy photometry and the Level 1 specification of uniformity across the sky. This will undoubtedly be the subject of much further discussion.....
Scans With Unacceptable Severe Airglow and the Jump Counter
G. Kopan originally developed a "jump counter" to detect the J background jumps caused by hardware problems that introduced "frame edges" in the coadds. Since severe airglow variation also produced "frame edges", the jump counter is also useful in detecting severe airglow variation. The quality analysts currently use the jump counter and background jumps correlated in color between the bands to detect scans with severe airglow.
This analysis has provided a much better way to detect scans affected by airglow, the residual background sigma, but it is of some interest to know how this correlates with the jump counter.
The jump counter is computed from the frame medians output by FREXAS. The algorithm differences the current and previous frame median. If the difference is greater than 0.5 times the rss of the computed noise of the two frames, then the jump counter is incremented for that scan for that band. The jump counter is thus the total number of increments per scan per band.
The computed noise of a frame of course includes any background variation caused by airglow. However, the 0.5 threshold used turns out to be fairly accurate in detecting scans with severe airglow. A plot of the maximum residual H coadd noise in a scan versus the H jump counter shows that large values of the jump counter always imply excess coadd noise. However, the reverse is not the case.
Acknowledgments
I have received a lot of help from T. Jarrett, D. Kirkpatrick, R. Hurt, G. Kopan and R. Cutri in sorting this problem out. They helped to straighten me out when I went down the wrong path. Noise is a tricky business, and one needs all the help one can get.
http://spider.ipac.caltech.edu/staff/tchester/2mass/analysis/galaxies/backgrounds/analysis.html
Comments and feedback: Tom Chester
Last update: 30 November 1998.
