The AllWISE Multiframe pipeline detects sources on the deep coadded Atlas Images, and then measures the sources through PSFfit photometry using the individual Singleexposures. Optimal source fluxes and positions are measured by fitting pixel data from all available Singleexposure images in all bands simultaneously. The magnitudes in the Source Catalog w?mpro columns are not simply a combination of flux measurements on the individual frames, but rather a simultaneous fit to all pixel data in all bands that makes the best use of all the information.
After the profilefit extraction for each deep detection source is performed, fluxes are then measured on the individual Singleexposures by solving for the PSF amplitude (i.e. the flux), forced at the sky position of the deep detection fit. These individual frame flux measurements and uncertainties are recorded in the AllWISE Multiepoch Photometry Database (MEP). The Singleexposure fluxes are calibrated and converted to magnitudes using the same procedures, zeropoints, and conventions as are used for the entries in the Source Catalog.
For faint deep detection sources, the individual Singleexposure flux measurements will have SNR<2, and magnitudes in the MEP Database therefore will be upper limits. In addition, the measurements in the MEP Database are limited to only those from Singleexposures that satisfied the quality requirements to be used for the AllWISE Multiframe processing. There may be Singleexposure measurements for images excluded from the AllWISE processing in the AllSky, 3Band Cryo, or PostCryo Singleexposure Source Working Databases. However, because of the shallower depth of the Singleexposures, the faintest sources may not have been detected, and the corresponding photometry will not be available.
A number of statistics are computed using the distribution of Singleexposure fluxes measured for each deep detection source. Equations 18 describe the basic flux distribution moments that are calculated, including the inverse varianceweighted mean, unbiased weighted sample variance and the standard deviation of the mean. For example, the w?magp values in the Source Catalog are magnitudes computed from the inverse variance weighted mean fluxes, and are on average very similar to the deep detection profilefit magnitudes, as illustrated in Figures 5ad in II.1.d.i. All of the Singleexposure flux distribution statistics and related parameters included in the Source Catalog and Reject Table are described in Table 1. These statistics are particularly useful for identifying and classifying flux variability, as described in V.3.b.vi.
Note that fluxes measured for saturated sources during the PostCryo phase of the mission are not used in the calculation of flux distribution statistics because of the positive flux bias (II.1.d.i.). These measures are included in the MEP Database, however.
(Eq. 1)

Here M is the total number of measurements, f_{i} is the flux of the i^{th} measurement, w_{i} is the weight of the i^{th} element, w_{t} is the sum of the weights.
Column Name  Description  

w?m  The number of individual frames that are available to make a deep detection profilefit measurement in band "?", where "?" = 1, 2, 3, or 4.  
w?nm  The number of individual frames on which WPRO extracted a flux measurement with SNR > 2.  
w?magp  Sigmaclipped and inverse varianceweighted integrated flux in magnitude units, in each band.  
w?sigp1  Unbiased, weighted sample standard deviation in magnitude units (1.0857*sqrt(Equation 6)/Equation 1).  
w?sigp2  Standard deviation of the mean flux in magnitude units (1.0857*Equation 7/Equation 1).  
w?k  Stetson Kindex (Stetson, P. 1996, PASP, 108, 851), which provides a robust measure of the kurtosis of the magnitude histogram in the band. The value of w?k tends to 1.0 when the variability is much larger than the uncertainties in individual observations, and to 0.798 when the photometric errors dominate over real variations.  
w?ndf  Number of degrees of freedom in the flux variability chisquare in band "?". This quantity is used for prefiltering in the variability flag computation.  
w?mlq  Probability measure that the source flux is variable in band ?. The value is log10(Q), where Q = 1P(chi2). P is the cumulative distribution probability for flux^{[1]}. The value is clipped at 9. This quantity is used as a component in the variability flag computation.  
w?mjdmin  The minimum modified Julian Date (mJD) of the frames used in the flux distribution computation in each band.  
w?mjdmax  The maximum modified Julian Date (mJD) of the frames used in the flux distribution computation in each band.  
w?mjdmean  The mean modified Julian Date (mJD) of the frames used in the flux distribution computation in each band.  
rho12  The correlation coefficient between the W1 and W2 singleframe flux measurements. The value is a signed 2digit integer, expressed as a percentage. Negative values indicate anticorrelation. This quantity is used as a component in the variability flag computation. Rho12 is equal to 100 times the J variability index of Stetson (1996 PASP, 108, 851) computed for W1 and W2.  
rho23  The correlation coefficient between the W2 and W3 singleframe flux measurements. The value is a signed 2digit integer, expressed as a percentage. Negative values indicate anticorrelation. This quantity is used as a component in the variability flag computation. Rho23 is approximately equal to 100 times the J variability index of Stetson (1996 PASP, 108, 851) computed for W2 and W3.  
rho34  The correlation coefficient between the W3 and W4 singleframe flux measurements. The value is a signed 2digit integer, expressed as a percentage. Negative values indicate anticorrelation. This quantity is used as a component in the variability flag computation. Rho34 is approximately equal to 100 times the J variability index of Stetson (1996 PASP, 108, 851) computed for W3 and W4.  
q12  Correlation significance between W1 and W2^{[2]}. The value is log10(Q2(rho12)), where Q2 is the twotailed fraction of all cases expected to show at least this much apparent positive or negative correlation when in fact there is no correlation. The value is clipped at 9. This quantity is used as a component in the variability flag computation.  
q23  Correlation significance between W2 and W3^{[2]}. The value is log10(Q2(rho23)), where Q2 is the twotailed fraction of all cases expected to show at least this much apparent positive or negative correlation when in fact there is no correlation. The value is clipped at 9. This quantity is used as a component in the variability flag computation.  
q34  Correlation significance between W3 and W4^{[2]}. The value is log10(Q2(rho34)), where Q2 is the twotailed fraction of all cases expected to show at least this much apparent positive or negative correlation when in fact there is no correlation. The value is clipped at 9. This quantity is used as a component in the variability flag computation).  
Notes to Table 1: [1] The Q value is the fraction of all cases to be expected if the null hypothesis is true. The null hypothesis is that the flux is emitted by a nonvariable astrophysical object. It may be false because the object is variable. It may also be false because the flux measurement is corrupted by artifacts such as cosmic rays, scattered light, etc. The smaller the Q value, the more implausible the null hypothesis, i.e., the more likely it is that the flux is either variable or corrupted or both. [2] When the number of measurements is large, the significance of correlation also tends to be large even though the correlations themselves may have a relatively small magnitude. This is a typical manifestation of statistical significance increasing as the sample size increases; eventually the high significance can be due to small correlated errors in background estimation or even roundoff errors. These effects tend to be small but become significant when there are enough observations of them. High flux correlation significance should be taken seriously only when the magnitude of the correlation is also fairly high. 
Last update: 19 November 2013