IV. 2MASS Data Processing
4. Point Source Detection and Photometry
c. Aperture Photometry, Curve of Growth Correction and Photometric Normalization
Aperture photometry is performed for each non-saturated source detection made on the Atlas Images to provide a reference to the absolute photometric scale for the profile-fit photometry, statistics on the detectability of an object, and as a back-up source of brightness information when profile-fitting fails to converge to a valid measurement.
As with the profile fitting,
the aperture photometric measurement is made at the position of a
detection on the individual frames. On each frame, the brightness is
measured in a series of apertures ranging in radius from 3´´ to
14´´, in 1´´ steps, by summing pixels entirely
within the aperture and interpolating
pixels partially within the aperture. The sky background for each object
is computed in an annulus with an inner radius of 14.0´´ and
an outer radius of 20.0´´. Pixels in the sky annulus are entirely
included or excluded based on the distance of their centers from the source.
The sky value is estimated by first excluding saturated, masked, or
unreasonably low pixels. A 
-trimmed median
of the surviving sky pixels is then used as the sky brightness estimate.
The aperture measurements from each of the six input frames are combined using an unweighted average which takes into account non-detections in frames to avoid flux-overestimation. Aperture measurements are usually possible on all six (and sometimes seven) frames that sample the position of each detection. However, if one of more of the frames contains a masked or saturated pixel within 4" of the source centroid, or if the source centroid falls within <4'' of a frame edge, that frame is excluded from the the measurement. The aperture measurements from each of the remaining available frames are combined using an unweighted average.
The statistics of the aperture measurements are compiled in
the ndet
parameter included in the PSC record. Ndet is a six-digit flag,
with two digits per band
(NJMJNHMHNKMK)
that tabulates for each band the number of frames on which a source
was detected with >3 in aperture the photometry,
Nb, and
the number of frames which were available for measurement, Mb.
Thus, the frame detection thresholds are also referred to
as the "N-out-of-M" criteria.
For example,
an ndet value of "665634" indicates that a source had
six >3 detections
on all six of the available frames in the J-band, five detections out of
six possible frames in the H-band, and three detection on four possible
frames in the Ks-band. For brighter sources, the
ndet parameter can be used as a reliability indicator
and is used in source selection for
the final PSC.
ii. Curve-of-Growth Correction
The "standard aperture" used for 2MASS aperture photometry had a 4'' radius (or ~2 camera pixels). However, the point-spread-function of the 2MASS optical system is broad enough that light from the wings of star images is not completely captured within this aperture. Depending on the atmospheric seeing conditions, between 2% and 15% of the total flux from a point source will be missed. To correct for the loss of light in the standard aperture, a curve-of-growth correction is applied to the measurements, and it is this corrected photometry that is listed in the standard aperture magnitudes (j_m_stdap, h_m_stdap, k_m_stdap) in the PSC source records.
The curve-of-growth correction is a constant factor that when added to the magnitudes measured in the 4'' radius aperture makes them equivalent to an "infinite" size aperture. Correcting small-aperture measurements rather than using much larger apertures avoids the degradation in signal to noise ratio due to increased sky photon noise and possible confusion with nearby sources that would result from simply using larger aperture measurements. However, the correction means that the aperture photometry quoted for 2MASS sources assumes that the sources are unresolved, and have a profile consistent with the point-spread-function of the optical system plus seeing. Resolved or multiple sources may not be accurately characterized by the standard aperture measurements.
The curve-of-growth corrections applied to standard aperture photometry during final 2MASS data processing were drawn from look-up tables indexed by atmospheric seeing. Photometry for all sources in a scan observed within specified ranges of measured seeing conditions were corrected using the same factor, per band. The correction-table values were derived empirically using the multi-aperture photometry of large ensembles of non-saturated sources (rd_flg="2") observed in relatively low source density scans from each observatory under a wide variety of seeing conditions. For each observatory, time period and seeing value, the differences between magnitudes in successive aperture were compiled, and the point at which the differences converge to zero was determined. The correction factor, in magnitudes, is the median difference between the 4´´ aperture magnitude and the magnitude in the aperture at which the magnitude differentials become indistinguishable from zero. The mean correction values for each band and each seeing range were internally consistent; the median and the mean values agree to <0.01 magnitudes.
J-band curves-of-growth evaluated during periods of good (2.5´´ FWHM) and bad (3.4´´ FWHM) seeing in scans from the Second Incremental Data Release are shown in Figure 1 and Figure 2, respectively. The x-axes show aperture radius in pixels (2´´/pixel), and the y-axes show the magnitude differences measured in successive aperture pairs vs. the outer radius of the pair. Indicated on the figures are the radius of the "standard aperture" (open circle), and the radius at which the curve-of-growth was determined to converge (open star). The good seeing case shown in Figure 1, converges at a smaller radius, 2.5 pix (5´´) than the poor seeing case, 4.0 pix (8´´). The curve-of-growth correction determined in these examples were -0.016±0.005 mags and -0.121±0.015 mags, respectively. Note that the net corrections in each case are the sum of the differentials for all pairs between 4'' and the convergence radii.
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| Figure 1 | Figure 2 |
iii. Photometric Normalization
Profile-fit Photometry
Curve-of-growth-corrected aperture photometry of high SNR, unconfused, non-saturated sources on the 1.3 s exposures best defines the true photometric scale for 2MASS. In the absence of confusion, such measurements best capture the total flux of points sources and are least influenced by effects such as focal plane distortion and differences between the seeing-influenced instantaneous point-spread-function and model point-spread-functions used in profile-fitting photometry. Therefore, both the profile-fitting magnitudes, and those derived from aperture photometry on the 51 ms "Read_1" frames are normalized to the curve-of-growth-corrected aperture photometry of bright, non-saturated sources measured on 1.3 s "Read_2" frames.
Normalization of the profile-fitting photometry was usually
done by deriving empirical offsets between the profile-fit and
curve-of-growth-corrected aperture magnitudes for high SNR sources
in each scan. Since the normalization changes with seeing,
different offsets were derived for sources in a scan having
different measured characteristic seeing values.
For a given band and seeing range, the normalization constants were
derived by measuring the median difference between profile-fit and
curve-of-growth-corrected aperture photometry for all sources in a scan
within that seeing range
using iterative 3 rejection.
The -rejection excluded confused sources
which can have contaminated aperture or profile-fit photometry, or both.
The resulting offset correction is added to the profile-fit photometry,
and this corrected value is the default magnitude
listed in the PSC record for sources with
rd_flg="2".
Figure 3 shows the relationship between
profile-fit and curve-of-growth-corrected aperture magnitudes for a scan
in the All-Sky Data Release,
after the normalization correction has been applied to the profile-fit
photometry.
In scans of Tiles with source densities too low to provide enough sources for the normalization derivation, or with source densities so high that confusion corrupts the aperture photometry (>41,000 deg-2), the photometric normalization constants could not be reliably determined empirically. The profile-fit photometry in these scans were selected from a look-up table indexed by the seeing. The correction tables were derived using the empirical corrections calculated in the preliminary processing, using all survey scans with fewer than 2000 sources per Atlas Image (17´ in length).
Bright Star Aperture Photometry
Normalization of all of the aperture photometry of bright stars measured on the 51 ms "Read 1" exposures was made using the corrections taken from a seeing-indexed look-up table. As with the curve-of-growth corrections, these normalization factors were derived before processing began using photometry of large ensembles of stars from both observatories taken under a wide range of seeing conditions that were bright enough to be detected in the 51 ms exposures, but not bright enough to be saturated in the 1.3 s "Read 2" exposures. There was typically 2-3 magnitudes of brightness overlap in which sources would satisfy this requirement. The mean offsets between curve-of-growth-corrected aperture magnitudes and the aperture magnitudes from the 51 ms exposures were derived for all stars within various seeing ranges. The results for each seeing range were internally consistent; the median and the mean values agree to better than 0.001 magnitude, and the standard deviation of the mean offset values were <0.01 mag.
The 51 ms exposure aperture photometry corrections ranged in amplitude from -0.02 mag to -0.12 mag for seeing values of ~2´´ to 3.5´´. These normalization factors were added to the 51 ms exposure aperture photometry, and the corrected magnitudes are listed in the default magnitude fields for the PSC sources with rd_flg="1"). Figure 4 shows the normalized 51 ms exposure aperture magnitudes plotted as a function of their corrected profile-fit magnitudes for a full night's data in the All-Sky Data Release. This figure also illustrates the overlap in the magnitude range over which both 51 ms and 1.3 s exposures provide useful measurements for determining the normalizations.
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| Figure 3 | Figure 4 |
vi. Curve-of-Growth and Photometric Normalization Errors
After the final 2MASS data processing was completed, it was discovered that out-of-date correction look-up-tables were used for the normalization of profil-fit photometry in the very high and low source density cases. The differences between the correct values and those used resulted in a systematic overestimate of source brightnesses after the correction, the amplitude of which is a function of seeing FWHM and the photometric band. The overestimation ranges from <0.01 mag in good seeing, to a maximum of 0.02-0.03 mag for the worst seeing in the Survey. Because the amplitude of the bias can be different in each band, this error can produce residual color-biases on ~17´ scales along a Tile, and ~8.5´ across Tile boundaries.
This bias is believed to cause at least part of the discrete color jumps correlated with Atlas Image boundaries seen in spatially-averaged color maps of high source density regions. An example of this is given in Figure 5 which shows a map of mean H-Ks source color made using the normalized profile-fit photometry of PSC sources in a 3°x6° field near the galactic center. However, the amplitude of these jumps can be as large as 0.05 mag, as seen in Figure 6 which shows the H-Ks colors of individual stars along one of the scans in Figure 5. Therefore, the observed discrete color biases cannot be fully accounted for by the PSF-normalization errors. We do not have a complete understanding of the origin of these color jumps, but they are known to be correlated to changes in the PSF used in profile-fit photometry. The biases are not seen in colors derived from aperture photometry.
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| Figure 5 | Figure 6 |
[Last Updated: 2003 March 11; by R. Cutri, T. Evans, J. Carpenter]
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