I. Background
Discussion about  the aperture curve-of-growth and psf-aperture normalizations can be found in John Gizis' webpage. Color biases were identified by John Carpenter in H-Ks color maps for high density fields. These biases result from the profile-fit/aperture normalizations used in the final processing (see Roc Cutri's webpage).

Color biases seen in the final processing are all places on the sky  where the PSF normalization toggled from calculated to look-up table. The following plots compare the calculated PSF normalizations with the look-up table used when calculated values are not available due to very high or low source density. The analysis is done for each hardware period.
 

II. PSF normalization value versus shape

In all plots surface density corresponds to empirical normalizations, squares are the look-up table values currently in use. The linear regression for the psf normalization versus the shape for each psfid is represented by lines.
Lines boundaries are obtained from the min and max psf shape range. Links below each image open a table which contains the psfid, a and b for psfnorm = b x shape + a, and the old look-up values.

Table 1

J - north a	J - north b	J - north cd	J - north e	J - south
H - north a	H - north b	H - north cd	H - north e	H - south
Ks - north a	Ks - north b	Ks - north cd	Ks - north e	Ks - south

 

III. PSF normalization versus point source density

Figure 1 represents the psf normalization distribution versus the star density. The black diamond indicates the median value of the empirical normalization (1.500) which is larger than the look-up value (1.492). There is no significant density effect on the psf normalization. Figure 2 shows the median and the sigma values of the normalization per density bin. These two plots are for the psf H9715 south which is one of the two psf responsible of the H-Ks color jump of the figure 4.
However, Tom Chester found some psf affected by the density. In these cases, the normalization increases by about 1% from low to high source density.
 

Fig. 1	Fig. 2

 

IV. Median difference between empirical and look-up values for each psfid:
 

J north a	H north a	Ks north a
9531  -0.005   9661  -0.014   9911    0.014 10091    0.012 10311    0.022 10471    0.020 10711    0.017 10911    0.025 11091    0.027 11281    0.025 11491    0.026 11691    0.026 11871    0.026 12091    0.026 12311    0.027 12521    0.025 12711    0.029 12921    0.029 13071    0.024 13301    0.021 13781    no look up value	9471  -0.006   9711    0.014   9891    0.016 10101    0.022 10301    0.026 10481    0.028 10691    0.028 10891    0.018 11101    0.027 11291    0.026 11501    0.024 11701    0.027 11861    0.020 12131    0.019 12291    0.024 12501    0.020 12721    0.022 12881    0.012	9261   -0.005   9481    0.005   9701    0.011   9901    0.022 10081    0.021 10291    0.023 10501    0.027 10701    0.031 10901    0.027 11111    0.028 11301    0.030 11511    0.032 11711    0.026 11881    0.030 12101    0.027 12301    0.032 12511    0.031 12681    0.008

 

J north b	H north b	Ks north b
9752    0.014   9902    0.008 10092    0.013 10302    0.020 10522    0.028 10692    0.023 10882    0.029 11082    0.025 11292    0.032 11472    0.034 11682    0.025 11882    0.026 12092    0.019 12322    0.018 12492    0.010 12912    no look up value	9762    0.017   9932    0.009 10082    0.010 10312    0.022 10482    0.025 10672    0.023 10902    0.033 11072    0.024 11302    0.027 11482    0.025 11692    0.028 11902    0.024 12112    0.012 12282    0.015 12552    no look up value	10122    0.025 10272    0.020 10512    no look up value 10702    0.027 10892    0.027 11092    0.024 11312    0.030 11502    0.036 11712    0.044 11872    0.031 12122    0.041 12332    0.058 12572    0.040 12832    no look up value

 

J north cd	H north cd	Ks north cd
9423   -0.002   9523    0.003   9713    0.007   9903    0.005 10093    0.009 10303    0.021 10483    0.020 10703    0.018 10903    0.026 11103    0.023 11293    0.022 11503    0.019 11703    0.022 11913    0.023 12093    0.023 12323    0.022 12483    0.021 12663    0.022 12873    0.020 13083    0.018 13253    0.020	9383    0.042   9503    0.004   9733    0.013   9873    0.015 10083    0.022 10293    0.015 10463    0.025 10693    0.019 10883    0.019 11063    0.016 11323    0.021 11543    0.021 11713    0.016 11893    0.020 12103    0.018 12303    0.019 12513    0.020 12713    0.016 12883    0.016 13073    no look up value	9223   -0.002   9273  -0.009   9543    0.020   9683    0.014   9923    0.023 10073    0.023 10313    0.023 10493    0.026 10753    0.021 10923    0.020 11113    0.019 11303    0.030 11493    0.024 11693    0.019 11883    0.022 12113    0.027 12313    0.024 12503    no look up value 12703    0.010 12903    no look up value

 

J north e	H north e	Ks north e
9334  -0.02   9524  -0.006   9644  -0.012   9874    0.002 10104    0.008 10304    0.019 10504    0.020 10724    0.026 10894    0.025 11104    0.019 11314    0.021 11504    0.021 11714    0.022 11884    0.025 12094    0.024 12304    0.022 12504    0.023 12714    0.021 12874    0.020 13104    0.020 13324    no look up value 13504    0.038	9154    0.00   9294    0.00   9464  -0.004   9654    0.007   9884    0.017 10114    0.023 10314    0.018 10494    0.019 10704    0.020 10914    0.021 11094    0.019 11294    0.019 11494    0.021 11694    0.022 11894    0.020 12104    0.021 12314    0.020 12494    0.025 12724    no look up value 12904    0.016	9344    0.012   9504    0.004   9704    0.013   9904    0.011 10074    0.023 10284    0.022 10514    0.028 10734    0.030 10924    0.033 11114    0.031 11334    0.033 11484    0.027 11684    0.028 11904    0.025 12114    0.028 12324    no look up value 12514    0.028 12704    no look up value

 

J south	H south	Ks south
9155   -0.002   9315  -0.005   9535    0.00   9695   -0.006   9875    0.005 10075    0.012 10285    0.021 10515    0.022 10705    0.022 10885    0.016 11095    0.014 11355    0.019 11495    0.020 11695    0.020 11905    0.018 12085    0.018 12325    0.020 12505    0.018 12715    0.021 12905    0.020 13095    0.019 13525    0.021	9115    0.003   9325    0.006   9505  -0.005   9715    0.008   9895    0.012 10085    0.018 10305    0.017 10495    0.011 10675    0.013 10905    0.021 11085    0.012 11285    0.013 11475    0.011 11705    0.012 11915    0.010 12105    0.011 12345    0.015 12615    0.007 13025    no look up value	9355    0.004   9545    0.015   9705    0.036   9905    0.025 10095    0.017 10315    0.025 10505    0.024 10715    0.017 10915    0.019 11105    0.016 11315    0.017 11485    0.020 11725    0.015 11885    0.022 12125    0.018 12305    0.022 12515    0.021 13055    no look up value

 

V. Normalization correction for the equator testfield 2 (see John Carpenter's webpage)

a) Color jump
These figures correspond to the right side of the John Carpenter's figure  which show H-Ks jumps for the equator testfield 2.
In figure 3, the left image is H-Ks derived from the database values, the middle image is H-Ks corrected using the above tables and the right image corresponds to the difference between them (i.e. the correction).
A cross section in the inscan direction is presented in figure 4. The original and the corrected sections are represented by the solid black and red lines, respectively. The dashed red line is the corrected section offseted to show the relative effect of the new normalization correction on the H-Ks jumps.
The 2 bottom lines give the PSFIDs along the scan for H and Ks.
 

Fig. 3	Fig. 4	Fig. 5

Fig.5 is obtained using the area of the coadd that overlaps with the Est and West coadds for which there is no PSF change. The solid line corresponds to the Est and West coadds, diamonds to the previous coadd that switches from the H9505s PSF to the H9715s. Dots shows how poor is the statistic. Since the color jump exists between coadds for the same sky area, PSF change seems to be the best explanation for the observed jumps, rather than any astrophysical effect.
 

b) Color analysis versus SNR

Fig. 6	Fig. 7	Fig. 8	Fig. 9	Fig. 10

Fig. 6, 7, and 8 correspond to H-Ks/Dec plots for H_snr and Ks_snr > 0, 20, and 50 , respectively. Jumps still exist at high SNR. This is also seen in the color/magnitude diagram in Fig. 9 which shows that color jumps do not depend on magnitude. Fig. 10 is similar to Fig. 9 but aperture photometry is used instead of psf photometry.These color/magnitude diagrams are obtained using only the 5 coadds involved in the 2 jumps presented in previous figures (Fig. 4 to Fig. 8), i.e. only sources with 7.6 < Dec < 8.8.

c) Additional plots from Tom Chester

-Tom Chester wrote:

i took the dupe sources from eq2 test field with j_snr > 20, and separated them by psfid.  i histogrammed the psf - aperture mags separately for dupe sources which had one dupe with psf id 9505, and which had the other dupe
with psf id 9715.  there is certainly not anything like a 0.10 mag change in the normalization - any such effect is clearly in the 0.01 mag range as calculated by laurent.  see:
http://spider.ipac.caltech.edu/staff/tchester/2mass/analysis/psc/aperture_corrections_eq2_testfield.gif
so we can now concentrate on looking for other sources of the color jump.
 

-Tom Chester wrote:
i looked at the difference in the photometry for the dupes, separating it by psf id, separately for both the psf and ap photometry.  it also shows that there is no effect larger than 0.01 mag when shifting from h psfid 9505 to h psfid 9715.  see:
http://spider.ipac.caltech.edu/staff/tchester/2mass/analysis/psc/dupe_src_photometry_by_psfid.gif
curiously, there is a significant mean difference between the psf mags of -0.010 mag from the lower dec version of a dupe source to the higher dec version of the dupe source, irrespective of whether the psfid changes!  the aperture photometry shows no such effect, with a mean of 0.000 mag:
mean difference (higher dec rendition - lower dec rendition)
psf 9505/9505   ap 9505/9505    psf 9505/9715   ap 9505/9715
-0.011          -0.001          -0.010          0.000
(these values are straight means over all dupe sources shown in the histogram.)
i think my analysis now clearly shows that overall, in eq2 test field, there are no problems larger than the 0.01 mag level in point source photometry in general in this area, at least wrt how we are determining the mags.
since laurent's and john's plots clearly show that SOMETHING is happening in at least one area, i think we need to look at the sources in that one area more closely.

d) Reprocessing withtout the pfs H9715

Ron has reprocessed the scan which contains the jumps with a config that prevents the psf switch (i.e. H9505 is used where H9715 is requested). Fig. 11 is equivalent to Fig. 9 with this new run. The color jump is no longer in the scan. The psf mismatch causes the color jumps.
 

Fig. 11

PSF mismatches has been studied (see Ken Marsh's webpage) and are expected when significant seing variations occur at the coadd timescale. However, the error for a 1-bin shape mismatch (as it is the case here) was believed to yield a 2-3% error at maximum. Although color jumps have only been detected in high density fields for statistical reasons, PSF mismatches are expected everywhere, and statistically should happen more often in low density fields.

e) Interpretation

Relevant psf parameters corresponding to the jumps are summarized in the following table:

H_psfid	9505	9715	9505	9715	9505
H_shape	0.955	0.963	0.958	0.963	0.953
H_shape_sig	0.042	0.045	0.035	0.038	0.034
n_src_shape	175	173	167	116	159

-Tom Chester wrote:
so basically the seeing was near the boundary between two psf-ids, and toggled back and forth.  converting your numbers to "% to the boundary", I get:
43%     -81%    71%     -81%    24%
100% means we are exactly at a boundary.  so in the coadds in question, the numbers are 71% and 81%, pretty close to the boundary.
so in the case where we see a 7% relative difference, we were within 29% of a boundary, and toggling back and forth.
so one immediate conclusion is that the psf fit is not as bad as we thought
- the error is probably only around 3.5%, since one psf-fit is ~3.5% too
high and the next one is ~3.5% too low.

so our first conclusion that there was a mag error of 7% is wrong.  the majority of the coadds with hpsfid 9505 are probably 3% too high, and the two coadds with hpsfid 9715 are probably 4% too low.

Figures 12, 13 and 14 support this interpretation: they plot the psf photometry - aperture photometry versus the distance to the center of the psf shape range. 0 is the center of the psf, 1 is the boundary with the adjacent psf.
It is important noting that the bias in the psf photometry depends on the psf, as it appears for the specific case of H9505 (fig. 13) and H9715 (fig. 14).
 

Fig. 12	Fig. 13	Fig. 14

 

Same figures for the field defined by hemis='s' and glat<-80 :
 

Fig. 15	Fig. 16	Fig. 17

For the eq2 field, psf are normalized with look-up values whereas empirical normalization is used for the low density field (glat<-80). Lower slopes for the low density field are the result of this difference: empirical values are computed for each shape within a psf but there is only 1 look-up value per psf, whatever is the shape.