INTRODUCTION
The active deblending capability of the new development-version of PROPHOT
has been tested against a truth table based on some higher-resolution
observations of a moderately dense region of the Galactic plane at K band.
The observations were made by John Carpenter et al using the University of
Hawaii 2.24 m telescope, and covered 23 separate regions of size 5' x 5'
in the vicinity of Galactic longitude 140 deg. The FWHM of the PSF was
approximately 0.6 arcsec. The magnitude range of the extractions was 11.5 to
17.5 (the lower limit of which was constrained by saturation), and the
extraction list included the RA and dec (J2000) and K magnitude. There were
systematic errors in position of the order of 2 arcsec.
ANALYSIS
PROPHOT was run on the set of scans which included the above regions, using
the following parameters:
adb_nmax = 2 (maximum number of actively-deblended components)
adb_magmax = no limit (maximum magnitude for an attempted active deblend)
adb_dchi = 1.0 (minimum improvement in reduced chi squared required by
active deblending algorithm)
chip = 2.0 (maximum allowed value of reduced chi squared for a
point source)
The output source list was matched up against the truth table based on
Carpenter's data, using the following prodedure:
(1) A list was made of all of the blended sources in Carpenter's data, where
a blend was defined as a pair of sources whose separation was less than
or equal to 4 arcsec (such sources represent complete or partial blends at
the 2MASS resolution). In the vast majority of cases, the blends were
doubles (for example, at a limiting magnitude of 15, only about 2% were
triples).
(2) For each of the above blends, the 2MASS source lists were searched for
the best match in position, with respect to the primary (defined as the
brightest source in a blend) and its neighbor(s). The positional tolerance
for a position match was 3 arcsec for the primary, and 2 arcsec in relative
position of the secondary with respect to the primary.
(3) For each attempted active deblend, the successful cases were identified
(defined as those for which the error in separation vector was less than
2 arcsec in both x and y). The standard deviation of the residuals in
K magnitude (2MASS - Carpenter) was then calculated, both for the blend as a
whole and for the individual components.
Steps (2) and (3) were done for a series of upper magnitude cutoffs.
RESULTS
The results are summarized in Table 1 as follows:
Kmax Nblends Npri Nall Nattempts Nsuccess sigK(blend) sigK(comp) 15 162 101 41 21 20 0.8 1.0 14 113 70 26 16 16 0.3 0.7 13 41 24 9 5 5 0.2 1.0 12 10 6 2 1 1 0.1 0.3 The column headings have the following meaning: Kmax = upper cutoff for K magnitude Nblends = number of blends identified in Carpenter's data Npri = number of those cases in which primary was present in 2MASS data Nall = no. of those cases in which all components present in 2MASS data Nattempts = number of active-deblend attempts Nsuccess = number of successful active deblends sigK(blend) = RMS magnitude residual (2MASS-Carpenter) for blend as a whole sigK(comp ) = RMS magnitude residual for individual component
ANALYSIS OF MAGNITUDE ERRORS
Since the magnitude errors, as inferred from the RMS magnitude residual in Table 1, were somewhat large, a detailed analysis was performed, in which the RMS residuals were evaluated separately for the primary and secondary components, and binned as a function of source separation and magitude difference of primary and secondary. In addition, these RMS residuals were compared with their theoretical values based on the combined errors of the 2MASS and Carpenter photometry.
The results of the error analysis were plotted as follows:
Figure 1:, RMS magnitude residual as a function of source separation.
Figure 2:, RMS magnitude residual as a function of (sec-pri) magnitude difference
Figure 3:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of source separation.
Figure 4:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of (sec-pri) magnitude difference.
In all 4 plots, the filled circles represent the primary components, and the open diamonds represent the secondaries.
Figure 1 shows the expected qualitative behavior in that the photometric errors increase with decreasing source separation.
From Figures 1 and 2, it is apparent that a large fraction of the magnitude
error reported in Table 1 is due to the secondary components. Examination
of Figures 3 and 4, however, reveals that the secondary magnitude errors
are entirely consistent with expectation.
Figure 3 also shows that the primary magnitude errors are larger than expected.
There appears to be a trend, in which the discrepancy
between the observed and expected magnitude errors becomes greater as the
source separation is decreased, but decreases down to the expected value
as the source separation increases. One possible explanation of this is
that the expression used for the variance of simulaneous estimates (based
on second derivatives of chi squared) assumed a linear measurement model
in the neighborhood of the maximum likelihood solution. This was
apparently a valid assumption in the case of an isolated source, but it
may break down in the case of multiple sources because the nonlinearities
may be more severe. Experiments with synthetic data show somewhat similar
behavior, but this needs to be investigated further.
UPDATES
=======
AUG 4
=====
Found an error in the deblending logic in prophot, whereby a deblended source would have been excluded if its final rchisq was below the "let's attempt to deblend" threshold. We now distinguish between the rchisq value ADB_CHIMAX above which a deblend will be attempted, and the value CHIP which determines if the final fit is satisfactory.
Repeated the prophot run for the counterparts of the Carpenter data, using the following parameters:
CHIP = 2.0
ADB_CHIMAX = 1.3
As a result of the above fix, and also the use of a smaller value of the deblend criterion, adb_chimax, many more deblended sources were found, thus improving the statistics. The new versions of Figs 1-4 above are:
New Figure 1:, RMS magnitude residual as a function of source separation.
New Figure 2:, RMS magnitude residual as a function of (sec-pri) magnitude difference
New Figure 3:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of source separation.
New Figure 4:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of (sec-pri) magnitude difference.
Some things to note from these figures:
(1) The primary magnitude error decreases with increasing pri/sec flux ratio, whereas the converse is true for the secondary. This behavior is expected, and furthermore, the primary magnitude error approaches the value for an isolated point source at large flux ratios.
(2) The primary magnitude error is about a factor of 2.5 larger than the expected value, except for small separations, when it increases to about 5. The secondary magnitude errors, are, however, consistent with expectation.
(3) The actual magnitude errors for primary and secondary (as opposed to the RMS residuals which are plotted), for the range 1-4 arcsec in source separation, are:
primary ~ 0.2 mag
secondary ~ 0.3-0.5 mag
AUG 7
=====
COMPARISON WITH SYNTHETIC DATA.
Synthetic 2MASS data were generated in order to check that the results obtained from John Carpenter's data are consistent with expected performance. The data were generated based on instrumental parameters appropriate to 2MASS, in terms of PSF shape, noise model (pixel gain, read noise, PSF variance) and frame-to-frame offsets. Synthetic images of blended source pairs were thereby generated for separations in the range 0.2 - 2.0 pixels (i.e., 0.4 - 4.0 arcsec) and magnitudes in the range 8-15 (the latter half of which overlaps with Carpenter's data). A constant flux ratio was assumed, corresponding to a sec-pri magnitude difference of 0.8 (the mean value for the blends in Carpenter's data).
The RMS magnitude errors for the primary and secondary were evaluated, and expressed both in magnitudes and in units of the expected error (a-posteriori standard deviation). These and other quantities of interest were tabulated as a function of source separation and primary magnitude, and the results were as follows:
Percentage of cases in which all blended components were found:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 33 37 66 13 3 13 56
9.0 | 0 6 13 44 63 3 0 16 63
10.0 | 0 3 13 51 56 6 0 23 73
11.0 | 0 10 23 58 73 6 0 30 76
12.0 | 0 3 23 41 73 20 0 13 83
13.0 | 0 0 10 44 90 50 17 40 80
14.0 | 0 0 3 27 50 26 17 33 83
15.0 | 0 0 0 0 0 0 6 6 26
Percentage of the above cases in which active deblending done:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 100 100 100 100 100 0 11
9.0 | 0 100 100 100 100 100 0 40 10
10.0 | 0 100 100 100 100 100 0 42 13
11.0 | 0 100 100 100 100 100 0 55 4
12.0 | 0 100 100 100 100 100 0 25 36
13.0 | 0 0 100 100 100 100 80 75 45
14.0 | 0 0 100 100 100 100 100 60 24
15.0 | 0 0 0 0 0 0 50 50 25
Position error [hundredths of a pixel]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 24 9 6 9 5 4 5
9.0 | 0 11 8 9 10 3 0 6 5
10.0 | 0 65 10 11 8 23 0 35 9
11.0 | 0 20 12 10 8 66 0 26 5
12.0 | 0 6 22 16 8 7 0 6 14
13.0 | 0 0 21 17 9 13 10 19 23
14.0 | 0 0 19 17 16 18 24 27 21
15.0 | 0 0 0 0 0 0 37 25 22
Primary magnitude error [hundredths of a magnitude]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 24 24 12 13 78 30 15
9.0 | 0 27 23 20 16 12 0 42 14
10.0 | 0 24 16 24 13 4 0 47 17
11.0 | 0 10 45 22 18 42 0 48 20
12.0 | 0 36 20 23 12 23 0 37 27
13.0 | 0 0 43 33 15 19 19 28 25
14.0 | 0 0 10 32 20 35 59 23 31
15.0 | 0 0 0 0 0 0 19 68 47
Secondary magnitude error [hundredths of a magnitude]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 37 27 15 11 12 6 26
9.0 | 0 46 15 33 27 2 0 26 27
10.0 | 0 100 41 33 24 30 0 12 8
11.0 | 0 25 46 28 19 73 0 18 13
12.0 | 0 27 66 50 16 15 0 13 39
13.0 | 0 0 57 31 12 23 4 17 36
14.0 | 0 0 1 41 23 20 17 29 26
15.0 | 0 0 0 0 0 0 23 62 42
Position error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 304 202 160 186 82 72 108
9.0 | 0 144 123 173 251 98 0 98 101
10.0 | 0 833 172 210 183 166 0 141 109
11.0 | 0 274 205 170 208 124 0 150 109
12.0 | 0 75 293 205 141 129 0 90 122
13.0 | 0 0 304 235 93 139 122 104 135
14.0 | 0 0 153 107 123 105 118 106 121
15.0 | 0 0 0 0 0 0 116 63 92
Primary magnitude error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 229 268 182 154 748 306 218
9.0 | 0 106 208 211 287 239 0 358 198
10.0 | 0 556 270 322 222 66 0 212 236
11.0 | 0 197 422 244 197 53 0 220 242
12.0 | 0 169 343 260 148 222 0 294 241
13.0 | 0 0 450 258 152 203 257 289 204
14.0 | 0 0 94 127 132 172 192 196 158
15.0 | 0 0 0 0 0 0 125 165 136
Secondary magnitude error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 269 229 222 100 167 97 233
9.0 | 0 201 60 198 473 44 0 259 261
10.0 | 0 511 181 257 307 178 0 63 139
11.0 | 0 221 583 218 239 63 0 131 206
12.0 | 0 124 712 253 145 184 0 120 330
13.0 | 0 0 370 317 75 121 41 175 164
14.0 | 0 0 10 168 96 113 81 474 104
15.0 | 0 0 0 0 0 0 81 118 132
A few things to note from the above:
(1) There appears to be the same trend which was apparent from the real data (i.e., the 2MASS/Carpenter comparison), whereby the relative magnitude error (in units of sigma) increases with decreasing source separation.
(2) The actual magnitude errors are quite consistent with those obtained
from the real data.
CONCLUSIONS:
Based on the results obtained from John Carpenter's data (K = 11.5-15), and the extrapolation to brighter sources using synthetic data (justified by the consistency with Carpenter's data in the overlap range), I draw the following conclusions:
(1) At a source separation of about 1 arcsec, for blends with magnitude differences in the range 0-1, active deblending gives magitude errors of typically 0.1-0.2 for the primary and 0.2-0.3 for the secondary.
(2) The errors get somewhat worse for smaller separations. Depending on the flux ratio, the secondary magnitude error can be 0.5 or more.
In terms of cpu time, the the cost of doing all this is about a factor of 4 per blend (over and above the time it takes to do 1 isolated source).
AUG 14
======
ERRORS OF TOTAL BLEND FLUX
The errors of the total blend flux were analysed both for the synthetic data and real (2MASS+Carpenter) data at K-band.
(a) Comparison of total blend flux for 2MASS (deblended) and Carpenter data:
Figure 5 shows a plot of the magnitude residual (2MASS - Carpenter) as a function of total blend magnitude.
In order to show how these magnitude residuals compare with the theoretical errors, the next figure (Figure 6) shows a plot of magnitude error divided by the expected sigma, taking into account the photometric errors of both 2MASS and the Carpenter results. This figure shows that the magitude residuals are entirely consistent with expectation.
(b) Total blend flux errors for synthetic data:
The total-blend magnitude errors have been evaluated for the K-band synthetic data, both in absolute units and in units of the expected error. The results are tabulated as follows:
Blend magnitude error [hundredths of a magnitude]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 13 6 7 11 40 18 10
9.0 | 0 8 11 10 6 7 0 35 13
10.0 | 0 3 9 9 8 10 0 25 13
11.0 | 0 7 9 9 9 11 0 32 15
12.0 | 0 11 6 11 7 14 0 24 26
13.0 | 0 0 12 10 9 11 14 18 19
14.0 | 0 0 7 10 13 18 35 17 24
15.0 | 0 0 0 0 0 0 20 24 31
Blend magnitude error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 97 53 91 89 397 139 105
9.0 | 0 35 64 70 83 130 0 271 127
10.0 | 0 16 43 81 80 26 0 131 169
11.0 | 0 68 44 66 93 8 0 159 164
12.0 | 0 42 64 68 69 121 0 151 132
13.0 | 0 0 55 50 64 100 131 118 93
14.0 | 0 0 44 44 51 79 99 111 84
15.0 | 0 0 0 0 0 0 65 50 58
These tables show that the magnitude errors of the total blend are
reasonable, and consistent with theoretical expectation.
AUG 24
======
PROBLEMS RELATED TO COMPLETENESS
The results with synthetic data, as presented in the Aug 7 update, indicated a severe dip in the completeness at a source separation of 1.4 pixels. The relevant portion of the results was as follows:
Percentage of cases in which all blended components were found:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
8.0 | 0 0 33 37 66 13 3 13 56
9.0 | 0 6 13 44 63 3 0 16 63
10.0 | 0 3 13 51 56 6 0 23 73
11.0 | 0 10 23 58 73 6 0 30 76
12.0 | 0 3 23 41 73 20 0 13 83
13.0 | 0 0 10 44 90 50 17 40 80
14.0 | 0 0 3 27 50 26 17 33 83
15.0 | 0 0 0 0 0 0 6 6 26
As it turns out, this dip is an indirect consequence of a long-standing typographical error in PROPHOT. This error occurred in the function subroutine FUNK which calculates the chi squared corresponding to an assumed source position (or set of positions in the case of either active or passive deblending). The section in which the fluxes are estimated contains the following piece of code:
c Now calculate the right hand sides. do j = 1,nblend xij = p(2*j-1) etak = p(2*j)
In the 4th line, however, the variable "etak", which represents the y-coordinate of the source, should have been "etaj". In the case of single sources, the location "etak" contained the correct value, and hence the photometry was not affected (which is why the problem has not been detected over the years). In the case of blended sources (either passive or active), however, the typo would have had serious consquences. It would have resulted in an error in flux estimation which depended on the relative y offsets of the components.
In the present tests, if the position angles of the separation vectors of the synthetic blends had been random, the above effect would have given rise to a random error. However, the synthetic data were generated in such a way that the position angle was correlated with the source separation. Specifically, as the scan progressed, the separation vector was systematically rotated and scaled so as to give a range of angles and separations for test purposes. It simply turned out that at a separation of 1.4 pixels, the separation vector was parallel to the y-axis, thus maximizing the y-offset-related error.
After fixing this, the completeness table then looked like:
Percentage of cases in which all blended components were found:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 0 0 3 0 3 13 56
8.0 | 0 3 16 17 20 10 20 36 63
9.0 | 0 0 23 62 70 80 75 80 93
10.0 | 0 3 20 65 80 80 93 90 100
11.0 | 0 0 10 65 90 93 96 100 100
12.0 | 0 0 6 75 96 96 96 96 100
13.0 | 0 0 6 48 80 100 100 96 100
14.0 | 0 0 0 3 6 23 58 70 83
Happily, the completeness dip at 1.4 pixels has now disappeared. Unhappily, though, there is a falloff in completeness with increasing source brightness (the range of magnitudes has been adjusted to go down to 7, so as to better illustrate this effect).
This problem turned out to be a dynamic range effect in the noise-model variance, resulting from the fact that the noise model for bright sources is PSF-dominated, and the variance is then proportional to the square of the flux. This causes precision problems in the computations, especially in the matrix inversion step. One solution is to convert much of the parameter-estimation section of the code to double precision. A simpler solution, which I believe is satisfactory, is to place a ceiling on the dynamic range of the variance. A value of 1000 seems to preserve the information content while not running afoul of single-precision limitations.
Based on that modification, the completeness table now looks quite satisfactory. The complete (no pun intended) set of results of the synthetic data analysis is as follows:
Percentage of cases in which all blended components were found:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 20 75 90 93 96 90 96
8.0 | 0 0 20 62 83 83 100 93 96
9.0 | 0 3 20 65 83 90 96 93 100
10.0 | 0 3 20 65 80 80 93 93 100
11.0 | 0 0 10 65 90 93 96 100 100
12.0 | 0 0 6 75 96 96 96 96 100
13.0 | 0 0 6 48 80 100 100 100 100
14.0 | 0 0 0 3 6 23 58 70 83
Percentage of the above cases in which active deblending done:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 100 100 100 100 96 77 20
8.0 | 0 0 100 100 100 100 100 67 13
9.0 | 0 100 100 100 100 100 100 75 16
10.0 | 0 100 100 100 100 100 100 71 10
11.0 | 0 0 100 100 100 100 100 73 6
12.0 | 0 0 100 100 100 100 96 79 26
13.0 | 0 0 100 100 100 100 100 73 13
14.0 | 0 0 0 100 100 100 94 38 12
Position error [hundredths of a pixel]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 6 6 8 8 6 4 4
8.0 | 0 0 7 7 8 7 6 4 4
9.0 | 0 6 9 9 8 7 6 4 5
10.0 | 0 7 10 7 7 6 7 4 4
11.0 | 0 0 10 9 8 5 4 4 3
12.0 | 0 0 4 8 7 9 5 6 4
13.0 | 0 0 14 14 12 9 7 9 6
14.0 | 0 0 0 33 19 12 13 13 13
Primary magnitude error [hundredths of a magnitude]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 8 8 7 9 10 4 7
8.0 | 0 0 10 12 8 7 6 5 5
9.0 | 0 10 11 10 8 10 10 6 8
10.0 | 0 6 17 10 9 7 7 9 5
11.0 | 0 0 15 12 10 7 6 5 5
12.0 | 0 0 10 11 11 6 6 7 5
13.0 | 0 0 9 12 5 7 7 6 7
14.0 | 0 0 0 2 17 6 10 10 16
Secondary magnitude error [hundredths of a magnitude]:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 25 21 21 19 10 6 5
8.0 | 0 0 26 23 22 15 10 6 5
9.0 | 0 21 21 24 18 9 11 5 5
10.0 | 0 15 32 19 18 11 8 5 4
11.0 | 0 0 32 24 21 10 7 7 4
12.0 | 0 0 15 23 15 11 6 10 7
13.0 | 0 0 32 25 15 16 9 14 10
14.0 | 0 0 0 22 26 13 16 19 19
Position error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 100 155 251 308 226 271 179
8.0 | 0 0 126 163 227 245 271 206 120
9.0 | 0 12 146 197 225 219 246 168 123
10.0 | 0 100 154 159 208 208 309 133 106
11.0 | 0 0 120 184 195 158 126 105 99
12.0 | 0 0 41 143 144 155 119 97 77
13.0 | 0 0 158 172 125 108 96 79 99
14.0 | 0 0 0 110 113 79 87 110 105
Primary magnitude error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 127 112 135 147 149 75 91
8.0 | 0 0 142 140 148 110 92 103 85
9.0 | 0 212 132 151 129 145 98 94 116
10.0 | 0 139 147 136 147 118 111 72 83
11.0 | 0 0 63 156 139 101 78 68 88
12.0 | 0 0 196 128 110 88 75 74 68
13.0 | 0 0 92 193 58 74 84 71 62
14.0 | 0 0 0 17 114 47 80 77 142
Secondary magnitude error as a percentage of theoretical value:
| Source separation [pixels] -->
Mag | 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8
-------------------------------------------------------------
7.0 | 0 0 181 182 328 471 227 313 272
8.0 | 0 0 223 166 312 268 310 332 127
9.0 | 0 228 139 245 252 226 345 244 99
10.0 | 0 194 162 190 278 265 284 123 115
11.0 | 0 0 148 183 248 220 163 100 106
12.0 | 0 0 135 193 144 136 123 105 85
13.0 | 0 0 206 211 108 128 71 61 76
14.0 | 0 0 0 84 125 80 93 93 104
Note that not only has the completeness been drastically improved, and shows no spurious trends, but the accuracy of the primary flux estimates has been improved by a factor of 2.
Additional note: Although the completeness dip turned out not to be due to an undersized solution radius (i.e. radius of the "data circle" -- the standard value is 2 pixels), I have increased this radius to 3 pixels for active deblending in order to avoid clipping the data for the secondary components. This was an oversight in the previous runs. For the final version of prophot, we need to retain the 2-pixel radius for single sources (as a computational economy measure), but increase it to 3 (or possibly even 4) pixels when the single-source chi squared indicates the need for active deblending.
AUG 30
======
Reran John Carpenter's data through the fixed version of prophot, using a data-circle radius of 3 pixels. The results were as follows:
New Figure 1:, RMS magnitude residual as a function of source separation.
New Figure 2:, RMS magnitude residual as a function of (sec-pri) magnitude difference
New Figure 3:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of source separation.
New Figure 4:, Relative RMS magnitude residual (in units of the theoretical a-posteriori standard deviation) as a function of (sec-pri) magnitude difference.
Comparing these results with those obtained previously (Aug 4 update), it is apparent that the magnitude errors have been reduced substantially. Interestingly, there is not much difference in the results when expressed in terms of the theoretical error. I suspect that this is due to the fact that theoretically-predicted errors have also decreased, probably because of the increased data-circle radius.