•   Purpose:  To understand psfchi numbers which are in current database (aug, 2000) and determine the psfchi cut and magnitude limit, for debelding: 1) what ranges of psfchi is worthwhile for deblending? Since psfchi is large could mean that the souce is non-single sources, deblending could resolve into multiple sources. 2) What magnitude ranges of sources are worthwhile for deblending. If the sources are too faint, then it will be hard to distinguish if they are a single source, multiple sources or extended sources. So to set up the upper mangnitude limit for debleding is needed, not to waste computer running time.

•    Definition:

•  Summary plots

 
• Summary plots for J band


The plots needed to determine the psfchi cut for deblending below.

Figure  A (55new1 below). Histogram Comparison of b=89, b=10, and b=0 cases (J band)
Figure  B (55new2 below). Cumulative histogram Comparison (SUM OF ALL MAGNITUDE RANGE): J band
Figure   C(53new1 below), Histogram of comparison for Jmag between 12 and 14.: J band
*The plots needed to determine the magnitude cut for deblending below
 Figure  D (44 below). Comparison of mag dependency  ofpsfchi<2 for b=0 and b=89 (before psfchi peak shifted): Jband
 Figure E(56a below). HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE.(b=89) after psfchi peaks were shifted
 Figure F(56b below) MAG VS. NORMALIZED HISTOGRAM (b=89) after psfchi2 peaks were shifted
 Figure G (57a  below) HISTOGRAM(b=0) Jband after psfchi peaks were shifted
 Figure  H(57b below) NORMALIZED HISTOGRAM (b=0) Jband after psfchi peaks were shifted.
 
 
 

• Summary plots for H band
 
 Figure  I(76a. below) HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE after psfchi peaks were shifted.
 Figure  J(76b below)  MAG VS. NORMALIZED HISTOGRAM after psfchi peaks were shifted
 Figure  K (77a below)  HISTOGRAM(b=0) after psfchi peaks were shifted
 Figure  L(77b below) NORMALIZED HISTOGRAM (b=0) after psfchi peaks were shifted.
 Figure  M (76-79 below). Comparison of mag dependency of psfchi<2. for b=0 and b=89 (after psfchi peak is shifted): H band
                  Small stepin b=0 case at 12 mag is not real (due to adjustment of the  psfchi peak so that you may ignore.
                  This plot suggests at least up to 13mag is worthwhile for deblending.
 Figure  N (75new3 below) Likely Extended source population (histogram for b=0 - histogram for b=89): H band
 
• Summary plots for K band


 Figure O(85b below). Magnitude vs. Normalized histogram (b=89) before psfchi peaks were shifted
 Figure P(86a below) . Magnitude vs. Normalized histogram (b=00) before psfchi peaks were shifted
 Figure Q(96a below). HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE (b=89).
 Figure  R(96b below) MAG VS. NORMALIZED HISTOGRAM (b=89) after  psfchi peaks were shifted
 Figure S (97a  below) HISTOGRAM(b=0) after psfchi peaks were shifted
 Figure T(97b  bwlow) NORMALIZED HISTOGRAM (b=0) after psfchi peaks were shifted.
 Figure U. Comparison of b=89 and b=00 for mag vs.normalized histogram (for psfchi<2)

   For example of J band,  the sources with psfchi > 2 is 18 percent, and psfch > 1.5 is 26 percent.
* Final statistics for band crossing for deblending. (see section D.1. for details below)
       Three band cross checking using psfchi>1 for deblending (using b=0 case)
               a) One band is deblended but the other two blands are not deblended:
                      The sources which will be deblended in one band but not in other bands, is about
                      6 percent  sources, using psfchi>2.
               b) Two bands are deblended but the third band is not deblended:
                    percent of sample with  (Jpsfchi > 2 and Hpsfchi >2  and  K psfchi <= 2 ) is  3 percent.
                    percent of sample with  (Kpsfchi > 2 and  Hpsfchi > 2 and K psfchi <= 2) is  7 percent.
 
 
 
 

    1) b=89 (l=20) case.
             Histogram and cumulative histogram
            Figure 1 JHK histogram
        Figure 1  b=89 (l=20) historgram  :

                 These histrograms (Fig. 1a and 1b) show most of   Psfchi is less than 2 and
                 it peaks at 1.  Only really small portion (about 5 percent has Psfch greater than 2).
                 Psfchi reanges from 0 to 13.
           Figure 2 Normalized Cumulative histogram (from Fig.1a)

                    Figure 3a Histogram with extended sources
                            This figures show histograms for both point sources (astricks) and extended sources (diamond).
                             For higher chisq (between 2-9), the percent of extended sources are higher, which tendency
                              is noticeable for redchi2 >2. Above redchi2=2, the sources probably starts blending sources,
                              rather than point sources (or true extended sources).
                     Figure  3b Histrogram with different chisq cut
                     Figure  3c Redchi2 vs percent of extended sources
                               Percent of extended sources gradually  increase until rechi2=2, and after that point, it remains
                               high (more than 50 percent).

           Figure  4. The ratio of Histrogram  normalized by the histogram (total)
           This is the ratio of histogram normalized by total histogram
                    (this is order from the top to the bottom).
          The  difference in the histograms is noticeable above 13 mag.

                This plot suggests the cutoff of the J magnitude is 17 mag.  Above 17 mag
               the data quality of chi2 is uncertain.
                  Figure 4b improved  (This figure is teh same as Fig. 2b, but with most sample point sources,
                                                            i.e. search was done for 5 degree radius).
           Figure 5. Histogram normalized by hist of chi<2
                        This figure shows that the reliability is bad for higher mag than 14.5 mag for chi<4.
                                                               the reliability is bad  for higher mag thatn14.5 mag for chi<5.
                                                                the reliability is bad for all mag if we include chi>5.

       2) b=10 (l=20)  case

           Figure 11a b=10 (l=20) histogram and cumulative histogram
                Figure 11b zoom
                Figure 11c zoom2

           Figure 12d Normalized cumulative histogram (from Fig. 3a)
                Figure 12e Histogram with Point and Extended sources
                     This histogram shows with extended sources (astricks). Since there are only 52 sources
                     are marked with extended sources, the percent of extended sources for each rechi2 is unclear.
                     Most of ext. sources have rechi2 less than 2 where most of point sources fall into. Above
                      redchi2 of 2, there are only 1-2 extended sources.
                 Figure 12f Histogram of point and extended sources (percent of extended sources)
                                When we compare this percent with that for b=89 case (figure 2ab),  extended
                                    percent for b=10 case shows much  smaller portion.
           Figure 13 Histrogram comparison for all chi cut

           Figure 13a The histrogram (with given chi2) normalized by total histogram
                      Figure 13a zoom
           *This plot shows the following implication.
              (1) Double stars can contribute the reduced chi2 lower as in jmag 10-15 mag.
                     The reason the hist/totalhist (for rechi2<2: blue plot) decreases bebtween 10
                      to 15mag is due to the confusion in double stars.
              (2) When jmag>15, the percent for rechi2<2 increases because S/N is limited.
              (3) For the bright stars (brighter than 10mag),  the faint nearby star(companion of
               the bright star) may not be able to be identified due to surrounding artifacts due to the bright star.
                which can contributed. However, when a single psf is fit to this bright star with a faint companion,
                it will give residuals (slightly higher redchi2).  At 9 mag, a sharp dip in the plot means that
                in that dip the data points have rechi2 >10 (not just >2).

           Figure 14b The histrogram (for given chi2) normalized by histogram of rechi2 <2
             Assuming the histogram of redchi2 (<2) is ideal, the histogram ratio
           with rechi2<2 show above 16.5 magnitude, the data quality is good for
            deblending.
 

    3) b=50 (l=20) case.
       data: data extraction region: 3 degree radius centered on b=50, l=20
           Figure 21a Psfchi distribution (histogram) in J, H and K bands
                J , H, and K dpsfchi distributions are similar to each other.
          Figure 22. Histogram for Psfchi distribution
                Figure 8b. Normalized inverse cumulative histogram
           Figure 23a Histogram for point sources (also marked extended sources)
                   Figure 23b Percent of point sources which marked as extended
          Figure  24a Magnitude vs. its histogram for different chi2 range
             Figure 24b Jmag vs. normalized histogram for point sources for different redchi2 cut
                          Figure  24b zoom

  4) b=0 case
      data: data extraction region: 1 degree radius centered on b=00, l=10

          Figure 31a. Histogram for Psfchi distribution
                Figure 31b. Normalized inverse cumulative histogram
           Figure 32a Histogram for point sources (also marked extended sources)
                   Figure 32b Percent of point sources which marked as extended
                   One clear noticeable fact is that the correlation between chi2 and extended source is really poor  for a dense region of b=0.
             Figure 33a Magnitude vs. its histogram for different chi2 range
             Figure 33b Jmag vs. normalized histogram for point sources for different redchi2 cut
                          Figure 33b  zoom

   5) Comparison between the two (b=89, b=10, and/or b=0)

      Figure 41 Comparison of histogram and cumulative histogram between b=10 and b=89

       Figure 42 Comparison of normalized histogram for b=10 and b=89
          b=89 data set has 1,844 data points and b=10 has 92,351 data points. So b=10 has 50 times as large as that of b=89.
          The normalized histogram is very similar. for the case fo b=10 shows more small changes in steps which is probably due to smaller samples. (92321 data points for b=10, 1844)
         Figure 43 Comparison of normalized histogram improved (b=89 and b=10). (for b=89 data, data amount is increased, r=5 degree).

         Figure 44. Comparison of mag dependency of psfchi<2 for b=0 and b=89

       Figure 45. Magnitude vs Psfchi for b=0 and b=89

  6) NEW COMPARISON for b=0 and b=89 (and/or b=10): REDUCED CHI2 is normalized for each
mag bin since there is a problem in absolute meaning of reduced psf chi2.

data: b=89 (l=20,5 degree radius, number of data points:105,943-15: This is not the same data set above.
                       previous data set has 1 degree radius and 5 degree radius sample is used to reduce the errors).
           b=10 (l=20, 1 degree radius, number of data points:92,336-15: This is the same data set above)

          New set b=0 (newplot)(l=10 which has data points of  205,680)

Figure 51new1.  Comparison for Jmag<9
               This figure shows chi2 greater than 5 is not good, requiring deblending; above rechi2 =2, the discrepancy
               is noticeable (so deblending can be attended to improve).
Figure 51new2. Non-Cumulative Histogram (Jmag<9mag)
Figure 51new3.Normalized Cumulative histogram (Jmag<9mag) after psfchi peak is shifted to 1
                This figure shows histograms of b=10 and b=0 are significantly different with that of b=89 above psfhci=5.
 
 

Figure 52new1: Histogram comparison for jmag between 9 and 12
                This plot shows deblending can be used above psfchi=1.3 (other option is above  2 for b=10, and
                above chi2=1.5 for b=0; more convervative solution).
Figure 52new2. Non-cumulative histogram
Figure 52new3. Normalized cumulative histogram (9<Jmag<12) after psfchi is shifted to 1.
                 1)This figure shows the histogram of b=10 is overall similar to that of b=89, but  that of
                       b=10 is different above psfchi=1.
                 2) In details,  signifiant difference of b=10 cumulative histogram in comparison with b=89 is noticeable above psfchi=1,
                      while significant difference of b=0 is noticeable above psfchi=2.5 (accurately above 1.5).
 
 

 Figure 53new1, Histogram of comparison for Jmag between 12 and 14.
                     This plot suggests that deblending can be used above 4 for b=10 and above 1.3 for b=0.
 Figure 53new2  Non-cumulative Histogram
 Figure 53new3. Normalized cumulative histogram (12<Jmag<14) after psfchi is shifted to 1
                      1)This figure shows the histogram of b=10 is overall similar to that of b=89, but  that of
                       b=10 is different above psfchi=1.
                      2) Signifiant difference of b=10 cumulative histogram in comparison with b=89 is noticeable above psfchi=5,
                      while significant difference of b=0 is noticeable above psfchi=1.
 

 Figure 54new1 Histogram comparison for Jmag greater than 14
                     This plot suggested that dblending can be used above rechi=1.5 for b=10, and above 1.3 for b=0.
 Figure 54new2 Non-cumulative histogram
 Figure 54new3. Normalized cumulative histogram (Jmag>14mag) after psfchi is shifted to 1
 
 

 Figure 55new1. Histogram Comparison of b=89, b=10, and b=0 cases
                    Figure 25new1 is obtained by summing all magnitude ranges histogram (which were shown above, sum of
                       histograms of Figure 21new2, Figure 22new2, Figure23new2, and figure24new2).
 Figure 55new2. Cumulative histogram Comparison (SUM OF ALL MAGNITUDE RANGE)
                    Figure 25new2 is obtained a summing all magnitude ranges histogram (which were shown above, i.e.
                     sum of  cumulative histograms of Figure 21new3, Figure 22new3, Figure23new3, and figure24new3).

 Figure 55new3. Likely Extended source population (histogram for b=0 - histogram for b=89).
                      The sources with psfchi=1.5-6 can be deblending to resolve into  multiple  point sources.
 

 Figure 56a. HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE.(b=89)
 Figure 56b MAG VS. NORMALIZED HISTOGRAM (b=89)

 Figure 57a HISTOGRAM(b=0) Jband
 Figure 57b NORMALIZED HISTOGRAM (b=0) Jband.
 Figure 58.  Magnitude and psfchi scatter plot (before shift and after shift)
 

Conclusion   from J band Analysis.
 1) The critical psfchi number for deblending is between 1.3 and 1.5
     (above psfchi=1 is worthwhile to attempt deblending).  This deblending
     effort will be critical the sources which has psfchi between 1.3 and 6.
 2) The deblending should be at least done the magnitudes less than 12-14mag
      and if possible we can try up to 15 mag limit.

B) H band
 
 

1) H Band Histogram
        Figure 61. H band histogram (also extended source counterpart)      (J and H similar but K different).
        Figure 62.  H band Extended counterpart percent histogram
        Figure 63. H band Histogram and cumulative histogram
        Figure 63b. H band Hist (point and ext)
        Figure 63c  H band Normalized histogram
Figure 64.  Hband Normalized chi2 distribution for different rechi2 cut

2) new comparison for H band: REDUCED CHI2 is normalized for each
mag bin since there is a problem in absolute meaning of reduced psf chi2.

Figure 71new1.  Non-cumulative Histogram for  Hmag<9  (histogram peak is shifted to 1).

Figure 71new2.  Normalized Cumulative  histogram (Jmag<9mag) after psfchi peak is shifted to 1

Figure 72new1. Non-Cumulative histogram

Figure 72new2. Normalized cumulative histogram (9<Jmag<12) after psfchi is shifted to 1.
 

Figure 73new1  Non-cumulative Histogram
Figure 73new2. Normalized cumulative histogram (12<Jmag<14) after psfchi is shifted to 1

Figure 74new1 Non-cumulative Histogram comparison for Jmag greater than 14

Figure 74new2. Normalized cumulative histogram (Jmag>14mag) after psfchi is shifted to 1
 

Figure 75new1. Histogram Comparison of b=89, b=10, and b=0 cases
                    Figure 35new1 is obtained by summing all magnitude ranges histogram (which were shown above, sum of
                       histograms of Figure 31new2, Figure 32new2, Figure33new2, and figure34new2).
Figure 75new2. Cumulative histogram Comparison (SUM OF ALL MAGNITUDE RANGE)
 

Figure 75new3. Likely Extended source population (histogram for b=0 - histogram for b=89).

***** Summary plots for H band  *****************************************************************

 Figure 76a. HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE.
 Figure 76b MAG VS. NORMALIZED HISTOGRAM
 Figure 77a HISTOGRAM(b=0)
 Figure 77b NORMALIZED HISTOGRAM (b=0).
 Figure 78.  Magnitude and psfchi scatter plot (before shift and after shift)
 

C) K  Band
1) Histogram
        Figure 81. K band histogram (also extended source counterpart)

       Figure  82 K  band Histogram and cumulative histogram
       Figure 83b. K band Hist (point and ext)
       Figure  83c  K band Normalized histogram
       Figure 84, K band Normalized chi2 distribution for different rechi2 cut (b=10)
       Figure 85a. Extended source percent as a function of redchi2( b=89)
       Figure 85b. Magnitude vs. Normalized histogram (b=89)

      Figure 86a. Magnitude vs. Normalized histogram (b=00)
      Figure 86b. Magnitude vs.  Histogram (b=00)
      Figure 86c. Extended source percent as a function of redchi2(b=00)
 

2) new comparison for K band: REDUCED CHI2 is normalized for each
mag bin since there is a problem in absolute meaning of reduced psf chi2.

Figure 91a.  Non-cumulative Histogram for  Kmag<9  (histogram peak is shifted to 1).

Figure 91b.  Normalized Cumulative  histogram (Kmag<9mag) after psfchi peak is shifted to 1

Figure 92a. Non-Cumulative histogram(9>Kmag<12)

Figure 92b. Normalized cumulative histogram (9<Kmag<12) after psfchi is shifted to 1.
 

Figure 93a. Non-cumulative Histogram (12<Kmag<14)
Figure 93b. Normalized cumulative histogram (12<Kmag<14) after psfchi is shifted to 1

Figure 94a. Non-cumulative Histogram comparison for Kmag greater than 14

Figure 94b. Normalized cumulative histogram (Kmag>14mag) after psfchi is shifted to 1
 

Figure 95a. Histogram Comparison of b=89, b=10,and b=0 cases
                    Figure 35new1 is obtained by summing all magnitude ranges histogram (which were shown above, sum of
                       histograms of Figure 31new2, Figure 32new2, Figure33new2, and figure34new2).
Figure 95b. Cumulative histogram Comparison (SUM OF ALL MAGNITUDE RANGE)
Figure 95c. Likely Extended source population (histogram for b=0 - histogram for b=89).

** ********SUMMARY PLOTS for  K band ******************************************************

 Figure 96a. HITOGRAM AFTER PEAK IS SHIFTED DEPENDING ONE THE MAG RANGE (b=89).
 Figure 96b MAG VS. NORMALIZED HISTOGRAM (b=89)
 Figure 96c.  Magnitude and psfchi scatter plot b=89(before shift and after shift)
 Figure 97a HISTOGRAM(b=0)
 Figure 97b NORMALIZED HISTOGRAM (b=0).
 Figure 97c.  Magnitude and psfchi scatter plot (before shift and after shift)

D) J, H, and K psfchi comparison

1) Correlation
b=89
 Figure 101a. J and H psfchi comparison
 Figure 101b. J and K psfchi comparison
  The percent of sample which gives chi difference between Jchi and Kchi is greater than 1,  is 3 percent (=3354/105928).
b=0
 Figure 102a. J and H chi comparison (b=0)
 Figure 102b. J and K psfchi comparison (b=0)
*The percent of sample which gives chi difference between Jchi and Kchi is greater than 1,  is 32 percent (=66681/205680).

* I have also examined percent of sample for possible deblending.
   1) when thresold for chicut is 2 for deblending.
            A)   Two band cross checking (using b=0 case)
                    percent of sample with Jpsfchi > 2 and K psfchi <= 2 is  8.5 percent.
                    percent of sample with Kpsfchi > 2 and J psfchi <= 2 is  13 percent.
                    percent of sample with Jpsfchi > 2 and H psfchi <= 2 is  7.0 percent.
                    percent of sample with Hpsfchi > 2 and J psfchi <= 2 is  10 percent.
                    percent of sample with H psfchi > 2 and K psfchi <= 2 is  6.0 percent.
                    percent of sample with K psfchi > 2 and H  psfchi <= 2 is   7.5percent.
           B)   Three band cross checking (using b=0 case)
                 a) one band is deblended but the other two blands are not deblended:
                    percent of sample with  (Jpsfchi > 2 and K psfchi <= 2 and Hpsfchi <=2) is  5.7 percent.
                    percent of sample with  (Kpsfchi > 2 and J psfchi <= 2  and Hpsfchi <=2) is  6.1 percent.
                                Therefore, the percent of sources which will be deblended in J (or K) band but not in other bands, is about
                                6 percent  of sources in the Galactic plane.
                 b)  two bands are deblended but the third band is not deblended:
                    percent of sample with  (Jpsfchi > 2 and Hpsfchi >2  and  K psfchi <= 2 ) is  3 percent.
                    percent of sample with  (Kpsfchi > 2 and  Hpsfchi > 2 and K psfchi <= 2) is  7 percent.
 

   2) when thresold for chicut is 1.5 : percent of sample with Jpsfchi > 1.5 and K psfchi <= 1.5 is  11 percent.
                                                            percent of sample with K psfchi > 1.5 and J  psfchi <= 1.5  is   15.5 percent.

2) Comparison with H and K band

   Figure 111. l=20 b=10 plot
 *Where solid line (J band), dashed line (H band), and dashed-dot line (K band):
  H istograms show that the chi peaks at 0.5-1 (0.55 for b=10, 0.95 for b=50, and 0.55 for b=89).
  The comparison plot for J, H, K shows the J and H bands have similar redchi2 values
  while K can use a higher rechi2 than those of J and H.
   Figure 112. l=50 l=20 chi distribution of J, H, and K band