Kiso Schmidt Plate Digitized Data NEW (KSQ) Astrometric Calibration
(Oct.2020)



New astrometric calbration using 'ARC-SIP' fittings is DONE.
The new calibrated FITS files are named 'KSQxxxxx'.

Notes
(1) Some browsers (for example, DS9 older then v.8.0) do not resolve SIP parameters correctly.
(2) Because SMOKA astrometric calibration is done for a whole area on the plate,
accurate calibration may be difficult.
If you want more accurate calibration, we recommend the partial area calibration by yourself.
(3) There are several difficulties in the determination of the center of stars:
the centers of line-shaped stars in "comet" plates are not well-defined,
the centers of stars on Objective Prism plates cannot be well-defined, and
multi-exposure plates (MUL2,MUL3) and sub-beam-prism plates (SB) lead mis-matching of Std.Stars.



2019-11-28
Results of the astrometric calibration are released for 5542 plates.

2020-10-21
Results of the NEW astrometric calibration are released for 4609 plates.



(1) Astrometric Calibrated Data:

The astrometric calibrated FITS files are modified their header keywords ;
CTYPE1 to "RA---ARC-SIP', CTYPE2 to 'DEC--ARC-SIP', RA2000, and DEC2000.
Additionally, several FITS header keywords are added to the FITS headers;
WCS keywords (CRVAL1, CRVAL2, CRPIX1, CRPIX2, CD1_1, CD1_2, CD2_1, and CD2_2),
3rd.order SIP keywords (A_ORDER=3,B_ORDER=3,A_0_2,A_1_1,A_0_2,A_2_1,A_1_2,A_3_0,A_0_3, B_0_2,B_1_1,B_0_2,B_2_1,B_1_2,B_3_0,B_0_), and
keywords about fitting results ( WCSNSTAR, WCSRESID, and WCSFLAGS );
WCSNSTAR : Number of adopted Std.Stars.
WCSRESID : Mean fitting residuals (arcsec).
WCSFLAGS : Distribution of adopted Std.Stars (8characters).
           1st.char. : W,V  min.value of X-coordinate >= 2/4,1/4 of X-size  
           2nd.char. : W,V  max.value of X-coordinate <= 2/4,3/4 of X-size  
           3rd.char. : W,V  min.value of Y-coordinate >= 2/4,1/4 of Y-size  
           4th.char. : W,V  max.value of Y-coordinate <= 2/4,3/4 of Y-size  
           5th.char. : M,N  center of gravity of X-coordinate <= 2/8,3/8 of X-size
                     : P,Q  center of gravity of X-coordinate >= 6/8,5/8 of X-size
           6th.char. : M,N  center of gravity of Y-coordinate <= 2/8,3/8 of Y-size
                     : P,Q  center of gravity of Y-coordinate >= 6/8,5/8 of Y-size
           7th.char. : DUMMY
           8th.char. : DUMMY


(2) Calibration Methods:

Star extraction program : SExtractor2.19.5
Standard stars catalog : UCAC4 with proper motions
Step.B Matching/Fitting program : imwcs in wcstools3.9.5
Steps C,D,and E Fitting program : minpack.lm on R-3.5.2

The NEW calibration uses the results of the previous calibration (Step.A-D);
  • Step.A : extract stars with SExtractor.
  • Step.B : Match/Fit Std.Stars with wcstools.
  • Step.C : Fit Std.Stars using the Step.B match list with "nls.lm" in "minpack.lm" package of R. Fit is done two times through 5 arcsec rejection.
  • Step.D : Match using the Step.C fitting parameters with threshold 10arcsec, then Fit Std.Stars with "nls.lm" in "minpack.lm" package of R. Fit is done two times through 3 or 5 arcsec rejection.
  • After Step.D of the previous calibration,
  • Step.E : Match using the Step.D fitting parameters with threshold 20arcsec, then Fit Std.Stars with "nls.lm" in "minpack.lm" package of R. (#) Fit is done two times through 3 arcsec rejection.
  • is DONE.
    (#) Fitting in Step.E ("ARC-SIP") is applied to minimize the sum of the value V
             V = sqrt( ( DX - HX ) **2 + ( DY - HY ) **2 ) )
    
             where
    
             TH = asin( sin(dc) * sin(dc0) + cos(dc) * cos(dc0) * cos(ra-ra0) )
             TZ = 90.0 * 3600.0 - TH * dr 
             dr = ( 180.0 * 3600.0 ) / pi 
             DX = TZ * ( cos(dc) * sin(ra-ra0) ) / cos(TH) 
             DY = TZ * ( sin(dc) * cos(dc0) - cos(dc) * sin(dc0) * cos(ra-ra0) ) / cos(TH)
    
             xx = x - xc
             yy = y - yc
             F  = a20 * xx**2 + a02 * yy**2 + a11 * xx * yy +
                  a21 * xx**2 * yy + a12 * xx * yy**2 + a30 * xx**3 + a03 * yy**3
             G  = b20 * xx**2 + b02 * yy**2 + b11 * xx * yy +
                  b21 * xx**2 * yy + b12 * xx * yy**2 + b30 * xx**3 + b03 * yy**3
             HX <- cd11 * ( xx + F ) + cd12 * ( yy + G )
             HY <- cd21 * ( xx + F ) + cd22 * ( yy + G ) 
    
             and
             (ra,dc) is the coordinate of each standard star,
             (x,y)   is the coordinate of each detected star on the plate.
                   
               Fitting parameters are 20 :(ra0,dc0) is a projection center, 
                                          (cd11,cd12,cd21,cd22) are CD-matrix elements, and
                   (a20,a02,a11,a21,a12,a30,a03,b20,b02,b11,b21,b12,b30,b03) are SIP parameters. 
               Shift parameters (xc,yc) are fixed to the image center.
    

    Finally, we only use the information on the NEW astrometric calibration
    with adopted Std.Stars >= 1000 ( in the case of plates with objective prism or small size plates >= 500 )
    AND better results than the previous calibration (i.e. many adopted Std.Stars and less mean residuals).



    (3) Characteristics of Calibration:

    Fitting Residuals:
    "2nd.step threshold" is 3 arcsec for all plates.
    Fig.3-1a Fig.3-1b





    (4) Residual Map for each plate:

    The map can be seen by clicking the NUMBER in the search results or each THUMBNAIL figure.
    The map shows;
  • matched stars and adopted stars (red) on the image coordinates (upper left)
  • distribution of residuals (RED|1"|ORN|3"|BLK|5"|BLU) on the image coordinates (upper right)
  • distribution of residuals (RED|1"|ORN|3"|BLK|5"|BLU) on the celestial sphere projection plane (lower left)
  • residual vectors (length 100X) on the celestial sphere projection plane (lower right)
  • with several parameters at the bottom area.

    The example figure (KSQ05555) :

    Fig4

    The example of objective prism plates is here



    (5) The strange pattern of the Residual Map (see the map of previous calibration)

    The pattern like vertical stripes is resolved in the NEW calibration.
    The pattern may be caused by the scanner.








    These figures are drawn using R.