4-PARAMETER TRANSFORMATION OF DIGITIZED ASTRONOMICAL IMAGES Yavor Chapanov 1 1 – National Institute of Geophysics, Geodesy and Geography, Bulgarian Academy of Sciences VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia

4-, 3- parameter transformation – Z, Cz, Rx and Ry are zeroes

DATA SIMULATION PLATE SCALE <100"/mm SCAN RESOLUTION 2400dpi IDENTICAL STAR SETS PRELIMINARY UNIFIED DATA REFRACTION AND DISTORTION CORRECTIONS ACCURACY: (I) 0”.5 – the best case, (II) 1”.0 – middle precision, (III) 5”.0 – poor accuracy Systematic errors: Image rotation 2 arcmin; Center shift 5 Scales 1*10 -4 ; 1*10 6 (  =2) VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia

Field Width: 02Ê00' Center RA: 02h 00m 00s, Center DE: 42Ê00'00º Equinox: J2000 North is Up, East is Left Source catalog: GSC-ACT Created by StarGazer version dev (C) by Rumen G.Bogdanovski STAR POSITIONS 317 stars

A MODEL OF TIPICAL ASTROMETRIC ERRORS Normally distributed numbers N (0, 0.1) Replaced by: 1% evenly distributed numbers from intervals (  0.8,  0.4], [0.4, 0.8); 6% evenly distributed numbers from intervals (  0.4,  0.1], [0.1, 0.4); 6% evenly distributed numbers from intervals (  0.06, 0.06). Resulting  =0.14 Re-scaling as: 0”.5; 1”.0; 5”.0 VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia

ERROR MODEL – I Standard 0.5 arcsec VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia Coordinate Frame Rotation 2 translations, 1 rotation, scale correction X vector [arcsec] Y vector [arcsec] Z angle [arcsec] Scale [ppm] Quality criteria 2.75 Maximum spatial residual [arcsec] 0.60 Average spatial residual [arcsec] 0.41 Root mean Square (RMS) of residuals [arcsec] X=180as, Y=240as, Rz=-120as, S=100ppm Max. errors <0”.05

ERROR MODEL – II Standard 1.0 arcsec VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia Coordinate Frame Rotation 2 translations, 1 rotation, scale correction X vector [arcsec] Y vector [arcsec] Z angle [arcsec] Scale [ppm] Quality criteria 5.23 Maximum spatial residual [arcsec] 0.86 Average spatial residual [arcsec] 0.66 Root mean Square (RMS) of residuals [arcsec] X=180as, Y=240as, Rz=-120as, S=100ppm Max. errors <0”.05

ERROR MODEL – III Standard 5.0 arcsec VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia Coordinate Frame Rotation 2 translations, 1 rotation, scale correction X vector [arcsec] Y vector [arcsec] Z angle [arcsec] Scale [ppm] Quality criteria Maximum spatial residual [arcsec] 6.07 Average spatial residual [arcsec] 4.31 Root mean Square (RMS) of residuals [arcsec] X=180as, Y=240as, Rz=-120as, S=100ppm Max. errors <0”.4

VII BSAC "ASTROINFORMATICS" – Chepelare, 1-4 June 2010 Position errors 0”.5 + PM errors 0”.5/a*10a Coordinate Frame Rotation 2 translations, 1 rotation, scale correction X vector [arcsec] Y vector [arcsec] Z angle [arcsec] Scale [ppm] Quality criteria Maximum spatial residual [arcsec] 5.55 Average spatial residual [arcsec] 4.46 Root mean Square (RMS) of residuals [arcsec] X=180as, Y=240as, Rz=-120as, S=100ppm Max. errors <0”.5 PROPER MOTION ERRORS

VII BSAC "ASTROINFORMATICS" – Chepelare, 1-4 June 2010 Standard 1.0 arcsec Coordinate Frame Rotation 2 translations, 1 rotation, scale correction X vector [arcsec] Y vector [arcsec] Z angle [arcsec] Scale [ppm] Quality criteria 5.5 Maximum spatial residual [arcsec] 1.2 Average spatial residual [arcsec] 0.8 Root mean Square (RMS) of residuals [arcsec] X=360as, Y=480as, Rz=-120as, S=1,  =2 Max. errors <0”.6 A CASE OF LARGE SCALE

CONCLUSIONS It is possible to estimate the rotation and image center of digitized astronomical plates by the 4-parameter Helmert transformation if the number of identical stars is more than 100. The estimation accuracy is better than 0.4as for plates with 100”/mm scale, scan resolution 2400dpi and total rms errors of star positions below 5as. The necessary preprocessing of digitized astronomical images are image convert to small scale, determination of identical stars from the image and star catalog and correction of the atmosphere refraction and distortions due to telescope optics and projection of celestial sphere over the focal plane. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia