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4-PARAMETER TRANSFORMATION OF DIGITIZED ASTRONOMICAL IMAGES

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

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4-PARAMETER TRANSFORMATION OF DIGITIZED ASTRONOMICAL IMAGES

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  1. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia 4-PARAMETER TRANSFORMATION OF DIGITIZED ASTRONOMICAL IMAGES Yavor Chapanov1 1 – National Institute of Geophysics, Geodesy and Geography, Bulgarian Academy of Sciences

  2. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia 4-, 3- parameter transformation – Z, Cz, Rx and Ry are zeroes

  3. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia 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*106 (m=2)

  4. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia STAR POSITIONS 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 1.3.0-dev (C)2001-2005 by Rumen G.Bogdanovski 317 stars

  5. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia A MODEL OF TIPICAL ASTROMETRIC ERRORS 10000 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 s=0.14 Re-scaling as: 0”.5; 1”.0; 5”.0

  6. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia ERROR MODEL – I Standard 0.5 arcsec X=180as, Y=240as, Rz=-120as, S=100ppm Coordinate Frame Rotation 2 translations, 1 rotation, scale correction 180.03 X vector [arcsec] 240.02 Y vector [arcsec] -119.48 Z angle [arcsec] 92.96 Scale [ppm] Max. errors <0”.05 Quality criteria 2.75 Maximum spatial residual [arcsec] 0.60 Average spatial residual [arcsec] 0.41 Root mean Square (RMS) of residuals [arcsec]

  7. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia ERROR MODEL – II Standard 1.0 arcsec X=180as, Y=240as, Rz=-120as, S=100ppm Coordinate Frame Rotation 2 translations, 1 rotation, scale correction 180.03 X vector [arcsec] 240.01 Y vector [arcsec] -121.28 Z angle [arcsec] 99.20 Scale [ppm] Max. errors <0”.05 Quality criteria 5.23 Maximum spatial residual [arcsec] 0.86 Average spatial residual [arcsec] 0.66 Root mean Square (RMS) of residuals [arcsec]

  8. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia ERROR MODEL – III Standard 5.0 arcsec X=180as, Y=240as, Rz=-120as, S=100ppm Coordinate Frame Rotation 2 translations, 1 rotation, scale correction 180.24 X vector [arcsec] 240.15 Y vector [arcsec] -112.12 Z angle [arcsec] 87.20 Scale [ppm] Max. errors <0”.4 Quality criteria 28.29 Maximum spatial residual [arcsec] 6.07 Average spatial residual [arcsec] 4.31 Root mean Square (RMS) of residuals [arcsec]

  9. VII BSAC  "ASTROINFORMATICS" – Chepelare, 1-4 June 2010 PROPER MOTION ERRORS Position errors 0”.5 + PM errors 0”.5/a*10a X=180as, Y=240as, Rz=-120as, S=100ppm Coordinate Frame Rotation 2 translations, 1 rotation, scale correction 180.22 X vector [arcsec] 240.15 Y vector [arcsec] -112.78 Z angle [arcsec] 143.54 Scale [ppm] Max. errors <0”.5 Quality criteria 39.46 Maximum spatial residual [arcsec] 5.55 Average spatial residual [arcsec] 4.46 Root mean Square (RMS) of residuals [arcsec]

  10. VII BSAC  "ASTROINFORMATICS" – Chepelare, 1-4 June 2010 A CASE OF LARGE SCALE Standard 1.0 arcsec X=360as, Y=480as, Rz=-120as, S=1, m=2 Coordinate Frame Rotation 2 translations, 1 rotation, scale correction 360.03 X vector [arcsec] 480.03 Y vector [arcsec] -119.47 Z angle [arcsec] 1000085.93 Scale [ppm] Max. errors <0”.6 Quality criteria 5.5 Maximum spatial residual [arcsec] 1.2 Average spatial residual [arcsec] 0.8 Root mean Square (RMS) of residuals [arcsec]

  11. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia 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.

  12. VIII Serbian-Bulgarian Astronomical Conference: 8-12 May 2012, Leskovac, Serbia THANK YOU FOR YOUR ATTENTION

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