4-PARAMETER TRANSFORMATION OF DIGITIZED ASTRONOMICAL IMAGES

Yavor Chapanov1

1 – National Institute of Geophysics, Geodesy and Geography, Bulgarian Academy of Sciences

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

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

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

DATA SIMULATIONPLATE 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 (=2)

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

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

Field Width: 02Ê00' Center RA: 02h 00m 00s, Center DE: 42Ê00'00ºEquinox: J2000North is Up, East is LeftSource catalog: GSC-ACTCreated by StarGazer version 1.3.0-dev(C)2001-2005by Rumen G.Bogdanovski

STAR POSITIONS

317 stars

Ðàçïðåäåëåíèå íà ãðåøêàòà íà ñèìóëèðàíèòå íàáëþäåíèÿ

Ôèò y = 10000 * 0.01769 * normal (x, 0.001654, 0.141115)

[arcsec]

Áðîé

íà íàáëþäåíè

ÿòà

0

50

100

150

200

250

300

350

400

450

500

550

600

650

-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

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 =0.14

Re-scaling as:0”.5; 1”.0; 5”.0

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

ERROR MODEL – IStandard 0.5 arcsec

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

Coordinate Frame Rotation2 translations, 1 rotation, scale correction 180.03 X vector [arcsec] 240.02 Y vector [arcsec] -119.48 Z angle [arcsec] 92.96 Scale [ppm]

Quality criteria2.75 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 – IIStandard 1.0 arcsec

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

Coordinate Frame Rotation2 translations, 1 rotation, scale correction 180.03 X vector [arcsec] 240.01 Y vector [arcsec]-121.28 Z angle [arcsec] 99.20 Scale [ppm]

Quality criteria5.23 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 – IIIStandard 5.0 arcsec

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

Coordinate Frame Rotation2 translations, 1 rotation, scale correction 180.24 X vector [arcsec] 240.15 Y vector [arcsec] -112.12 Z angle [arcsec] 87.20 Scale [ppm]

Quality criteria28.29 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 Rotation2 translations, 1 rotation, scale correction 180.22 X vector [arcsec] 240.15 Y vector [arcsec] -112.78 Z angle [arcsec] 143.54 Scale [ppm]

Quality criteria39.46 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 Rotation2 translations, 1 rotation, scale correction 360.03 X vector [arcsec] 480.03 Y vector [arcsec] -119.47 Z angle [arcsec] 1000085.93 Scale [ppm]

Quality criteria5.5 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

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