Abstract

Detection accuracy is an important performance indicator of ground-based telescopes and is affected mainly by pointing error, geometric distortion of the optical system, and parameter errors caused by machining error and installation error. To improve detection accuracy, a modified algorithm based on a simulated annealing algorithm is proposed in this paper; this algorithm is able to correct pointing, derive a geometric distortion solution, and re-estimate some parameters of telescopes simultaneously. The efficiency of the proposed method is verified by using the observation data of the telescope, whose aperture is 600 mm under two distortion models (the physical model and polynomial fitting model). The results show that the method presented in this paper can effectively solve the problem of nonconvergence of the distortion solution with a pointing error. The final angle error under the polynomial fitting model is 1.07″, and the pixel error is 0.06 pixels; the errors under the physical model are 1.08″ and 0.07 pixels. The correction effect under the two distortion models is basically the same, but the averaged operation speed based on the physical model is 19.45% faster.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. J. Anderson and I. R. King, “An improved distortion solution for the Hubble space telescope’s WFPC2,” Publ. Astron. Soc. Pac. 115, 113–131 (2003).
    [Crossref]
  2. J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
    [Crossref]
  3. S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
    [Crossref]
  4. E. Bertin and S. Arnouts, “SExtractor: software for source extraction,” Astron. Astrophys. 117, 393–404 (1996).
    [Crossref]
  5. Stetson and B. Peter, “DAOPHOT—a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191–222 (1987).
    [Crossref]
  6. P. L. Schechter and M. A. Saha, “DoPHOT, a CCD photometry program: description and tests,” Publ. Astron. Soc. Pac. 105, 1342–1353 (1993).
    [Crossref]
  7. J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
    [Crossref]
  8. G. J. Zhang, Star Identification (Springer, 2017).
  9. A. Bellini and L. R. Bedin, “Ground-based CCD astrometry with wide field imagers. IV. An improved geometric distortion correction for the blue prime-focus camera at the LBT,” Astron. Astrophys. 517, A34 (2010).
    [Crossref]
  10. W. C. Xu and T. G. Chu, “A high-precision algorithm for centroid location of star pattern recognition with application to optical imaging distortion correction,” Sys. Sci. Math. Scis. 30, 850–858 (2010).
  11. http://www.iausofa.org/ .
  12. B. S. Liu, C. K. Liu, and H. T. Du, Accuracy Appraisal of Outside Measuring Equipment in Shooting Range (National Defense Industry, 2008).
  13. Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).
  14. C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).
  15. M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
    [Crossref]

2016 (1)

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

2012 (1)

Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).

2010 (3)

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

A. Bellini and L. R. Bedin, “Ground-based CCD astrometry with wide field imagers. IV. An improved geometric distortion correction for the blue prime-focus camera at the LBT,” Astron. Astrophys. 517, A34 (2010).
[Crossref]

W. C. Xu and T. G. Chu, “A high-precision algorithm for centroid location of star pattern recognition with application to optical imaging distortion correction,” Sys. Sci. Math. Scis. 30, 850–858 (2010).

2006 (1)

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

2003 (1)

J. Anderson and I. R. King, “An improved distortion solution for the Hubble space telescope’s WFPC2,” Publ. Astron. Soc. Pac. 115, 113–131 (2003).
[Crossref]

2000 (1)

J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
[Crossref]

1996 (1)

E. Bertin and S. Arnouts, “SExtractor: software for source extraction,” Astron. Astrophys. 117, 393–404 (1996).
[Crossref]

1993 (1)

P. L. Schechter and M. A. Saha, “DoPHOT, a CCD photometry program: description and tests,” Publ. Astron. Soc. Pac. 105, 1342–1353 (1993).
[Crossref]

1987 (1)

Stetson and B. Peter, “DAOPHOT—a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191–222 (1987).
[Crossref]

Anderson, J.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

J. Anderson and I. R. King, “An improved distortion solution for the Hubble space telescope’s WFPC2,” Publ. Astron. Soc. Pac. 115, 113–131 (2003).
[Crossref]

J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
[Crossref]

Arnouts, S.

E. Bertin and S. Arnouts, “SExtractor: software for source extraction,” Astron. Astrophys. 117, 393–404 (1996).
[Crossref]

Bedin, L. R.

A. Bellini and L. R. Bedin, “Ground-based CCD astrometry with wide field imagers. IV. An improved geometric distortion correction for the blue prime-focus camera at the LBT,” Astron. Astrophys. 517, A34 (2010).
[Crossref]

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

Bellini, A.

A. Bellini and L. R. Bedin, “Ground-based CCD astrometry with wide field imagers. IV. An improved geometric distortion correction for the blue prime-focus camera at the LBT,” Astron. Astrophys. 517, A34 (2010).
[Crossref]

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

Bergeron, E.

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

Bertin, E.

E. Bertin and S. Arnouts, “SExtractor: software for source extraction,” Astron. Astrophys. 117, 393–404 (1996).
[Crossref]

Campbell, R.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

Chu, T. G.

W. C. Xu and T. G. Chu, “A high-precision algorithm for centroid location of star pattern recognition with application to optical imaging distortion correction,” Sys. Sci. Math. Scis. 30, 850–858 (2010).

Clarkson, W.

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Cox, C.

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

Do, T.

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Du, H. T.

B. S. Liu, C. K. Liu, and H. T. Du, Accuracy Appraisal of Outside Measuring Equipment in Shooting Range (National Defense Industry, 2008).

Fan, Q. Y.

Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).

Ghez, A. M.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

King, I. R.

J. Anderson and I. R. King, “An improved distortion solution for the Hubble space telescope’s WFPC2,” Publ. Astron. Soc. Pac. 115, 113–131 (2003).
[Crossref]

J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
[Crossref]

Li, X. J.

Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).

Liu, B. S.

B. S. Liu, C. K. Liu, and H. T. Du, Accuracy Appraisal of Outside Measuring Equipment in Shooting Range (National Defense Industry, 2008).

Liu, C. K.

B. S. Liu, C. K. Liu, and H. T. Du, Accuracy Appraisal of Outside Measuring Equipment in Shooting Range (National Defense Industry, 2008).

Lu, J. R.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Mackenty, J.

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

Matthews, K.

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Noll, K.

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

Peter, B.

Stetson and B. Peter, “DAOPHOT—a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191–222 (1987).
[Crossref]

Piotto, G.

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

Ritchie, C.

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

Saha, M. A.

P. L. Schechter and M. A. Saha, “DoPHOT, a CCD photometry program: description and tests,” Publ. Astron. Soc. Pac. 105, 1342–1353 (1993).
[Crossref]

Schechter, P. L.

P. L. Schechter and M. A. Saha, “DoPHOT, a CCD photometry program: description and tests,” Publ. Astron. Soc. Pac. 105, 1342–1353 (1993).
[Crossref]

Service, M.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

Sitarski, B. N.

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

Stetson,

Stetson and B. Peter, “DAOPHOT—a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191–222 (1987).
[Crossref]

Xu, W. C.

W. C. Xu and T. G. Chu, “A high-precision algorithm for centroid location of star pattern recognition with application to optical imaging distortion correction,” Sys. Sci. Math. Scis. 30, 850–858 (2010).

Yadav, R. S.

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

Yelda, S.

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Zhang, G. J.

Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).

G. J. Zhang, Star Identification (Springer, 2017).

Astron. Astrophys. (3)

E. Bertin and S. Arnouts, “SExtractor: software for source extraction,” Astron. Astrophys. 117, 393–404 (1996).
[Crossref]

A. Bellini and L. R. Bedin, “Ground-based CCD astrometry with wide field imagers. IV. An improved geometric distortion correction for the blue prime-focus camera at the LBT,” Astron. Astrophys. 517, A34 (2010).
[Crossref]

J. Anderson, L. R. Bedin, G. Piotto, R. S. Yadav, and A. Bellini, “Ground-based CCD astrometry with wide field imagers. I. Observations just a few years apart allow decontamination of field objects from members in two globular clusters,” Astron. Astrophys. 454, 1029–1045 (2006).
[Crossref]

Astrophys. J. (1)

S. Yelda, J. R. Lu, A. M. Ghez, W. Clarkson, J. Anderson, T. Do, and K. Matthews, “Improving galactic center astrometry by reducing the effects of geometric distortion,” Astrophys. J. 725, 331–352 (2010).
[Crossref]

Infrared Laser Eng. (1)

Q. Y. Fan, X. J. Li, and G. J. Zhang, “Selection of star sensor lens aberration model,” Infrared Laser Eng. 41, 665–670 (2012).

Publ. Astron. Soc. Pac. (5)

J. Anderson and I. R. King, “An improved distortion solution for the Hubble space telescope’s WFPC2,” Publ. Astron. Soc. Pac. 115, 113–131 (2003).
[Crossref]

M. Service, J. R. Lu, R. Campbell, B. N. Sitarski, A. M. Ghez, and J. Anderson, “A new distortion solution for NIRC2 on the Keck II telescope,” Publ. Astron. Soc. Pac. 128, 095004 (2016).
[Crossref]

Stetson and B. Peter, “DAOPHOT—a computer program for crowded-field stellar photometry,” Publ. Astron. Soc. Pac. 99, 191–222 (1987).
[Crossref]

P. L. Schechter and M. A. Saha, “DoPHOT, a CCD photometry program: description and tests,” Publ. Astron. Soc. Pac. 105, 1342–1353 (1993).
[Crossref]

J. Anderson and I. R. King, “Toward high-precision astrometry with WFPC2. I. Deriving an accurate point-spread function,” Publ. Astron. Soc. Pac. 112, 1360–1382 (2000).
[Crossref]

Sys. Sci. Math. Scis. (1)

W. C. Xu and T. G. Chu, “A high-precision algorithm for centroid location of star pattern recognition with application to optical imaging distortion correction,” Sys. Sci. Math. Scis. 30, 850–858 (2010).

Other (4)

http://www.iausofa.org/ .

B. S. Liu, C. K. Liu, and H. T. Du, Accuracy Appraisal of Outside Measuring Equipment in Shooting Range (National Defense Industry, 2008).

G. J. Zhang, Star Identification (Springer, 2017).

C. Cox, C. Ritchie, E. Bergeron, J. Mackenty, and K. Noll, “NICMOS distortion correction,” (1997).

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Figures (9)

Fig. 1.
Fig. 1. Projection diagram of miss distance.
Fig. 2.
Fig. 2. Flow chart of the simulated annealing algorithm.
Fig. 3.
Fig. 3. Algorithm flow chart.
Fig. 4.
Fig. 4. Image filtering. (a) Original image and (b) filtered image.
Fig. 5.
Fig. 5. Images used to calibrate the errors of our telescope. The coordinates of the center of the field are RA = 04 h 08 m 15 s ; DEC = 28 ° 08 32 (J2000.0). Stars used in calibration are highlighted with a green circle.
Fig. 6.
Fig. 6. Star position error before correction, the position error in the middle image has been exaggerated by a factor of 5.
Fig. 7.
Fig. 7. Result of distortion correction without pointing correction.
Fig. 8.
Fig. 8. Result of distortion correction with pointing correction. (a) Result under the physical model and (b) under the polynomial fitting model.
Fig. 9.
Fig. 9. Result of distortion correction with pointing correction. (a) Modified result under the physical model and (b) under the polynomial fitting model.

Tables (2)

Tables Icon

Table 1. Parameters to Be Estimated in This Paper

Tables Icon

Table 2. Parameter Correction Result

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

F ( X , Y ) = { f ( X , Y ) T f ( X , Y ) T 0 f ( X , Y ) < T ,
{ X 0 = X = 1 m Y = 1 n F ( X , Y ) X X = 1 m Y = 1 n F ( X , Y ) , Y 0 = X = 1 m Y = 1 n F ( X , Y ) Y X = 1 m Y = 1 n F ( X , Y ) ,
{ x = tan Δ A · ( f cos E 0 y sin E 0 ) , y = f · tan E · cos E 0 cos Δ A · sin E 0 tan E · sin E 0 + cos Δ A · cos E 0 Δ A = A A 0 , ,
{ x r = x cos ( α ) y sin ( α ) , y r = x sin ( α ) + y cos ( α ) ,
{ X = x r / p x + X 0 , Y = Y 0 y r / p y ,
{ δ x r = i = 1 n q i x r 2 i , δ y r = i = 1 n q i y r 2 i .
{ δ x t = p 1 ( 3 x 2 + y 2 ) + 2 p 2 x y + O [ ( x , y ) 4 ] , δ y t = 2 p 1 x y + p 2 ( x 2 + 3 y 2 ) + O [ ( x , y ) 4 ] .
{ δ x p = s 1 ( x 2 + y 2 ) + O [ ( u , v ) 4 ] , δ y p = s 2 ( x 2 + y 2 ) + O [ ( u , v ) 4 ] .
{ δ x = δ x r + δ x t + δ x p , δ y = δ y r + δ y t + δ y p .
{ δ x = l 1 x + l 2 y + l 3 x 2 + l 4 x y + l 5 y 2 + l 6 x 3 + l 7 x 2 y + l 8 x y 2 + l 9 y 3 , δ y = m 1 x + m 2 y + m 3 x 2 + m 4 x y + m 5 y 2 + m 6 x 3 + m 7 x 2 y + m 8 x y 2 + m 9 y 3 .
J ( ω ) = i = 1 N [ ( X i corrected X i theoretical ) 2 + ( Y i corrected Y i theoretical ) 2 ] N .

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