Abstract

Since the cylinder surface is closed and periodic in the azimuthal direction, traditional stitching interferometry cannot be used to yield the 360° form map. This paper describes a full cylinder stitching interferometry based on the first-order approximation of cylindrical coordinate transformation. First, it introduces cylindrical projection, which allows us to determine the overlap region of the cylinder without ambiguity. Second, the relationship between the variations of radial coordinates and the movement errors of the rotational stage is derived from the first-order approximation of cylindrical coordinate transformation. Based on this relation, a cylinder stitching model is built to connect all sub-apertures together. Finally, we experimentally validate the proposed method by measuring a precision metal shaft. The high resolution and repeatability shown in the experimental results demonstrate our approach to be an attractive and promising technique in the field of precision measurement.

© 2017 Optical Society of America

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References

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  1. M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
    [Crossref]
  2. T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).
  3. H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
    [Crossref]
  4. K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
    [Crossref]
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    [Crossref]
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    [Crossref]
  12. P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
    [Crossref]
  13. P. Murphy and J. Fleig, “Subaperture stitching interferometry for testing mild aspheres,” in Proc. SPIE, (2006), paper 62930J.
    [Crossref]
  14. M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
    [Crossref]
  15. J. Peng, Q. Wang, X. Peng, and Y. Yu, “Stitching interferometry of high numerical aperture cylindrical optics without using a fringe-nulling routine,” J. Opt. Soc. Am. A 32, 1964–1972 (2015).
    [Crossref]
  16. V. N. Mahajan, “Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils,” Appl. Opt. 49, 6924–6929 (2010).
    [Crossref] [PubMed]
  17. J. Peng, D. Ge, Y. Yu, K. Wang, and M. Chen, “Method of misalignment aberrations removal in null test of cylindrical surface,” Appl. Opt. 52, 7311–7323 (2013).
    [Crossref] [PubMed]
  18. “Encoding and fabrication report: CGH cylinder null H80F3C,” Tech. Rep. C1437, Diffraction International, 5810 Baker Road, Suite 225 Minnetonka, Minnesota 55345–5982 USA (2014).
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    [Crossref]
  20. P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
    [Crossref]
  21. J. Peng, Y. Yu, and H. Xu, “Compensation of high-order misalignment aberrations in cylindrical interferometry,” Appl. Opt. 53, 4947–4956 (2014).
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2015 (1)

2014 (2)

2013 (1)

2012 (2)

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).

2010 (2)

M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
[Crossref]

V. N. Mahajan, “Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils,” Appl. Opt. 49, 6924–6929 (2010).
[Crossref] [PubMed]

2008 (1)

H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
[Crossref]

2006 (1)

2003 (2)

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
[Crossref]

H. Guo and M. Chen, “Multiview connection technique for 360◦ three-dimensional measurement,” Opt. Eng. 42, 900–905 (2003).
[Crossref]

2002 (1)

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

2001 (1)

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

1998 (1)

1994 (1)

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608–613 (1994).
[Crossref]

1982 (1)

Anand, S.

H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
[Crossref]

Baldwin, J.

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Bauer, M.

M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
[Crossref]

Brinkmann, S.

Brown, C.

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Bruning, J.

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

Bryan, J.

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

Cassou, R.

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Chen, M.

J. Peng, D. Ge, Y. Yu, K. Wang, and M. Chen, “Method of misalignment aberrations removal in null test of cylindrical surface,” Appl. Opt. 52, 7311–7323 (2013).
[Crossref] [PubMed]

H. Guo and M. Chen, “Multiview connection technique for 360◦ three-dimensional measurement,” Opt. Eng. 42, 900–905 (2003).
[Crossref]

Chen, S.

Chen, Y.-C.

P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
[Crossref]

Dai, Y.

Dresel, T.

Fleig, J.

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
[Crossref]

P. Murphy and J. Fleig, “Subaperture stitching interferometry for testing mild aspheres,” in Proc. SPIE, (2006), paper 62930J.
[Crossref]

Forbes, G.

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
[Crossref]

Ge, D.

Gerhardt, U.

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

Guo, H.

H. Guo and M. Chen, “Multiview connection technique for 360◦ three-dimensional measurement,” Opt. Eng. 42, 900–905 (2003).
[Crossref]

Henke, R.

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Kanagaraj, S.

H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
[Crossref]

Kim, C. -J.

Knight, P.

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

Kühnel, M.

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

Kulawiec, A.

M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
[Crossref]

Lee, C.-M.

P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
[Crossref]

Li, S.

Liang, C.-W.

P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
[Crossref]

Lin, P.-C.

P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
[Crossref]

Mahajan, V. N.

Manske, E.

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

McElroy, R.

T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).

Murphy, P.

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
[Crossref]

P. Murphy and J. Fleig, “Subaperture stitching interferometry for testing mild aspheres,” in Proc. SPIE, (2006), paper 62930J.
[Crossref]

Okada, K.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608–613 (1994).
[Crossref]

Ollison, T. E.

T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).

Otsubo, M.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608–613 (1994).
[Crossref]

Patterson, S.

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

Peng, J.

Peng, X.

Ramaswami, H.

H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
[Crossref]

Schreiner, R.

Schwider, J.

Summerhays, K.

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Tricard, M.

M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
[Crossref]

Tsujiuchi, J.

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608–613 (1994).
[Crossref]

Ullmann, V.

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

Ulmer, J. M.

T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).

Wang, K.

Wang, Q.

Weckenmann, A.

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

Xu, H.

Yu, Y.

Zheng, Z.

Appl. Opt. (5)

CIRP Ann.-Manuf. Techn. (1)

A. Weckenmann, J. Bruning, S. Patterson, P. Knight, and J. Bryan, “Grazing inciden interferometry for high precision measurement of cylindrical form deviations,” CIRP Ann.-Manuf. Techn. 50, 381–384 (2001).
[Crossref]

CIRP Annals-Manuf. Technol. (1)

M. Tricard, A. Kulawiec, and M. Bauer, “Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null,” CIRP Annals-Manuf. Technol. 59, 547–550 (2010).
[Crossref]

Int. J. Adv. Manuf. Tech. (1)

H. Ramaswami, S. Kanagaraj, and S. Anand, “An inspection advisor for form error in cylindrical features,” Int. J. Adv. Manuf. Tech. 40, 128–143 (2008).
[Crossref]

Int. J. Eng. Res. Innovation (1)

T. E. Ollison, J. M. Ulmer, and R. McElroy, “Coordinate measurement technology: A comparison of scanning versus touch trigger probe data capture,” Int. J. Eng. Res. Innovation 4, 60–67 (2012).

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

M. Kühnel, V. Ullmann, U. Gerhardt, and E. Manske, “Automated setup for non-tactile high-precision measurements of roundness and cylindricity using two laser interferometers,” Meas. Sci. Technol. 23(7), 074016 (2012).
[Crossref]

Opt. Eng. (2)

M. Otsubo, K. Okada, and J. Tsujiuchi, “Measurement of large plane surface shapes by connecting small-aperture interferograms,” Opt. Eng. 33, 608–613 (1994).
[Crossref]

H. Guo and M. Chen, “Multiview connection technique for 360◦ three-dimensional measurement,” Opt. Eng. 42, 900–905 (2003).
[Crossref]

Opt. Photonics News (1)

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photonics News 14, 39–43 (2003).
[Crossref]

Precis. Eng. (1)

K. Summerhays, R. Henke, J. Baldwin, R. Cassou, and C. Brown, “Optimizing discrete point sample patterns and measurement data analysis on internal cylindrical surfaces with systematic form deviations,” Precis. Eng. 26, 105–121 (2002).
[Crossref]

Other (4)

http://diffraction.com/cylinder.php .

P. Murphy and J. Fleig, “Subaperture stitching interferometry for testing mild aspheres,” in Proc. SPIE, (2006), paper 62930J.
[Crossref]

“Encoding and fabrication report: CGH cylinder null H80F3C,” Tech. Rep. C1437, Diffraction International, 5810 Baker Road, Suite 225 Minnetonka, Minnesota 55345–5982 USA (2014).

P.-C. Lin, Y.-C. Chen, C.-M. Lee, and C.-W. Liang, “A subaperture stitching algorithm for aspheric surfaces,” in Proc. SPIE, P. H. Lehmann, W. Osten, and K. Gastinger, eds. (2011), p. 80821G.
[Crossref]

Supplementary Material (2)

NameDescription
» Visualization 1: AVI (20152 KB)      3D video of stitching result
» Visualization 2: MP4 (56206 KB)      Video of cylindricity measured by Taylor Hobson 585

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Figures (10)

Fig. 1
Fig. 1 Sketch map of the cylindricity measuring system.
Fig. 2
Fig. 2 Flowchart of the stitching procedure.
Fig. 3
Fig. 3 The geometric sketch of coordinate transformation: (a) footprint on the CGH, (b) test configuration.
Fig. 4
Fig. 4 Schematic diagram of stitching interferometry for cylinder.
Fig. 5
Fig. 5 Overlap calculation of cylinder.
Fig. 6
Fig. 6 Experimental setup and measurement region: (a) Experimental setup, (b) measurement region (unit: mm).
Fig. 7
Fig. 7 Sub-aperture Data: (a) recorded interfergrams, (b) phase map after removing the misalignment aberrations.
Fig. 8
Fig. 8 Experimental result: (a) stitching result, (b) mismatch map.
Fig. 9
Fig. 9 Stitching results when different sub-apertures were set as datum: (a) Sub-aperture 310 was set as datum, (b) Sub-aperture 260 was set as datum.
Fig. 10
Fig. 10 Comparison between the roundness measurement instrument and the proposed method: (a) 3D view of the stitched results (see Visualization 1), (b) 3D cylindricity map obtained by cylindricity measuring instrument (see Visualization 2).

Tables (1)

Tables Icon

Table 1 Reproducibility of the proposed method (Unit: μm).

Equations (9)

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[ x θ Δ ρ ] = [ s u tan 1 ( s v r b f ) φ λ 2 π ] ,
X = x + x 0 , Θ = θ + θ 0 ,
[ ρ 2 Θ 2 X 2 ] = [ ρ 1 Θ 1 X 1 ] + [ cos Θ 1 sin Θ 1 0 X 1 sin Θ 1 X 1 cos Θ 1 0 sin Θ 1 / ρ 1 cos Θ 1 / ρ 1 0 X 1 cos Θ 1 / ρ 1 X 1 sin Θ 1 / ρ 1 1 0 0 1 ρ 1 sin Θ 1 ρ 1 cos Θ 1 0 ] [ Δ z Δ y Δ x Δ γ Δ β Δ α ] ,
Δ ρ s t i t c h e d ( X , Θ ) = Δ ρ s u b ( X , Θ ) + Δ z cos Θ + Δ y sin Θ Δ γ X sin Θ + Δ β X cos Θ .
k l { [ Δ ρ s u b , k ( X , Θ ) + Δ z k cos Θ + Δ y k sin Θ Δ γ k X sin Θ + Δ β k X cos Θ ] [ Δ ρ s u b , l ( X , Θ ) + Δ z l cos Θ + Δ y l sin Θ Δ γ l X sin Θ + Δ β l X cos Θ ] } 2 min
[ cos 2 Θ cos Θ sin Θ X cos Θ sin Θ X cos 2 Θ cos Θ sin Θ sin 2 Θ X sin 2 Θ X cos Θ sin Θ X sin Θ cos Θ X sin 2 Θ X 2 sin 2 Θ X 2 sin Θ cos Θ X cos 2 Θ X cos Θ sin Θ X 2 cos Θ sin Θ X 2 cos 2 Θ ] [ Δ z Δ y Δ γ Δ β ] = [ Δ ρ Δ z Δ ρ Δ y Δ ρ Δ γ Δ ρ Δ β ] ,
1 2 [ ( Δ ρ s u b , 1 Δ ρ s u b , 2 ) + Δ z 1 cos Θ + Δ y 1 sin Θ Δ γ 1 X sin Θ + Δ β 1 X cos Θ ] 2 + 2 3 [ ( Δ ρ s u b , 2 Δ ρ s u b , 3 ) + Δ z 2 cos Θ + Δ y 2 sin Θ Δ γ 2 X sin Θ + Δ β 2 X cos Θ ] 2 + + n 1 n [ ( Δ ρ s u b , n 1 Δ ρ s u b , n ) + Δ z n 1 cos Θ + Δ y n 1 sin Θ Δ γ n 1 X sin Θ + Δ β n 1 X cos Θ ] 2 + 1 n [ ( Δ ρ s u b , 1 Δ ρ s u b , n ) + ( Δ z 1 + + Δ z n 1 ) cos Θ + ( Δ y 1 + + Δ y n 1 ) sin Θ ( Δ γ 1 + + Δ γ n 1 ) X sin Θ + ( Δ β 1 + + Δ β n 1 ) X cos Θ ] 2 min .
[ A 1 + B B B B B A 2 + B B B B B A 3 + B B B B B B A N 1 + B ] [ M 1 M 2 M 3 M N 1 ] = [ f 1 + g f 2 + g f 3 + g f N 1 + g ] ,
Δ ρ 1 ^ = Δ ρ 1 , Δ ρ 2 ^ = Δ ρ 2 + ( Δ z 1 cos Θ + Δ y 1 sin Θ Δ γ 1 X sin Θ + Δ β 1 X cos Θ ) , Δ ρ 3 ^ = Δ ρ 3 + ( ( Δ z 1 + Δ z 2 ) cos Θ + ( Δ y 1 + Δ y 2 ) sin Θ ( Δ γ 1 + γ 2 ) X sin Θ + ( Δ β 1 + Δ β 2 ) X cos Θ ) , Δ ρ N ^ = Δ ρ N + ( ( Δ z 1 + + Δ z N 1 ) cos Θ + ( Δ y 1 + + Δ y N 1 ) sin Θ ( Δ γ 1 + + γ N 1 ) X sin Θ + ( Δ β 1 + + Δ β N 1 ) X cos Θ ) .

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