Abstract

In this paper, a modified stitching algorithm for annular subaperture stitching interferometry (ASSI) for aspheric surfaces is proposed. The mathematical model of adjustment error is deduced based on the wavefront aberration theory and rigid body movement; meanwhile, its basic principle and theory are introduced. The modified stitching algorithm is established based on the mathematical model and the simultaneous least-squares method, which keeps the error from transmitting and accumulating. So the adjustment error can be compensated efficiently. In addition, the standard deviation (SD) in the overlapped regions is used as the figure of merit to determine the stitching accuracy. Finally, simulations and experiments are given to verify the validity and rationality of the proposed algorithm. The results show that the introduced method is quite efficient.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. X. K. Wang, “Annular sub-aperture stitching interferometry for testing of large aspherical surfaces,” Proc. SPIE 6624, 66240A (2007).
    [CrossRef]
  15. X. K. Wang and L. H. Wang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 11, 645–647 (2007).
  16. J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
    [CrossRef]
  17. S. Y. Chen, S. Y. Li, and Y. F. Dai, “Experimental study on subaperture testing with iterative stitching algorithm,” Opt. Express 16, 4760–4765 (2008).
    [CrossRef]

2010

2009

M. BrayMBO-Metrology, “Stitching interferometry: the practical side of things,” Proc. SPIE 7426, 74260Q (2009).
[CrossRef]

2008

2007

X. Hou, F. Wu, L. Yang, and Q. Chen, “Experimental study on measurement of aspheric surface shape with complementary annular subaperture interferometric method,” Opt. Express 15, 12890–12899 (2007).
[CrossRef]

X. K. Wang, “Annular sub-aperture stitching interferometry for testing of large aspherical surfaces,” Proc. SPIE 6624, 66240A (2007).
[CrossRef]

X. K. Wang and L. H. Wang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 11, 645–647 (2007).

2006

S. Chen, S. Li, and Y. Dai, “Lattice design for subaperture stitching test of a concave paraboloid surface,” Appl. Opt. 45, 2280–2286 (2006).
[CrossRef]

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930 (2006).
[CrossRef]

2004

F. Granados-Agustin, “Testing parabolic surfaces with annular subaperture interferograms,” Opt. Rev. 11, 82–86 (2004).
[CrossRef]

2003

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003).
[CrossRef]

1995

S. M. Arnold, “Verification and certification of CGH aspheric nulls,” Proc. SPIE 2536, 117–126 (1995).
[CrossRef]

1992

M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multi-aperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1992).

M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspherical surfaces using multiple annular interferograms,” Proc. SPIE 1781, 232–240 (1992).
[CrossRef]

1988

1982

1972

Arnold, S. M.

S. M. Arnold, “Verification and certification of CGH aspheric nulls,” Proc. SPIE 2536, 117–126 (1995).
[CrossRef]

Bennett, V. P.

Bray, M.

M. BrayMBO-Metrology, “Stitching interferometry: the practical side of things,” Proc. SPIE 7426, 74260Q (2009).
[CrossRef]

Chen, M. Y.

M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multi-aperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1992).

Chen, Q.

Chen, S.

Chen, S. Y.

Cheng, W. M.

M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multi-aperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1992).

Dai, Y.

Dai, Y. F.

Dumas, P.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Fleig, J.

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930 (2006).
[CrossRef]

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003).
[CrossRef]

Forbes, G.

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930 (2006).
[CrossRef]

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003).
[CrossRef]

Forbes, G. W.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Granados-Agustin, F.

F. Granados-Agustin, “Testing parabolic surfaces with annular subaperture interferograms,” Opt. Rev. 11, 82–86 (2004).
[CrossRef]

Hou, X.

Kim, C. J.

Koliopoulos, C. L.

Lawrence, G. N.

Li, J.

Li, S.

Li, S. Y.

Liu, Y.

Mazzoni, A.

M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspherical surfaces using multiple annular interferograms,” Proc. SPIE 1781, 232–240 (1992).
[CrossRef]

Melozzi, M.

M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspherical surfaces using multiple annular interferograms,” Proc. SPIE 1781, 232–240 (1992).
[CrossRef]

Murphy, P.

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930 (2006).
[CrossRef]

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003).
[CrossRef]

Murphy, P. E.

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

Pezzati, L.

M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspherical surfaces using multiple annular interferograms,” Proc. SPIE 1781, 232–240 (1992).
[CrossRef]

Wang, C. W.

M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multi-aperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1992).

Wang, L. H.

X. K. Wang and L. H. Wang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 11, 645–647 (2007).

Wang, X. K.

X. K. Wang and L. H. Wang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 11, 645–647 (2007).

X. K. Wang, “Annular sub-aperture stitching interferometry for testing of large aspherical surfaces,” Proc. SPIE 6624, 66240A (2007).
[CrossRef]

Wu, F.

Wyant, J. C.

Yang, L.

Zhang, P.

Zhao, H.

Zhou, X.

Appl. Opt.

Chin. Opt. Lett.

X. K. Wang and L. H. Wang, “Measurement of large aspheric surfaces by annular subaperture stitching interferometry,” Chin. Opt. Lett. 11, 645–647 (2007).

Opt. Express

Opt. Photon. News

P. Murphy, G. Forbes, and J. Fleig, “Stitching interferometry: a flexible solution for surface metrology,” Opt. Photon. News 14(5), 38–43 (2003).
[CrossRef]

Opt. Rev.

F. Granados-Agustin, “Testing parabolic surfaces with annular subaperture interferograms,” Opt. Rev. 11, 82–86 (2004).
[CrossRef]

Proc. SPIE

X. K. Wang, “Annular sub-aperture stitching interferometry for testing of large aspherical surfaces,” Proc. SPIE 6624, 66240A (2007).
[CrossRef]

J. Fleig, P. Dumas, P. E. Murphy, and G. W. Forbes, “An automated subaperture stitching interferometer workstation for spherical and aspherical surfaces,” Proc. SPIE 5188, 296–307 (2003).
[CrossRef]

M. Melozzi, L. Pezzati, and A. Mazzoni, “Testing aspherical surfaces using multiple annular interferograms,” Proc. SPIE 1781, 232–240 (1992).
[CrossRef]

S. M. Arnold, “Verification and certification of CGH aspheric nulls,” Proc. SPIE 2536, 117–126 (1995).
[CrossRef]

P. Murphy, J. Fleig, and G. Forbes, “Subaperture stitching interferometry for testing mild aspheres,” Proc. SPIE 6293, 62930 (2006).
[CrossRef]

M. BrayMBO-Metrology, “Stitching interferometry: the practical side of things,” Proc. SPIE 7426, 74260Q (2009).
[CrossRef]

M. Y. Chen, W. M. Cheng, and C. W. Wang, “Multi-aperture overlap-scanning technique for large-aperture test,” Proc. SPIE 1553, 626–635 (1992).

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Figures (10)

Fig. 1.
Fig. 1.

Sketch map of ASSI.

Fig. 2.
Fig. 2.

Paraboloid phase datum and its two subaperture phase data: (a) full-aperture, (b) subaperture 1, and (c) subaperture 2.

Fig. 3.
Fig. 3.

Subaperture 2 data with different adjustment errors: (a) simulation 1 and (b) simulation 2

Fig. 4.
Fig. 4.

Simulation result 1: (a)–(c) are the results of the traditional stitching method: (a) is the stitching result, (b) is the residual error, (c) is the SD map; (d)–(f) are the proposed method: (d) is the stitching result; (e) is the residual error; (f) is the SD map.

Fig. 5.
Fig. 5.

Simulation result 2: (a)–(c) are the results of the traditional stitching method: (a) is the stitching result, (b) is the residual error, (c) is the SD map; (d)–(f) are the proposed methods: (d) is the stitching result, (e) is the residual error, (f) is the SD map.

Fig. 6.
Fig. 6.

Experiment setup.

Fig. 7.
Fig. 7.

Subapertures data of paraboloid mirror.

Fig. 8.
Fig. 8.

Experiment results: (a) and (b) are the traditional methods, (c) and (d) are the proposed methods.

Fig. 9.
Fig. 9.

Measured subapertures of the hyperboloid mirror: (a) subaperture 1 and (b) subaperture 2.

Fig. 10.
Fig. 10.

Final results: (a) and (b) are the traditional method; (b) and (c) are the proposed method.

Tables (2)

Tables Icon

Table 1. Coefficients of Adjustment Error

Tables Icon

Table 2. Stitching Coefficients of Two Methods

Equations (11)

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

(x,y,z,1)=T·(x,y,z,1),
T=[cosβ0sinβdxsinαsinβcosαsinαcosβdycosαsinβsinαcosαcosβdz0001].
Δp=p(x,y,z)p(x,y,z)=[zβ+dxzα+dyxβyα+dz]T.
W(x,y)=21+(zx)2+(zy)2[zxΔp⃗xzyΔp⃗y+Δp⃗z].
z=12cs2+(1e2)8c3s4+(1e2)216c5s6+,
W(x,y)=2dzpiston2(czβdx+β)xx-tilt+2(czα+dy+α)yy-tilt+c2dzs2focus[c2β(e2cz+1)+(2e2c3)dx]xs2x-coma[c2α(e2cz+1)+e2dy]ys2y-coma2(1e2)c4dzs4spherical.
wa=w+bk1+k2x+k3y+k4(x2+y2)+k5x(x2+y2)+k6y(x2+y2)+k7(x2+y2)2,
w0=w1+k11+k21x+k31y+k41(x2+y2)+k51x(x2+y2)+k61y(x2+y2)+k71(x2+y2)2=w2+k12+k22x+k32y+k42(x2+y2)+k52x(x2+y2)+k62y(x2+y2)+k72(x2+y2)2=wm1+k1m1+k2m1x+k3m1y+k4m1(x2+y2)+k5m1x(x2+y2)+k6m1y(x2+y2)+k7m1(x2+y2)2,
i=1n{Δw[k1+k2x+k3y+k4(x2+y2)+k5x(x2+y2)+k6y(x2+y2)+k7(x2+y2)2]}min.
[k1k2k6k7]=[nxy(x2+y2)(x2+y2)2xx2xy(x2+y2)x(x2+y2)2y(x2+y2)xy(x2+y2)y2(x2+y2)2y(x2+y2)3(x2+y2)2x(x2+y2)2y(x2+y2)3(x2+y2)4]1[ΔwxΔwy(x2+y2)Δw(x2+y2)2Δw].
SD=1N(x,y)i=1N[wi(x,y)w¯(x,y)],

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