Abstract

Alignment of optical components is crucial for the assembly of optical systems to ensure their full functionality. In this paper we present a novel predictor-corrector framework for the sequential assembly of serial optical systems. Therein, we use a hybrid optical simulation model that comprises virtual and identified component positions. The hybrid model is constantly adapted throughout the assembly process with the help of nonlinear identification techniques and wavefront measurements. This enables prediction of the future wavefront at the detector plane and therefore allows for taking corrective measures accordingly during the assembly process if a user-defined tolerance on the wavefront error is violated. We present a novel notation for the so-called hybrid model and outline the work flow of the presented predictor-corrector framework. A beam expander is assembled as demonstrator for experimental verification of the framework. The optical setup consists of a laser, two bi-convex spherical lenses each mounted to a five degree-of-freedom stage to misalign and correct components, and a Shack-Hartmann sensor for wavefront measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (1)

F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

2016 (3)

2015 (2)

N. Patel and C. S. Narayanamurthy, “Measurement of optical misalignment using wavefront sensing,” Opt. Eng. 54, 104106 (2015).
[Crossref]

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
[Crossref]

2014 (1)

2013 (1)

L. M. Rios and N. V. Sahinidis, “Derivative-free optimization: a review of algorithms and comparison of software implementations,” J. Glob. Optim. 56, 1247–1293 (2013).
[Crossref]

2011 (1)

H. Butler, “Position control in lithographic equipment,” IEEE Control. Syst. Mag. 31, 28–47 (2011).
[Crossref]

2010 (2)

J. Sin, W. H. Lee, and H. E. Stephanou, “Sensitivity analysis of an assembled fourier transform microspectrometer,” Proc. SPIE 768076800T (2010).

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

2009 (1)

A. N. Das, D. O. Popa, J. Sin, and H. E. Stephanou, “Precision alignment and assembly of a fourier transform microspectrometer,” J. Micro-Nano Mechatronics 5, 15 (2009).
[Crossref]

2007 (2)

2006 (3)

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

2005 (1)

2004 (2)

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

1994 (1)

1985 (1)

W. Shaomin, “Matrix methods in treating decentred optical systems,” Opt. quantum electronics 17, 1–14 (1985).
[Crossref]

Abbink, R. E.

R. E. Abbink, “Interferometer alignment,” (2005). US Patent 6,952,266.

Acernese, F.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Adil, F. Z.

F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

Adil, Ö. F.

F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

Al-Shourbagy, M.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Amico, P.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Aoudia, S.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Atcheson, P.

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

Avino, S.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Babusci, D.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Balkan, T.

F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

Ballardin, G.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Barillé, R.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Barone, F.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Barsotti, L.

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

Brecher, C.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Butler, H.

H. Butler, “Position control in lithographic equipment,” IEEE Control. Syst. Mag. 31, 28–47 (2011).
[Crossref]

Casey, M. M.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Cenko, A.

A. Cenko, “Automatic interferometric alignment of a free-space optical coherence tomography system,” Ph.D. thesis (2011).

Cheng, S.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Choi, S. C.

Choi, Y.-W.

Dalton, G. B.

Das, A. N.

A. N. Das, D. O. Popa, J. Sin, and H. E. Stephanou, “Precision alignment and assembly of a fourier transform microspectrometer,” J. Micro-Nano Mechatronics 5, 15 (2009).
[Crossref]

Duan, H.-Z.

Edmunds, J. M.

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

Fang, J.

Freise, A.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Ganesan, A. R.

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
[Crossref]

Gao, M.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Gatej, A.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Genest, J.

C. G. Prevost and J. Genest, “Dynamic alignment of a michelson interferometer using a position-sensitive device,” in “Proc. of the SPIE 49th Annual Meeting,” (2004), pp. 293–304.

Gossler, S.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Grote, H.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Haag, S.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Heinzel, G.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Holters, M.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Jin, L.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Kalamatianos, D.

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

Kalikivayi, V.

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
[Crossref]

Kang, M.-S.

Kannan, K.

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
[Crossref]

Kim, E. D.

Kim, S.

Kim, S.-H.

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Kim, S.-W.

Kim, Y.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

Kima, S.-W.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

Kimc, S.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

Konukseven, E. I.

F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

Kumar, V. C. P.

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
[Crossref]

Lee, H.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

H. Lee, G. B. Dalton, I. A. Tosh, and S.-W. Kim, “Computer-guided alignment ii: Optical system alignment using differential wavefront sampling,” Opt. Express 15, 15424–15437 (2007).
[Crossref] [PubMed]

Lee, H.-Y.

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Lee, I.-W.

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Lee, J.-H.

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Lee, W. H.

J. Sin, W. H. Lee, and H. E. Stephanou, “Sensitivity analysis of an assembled fourier transform microspectrometer,” Proc. SPIE 768076800T (2010).

Lee, Y.-W.

S. Kim, H.-S. Yang, Y.-W. Lee, and S.-W. Kim, “Merit function regression method for efficient alignment control of two-mirror optical systems,” Opt. Express 15, 5059–5068 (2007).
[Crossref] [PubMed]

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Li, S.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Liang, Y.-R.

Liatsis, P.

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

Loosen, P.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Lou, J. Z.

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

Lück, H.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Mansell, J.

D. R. Neal and J. Mansell, “Application of shack-hartmann wavefront sensors to optical system calibration and alignment,” in “Proc. 2nd Int. Workshop on Adaptive Optics for Industry and Medicine,” (2000), pp. 234–243.

Meers, B. J.

Morrison, E.

Müller, T.

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

Narayanamurthy, C. S.

N. Patel and C. S. Narayanamurthy, “Measurement of optical misalignment using wavefront sensing,” Opt. Eng. 54, 104106 (2015).
[Crossref]

Neal, D. R.

D. R. Neal and J. Mansell, “Application of shack-hartmann wavefront sensors to optical system calibration and alignment,” in “Proc. 2nd Int. Workshop on Adaptive Optics for Industry and Medicine,” (2000), pp. 234–243.

Oh, E.-S.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

Patel, N.

N. Patel and C. S. Narayanamurthy, “Measurement of optical misalignment using wavefront sensing,” Opt. Eng. 54, 104106 (2015).
[Crossref]

Popa, D. O.

A. N. Das, D. O. Popa, J. Sin, and H. E. Stephanou, “Precision alignment and assembly of a fourier transform microspectrometer,” J. Micro-Nano Mechatronics 5, 15 (2009).
[Crossref]

Prevost, C. G.

C. G. Prevost and J. Genest, “Dynamic alignment of a michelson interferometer using a position-sensitive device,” in “Proc. of the SPIE 49th Annual Meeting,” (2004), pp. 293–304.

Raasch, T. W.

Redding, D.

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

Rhee, H.-G.

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Rios, L. M.

L. M. Rios and N. V. Sahinidis, “Derivative-free optimization: a review of algorithms and comparison of software implementations,” J. Glob. Optim. 56, 1247–1293 (2013).
[Crossref]

Robertson, D.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

Robertson, D. I.

Sahinidis, N. V.

L. M. Rios and N. V. Sahinidis, “Derivative-free optimization: a review of algorithms and comparison of software implementations,” J. Glob. Optim. 56, 1247–1293 (2013).
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Savransky, D.

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W. Shaomin, “Matrix methods in treating decentred optical systems,” Opt. quantum electronics 17, 1–14 (1985).
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D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

Sin, J.

J. Sin, W. H. Lee, and H. E. Stephanou, “Sensitivity analysis of an assembled fourier transform microspectrometer,” Proc. SPIE 768076800T (2010).

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[Crossref]

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H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Stephanou, H. E.

J. Sin, W. H. Lee, and H. E. Stephanou, “Sensitivity analysis of an assembled fourier transform microspectrometer,” Proc. SPIE 768076800T (2010).

A. N. Das, D. O. Popa, J. Sin, and H. E. Stephanou, “Precision alignment and assembly of a fourier transform microspectrometer,” J. Micro-Nano Mechatronics 5, 15 (2009).
[Crossref]

Strain, K. A.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
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Tong, J.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Tosh, I. A.

Ward, H.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
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S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Wellstead, P. E.

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

Willke, B.

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
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S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Yang, H.-S.

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

S. Kim, H.-S. Yang, Y.-W. Lee, and S.-W. Kim, “Merit function regression method for efficient alignment control of two-mirror optical systems,” Opt. Express 15, 5059–5068 (2007).
[Crossref] [PubMed]

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Yeh, H.-C.

Zhang, Y.

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

Appl. Opt. (2)

Class. Quantum Gravity (2)

H. Grote, G. Heinzel, A. Freise, S. Gossler, B. Willke, H. Lück, H. Ward, M. M. Casey, K. A. Strain, D. Robertson, and et al., “Alignment control of geo 600,” Class. Quantum Gravity 21, S441 (2004).
[Crossref]

F. Acernese, P. Amico, M. Al-Shourbagy, S. Aoudia, S. Avino, D. Babusci, G. Ballardin, R. Barillé, F. Barone, L. Barsotti, and et al., “The virgo automatic alignment system,” Class. Quantum Gravity 23, S91 (2006).
[Crossref]

IEEE Control. Syst. Mag. (1)

H. Butler, “Position control in lithographic equipment,” IEEE Control. Syst. Mag. 31, 28–47 (2011).
[Crossref]

Int. J. Comput. Integr. Manuf. (1)

M. Holters, A. Gatej, S. Haag, T. Müller, P. Loosen, and C. Brecher, “Approach for self-optimising assembly of optical systems,” Int. J. Comput. Integr. Manuf. 29, 1227–1237 (2016).
[Crossref]

J. Glob. Optim. (1)

L. M. Rios and N. V. Sahinidis, “Derivative-free optimization: a review of algorithms and comparison of software implementations,” J. Glob. Optim. 56, 1247–1293 (2013).
[Crossref]

J. Micro-Nano Mechatronics (1)

A. N. Das, D. O. Popa, J. Sin, and H. E. Stephanou, “Precision alignment and assembly of a fourier transform microspectrometer,” J. Micro-Nano Mechatronics 5, 15 (2009).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Korea (1)

Opt. Eng. (3)

N. Patel and C. S. Narayanamurthy, “Measurement of optical misalignment using wavefront sensing,” Opt. Eng. 54, 104106 (2015).
[Crossref]

V. Kalikivayi, V. C. P. Kumar, K. Kannan, and A. R. Ganesan, “Tolerance analysis of misalignment in an optical system using shack–hartmann wavefront sensor: experimental study,” Opt. Eng. 54, 075104 (2015).
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F. Z. Adil, E. İ. Konukseven, T. Balkan, and Ö. F. Adil, “Optical alignment procedure utilizing neural networks combined with shack–hartmann wavefront sensor,” Opt. Eng. 56, 051402 (2017).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. quantum electronics (1)

W. Shaomin, “Matrix methods in treating decentred optical systems,” Opt. quantum electronics 17, 1–14 (1985).
[Crossref]

Proc. SPIE (4)

J. Sin, W. H. Lee, and H. E. Stephanou, “Sensitivity analysis of an assembled fourier transform microspectrometer,” Proc. SPIE 768076800T (2010).

D. Redding, N. Sigrist, J. Z. Lou, Y. Zhang, and P. Atcheson, “Optical state estimation using wavefront data,” Proc. SPIE 5523, 212–224 (2004).

E.-S. Oh, S. Kimc, Y. Kim, H. Lee, S.-W. Kima, and H.-S. Yang, “Integration of differential wavefront sampling with merit function regression for efficient alignment of three-mirror anastigmat optical system,” Proc. SPIE 7793, 77930 (2010).

H.-S. Yang, S.-H. Kim, Y.-W. Lee, J.-B. Song, H.-G. Rhee, H.-Y. Lee, J.-H. Lee, I.-W. Lee, and S.-W. Kim, “Computer aided alignment using zernike coefficients,” Proc. SPIE 6293, 62930I (2006).

Rev. Sci. Instrum. (1)

D. Kalamatianos, P. E. Wellstead, J. M. Edmunds, and P. Liatsis, “Active alignment for two-beam interferometers,” Rev. Sci. Instrum. 77, 013103 (2006).
[Crossref]

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C. G. Prevost and J. Genest, “Dynamic alignment of a michelson interferometer using a position-sensitive device,” in “Proc. of the SPIE 49th Annual Meeting,” (2004), pp. 293–304.

S. Li, Y. Zhang, M. Gao, L. Xu, X. Wei, J. Tong, L. Jin, and S. Cheng, A Moving Mirror Driving System of FT-IR Spectrometer for Atmospheric Analysis (Springer, 2011), pp. 371–377.

D. R. Neal and J. Mansell, “Application of shack-hartmann wavefront sensors to optical system calibration and alignment,” in “Proc. 2nd Int. Workshop on Adaptive Optics for Industry and Medicine,” (2000), pp. 234–243.

R. E. Abbink, “Interferometer alignment,” (2005). US Patent 6,952,266.

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Figures (4)

Fig. 1
Fig. 1 Flow diagram of the proposed predictor-corrector framework.
Fig. 2
Fig. 2 Experimental beam expander setup (a, ND filter not depicted) and schematic depiction of the three configurations (0,1,2) during the beam expander assembly process (b).
Fig. 3
Fig. 3 Identification step (model update) in first assembly step of experiment (a): Iteration of cost function value (a) and corresponding predicted wavefront deviation (reconstructed from Zernike coefficient error) and simulated/obtained wavefront at iteration 0 (maximum wavefront error 22.83 waves) (b)–(c) and iteration 120 (maximum wavefront error 1.41 waves) (d)–(e). A selection of corresponding Zernike coefficients for this identification process are given in Tab. 2
Fig. 4
Fig. 4 Two consecutive predictor-corrector cycles in experiment (a): Measured wavefront in configuration 1 (a) followed by the predicted and subsequently corrected wavefront in simulation (b). The same is done in the second assembly step where a wavefront is obtained (c), and subsequent prediction-correction simulation calculations (d). The wavefront of the assembled beam expander is shown in (e).

Tables (4)

Tables Icon

Algorithm 1 Predictor-Corrector Framework (PCF)

Tables Icon

Table 1 Utilized Zernike standard polynomials with corresponding coefficients.

Tables Icon

Table 2 Iteration of first four Zernike coefficients (in waves) at selected iterations (1, 5, 10, 50, 80, 120) during the first identification step in experiment (a). The remaining Zernike coefficients (z5z10) are zero since they do not influence the wavefront (see sensitivity matrix S1 from (8)).

Tables Icon

Table 3 Iterative assembly process for the beam expander in experiment (a) and (b). Values for lens positions provided by initial design / simulation (blue) and values provided by identification (red). The corresponding predicted cost (green if below tolerance, red if above tolerance) is shown below.

Equations (13)

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

X i * : = ( x 1 * , , x i * )
X S , i : = ( x S , i + 1 , , x S , n ) .
X H , i : = ( X i * , X S , i )
z = h ( X ) .
X = h 1 ( z ) .
x * = arg min x X J ( X , z )
J ( X , z ) = z h ( X ) W = ( z h ( X ) ) T W ( z h ( X ) ) .
z d z p W = z d h ( X i * , X S , i ) W TOL .
X ^ S , i = arg min X S , i X H , i J ( X H , i , z d ) .
z d h ( X i * , X ^ S , i ) W TOL .
x ^ i = arg min x i X H , i J ( X H , i , z d ) .
z d h ( X i 1 * , x ^ i , X S , i ) W TOL .
S 1 = ( 0 0 0 0 0.12 33.51 0 0 2.05 0 0 33.51 2.05 0 0 0 0 0 0 0.07 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ) and S 2 = ( 0 0 0 0 0.57 75.63 0 0 1.58 0 0 75.63 1.58 0 0 0 0 0 0 0.33 0 0 0 0 0 0 0 0 0 0 0 0.02 0.01 0 0 0.02 0 0 0.01 0 0 0 0 0 0 0 0 0 0 0 ) .

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