Abstract

This paper aims at decreasing the assembly difficulty and reducing the cost of optical systems using multiple components. A strategy is proposed to substitute one freeform surface for multi-separated surfaces. A freeform-objective Chernin multipass cell is implemented as a typical instance for assembly simplification. The application of a freeform surface helps in decreasing the degree of objective assembly tolerances from 24 to 4, by representing the original four objectives with a linear combination of a 2D Gaussian radial basis function, which is analytical, global C smooth, and locally influencing. The simulation result verifies the feasibility and performance of the designed freeform-objective Chernin multipass cell, whose base length is 0.2 m, volume is less than 0.8 L, and adjustable optical length is 0.4–34 m. Results prove that by using a proper approach to approximate the original surfaces as an integrated freeform, one can simultaneously reduce the assembly cost and the assembly difficulty.

© 2017 Optical Society of America

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References

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    [Crossref]
  2. K. Fuerschbach, G. E. Davis, K. P. Thompson, and J. P. Rolland, “Assembly of a freeform off-axis optical system employing three ϕ-polynomial Zernike mirrors,” Opt. Lett. 39, 2896–2899 (2014).
    [Crossref]
  3. I. M. Egdall, “Manufacture of a three-mirror wide-field optical system,” Opt. Eng. 24, 242285 (1985).
    [Crossref]
  4. H. J. Jeong, G. N. Lawrence, and K. B. Nahm, “Auto-alignment of a three-mirror off-axis telescope by reverse optimization and end-to-end aberration measurements,” Proc. SPIE 0818, 419–430 (1987).
    [Crossref]
  5. J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
    [Crossref]
  6. S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
    [Crossref]
  7. S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
    [Crossref]
  8. F. Z. Fang and X. D. Zhang, “Off-axis parabolic multi-lens system integrated machining method,” CN patent104841951 A (19August2015).
  9. F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
    [Crossref]
  10. P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.
  11. V. P. Korolkov, A. G. Poleshchuk, and A. F. Ivanov, “Freeform corrector for laser with large aperture YAG:ND3+ active element,” Opt. Eng. 53, 075105 (2014).
    [Crossref]
  12. K. Wang, F. Chen, Z. Liu, X. Luo, and S. Liu, “Design of compact freeform lens for application specific light-emitting diode packaging,” Opt. Express 18, 413–425 (2010).
    [Crossref]
  13. Y. Luo, Z. Feng, Y. Han, and H. Li, “Design of compact and smooth free-form optical system with uniform illuminance for LED source,” Opt. Express 18, 9055–9063 (2010).
    [Crossref]
  14. Q. Y. Meng, W. Wang, H. C. Ma, and J. H. Dong, “Easy-aligned off-axis three-mirror system with wide field of view using freeform surface based on integration of primary and tertiary mirror,” Appl. Opt. 53, 3028–3034 (2014).
    [Crossref]
  15. M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
    [Crossref]
  16. J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
    [Crossref]
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    [Crossref]
  18. S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
    [Crossref]
  19. F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
    [Crossref]
  20. F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16, 7323–7329 (2008).
    [Crossref]
  21. Y. Cheng, F. Z. Fang, and X. D. Zhang, “Design and manufacture of off-axis optical reflective integrator with faceted structure,” Opt. Eng. 51, 94001 (2012).
    [Crossref]
  22. X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
    [Crossref]

2015 (2)

2014 (3)

2013 (2)

F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

2012 (2)

Y. Cheng, F. Z. Fang, and X. D. Zhang, “Design and manufacture of off-axis optical reflective integrator with faceted structure,” Opt. Eng. 51, 94001 (2012).
[Crossref]

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

2010 (3)

2008 (2)

2000 (1)

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

1991 (2)

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
[Crossref]

S. M. Chernin and E. G. Barskaya, “Optical multipass matrix systems,” Appl. Opt. 30, 51–58 (1991).
[Crossref]

1989 (1)

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

1987 (1)

H. J. Jeong, G. N. Lawrence, and K. B. Nahm, “Auto-alignment of a three-mirror off-axis telescope by reverse optimization and end-to-end aberration measurements,” Proc. SPIE 0818, 419–430 (1987).
[Crossref]

1985 (1)

I. M. Egdall, “Manufacture of a three-mirror wide-field optical system,” Opt. Eng. 24, 242285 (1985).
[Crossref]

Alvarez, R.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Barskaya, E. G.

Beier, M.

Benitez, P.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Buljan, M.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Cakmakci, O.

Chen, F.

Chen, S.

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
[Crossref]

Cheng, Y.

F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
[Crossref]

Y. Cheng, F. Z. Fang, and X. D. Zhang, “Design and manufacture of off-axis optical reflective integrator with faceted structure,” Opt. Eng. 51, 94001 (2012).
[Crossref]

Chernin, S. M.

Cowan, C. F. N.

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
[Crossref]

Cvetkovic, A.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Damm, C.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Davis, G. E.

Dong, J. H.

Dross, O.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Eberhardt, R.

Egdall, I. M.

I. M. Egdall, “Manufacture of a three-mirror wide-field optical system,” Opt. Eng. 24, 242285 (1985).
[Crossref]

Evans, C.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

Fang, F. Z.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
[Crossref]

Y. Cheng, F. Z. Fang, and X. D. Zhang, “Design and manufacture of off-axis optical reflective integrator with faceted structure,” Opt. Eng. 51, 94001 (2012).
[Crossref]

F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16, 7323–7329 (2008).
[Crossref]

F. Z. Fang and X. D. Zhang, “Off-axis parabolic multi-lens system integrated machining method,” CN patent104841951 A (19August2015).

Feng, Z.

Figoski, J. W.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Foroosh, H.

Fuerschbach, K.

Gao, H. M.

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

Gebhardt, A.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Grant, P. M.

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
[Crossref]

Guo, Y. W.

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

Han, Y.

Hartung, J.

Hernández, M.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Holota, W.

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Hou, W.

J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
[Crossref]

Hu, X. T.

Irie, S.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Ivanov, A. F.

V. P. Korolkov, A. G. Poleshchuk, and A. F. Ivanov, “Freeform corrector for laser with large aperture YAG:ND3+ active element,” Opt. Eng. 53, 075105 (2014).
[Crossref]

Jeong, H. J.

H. J. Jeong, G. N. Lawrence, and K. B. Nahm, “Auto-alignment of a three-mirror off-axis telescope by reverse optimization and end-to-end aberration measurements,” Proc. SPIE 0818, 419–430 (1987).
[Crossref]

Jin, G. F.

J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
[Crossref]

Kinoshita, H.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Korolkov, V. P.

V. P. Korolkov, A. G. Poleshchuk, and A. F. Ivanov, “Freeform corrector for laser with large aperture YAG:ND3+ active element,” Opt. Eng. 53, 075105 (2014).
[Crossref]

Lawrence, G. N.

H. J. Jeong, G. N. Lawrence, and K. B. Nahm, “Auto-alignment of a three-mirror off-axis telescope by reverse optimization and end-to-end aberration measurements,” Proc. SPIE 0818, 419–430 (1987).
[Crossref]

Li, H.

Liu, S.

Liu, Z.

Luo, X.

Luo, Y.

Ma, H. C.

Meng, Q. Y.

Miñano, J. C.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Miyafuji, A.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Moore, B.

Moore, G. F.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Murkami, K.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Nahm, K. B.

H. J. Jeong, G. N. Lawrence, and K. B. Nahm, “Auto-alignment of a three-mirror off-axis telescope by reverse optimization and end-to-end aberration measurements,” Proc. SPIE 0818, 419–430 (1987).
[Crossref]

Oshino, T.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Peschel, T.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Poleshchuk, A. G.

V. P. Korolkov, A. G. Poleshchuk, and A. F. Ivanov, “Freeform corrector for laser with large aperture YAG:ND3+ active element,” Opt. Eng. 53, 075105 (2014).
[Crossref]

Risse, S.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Rolland, J. P.

Santamaria, A.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Scheiding, S.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Shrode, T. E.

J. W. Figoski, T. E. Shrode, and G. F. Moore, “Computer-aided alignment of a wide-field, three-mirror, unobscured, high-resolution sensor,” Proc. SPIE 1049, 166–177 (1989).
[Crossref]

Stumpf, D.

Sugisaki, K.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Thompson, K. P.

Tünnermann, A.

M. Beier, J. Hartung, T. Peschel, C. Damm, A. Gebhardt, S. Scheiding, D. Stumpf, U. D. Zeitner, S. Risse, R. Eberhardt, and A. Tünnermann, “Development, fabrication, and testing of an anamorphic imaging snap-together freeform telescope,” Appl. Opt. 54, 3530–3542 (2015).
[Crossref]

S. Scheiding, C. Damm, W. Holota, T. Peschel, A. Gebhardt, S. Risse, and A. Tünnermann, “Ultra precisely manufactured mirror assemblies with well defined reference structures,” Proc. SPIE 7739, 773908 (2010).
[Crossref]

Wang, K.

Wang, W.

Watanabe, T.

S. Irie, T. Watanabe, H. Kinoshita, A. Miyafuji, K. Sugisaki, T. Oshino, and K. Murkami, “Development for the alignment procedure of three-aspherical-mirror optics,” Proc. SPIE 3997, 807–813 (2000).
[Crossref]

Weckenmann, A.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

Zamora, P.

P. Zamora, A. Cvetkovic, M. Buljan, M. Hernández, P. Benitez, J. C. Miñano, O. Dross, R. Alvarez, and A. Santamaria, “Advanced PV concentrators,” in IEEE Photovoltaic Specialists Conference (PVSC), (2009), p. 000929–000932.

Zeitner, U. D.

Zhang, G. X.

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

Zhang, X. D.

J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
[Crossref]

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
[Crossref]

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

Y. Cheng, F. Z. Fang, and X. D. Zhang, “Design and manufacture of off-axis optical reflective integrator with faceted structure,” Opt. Eng. 51, 94001 (2012).
[Crossref]

F. Z. Fang, X. D. Zhang, and X. T. Hu, “Cylindrical coordinate machining of optical freeform surfaces,” Opt. Express 16, 7323–7329 (2008).
[Crossref]

F. Z. Fang and X. D. Zhang, “Off-axis parabolic multi-lens system integrated machining method,” CN patent104841951 A (19August2015).

Zhu, J.

J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
[Crossref]

Adv. Opt. Technol. (1)

F. Z. Fang, Y. Cheng, and X. D. Zhang, “Design of freeform optics,” Adv. Opt. Technol. 2, 445–453 (2013).
[Crossref]

Appl. Opt. (3)

CIRP Ann. (2)

F. Z. Fang, X. D. Zhang, A. Weckenmann, G. X. Zhang, and C. Evans, “Manufacturing and measurement of freeform optics,” CIRP Ann. 62, 823–846 (2013).
[Crossref]

X. D. Zhang, H. M. Gao, Y. W. Guo, and G. X. Zhang, “Machining of optical freeform prisms by rotating tools turning,” CIRP Ann. 61, 519–522 (2012).
[Crossref]

IEEE Trans. Neural Netw. (1)

S. Chen, C. F. N. Cowan, and P. M. Grant, “Orthogonal least squares learning algorithm for radial basis function networks,” IEEE Trans. Neural Netw. 2, 302–309 (1991).
[Crossref]

J. Opt. (1)

J. Zhu, W. Hou, X. D. Zhang, and G. F. Jin, “Design of a low F-number freeform off-axis three-mirror system with rectangular field-of-view,” J. Opt. 17, 15605 (2015).
[Crossref]

Opt. Eng. (3)

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[Crossref]

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[Crossref]

Opt. Express (4)

Opt. Lett. (1)

Proc. SPIE (4)

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[Crossref]

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Figures (10)

Fig. 1.
Fig. 1.

Configuration of the four-objective Chernin multipass cell.

Fig. 2.
Fig. 2.

Tolerances of the four objectives: (a) x decenter; (b) y decenter; (c) z decenter; (d) pitch; (e) yaw; and (f) roll.

Fig. 3.
Fig. 3.

Diagram illustrating the simplification of four-objective Chernin multipass cell by freeform.

Fig. 4.
Fig. 4.

Matrices of focal points during adjustment of objectives.

Fig. 5.
Fig. 5.

Focal points at two base lengths of Chernin cell: (a) 1200 mm and (b) 600 mm.

Fig. 6.
Fig. 6.

Parameters of the four-objective Chernin multipass cell (unit: mm): (a) parameters of objectives and (b) parameters of principal and auxiliary field mirrors.

Fig. 7.
Fig. 7.

Linear combination of 2D Gaussian RBF to approximate the four objectives as the freeform objective: (a) four-objective surfaces; (b) 2D Gaussian RBF center’s position; (c) freeform-objective surface; and (d) approximation of sag error.

Fig. 8.
Fig. 8.

Simulation results of the freeform-objective Chernin multipass cell at maximum optical length: (a) ray-tracing simulation and (b) maximum optical absorption length.

Fig. 9.
Fig. 9.

Beam shape and intensity distribution analysis of the light incident on the sensor: (a) four-objective Chernin multipass cell without assembling errors; (b) freeform-objective Chernin multipass cell without assembling errors; (c) four-objective Chernin multipass cell with 0.2° roll error of O3; and (d) freeform-objective Chernin multipass cell with 0.2° roll error of freeform objective.

Fig. 10.
Fig. 10.

Tolerances of freeform objective: (a) roll; (b) x decenter; (c) y decenter; and (d) z decenter.

Tables (2)

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Table 1. Tolerance Analysis of the Four Objectives

Tables Icon

Table 2. Tolerance Analysis of the Freeform Objectives

Equations (3)

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ln(IinIinIout)=nαn(λ)CnL,
N=(m1)(4n2),
z(x,y)=i=1n(αie(λi((xxi)2+(yyi)2))+βi),

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