Abstract

The classic Czerny-Turner spectrometer consists of a plane grating and two spherical mirrors. The optical path geometry adopted for incident and grating dispersed light is off-axis reflection, so the spherical collimating and focusing mirrors introduce coma and astigmatism. The conventional configuration is asymmetrical for coma automatic compensation, but suffers from astigmatism. We substitute the off-axis parabolic (OAP) surfaces for spherical surfaces of the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free configuration. The multiple OAP surfaces are then expanded and mixed, to construct a freeform surface integrating the collimating and focusing mirrors into a single element. Results show that a 0.1 nm spectral resolution is achieved over a bandwidth of 400 nm centered at 800 nm, in the designed spectrometer comprised of a plane grating and one freeform mirror. The construction method is advantageous to integrated optic design, and the resulting freeform mirror spectrometer is compact, and simplifies manufacture and alignment.

© 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. D. Korsch, “Anastigmatic three-mirror telescope,” Appl. Opt. 16(8), 2074–2077 (1977).
    [Crossref] [PubMed]
  2. K. Fuerschbach, J. P. Rolland, and K. P. Thompson, “A new family of optical systems employing φ-polynomial surfaces,” Opt. Express 19(22), 21919–21928 (2011).
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    [Crossref] [PubMed]
  4. M. R. Torr and D. G. Torr, “Compact imaging spectrograph for broadband spectral simultaneity,” Appl. Opt. 34(34), 7888–7898 (1995).
    [Crossref] [PubMed]
  5. M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11–12), 792–797 (1930).
    [Crossref]
  6. A. B. Shafer, L. R. Megill, and L. Droppleman, “Optimization of the Czerny–Turner spectrometer,” J. Opt. Soc. Am. 54(7), 879–887 (1964).
    [Crossref]
  7. Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
    [Crossref]
  8. D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48(19), 3846–3853 (2009).
    [Crossref] [PubMed]
  9. M. D. Mouriz, E. L. Lago, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Schwarzschild spectrometer,” Appl. Opt. 50(16), 2418–2424 (2011).
    [Crossref] [PubMed]
  10. T. A. Chen, Y. Tang, L. J. Zhang, Y. E. Chang, and C. Zheng, “Correction of astigmatism and coma using analytic theory of aberrations in imaging spectrometer based on concentric off-axis dual reflector system,” Appl. Opt. 53(4), 565–576 (2014).
    [Crossref] [PubMed]
  11. Q. Xue, S. Wang, and F. Lu, “Aberration-corrected Czerny-Turner imaging spectrometer with a wide spectral region,” Appl. Opt. 48(1), 11–16 (2009).
    [Crossref] [PubMed]
  12. G. Xia, S. Wu, G. Wang, M. Hu, and J. Xing, “Astigmatism-free Czerny-Turner compact spectrometer with cylindrical mirrors,” Appl. Opt. 56(32), 9069–9073 (2017).
    [Crossref] [PubMed]
  13. L. Xu, K. Chen, Q. He, and G. Jin, “Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism,” Appl. Opt. 48(15), 2871–2879 (2009).
    [Crossref] [PubMed]
  14. E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
    [Crossref]
  15. C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
    [Crossref] [PubMed]
  16. K. S. Lee, K. P. Thompson, and J. P. Rolland, “Broadband astigmatism-corrected Czerny-Turner spectrometer,” Opt. Express 18(22), 23378–23384 (2010).
    [Crossref] [PubMed]
  17. Q. Xue, “Astigmatism-corrected Czerny-Turner imaging spectrometer for broadband spectral simultaneity,” Appl. Opt. 50(10), 1338–1344 (2011).
    [Crossref] [PubMed]
  18. G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).
  19. X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
    [Crossref]
  20. X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
    [Crossref]
  21. S. H. Kim, H. J. Kong, and S. Chang, “Aberration analysis of a concentric imaging spectrometer with a convex grating,” Opt. Commun. 333, 6–10 (2014).
    [Crossref]
  22. J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
    [Crossref] [PubMed]
  23. J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
    [Crossref] [PubMed]
  24. Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
    [Crossref] [PubMed]
  25. T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

2017 (3)

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

G. Xia, S. Wu, G. Wang, M. Hu, and J. Xing, “Astigmatism-free Czerny-Turner compact spectrometer with cylindrical mirrors,” Appl. Opt. 56(32), 9069–9073 (2017).
[Crossref] [PubMed]

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref] [PubMed]

2016 (2)

Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
[Crossref] [PubMed]

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

2015 (2)

X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
[Crossref]

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

2014 (4)

2012 (1)

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

2011 (3)

2010 (2)

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
[Crossref] [PubMed]

K. S. Lee, K. P. Thompson, and J. P. Rolland, “Broadband astigmatism-corrected Czerny-Turner spectrometer,” Opt. Express 18(22), 23378–23384 (2010).
[Crossref] [PubMed]

2009 (3)

2008 (1)

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
[Crossref]

1995 (1)

1977 (1)

1964 (1)

1930 (1)

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11–12), 792–797 (1930).
[Crossref]

Austin, D. R.

Bauer, A.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref] [PubMed]

Bu, Z.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Burrell, K. H.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
[Crossref] [PubMed]

Chang, S.

S. H. Kim, H. J. Kong, and S. Chang, “Aberration analysis of a concentric imaging spectrometer with a convex grating,” Opt. Commun. 333, 6–10 (2014).
[Crossref]

Chang, Y. E.

Chen, H.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Chen, K.

Chen, S.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Chen, T. A.

Chen, Y.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

Chrystal, C.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
[Crossref] [PubMed]

Czerny, M.

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11–12), 792–797 (1930).
[Crossref]

de la Fuente, R.

Droppleman, L.

Fuerschbach, K.

Gao, Z.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

Ge, X.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

González-Núñez, H.

Gulis, I. M.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
[Crossref]

Guo, P.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Guo, Z.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

He, Q.

Hu, M.

Ji, Z.

Jin, G.

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
[Crossref]

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
[Crossref] [PubMed]

L. Xu, K. Chen, Q. He, and G. Jin, “Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism,” Appl. Opt. 48(15), 2871–2879 (2009).
[Crossref] [PubMed]

Kim, S. H.

S. H. Kim, H. J. Kong, and S. Chang, “Aberration analysis of a concentric imaging spectrometer with a convex grating,” Opt. Commun. 333, 6–10 (2014).
[Crossref]

Kong, H. J.

S. H. Kim, H. J. Kong, and S. Chang, “Aberration analysis of a concentric imaging spectrometer with a convex grating,” Opt. Commun. 333, 6–10 (2014).
[Crossref]

Korsch, D.

Kupreev, A. G.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
[Crossref]

Lago, E. L.

Lee, K. S.

Liu, P.

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

Lu, F.

Megill, L. R.

Meng, Q.

Mouriz, M. D.

Mu, T.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Pablant, N. A.

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
[Crossref] [PubMed]

Prieto-Blanco, X.

Qu, B. X.

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

Reimers, J.

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref] [PubMed]

Rolland, J. P.

Shafer, A. B.

Shi, G.

Tang, Y.

Thompson, K. P.

Torr, D. G.

Torr, M. R.

Turner, A. F.

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11–12), 792–797 (1930).
[Crossref]

Voropai, E. S.

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
[Crossref]

Walmsley, I. A.

Wang, D.

Wang, G.

Wang, H.

Wang, K.

Wang, S.

Wang, Y.

Witting, T.

Wu, H.

Wu, S.

Wu, X.

Xia, G.

G. Xia, S. Wu, G. Wang, M. Hu, and J. Xing, “Astigmatism-free Czerny-Turner compact spectrometer with cylindrical mirrors,” Appl. Opt. 56(32), 9069–9073 (2017).
[Crossref] [PubMed]

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

Xing, J.

Xu, L.

Xue, Q.

Yang, J.

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Yang, T.

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
[Crossref] [PubMed]

Yu, F.

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

Yuan, Q.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

Zeng, F.

Zhang, J.

Zhang, L. J.

Zhang, X.

Zhang, Y.

X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
[Crossref]

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Zheng, C.

Zhong, X.

X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
[Crossref]

Zhu, D.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

Zhu, J.

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

J. Zhu, X. Wu, T. Yang, and G. Jin, “Generating optical freeform surfaces considering both coordinates and normals of discrete data points,” J. Opt. Soc. Am. A 31(11), 2401–2408 (2014).
[Crossref] [PubMed]

Zuo, C.

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

Appl. Opt. (10)

D. R. Austin, T. Witting, and I. A. Walmsley, “Broadband astigmatism-free Czerny-Turner imaging spectrometer using spherical mirrors,” Appl. Opt. 48(19), 3846–3853 (2009).
[Crossref] [PubMed]

M. D. Mouriz, E. L. Lago, X. Prieto-Blanco, H. González-Núñez, and R. de la Fuente, “Schwarzschild spectrometer,” Appl. Opt. 50(16), 2418–2424 (2011).
[Crossref] [PubMed]

T. A. Chen, Y. Tang, L. J. Zhang, Y. E. Chang, and C. Zheng, “Correction of astigmatism and coma using analytic theory of aberrations in imaging spectrometer based on concentric off-axis dual reflector system,” Appl. Opt. 53(4), 565–576 (2014).
[Crossref] [PubMed]

Q. Xue, S. Wang, and F. Lu, “Aberration-corrected Czerny-Turner imaging spectrometer with a wide spectral region,” Appl. Opt. 48(1), 11–16 (2009).
[Crossref] [PubMed]

G. Xia, S. Wu, G. Wang, M. Hu, and J. Xing, “Astigmatism-free Czerny-Turner compact spectrometer with cylindrical mirrors,” Appl. Opt. 56(32), 9069–9073 (2017).
[Crossref] [PubMed]

L. Xu, K. Chen, Q. He, and G. Jin, “Design of freeform mirrors in Czerny-Turner spectrometers to suppress astigmatism,” Appl. Opt. 48(15), 2871–2879 (2009).
[Crossref] [PubMed]

D. Korsch, “Anastigmatic three-mirror telescope,” Appl. Opt. 16(8), 2074–2077 (1977).
[Crossref] [PubMed]

M. R. Torr and D. G. Torr, “Compact imaging spectrograph for broadband spectral simultaneity,” Appl. Opt. 34(34), 7888–7898 (1995).
[Crossref] [PubMed]

Q. Xue, “Astigmatism-corrected Czerny-Turner imaging spectrometer for broadband spectral simultaneity,” Appl. Opt. 50(10), 1338–1344 (2011).
[Crossref] [PubMed]

Q. Meng, H. Wang, K. Wang, Y. Wang, Z. Ji, and D. Wang, “Off-axis three-mirror freeform telescope with a large linear field of view based on an integration mirror,” Appl. Opt. 55(32), 8962–8970 (2016).
[Crossref] [PubMed]

Chin. Opt. Lett. (2)

T. Yang, J. Zhu, and G. Jin, “Compact freeform off-axis three-mirror imaging system based on the integration of primary and tertiary mirrors on one single surface,” Chin. Opt. Lett. 14(6), 26–30 (2016).

G. Xia, B. X. Qu, P. Liu, and F. Yu, “Astigmatism–corrected miniature Czerny–Turner spectrometer with freeform cylindrical lens,” Chin. Opt. Lett. 10(8), 23–26 (2012).

J. Appl. Spectrosc. (1)

E. S. Voropai, I. M. Gulis, and A. G. Kupreev, “Astigmatism correction for a large-aperture dispersive spectrometer,” J. Appl. Spectrosc. 75(1), 150–155 (2008).
[Crossref]

J. Opt. Soc. Am. (1)

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

Light Sci. Appl. (1)

J. Reimers, A. Bauer, K. P. Thompson, and J. P. Rolland, “Freeform spectrometer enabling increased compactness,” Light Sci. Appl. 6(7), e17026 (2017).
[Crossref] [PubMed]

Opt. Commun. (3)

Q. Yuan, D. Zhu, Y. Chen, Z. Guo, C. Zuo, and Z. Gao, “Comparative assessment of astigmatism–corrected Czerny-Turner imaging spectrometer using off-the-shelf optics,” Opt. Commun. 388, 53–61 (2017).
[Crossref]

S. H. Kim, H. J. Kong, and S. Chang, “Aberration analysis of a concentric imaging spectrometer with a convex grating,” Opt. Commun. 333, 6–10 (2014).
[Crossref]

X. Zhong, Y. Zhang, and G. Jin, “High performance Czerny-Turner imaging spectrometer with aberrations corrected by tilted lenses,” Opt. Commun. 338, 73–76 (2015).
[Crossref]

Opt. Express (3)

Opt. Laser Technol. (1)

X. Ge, S. Chen, Y. Zhang, H. Chen, P. Guo, T. Mu, J. Yang, and Z. Bu, “Broadband astigmatism–corrected spectrometer design using a toroidal lens and a special filter,” Opt. Laser Technol. 65, 88–93 (2015).
[Crossref]

Rev. Sci. Instrum. (1)

C. Chrystal, K. H. Burrell, and N. A. Pablant, “Straightforward correction for the astigmatism of a Czerny-Turner spectrometer,” Rev. Sci. Instrum. 81(2), 023503 (2010).
[Crossref] [PubMed]

Z. Phys. (1)

M. Czerny and A. F. Turner, “On the Astigmatism of Mirror Spectrometers,” Z. Phys. 61(11–12), 792–797 (1930).
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 Optical layout of the classic Czerny-Turner spectrometer.
Fig. 2
Fig. 2 Optical layout of the OAP mirror.
Fig. 3
Fig. 3 Schemes for the multiple OAP surfaces substitutions.
Fig. 4
Fig. 4 Specification calculation scheme for the OAP segments.
Fig. 5
Fig. 5 Flowchart showing the parameter calculation for the OAP surfaces.
Fig. 6
Fig. 6 Coordinate transformation for the OAP segments.
Fig. 7
Fig. 7 Surface profiles along YF direction defined in the global coordinate system XF-YF-ZF (a) for each OAP segment and the OAP base (b) for differences between neighboring OAP segments in the overlapping area.
Fig. 8
Fig. 8 The update strategy of the OAP segment for λ4.
Fig. 9
Fig. 9 Flowchart of OAP surface expansion and mixing.
Fig. 10
Fig. 10 Optical layout of the freeform spectrometer.
Fig. 11
Fig. 11 Optical performance of the constructed freeform spectrometer. (a) Wavefront aberration of the collimated beam after the first reflection by the freeform mirror, (b) RMS spot radius on the detector as a function of wavelength across the spectrum range, (c) spot diagrams on the detector for the nine sampling wavelengths.
Fig. 12
Fig. 12 Surface sag of the optimized freeform mirror. (a) XY polynomials, (b) with the base spherical surface added.
Fig. 13
Fig. 13 Optical performance of the optimized freeform spectrometer. (a) Wavefront aberration of the collimated beam after the first reflection from the freeform mirror, (b) RMS spot radius on the detector as a function of wavelength across the spectrum range, (c) spot diagrams on the detector for the nine sampling wavelengths.

Tables (5)

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Table 1 OAP base and OAP segment parameters.

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Table 2 Updated OAP segment parameters.

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Table 3 Constructed and optimized parameters for the freeform mirror.

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Table 4 Constructed and optimized parameters for the freeform spectrometer.

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Table 5 Inclined incidence angles on the detector.

Equations (27)

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d(sini+sinθ)=mλ
s= D 2 2R = D 2 4f
f ^ =f+s
tanβ= D fs = 2RD R 2 D 2
D= R(1cosβ) sinβ
θ ctrl θ min + β min = β ctrl
θ ctrl θ max + β max = β ctrl
D B-max D B-min =L
f ^ S-ctrl + f ^ B-ctrl = f ^ S-min + f ^ B-min = f ^ S-max + f ^ B-max
β C = β 1 = θ 1 i 2
z ctrl = f ^ B-ctrl + s ctrl + x ctrl 2 + ( y ctrl + D S-ctrl ) 2 2 R ctrl
y 0 = f ^ B-ctrl sin β ctrl 2
z 0 = f ^ B-ctrl cos β ctrl 2
x ctrl-F = x ctrl
y ctrl-F = y ctrl cos β ctrl 2 z ctrl sin β ctrl 2 + y 0
z ctrl-F = y ctrl sin β ctrl 2 + z ctrl cos β ctrl 2 + z 0
x min-F = x min
y min-F = y min cos( θ min θ ctrl + β ctrl 2 ) z min sin( θ min θ ctrl + β ctrl 2 )+ y 0
z min-F = y min sin( θ min θ ctrl + β ctrl 2 )+ z min cos( θ min θ ctrl + β ctrl 2 )+ z 0
Φ x = Φ cosi
Φy= Φcos(θi) cosi
ε 4 = S 45 δ 45
β 4 = β 4 +2 ε 4
Δ 4 = d 45 tan ε 4
L GF4 = L GF4 Δ 4 = f ^ B4 Δ 4
L FD4 = f ^ S4 = L FD4 cos2 ε 4 Δ 4 = f ^ S4 cos2 ε 4 Δ 4
z F = R S + R S 2 ( x F 2 + y F 2 ) + p 20 x 2 + p 02 y 2 + p 21 x 2 y+ p 03 y 3 + p 40 x 4 + p 22 x 2 y 2 + p 04 y 4 + p 41 x 4 y+ p 23 x 2 y 3 + p 05 y 5

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