Abstract

We present a generalized method for designing a novel circular multi-pass cell (MPC) with multifold overall optical path length, or alternatively enlarged path-to-volume ratio in the same magnification compared to traditional version, by exploiting the vertical dimension of cavity mirrors. Multiple rows of reflection spots can be generated on arbitrary number of different horizontal planes within the cell that consists of two easy-fabricating circular spherical mirrors. Base on this method, one can arbitrarily determine the interval of reflection spots in both horizontal and vertical directions, so that almost seamless and regular distributed dense spot pattern, and consequently large path-to-volume ratio can be achieved. A series of q-preserving configurations of the multiple-row circular multi-pass cell are calculated and simulated, in which the q-parameters of probe Gaussian beams can be approximately unchanged after the whole transmission within the cells. The maximum optical path length among these simulation cases is 201.8 m within 427.2 mL volume. Furthermore, we demonstrate a practical optical setup with 21.9 m optical path length within 100.1 mL, which is the smallest volume case among the existing actual MPCs with similar overall optical path lengths.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Generalized method for seeking q-preserving configurations of multi-pass cells

Zheng Yang, Mingli Zou, and Liqun Sun
Opt. Express 27(10) 14054-14063 (2019)

Acetylene sensing system based on wavelength modulation spectroscopy using a triple-row circular multi-pass cell

Mingli Zou, Zheng Yang, Liqun Sun, and Xianshun Ming
Opt. Express 28(8) 11573-11582 (2020)

Optical design and analysis of a two-spherical-mirror-based multipass cell

Rong Kong, Tao Sun, Peng Liu, and Xin Zhou
Appl. Opt. 59(6) 1545-1552 (2020)

References

  • View by:
  • |
  • |
  • |

  1. S. M. Chernin, “Multipass systems of new generation in high-resolution spectroscopy for fundamental and applied atmosphere investigations,” Proc. SPIE 2366, 408–418 (1995).
    [Crossref]
  2. S. M. Chernin, “New generation of multipass systems in high resolution spectroscopy,” Spectrochim. Acta, Part A 52(8), 1009–1022 (1996).
    [Crossref]
  3. J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
    [Crossref]
  4. B. E. Bernacki, Multipass Optical device and process for gas and analyte determination. U.S. Patent 7876443 (25 January 2011).
  5. A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
    [Crossref]
  6. B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
    [Crossref]
  7. P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
    [Crossref]
  8. M. Graf, H. Looser, L. Emmenegger, and B. Tuzson, “Beam folding analysis and optimization of mask-enhanced toroidal multipass cells,” Opt. Lett. 42(16), 3137–3140 (2017).
    [Crossref]
  9. M. Markus, B. Tuzson, M. Hundt, J. Jágerská, H. Looser, and L. Emmenegger, “Circular paraboloid reflection cell for laser spectroscopic trace gas analysis,” J. Opt. Soc. Am. A 33(5), 913–919 (2016).
    [Crossref]
  10. Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
    [Crossref]
  11. Z. Yang, M. Zou, and L. Sun, “Generalized method for seeking q-preserving configurations of multi-pass cells,” Opt. Express 27(10), 14054–14063 (2019).
    [Crossref]
  12. D. Herriott, H. Kogelnik, and R. Kompfner, “Off-axis paths in spherical mirror interferometers,” Appl. Opt. 3(4), 523–526 (1964).
    [Crossref]
  13. D. R. Herriott and H. J. Schulte, “Folded optical delay lines,” Appl. Opt. 4(8), 883–889 (1965).
    [Crossref]
  14. J. Schulte, T. Sartorius, J. Weitenberg, A. Vernaleken, and P. Russbueldt, “Nonlinear pulse compression in a multi-pass cell,” Opt. Lett. 41(19), 4511–4514 (2016).
    [Crossref]
  15. M. Ueffing, S. Reiger, M. Kaumanns, V. Pervak, M. Trubetskov, T. Nubbemeyer, and F. Krausz, “Nonlinear pulse compression in a gas-filled multipass cell,” Opt. Lett. 43(9), 2070–2073 (2018).
    [Crossref]
  16. L. Lavenu, M. Natile, F. Guichard, Y. Zaouter, X. Delen, M. Hanna, E. Mottay, and P. Georges, “Nonlinear pulse compression based on a gas-filled multipass cell,” Opt. Lett. 43(10), 2252–2255 (2018).
    [Crossref]

2019 (1)

2018 (3)

2017 (1)

2016 (2)

2014 (1)

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

2013 (1)

2012 (1)

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

2008 (1)

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

1996 (1)

S. M. Chernin, “New generation of multipass systems in high resolution spectroscopy,” Spectrochim. Acta, Part A 52(8), 1009–1022 (1996).
[Crossref]

1995 (1)

S. M. Chernin, “Multipass systems of new generation in high-resolution spectroscopy for fundamental and applied atmosphere investigations,” Proc. SPIE 2366, 408–418 (1995).
[Crossref]

1965 (1)

1964 (1)

Bernacki, B. E.

B. E. Bernacki, Multipass Optical device and process for gas and analyte determination. U.S. Patent 7876443 (25 January 2011).

Bonetti, Y.

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

Chang, Y. C.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Chernin, S. M.

S. M. Chernin, “New generation of multipass systems in high resolution spectroscopy,” Spectrochim. Acta, Part A 52(8), 1009–1022 (1996).
[Crossref]

S. M. Chernin, “Multipass systems of new generation in high-resolution spectroscopy for fundamental and applied atmosphere investigations,” Proc. SPIE 2366, 408–418 (1995).
[Crossref]

de Rooij, N. F.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Delen, X.

Emmenegger, L.

M. Graf, H. Looser, L. Emmenegger, and B. Tuzson, “Beam folding analysis and optimization of mask-enhanced toroidal multipass cells,” Opt. Lett. 42(16), 3137–3140 (2017).
[Crossref]

M. Markus, B. Tuzson, M. Hundt, J. Jágerská, H. Looser, and L. Emmenegger, “Circular paraboloid reflection cell for laser spectroscopic trace gas analysis,” J. Opt. Soc. Am. A 33(5), 913–919 (2016).
[Crossref]

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
[Crossref]

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

Faist, J.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Georges, P.

Graf, M.

Guichard, F.

Guo, Y.

Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
[Crossref]

Hanna, M.

Herriott, D.

Herriott, D. R.

Herzig, H. P.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Hofstetter, D.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Homsy, A.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Hundt, M.

Hvozdara, L.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Jágerská, J.

Jouy, P.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Kaumanns, M.

Kawamata, H.

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

Kogelnik, H.

Kompfner, R.

Krausz, F.

Lavenu, L.

Liu, K.

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

Looser, H.

M. Graf, H. Looser, L. Emmenegger, and B. Tuzson, “Beam folding analysis and optimization of mask-enhanced toroidal multipass cells,” Opt. Lett. 42(16), 3137–3140 (2017).
[Crossref]

M. Markus, B. Tuzson, M. Hundt, J. Jágerská, H. Looser, and L. Emmenegger, “Circular paraboloid reflection cell for laser spectroscopic trace gas analysis,” J. Opt. Soc. Am. A 33(5), 913–919 (2016).
[Crossref]

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
[Crossref]

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

Mangold, M.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
[Crossref]

Manninen, A.

B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
[Crossref]

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

Markus, M.

Ming, X.

Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
[Crossref]

Mottay, E.

Natile, M.

Nubbemeyer, T.

Pervak, V.

Reiger, S.

Riedel, J.

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

Russbueldt, P.

Sartorius, T.

Schulte, H. J.

Schulte, J.

Sun, L.

Z. Yang, M. Zou, and L. Sun, “Generalized method for seeking q-preserving configurations of multi-pass cells,” Opt. Express 27(10), 14054–14063 (2019).
[Crossref]

Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
[Crossref]

Trubetskov, M.

Tuzson, B.

M. Graf, H. Looser, L. Emmenegger, and B. Tuzson, “Beam folding analysis and optimization of mask-enhanced toroidal multipass cells,” Opt. Lett. 42(16), 3137–3140 (2017).
[Crossref]

M. Markus, B. Tuzson, M. Hundt, J. Jágerská, H. Looser, and L. Emmenegger, “Circular paraboloid reflection cell for laser spectroscopic trace gas analysis,” J. Opt. Soc. Am. A 33(5), 913–919 (2016).
[Crossref]

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

B. Tuzson, M. Mangold, H. Looser, A. Manninen, and L. Emmenegger, “Compact multipass optical cell for laser spectroscopy,” Opt. Lett. 38(3), 257–259 (2013).
[Crossref]

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

Ueffing, M.

Vernaleken, A.

Wägli, P.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Weitenberg, J.

Wirthmueller, A.

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Yan, S.

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

Yang, Z.

Z. Yang, M. Zou, and L. Sun, “Generalized method for seeking q-preserving configurations of multi-pass cells,” Opt. Express 27(10), 14054–14063 (2019).
[Crossref]

Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
[Crossref]

Zaouter, Y.

Zou, M.

Analyst (1)

P. Jouy, M. Mangold, B. Tuzson, L. Emmenegger, Y. C. Chang, L. Hvozdara, H. P. Herzig, P. Wägli, A. Homsy, N. F. de Rooij, A. Wirthmueller, D. Hofstetter, H. Looser, and J. Faist, “Mid-infrared spectroscopy for gases and liquids based on quantum cascade technologies,” Analyst 139(9), 2039–2046 (2014).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B: Lasers Opt. (1)

A. Manninen, B. Tuzson, H. Looser, Y. Bonetti, and L. Emmenegger, “Versatile multipass cell for laser spectroscopic trace gas analysis,” Appl. Phys. B: Lasers Opt. 109(3), 461–466 (2012).
[Crossref]

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

Opt. Express (1)

Opt. Lett. (5)

Proc. SPIE (1)

S. M. Chernin, “Multipass systems of new generation in high-resolution spectroscopy for fundamental and applied atmosphere investigations,” Proc. SPIE 2366, 408–418 (1995).
[Crossref]

Rev. Sci. Instrum. (1)

J. Riedel, S. Yan, H. Kawamata, and K. Liu, “A simple yet effective multipass reflector for vibrational excitation in molecular beams,” Rev. Sci. Instrum. 79(3), 033105 (2008).
[Crossref]

Sensors (1)

Z. Yang, Y. Guo, X. Ming, and L. Sun, “Generalized optical design of the Double-row circular multi-pass cell,” Sensors 18(8), 2680 (2018).
[Crossref]

Spectrochim. Acta, Part A (1)

S. M. Chernin, “New generation of multipass systems in high resolution spectroscopy,” Spectrochim. Acta, Part A 52(8), 1009–1022 (1996).
[Crossref]

Other (1)

B. E. Bernacki, Multipass Optical device and process for gas and analyte determination. U.S. Patent 7876443 (25 January 2011).

Supplementary Material (1)

NameDescription
» Visualization 1       A rotating view of the actual optical setup and folded beam path of MR-CMPC, visualized by aerating smog. the first several folded beams are clearly visible, and all of the through-holes on the mask (corresponding to designated positions of reflectio

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1.
Fig. 1. The optical configuration of MR-CMPC when (a) N is an even number; (b) N is an odd number. Two samples of reflection sequences, with parameters of (c) N = 4, p = 14, q = 5; (d) N = 3, p = 14, q = 5. The brown circles represent the positions of reflection spots, while the number on them represent the sequences of appearance. For the clarity, the height of each circular mirror are dramatically exaggerated.
Fig. 2.
Fig. 2. With the change of parameter c, the deviations between the transfer matrixes of MR-CMPCs and identity matrix (a) while N = 3, (p, q) = (146, 71), (170, 83) and (194, 95); (b) while N = 4, (p, q) = (146, 71), (170, 83) and (194, 95); (c) N = 5, (p, q) = (162, 79), (182, 89) and (202, 99)
Fig. 3.
Fig. 3. Optical path simulations of MR-CMPC samples with parameters of R = 100 mm, (a) N = 3, p = 146, q = 71, c = 2.201 mm, and φ=350.162°; (b) N = 3, p = 170, q = 83, c = 1.883 mm, and φ=351.545°; (c) N = 3, p = 194, q = 95, c = 1.641 mm, and φ=352.588°; (d) N = 4, p = 146, q = 71, c = 1.262 mm, and φ=165.222°; (e) N = 4, p = 170, q = 83, c = 1.063 mm, and φ=167.300°; (f) N = 4, p = 194, q = 95, c = 0.918 mm, and φ=168.868°; (g) N = 5, p = 162, q = 79, c = 1.109 mm, and φ=342.252°; (h) N = 5, p = 182, q = 89, c = 0.967 mm, and φ=344.208°; (i) N = 5, p = 202, q = 99, c = 0.859 mm, and φ=345.772°.
Fig. 4.
Fig. 4. Three views and OPL plot of MR-CMPC with parameters of N = 5, R = 100 mm, p = 202, q = 99, c = 0.859 mm, and φ=345.772°. (a) Front view; (b) Side view; (c) Top view; (d) OPL plot at a dummy surface near the exit aperture, generated by TracePro.
Fig. 5.
Fig. 5. (a) Optical simulation of the design with parameter sets of N = 3, R = 50 mm, p = 74, q = 35, c = 1.5 mm, φ=340.632°; (b) The actual optical setup and folded beam path, visualized by aerating smog. A rotating view of the entire circular cell can be seen in Visualization 1.

Tables (1)

Tables Icon

Table 1. The minimum deviations of each set of parameter after optimization

Equations (13)

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

θ 0 = p 2 q 2 p π
θ = κ θ 0 = { 1 c 2 R 2 p sin 2 θ 0 ( 2 N p 1 ) θ 0 { { e j ( N 2 ) 2 θ 0 + sin [ 2 ( N 2 ) ] θ 0 sin 2 θ 0 e j 2 θ 0 } 3 + 2 { e j ( N 2 ) 2 θ 0 + sin [ 2 ( N 2 ) ] θ 0 sin 2 θ 0 e j 2 θ 0 } 2 + 2 N 5 + { e j N π 4 cos 2 θ 0 1 + e j ( 2 θ 0 ) [ k = 0 N 3 e j k ( 2 θ 0 + π ) sin 2 ( N 2 ) θ 0 sin 2 θ 0 e j [ ( N 1 ) π 2 θ 0 ] ] + e j N π } { { e j ( N 2 ) 2 θ 0 + sin [ 2 ( N 2 ) ] θ 0 sin 2 θ 0 e j 2 θ 0 } 2 + 1 } } } θ 0 , ( N = 3 , 4 , 5 )
κ = 1 c 2 R 2 ( 12 cos 2 2 θ + 4 cos 2 θ ) p sin 2 θ 0 ( 6 p 1 ) θ 0
φ = ( N 1 ) π 2 ( N 1 + 2 N n ) θ , ( n = 0 ,   1 ,   2 ,     ,   p 2 2 )
N u m = N p ( N 1 + 2 N n ) , ( n = 0 ,   1 ,   2 ,     ,   p 2 2 )
c N = 4 c cos 2 θ 1 + e j ( 2 θ ) ( e j ( N 1 ) 2 θ + e j N π e j ( 2 θ ) + 1 + e j [ 2 ( N 2 ) θ ] e j ( 2 N θ ) 2 j sin 2 θ ) c e j ( N 2 ) 2 θ sin [ 2 ( N 2 ) ] θ sin 2 θ c e j 2 θ
D i s h o r 2 π R p
D i s v e r 4 c
D e v = | | M I | | F = i = 1 4 j = 1 4 | m i j i i j | 2 = i = 1 4 σ i 2 ( M I )
M = P ( z O ) i = 1 N p [ Λ ( Θ i , α i ) P ( z i ) ]
M 1 = [ 1.003480873 0.004274561 0.001525937 0.005155892 0.000600288 0.995831833 0.005111647 0.001375134 0.035645475 0.001229019 0.996589933 0.000419473 0.001412132 0.034283772 0.004455679 1.004142834 ]
M 2 = [ 0.999187219 0.011871174 0.028308511 0.008164144 0.024620285 1.004006157 0.008573358 0.02758146 0.046852033 0.00040316 0.999193354 0.024913417 0.001229304 0.043901703 0.011450752 0.996924577 ]
M 3 = [ 0.996521324 0.026682949 0.012923366 0.003614159 0.042310145 1.003276671 0.003837331 0.013072316 0.009113667 0.000306078 1.002478947 0.042245634 0.000820163 0.006491543 0.026690505 0.995526994 ]

Metrics