Abstract

This paper proposes a new design paradigm which allows for a modular approach to replacing a homogeneous optical lens system with a higher-performance GRadient-INdex (GRIN) lens system using a WaveFront Matching (WFM) method. In multi-lens GRIN systems, a full-system-optimization approach can be challenging due to the large number of design variables. The proposed WFM design paradigm enables optimization of each component independently by explicitly matching the WaveFront Error (WFE) of the original homogeneous component at the exit pupil, resulting in an efficient design procedure for complex multi-lens systems.

© 2016 Optical Society of America

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References

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  1. M. J. Kidger, Fundamental Optical Design (SPIE Publications, 2001).
  2. R. Fischer, Optical System Design (McGraw-Hill Education, 2008).
  3. E. W. Marchand, Gradient Index Optics (Academic Press, 1978).
  4. G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient Index Elements and Systems (SPIE Publications, 1997).
  5. P. J. Sands, “Aberrations of lenses with axial index distributions,” J. Opt. Soc. Am. 61(8), 1086–10917 (1971).
    [Crossref]
  6. D. J. Fischer, C. J. Harkrider, and D. T. Moore, “Design and manufacture of a gradient-index axicon,” Appl. Opt. 39(16), 2687–2694 (2000).
    [Crossref] [PubMed]
  7. A. C. Urness, K. Anderson, C. Ye, W. L. Wilson, and R. R. McLeod, “Arbitrary GRIN component fabrication in optically driven diffusive photopolymers,” Opt. Express 23(1), 264–273 (2015).
    [Crossref] [PubMed]
  8. F. Bociort, “Chromatic paraxial aberration coefficients for radial gradient-index lenses,” J. Opt. Soc. Am. A 13(6), 1277–1284 (1996).
    [Crossref]
  9. S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.
  10. A. Sharma, D. V. Kumar, and A. K. Ghatak, “Tracing rays through graded-index media: a new method,” Appl. Opt. 21(6), 984–987 (1982).
    [Crossref] [PubMed]
  11. D. R. Smith, Y. Urzhumov, N. B. Kundtz, and N. I. Landy, “Enhancing imaging systems using transformation optics,” Opt. Express 18(20), 21238–21251 (2010).
    [Crossref] [PubMed]
  12. J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
    [Crossref] [PubMed]
  13. D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
    [Crossref]
  14. J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
    [Crossref]
  15. N. Hansen and A. Ostermeier, “Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation,” in Proceedings of the 1996 IEEE Intern. Conf. on Evolutionary Computation (IEEE, 1996), pp. 312–317.
    [Crossref]
  16. M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
    [Crossref]
  17. N. Hansen and A. Ostermeier, “Convergence properties of evolution strategies with the derandomized covariance matrix adaptation: the (μ/μ_I,λ)-CMA-ES,” in 5th European Congress on Intelligent Techniques and Soft Computing (Verlag Mainz, 1997), pp. 650–654.
  18. C. P. Grover and H. M. van Driel, “Autocorrelation method for measuring the transfer function of optical systems,” Appl. Opt. 19(6), 900–904 (1980).
    [Crossref] [PubMed]
  19. J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
    [Crossref]

2015 (1)

2014 (2)

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

2013 (1)

J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
[Crossref]

2011 (1)

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

2010 (1)

2008 (1)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

2000 (1)

1996 (1)

1982 (1)

1980 (1)

1971 (1)

Anderson, K.

Bayraktar, Z.

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

Bociort, F.

Brocker, D. E.

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.

Campbell, S. D.

S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.

Chen, R.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Corsetti, J. A.

J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
[Crossref]

Fischer, D. J.

Ghatak, A. K.

Gregory, M. D.

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

Grover, C. P.

Hansen, N.

N. Hansen and A. Ostermeier, “Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation,” in Proceedings of the 1996 IEEE Intern. Conf. on Evolutionary Computation (IEEE, 1996), pp. 312–317.
[Crossref]

Harkrider, C. J.

Jin, S.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Kim, T. K.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Kong, S. D.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Kumar, D. V.

Kundtz, N. B.

Landy, N. I.

Li, J.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Liu, Z.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Lu, D.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

McCarthy, P.

J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
[Crossref]

McLeod, R. R.

Moon, J.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Moore, D. T.

J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
[Crossref]

D. J. Fischer, C. J. Harkrider, and D. T. Moore, “Design and manufacture of a gradient-index axicon,” Appl. Opt. 39(16), 2687–2694 (2000).
[Crossref] [PubMed]

Nagar, J.

S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.

Ostermeier, A.

N. Hansen and A. Ostermeier, “Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation,” in Proceedings of the 1996 IEEE Intern. Conf. on Evolutionary Computation (IEEE, 1996), pp. 312–317.
[Crossref]

Pendry, J. B.

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Sands, P. J.

Sharma, A.

Smith, D. R.

Turpin, J. P.

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

Urness, A. C.

Urzhumov, Y.

van Driel, H. M.

VanSaders, B.

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Werner, D. H.

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.

Werner, P. L.

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

Wilson, W. L.

Ye, C.

Appl. Opt. (3)

IEEE Antennas Wirel. Propag. Lett. (1)

D. E. Brocker, J. P. Turpin, P. L. Werner, and D. H. Werner, “Optimization of gradient index lenses using quasi-conformal contour transformations,” IEEE Antennas Wirel. Propag. Lett. 13, 1787–1791 (2014).
[Crossref]

IEEE Trans. Antenn. Propag. (1)

M. D. Gregory, Z. Bayraktar, and D. H. Werner, “Fast optimization of electromagnetics design problems through the CMA evolutionary strategy,” IEEE Trans. Antenn. Propag. 59(4), 1275–1285 (2011).
[Crossref]

J. Opt. Soc. Am. (1)

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

Nano Energy (1)

J. Moon, D. Lu, B. VanSaders, T. K. Kim, S. D. Kong, S. Jin, R. Chen, and Z. Liu, “High performance multi-scaled nanostructured selective coating for concentrating solar power,” Nano Energy 8, 238–246 (2014).
[Crossref]

Opt. Eng. (1)

J. A. Corsetti, P. McCarthy, and D. T. Moore, “Color correction in the infrared using gradient-index materials,” Opt. Eng. 52(11), 112109 (2013).
[Crossref]

Opt. Express (2)

Phys. Rev. Lett. (1)

J. Li and J. B. Pendry, “Hiding under the carpet: a new strategy for cloaking,” Phys. Rev. Lett. 101(20), 203901 (2008).
[Crossref] [PubMed]

Other (7)

N. Hansen and A. Ostermeier, “Adapting arbitrary normal mutation distributions in evolution strategies: the covariance matrix adaptation,” in Proceedings of the 1996 IEEE Intern. Conf. on Evolutionary Computation (IEEE, 1996), pp. 312–317.
[Crossref]

N. Hansen and A. Ostermeier, “Convergence properties of evolution strategies with the derandomized covariance matrix adaptation: the (μ/μ_I,λ)-CMA-ES,” in 5th European Congress on Intelligent Techniques and Soft Computing (Verlag Mainz, 1997), pp. 650–654.

S. D. Campbell, J. Nagar, D. E. Brocker, and D. H. Werner, “On the use of surrogate models in the analytical decompositions of refractive index gradients obtained through quasiconformal transformation optics,” J. Opt. Soc. Am.in press.

M. J. Kidger, Fundamental Optical Design (SPIE Publications, 2001).

R. Fischer, Optical System Design (McGraw-Hill Education, 2008).

E. W. Marchand, Gradient Index Optics (Academic Press, 1978).

G. I. Greisukh, S. T. Bobrov, and S. A. Stepanov, Optics of Diffractive and Gradient Index Elements and Systems (SPIE Publications, 1997).

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Figures (10)

Fig. 1
Fig. 1 Homogeneous focusing lens system.
Fig. 2
Fig. 2 Five randomly seeded convergence curves for full system.
Fig. 3
Fig. 3 Spot diagram and WFE on the exit pupil at λ = 3 μm and on-axis illumination for (a) the first doublet and (b) the focusing lens system.
Fig. 4
Fig. 4 Depiction of the wavefront matching principle. The exit pupils, shown by the dashed lines, are aligned in both systems, and this is where the wavefront errors need to match for the systems to be identical. (a) Original homogeneous lens. (b) GRIN replacement.
Fig. 5
Fig. 5 Spot diagram and wavefront error on the exit pupil for the first GRIN singlet for λ = 3 μm and on-axis illumination.
Fig. 6
Fig. 6 Focusing lens system with GRIN singlet and homogeneous doublet.
Fig. 7
Fig. 7 Five randomly seeded convergence curves for wavefront matching of the first doublet.
Fig. 8
Fig. 8 Five randomly seeded convergence curves for wavefront matching of the second doublet.
Fig. 9
Fig. 9 Focusing lens system with two GRIN singlets.
Fig. 10
Fig. 10 MTF at θ = 2° and λ = 3 μm along the tangential and radial cuts for (left) the homogeneous and (right) the all-GRIN system.

Tables (5)

Tables Icon

Table 1 Strehl ratios for homogeneous focusing lens system.

Tables Icon

Table 2 Strehl ratios for GRIN focusing lens system using simple optimization.

Tables Icon

Table 3 Error in WFE match for first doublet.

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Table 4 Error in WFE match for second doublet.

Tables Icon

Table 5 Strehl ratios for all-GRIN focusing lens system using WFM.

Equations (3)

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COST= max P { abs[ W orig ( x p , y p ) W GRIN ( x p , y p ) ] }
H( f x , f y )= 1 1 ψ( x p + f x 2 , y p + f y 2 ) ψ * ( x p f x 2 , y p f y 2 )d x p d y p 1 1 | ψ( x p , y p ) | 2 d x p d y p ψ( x p , y p )=exp[ jkW( x p , y p ) ]
n(r,z)= n 0 + a 1 r 2 + a 2 r 4 + a 3 z+ a 4 z 2 + a 5 r 2 z+ a 6 r 2 z 2 + a 7 r 4 z+ a 8 r 4 z 2

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