Achromatic GRIN singlet lens design

doi:10.1364/OE.21.004970

Achromatic GRIN singlet lens design

Richard A. Flynn, E. F. Fleet, Guy Beadie, and James S. Shirk »View Author Affiliations

Optics Express, Vol. 21, Issue 4, pp. 4970-4978 (2013)
http://dx.doi.org/10.1364/OE.21.004970

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Abstract

Gradient refractive index (GRIN) materials are attractive candidates for improved optical design, especially in compact systems. For GRIN lenses cut from spherically symmetric GRIN material, we derive an analogue of the “lens maker’s” equation. Using this equation, we predict and demonstrate via ray tracing that an achromatic singlet lens can be designed, where the chromatic properties of the GRIN counterbalance those of the lens shape. Modeling the lens with realistic materials and realistic fabrication geometries, we predict we can make an achromatic singlet with a 19 mm focal length using a matrix of known polymers.

OCIS Codes
(080.3630) Geometric optics : Lenses
(110.2760) Imaging systems : Gradient-index lenses
(220.3630) Optical design and fabrication : Lenses
(080.5692) Geometric optics : Ray trajectories in inhomogeneous media

ToC Category:
Optical Design and Fabrication

History
Original Manuscript: November 20, 2012
Revised Manuscript: January 14, 2013
Manuscript Accepted: January 16, 2013
Published: February 21, 2013

Citation
Richard A. Flynn, E. F. Fleet, Guy Beadie, and James S. Shirk, "Achromatic GRIN singlet lens design," Opt. Express 21, 4970-4978 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4970

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References

D. T. Moore, “Design of singlets with continuously varying indices of refraction,” J. Opt. Soc. Am.61(7), 886–894 (1971). [CrossRef]
J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt.39(22), 3825–3832 (2000). [CrossRef] [PubMed]
V. I. Tarkhanov, “Lens with a spherical gradient of refractive index, ideally focusing for an object at a finite distance,” J. Opt. A, Pure Appl. Opt.8(6), 610–615 (2006). [CrossRef]
D. T. Moore, “Gradient-index optics: a review,” Appl. Opt.19(7), 1035–1038 (1980). [CrossRef] [PubMed]
G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express16(15), 11540–11547 (2008). [PubMed]
C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, “Novel structures by microlayer coextrusion - talc-filled PP, PC/SAN, and HDPE/LLDPE,” Polym. Eng. Sci.37(2), 355–362 (1997). [CrossRef]
Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci.103(3), 1834–1841 (2007). [CrossRef]
K. S. R. Krishna and A. Sharma, “Chromatic aberrations of radial gradient-index lenses. I. Theory,” Appl. Opt.35(7), 1032–1036 (1996). [CrossRef] [PubMed]
F. Bociort, “Chromatic paraxial aberration coefficients for radial gradient-index lenses,” J. Opt. Soc. Am. A13(6), 1277–1284 (1996). [CrossRef]
P. J. Sands, “Inhomogeneous lenses. II. Chromatic paraxial aberrations,” J. Opt. Soc. Am.61(6), 777–783 (1971). [CrossRef] [PubMed]
P. J. Sands, “Inhomogeneous lenses. 5. Chromatic paraxial aberrations of lenses with axial or cylindrical index distributions,” J. Opt. Soc. Am.61(11), 1495–1500 (1971). [CrossRef]
P. K. Manhart and R. Blankenbecler, “Fundamentals of macro axial gradient index optical design and engineering,” Opt. Eng.36(6), 1607–1621 (1997). [CrossRef]
ZEMAX software, Zemax Development Corp, www.zemax.com
G. Beadie and J. S. Shirk, “Effects of diffraction and partial reflection in multilayered gradient index polymer lenses,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2010), paper FThU3.
R. Ditteon, Modern Geometrical Optics (John Wiley & Sons, 1998).
B. D. Stone and G. W. Forbes, “Differential ray tracing in inhomogeneous media,” J. Opt. Soc. Am. A14(10), 2824–2836 (1997). [CrossRef]
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]

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[1] D. T. Moore, “Design of singlets with continuously varying indices of refraction,” J. Opt. Soc. Am.61(7), 886–894 (1971). [CrossRef]

[2] J. M. Gordon, “Spherical gradient-index lenses as perfect imaging and maximum power transfer devices,” Appl. Opt.39(22), 3825–3832 (2000). [CrossRef] [PubMed]

[3] V. I. Tarkhanov, “Lens with a spherical gradient of refractive index, ideally focusing for an object at a finite distance,” J. Opt. A, Pure Appl. Opt.8(6), 610–615 (2006). [CrossRef]

[4] D. T. Moore, “Gradient-index optics: a review,” Appl. Opt.19(7), 1035–1038 (1980). [CrossRef] [PubMed]

[5] G. Beadie, J. S. Shirk, A. Rosenberg, P. A. Lane, E. Fleet, A. R. Kamdar, Y. Jin, M. Ponting, T. Kazmierczak, Y. Yang, A. Hiltner, and E. Baer, “Optical properties of a bio-inspired gradient refractive index polymer lens,” Opt. Express16(15), 11540–11547 (2008). [PubMed]

[6] C. D. Mueller, S. Nazarenko, T. Ebeling, T. L. Schuman, A. Hiltner, and E. Baer, “Novel structures by microlayer coextrusion - talc-filled PP, PC/SAN, and HDPE/LLDPE,” Polym. Eng. Sci.37(2), 355–362 (1997). [CrossRef]

[7] Y. Jin, H. Tai, A. Hiltner, E. Baer, and J. S. Shirk, “New class of bioinspired lenses with a gradient refractive index,” J. Appl. Polym. Sci.103(3), 1834–1841 (2007). [CrossRef]

[8] K. S. R. Krishna and A. Sharma, “Chromatic aberrations of radial gradient-index lenses. I. Theory,” Appl. Opt.35(7), 1032–1036 (1996). [CrossRef] [PubMed]

[9] F. Bociort, “Chromatic paraxial aberration coefficients for radial gradient-index lenses,” J. Opt. Soc. Am. A13(6), 1277–1284 (1996). [CrossRef]

[10] P. J. Sands, “Inhomogeneous lenses. II. Chromatic paraxial aberrations,” J. Opt. Soc. Am.61(6), 777–783 (1971). [CrossRef] [PubMed]

[11] P. J. Sands, “Inhomogeneous lenses. 5. Chromatic paraxial aberrations of lenses with axial or cylindrical index distributions,” J. Opt. Soc. Am.61(11), 1495–1500 (1971). [CrossRef]

[12] P. K. Manhart and R. Blankenbecler, “Fundamentals of macro axial gradient index optical design and engineering,” Opt. Eng.36(6), 1607–1621 (1997). [CrossRef]

[13] ZEMAX software, Zemax Development Corp, www.zemax.com

[14] G. Beadie and J. S. Shirk, “Effects of diffraction and partial reflection in multilayered gradient index polymer lenses,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2010), paper FThU3.

[15] R. Ditteon, Modern Geometrical Optics (John Wiley & Sons, 1998).

[16] B. D. Stone and G. W. Forbes, “Differential ray tracing in inhomogeneous media,” J. Opt. Soc. Am. A14(10), 2824–2836 (1997). [CrossRef]

[17] 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]

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Achromatic GRIN singlet lens design