Abstract

In this paper, we develop the methodology, including the refraction correction, geometrical thickness correction, coordinate transformation, and layer segmentation algorithms, for 3D rendering and metrology of a layered spherical gradient refractive index (S-GRIN) lens based on the imaging data collected by an angular scan optical coherence tomography (OCT) system. The 3D mapping and rendering enables direct 3D visualization and internal defect inspection of the lens. The metrology provides assessment of the surface geometry, the lens thickness, the radii of curvature of the internal layer interfaces, and the misalignment of the internal S-GRIN distribution with respect to the lens surface. The OCT metrology results identify the manufacturing defects, and enable targeted process development for optimizing the manufacturing parameters. The newly fabricated S-GRIN lenses show up to a 7x spherical aberration reduction that allows a significantly increased utilizable effective aperture.

© 2016 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms

Jianing Yao, Panomsak Meemon, Michael Ponting, and Jannick P. Rolland
Opt. Express 23(5) 6428-6443 (2015)

In vivo human crystalline lens topography

Sergio Ortiz, Pablo Pérez-Merino, Enrique Gambra, Alberto de Castro, and Susana Marcos
Biomed. Opt. Express 3(10) 2471-2488 (2012)

Correction of geometric and refractive image distortions in optical coherence tomography applying Fermat’s principle

Volker Westphal, Andrew M. Rollins, Sunita Radhakrishnan, and Joseph A. Izatt
Opt. Express 10(9) 397-404 (2002)

References

  • View by:
  • |
  • |
  • |

  1. R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
    [Crossref]
  2. P. Kotsidas, V. Modi, and J. M. Gordon, “Nominally stationary high-concentration solar optics by gradient-index lenses,” Opt. Express 19(3), 2325–2334 (2011).
    [Crossref] [PubMed]
  3. R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21(4), 4970–4978 (2013).
    [Crossref] [PubMed]
  4. J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
    [Crossref] [PubMed]
  5. S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
    [Crossref]
  6. M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010).
    [Crossref]
  7. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
    [Crossref]
  8. P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
    [Crossref]
  9. T. Yamagishi, K. Fujii, and I. Kitano, “Gradient-index rod lens with high N.A,” Appl. Opt. 22(3), 400–403 (1983).
    [Crossref] [PubMed]
  10. W. A. Reed, M. F. Yan, and M. J. Schnitzer, “Gradient-index fiber-optic microprobes for minimally invasive in vivo low-coherence interferometry,” Opt. Lett. 27(20), 1794–1796 (2002).
    [Crossref] [PubMed]
  11. Y. Koike, Y. Takezawa, and Y. Ohtsuka, “New interfacial-gel copolymerization technique for steric GRIN polymer optical waveguides and lens arrays,” Appl. Opt. 27(3), 486–491 (1988).
    [Crossref] [PubMed]
  12. M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
    [Crossref] [PubMed]
  13. J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signal-to-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett. 28(21), 2067–2069 (2003).
    [Crossref] [PubMed]
  14. P. Ossowski, A. Raiter-Smiljanic, A. Szkulmowska, D. Bukowska, M. Wiese, L. Derzsi, A. Eljaszewicz, P. Garstecki, and M. Wojtkowski, “Differentiation of morphotic elements in human blood using optical coherence tomography and a microfluidic setup,” Opt. Express 23(21), 27724–27738 (2015).
    [Crossref] [PubMed]
  15. P. Tankam, Z. He, Y. J. Chu, J. Won, C. Canavesi, T. Lepine, H. B. Hindman, D. J. Topham, P. Gain, G. Thuret, and J. P. Rolland, “Assessing microstructures of the cornea with Gabor-domain optical coherence microscopy: pathway for corneal physiology and diseases,” Opt. Lett. 40(6), 1113–1116 (2015).
    [Crossref] [PubMed]
  16. A. Curatolo, M. Villiger, D. Lorenser, P. Wijesinghe, A. Fritz, B. F. Kennedy, and D. D. Sampson, “Ultrahigh-resolution optical coherence elastography,” Opt. Lett. 41(1), 21–24 (2016).
    [Crossref] [PubMed]
  17. Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
    [Crossref]
  18. S. Ortiz, P. Pérez-Merino, E. Gambra, A. de Castro, and S. Marcos, “In vivo human crystalline lens topography,” Biomed. Opt. Express 3(10), 2471–2488 (2012).
    [Crossref] [PubMed]
  19. S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010).
    [Crossref] [PubMed]
  20. J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
    [Crossref]
  21. J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
    [Crossref] [PubMed]
  22. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).
  23. K. Karnowski, I. Grulkowski, N. Mohan, I. Cox, and M. Wojtkowski, “Quantitative optical inspection of contact lenses immersed in wet cell using swept source OCT,” Opt. Lett. 39(16), 4727–4730 (2014).
    [Crossref] [PubMed]

2016 (1)

2015 (4)

2014 (1)

2013 (4)

R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21(4), 4970–4978 (2013).
[Crossref] [PubMed]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

2012 (1)

2011 (1)

2010 (2)

2008 (1)

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

2007 (1)

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

2003 (2)

2002 (1)

1996 (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

1988 (1)

1983 (1)

Baer, E.

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010).
[Crossref]

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Beadie, G.

Bouma, B. E.

Brister, A.

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Bukowska, D.

Bunch, R. M.

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Canavesi, C.

Cense, B.

Choma, M.

Chu, Y. J.

Cox, I.

Curatolo, A.

de Boer, J. F.

de Castro, A.

Derzsi, L.

Eljaszewicz, A.

Fleet, E. F.

Flynn, R. A.

Fritz, A.

Fujii, K.

Gain, P.

Gambra, E.

Garstecki, P.

Gordon, J. M.

Grulkowski, I.

Gupta, P.

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

He, Z.

Hiltner, A.

M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010).
[Crossref]

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Hindman, H. B.

Huang, J.

Izatt, J.

Ji, S.

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Karnowski, K.

Kennedy, B. F.

Kitano, I.

Koike, Y.

Kotsidas, P.

Lalanne, P.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Lee, K. S.

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

Lemercier-Lalanne, D.

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Lepine, T.

Lepkowicz, R. S.

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Lorenser, D.

Mackey, M.

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Marcos, S.

Meemon, P.

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

Modi, V.

Mohan, N.

Ohtsuka, Y.

Ortiz, S.

Ossowski, P.

Park, B. H.

Pascual, D.

Patel, H.

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

Pérez-Merino, P.

Pierce, M. C.

Ponting, M.

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010).
[Crossref]

Raiter-Smiljanic, A.

Rao, K.

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

Reed, W. A.

Remon, L.

Rolland, J. P.

Sampson, D. D.

Sarunic, M.

Schnitzer, M. J.

Shirk, J. S.

Siedlecki, D.

Suresh, M.

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

Szkulmowska, A.

Takezawa, Y.

Tankam, P.

Tearney, G. J.

Thompson, K. P.

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

Thuret, G.

Topham, D. J.

Verma, Y.

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

Villiger, M.

Wiese, M.

Wijesinghe, P.

Wojtkowski, M.

Won, J.

Yamagishi, T.

Yan, M. F.

Yang, C.

Yao, J.

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

Yin, K.

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Zahreddine, R. N.

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Appl. Opt. (2)

Appl. Phys. B (1)

Y. Verma, K. Rao, M. Suresh, H. Patel, and P. Gupta, “Measurement of gradient refractive index profile of crystalline lens of fish eye in vivo using optical coherence tomography,” Appl. Phys. B 87(4), 607–610 (2007).
[Crossref]

Biomed. Opt. Express (1)

J. Mod. Opt. (1)

P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996).
[Crossref]

Macromol. Symp. (1)

M. Ponting, A. Hiltner, and E. Baer, “Polymer nanostructures by forced assembly: process, structure and properties,” Macromol. Symp. 294(1), 19–32 (2010).
[Crossref]

Opt. Eng. (2)

S. Ji, K. Yin, M. Mackey, A. Brister, M. Ponting, and E. Baer, “Polymeric nanolayered gradient refractive index lenses: technology review and introduction of spherical gradient refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

J. Yao, P. Meemon, K. S. Lee, and J. P. Rolland, “Nondestructive metrology by optical coherence tomography empowering manufacturing iterations of layered polymeric optical materials,” Opt. Eng. 52(11), 112111 (2013).
[Crossref]

Opt. Express (7)

J. Yao, J. Huang, P. Meemon, M. Ponting, and J. P. Rolland, “Simultaneous estimation of thickness and refractive index of layered gradient refractive index optics using a hybrid confocal-scan swept-source optical coherence tomography system,” Opt. Express 23(23), 30149–30164 (2015).
[Crossref] [PubMed]

S. Ortiz, D. Siedlecki, I. Grulkowski, L. Remon, D. Pascual, M. Wojtkowski, and S. Marcos, “Optical distortion correction in optical coherence tomography for quantitative ocular anterior segment by three-dimensional imaging,” Opt. Express 18(3), 2782–2796 (2010).
[Crossref] [PubMed]

M. Choma, M. Sarunic, C. Yang, and J. Izatt, “Sensitivity advantage of swept source and Fourier domain optical coherence tomography,” Opt. Express 11(18), 2183–2189 (2003).
[Crossref] [PubMed]

P. Ossowski, A. Raiter-Smiljanic, A. Szkulmowska, D. Bukowska, M. Wiese, L. Derzsi, A. Eljaszewicz, P. Garstecki, and M. Wojtkowski, “Differentiation of morphotic elements in human blood using optical coherence tomography and a microfluidic setup,” Opt. Express 23(21), 27724–27738 (2015).
[Crossref] [PubMed]

P. Kotsidas, V. Modi, and J. M. Gordon, “Nominally stationary high-concentration solar optics by gradient-index lenses,” Opt. Express 19(3), 2325–2334 (2011).
[Crossref] [PubMed]

R. A. Flynn, E. F. Fleet, G. Beadie, and J. S. Shirk, “Achromatic GRIN singlet lens design,” Opt. Express 21(4), 4970–4978 (2013).
[Crossref] [PubMed]

J. Yao, P. Meemon, M. Ponting, and J. P. Rolland, “Angular scan optical coherence tomography imaging and metrology of spherical gradient refractive index preforms,” Opt. Express 23(5), 6428–6443 (2015).
[Crossref] [PubMed]

Opt. Lett. (5)

Proc. SPIE (1)

R. N. Zahreddine, R. S. Lepkowicz, R. M. Bunch, E. Baer, and A. Hiltner, “Beam shaping system based on polymer spherical gradient refractive index lenses,” Proc. SPIE 7062, 706214 (2008).
[Crossref]

Sci. Rep. (1)

P. Meemon, J. Yao, K. S. Lee, K. P. Thompson, M. Ponting, E. Baer, and J. P. Rolland, “Optical coherence tomography enabling non destructive metrology of layered polymeric GRIN material,” Sci. Rep. 3, 1709 (2013).
[Crossref]

Other (1)

M. Born and E. Wolf, Principles of Optics (Cambridge University Press, 1998).

Supplementary Material (1)

NameDescription
» Visualization 1: MP4 (8858 KB)      Volumetric rendering of an S-GRIN lens based on a 3D imaging data set acquired by the angular-scan OCT

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 (10)

Fig. 1
Fig. 1

Geometrical specifications of (a) an S-GRIN preform and (b) an S-GRIN lens cut out of the preform (the color scheme is to indicate the S-GRIN profile). (c) A photograph of an S-GRIN lens. (d) Estimated refractive index profile of the lens through its center thickness from material composition.

Fig. 2
Fig. 2

Schematic layout of the angular-scan OCT system.

Fig. 3
Fig. 3

Protocol of imaging space characterization (with a CaliBall), coordinate transformation, and 3D rendering of a lens sample acquired by the angular-scan OCT system (using normal incidence on the sample surface as an example).

Fig. 4
Fig. 4

(a) A raw 2D cross-sectional OCT image of a lens in polar coordinates and (b) remapped image in Cartesian coordinates, under the imaging condition shown in (c) where the θ-scanner trajectory and the convex lens surface were concentric. (d) A raw cross-sectional OCT image in polar coordinates and (e) remapped image in Cartesian coordinates, under the imaging condition shown in (f) where the θ-scanner trajectory and the convex lens surface were longitudinally shifted in their centers of curvature.

Fig. 5
Fig. 5

(a) Illustration of the refraction correction strategy based on the angular-scan imaging setup. (b) Interpretation of a raw cross-sectional polar image obtained from angular-scan imaging.

Fig. 6
Fig. 6

(a) Layer section segmentation on a raw cross-sectional image of an S-GRIN lens. (b) Identified layer structure remapped in the reconstructed Cartesian S-GRIN image. (c) 3D topographies of segmented surfaces/ layer section interfaces (note that the topographies are purposely offset along z for better visualization).

Fig. 7
Fig. 7

(a) and (b) are snapshots of the 3D view of the S-GRIN lens based on a volumetrically rendered OCT imaging data set. (c-f) are en face images at 0.5, 1, 1.5 and 2 mm depth, respectively, as denoted by the red dashed lines in (a). A video clip of the volumetric rendering of the lens is presented in Visualization 1.

Fig. 8
Fig. 8

The estimated (a) longitudinal shift in the centers of curvature and (b) radii of curvature of the first 20 segmented surface and layer section interfaces (i.e., with refractive index change on both sides).

Fig. 9
Fig. 9

(a) A simulated, approximate interferogram of the as-built S-GRIN lens. (b) An experimentally-obtained interferogram of the S-GRIN lens using the transmitted wavefront measurement configuration shown in (c). Due to the double-pass testing configuration, two fringes on an interferogram represent one wave of test part defect at 633 nm.

Fig. 10
Fig. 10

Interferograms of two new S-GRIN lenses measured with a Fizeau interferometer.

Equations (13)

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

P L = n1 R L ,
P L = n l R 1 l S ,
l R = n R L l S l S (n1)+ R L .
θ Scan =d θ Scan ( p 0 p),
R Scan (p= p max )= R Scan ( θ Scan = θ Scan max )= R L sin θ L max sin θ Scan max ,
R Scan (p)= R Scan ( p max )+[ f( p max )f(p) ]dR,
θ Ref = θ Scan ( n1 ) l s + R L n R L .
d θ Ref =d θ Scan ( n1 ) l s + R L n R L .
R Ref ( θ Ref )= R Scan ( θ Scan ) sin θ Scan sin θ Ref .
R Ref ( p )= R Scan ( p )sin[ d θ Scan ( p 0 p) ] sin[ d θ Scan ( p 0 p) ( n1 ) l s + R L n R L ] .
θ(p,q)=( p 0 p )d θ Ref + π 2 ,
R(p,q)= R Ref (p)+[ f(p)q ]dR.
dR'(p,q)= dR n g (p,q) .

Metrics