Abstract

The fabrication of high-performance spherical gradient refractive index (S-GRIN) optics requires nondestructive metrology techniques to inspect the samples. We have developed an angular-scan, swept-source-based, Fourier-domain optical coherence tomography (OCT) system centered at 1318 nm with 5 mm imaging depth capable of 180° polar scan and 360° azimuthal scan to investigate polymeric S-GRIN preforms. We demonstrate a method that enables simultaneous mapping of the group optical thickness, physical thickness, the radially-averaged group refractive index, and the transmitted wavefront of the S-GRIN preforms. The angular scan OCT imaging and metrology enables direct visualization, molding uniformity characterization, and optical property evaluations of the preforms. The results on two generations of S-GRIN preforms are discussed that showcase the evolution of the manufacturing process in response to the OCT metrology feedback.

© 2015 Optical Society of America

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References

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2013 (5)

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]

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 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]

Y. Zhou, K. K. H. Chan, T. Lai, and S. Tang, “Characterizing refractive index and thickness of biological tissues using combined multiphoton microscopy and optical coherence tomography,” Biomed. Opt. Express 4(1), 38–50 (2013).
[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).
[PubMed]

2011 (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]

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

2010 (4)

2008 (3)

S. Kim, J. Na, M. J. Kim, and B. H. Lee, “Simultaneous measurement of refractive index and thickness by combining low-coherence interferometry and confocal optics,” Opt. Express 16(8), 5516–5526 (2008).
[Crossref] [PubMed]

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]

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

2007 (3)

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]

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[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]

2005 (1)

2003 (2)

2002 (1)

P. de Groot, “Optical thickness measurement of substrates using a transmitted wavefront test at two wavelengths to average out multiple reflection errors,” Proc. SPIE 4777, 177–183 (2002).
[Crossref]

2000 (1)

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

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]

1995 (2)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995).
[Crossref] [PubMed]

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1980 (1)

Akcay, A. C.

Baer, E.

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]

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (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]

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]

Beadie, G.

Borja, D.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

Bouma, B. E.

Brezinski, M. 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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

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]

Cense, B.

Chan, K. K. H.

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Choma, M. A.

Clarkson, E.

Cotton, C.

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[Crossref]

Dallas, W.

de Boer, J. F.

de Castro, A.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, “Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging,” Opt. Express 18(21), 21905–21917 (2010).
[Crossref] [PubMed]

de Groot, P.

P. de Groot, “Optical thickness measurement of substrates using a transmitted wavefront test at two wavelengths to average out multiple reflection errors,” Proc. SPIE 4777, 177–183 (2002).
[Crossref]

Delemos, T.

Diehl, D. W.

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[Crossref]

Ditchman, C. J.

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[Crossref]

El-Zaiat, S. Y.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

et,

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Fercher, A. F.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Fleet, E. F.

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Flynn, R. A.

Fujimoto, J. G.

Gambra, E.

Gordon, J. M.

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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]

Haruna, M.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

Hee, M. R.

G. J. Tearney, M. E. Brezinski, J. F. Southern, B. E. Bouma, M. R. Hee, and J. G. Fujimoto, “Determination of the refractive index of highly scattering human tissue by optical coherence tomography,” Opt. Lett. 20(21), 2258–2260 (1995).
[Crossref] [PubMed]

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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]

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]

Hitzenberger, C. K.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Hsu, K.

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Izatt, J. A.

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Jin, Y.

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]

Kamp, G.

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Kim, M. J.

Kim, S.

Kotsidas, P.

Lai, T.

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, B. H.

Lee, K. S.

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]

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett. 35(7), 1058–1060 (2010).
[Crossref] [PubMed]

K. S. Lee, A. C. Akcay, T. Delemos, E. Clarkson, and J. P. Rolland, “Dispersion control with a Fourier-domain optical delay line in a fiber-optic imaging interferometer,” Appl. Opt. 44(19), 4009–4022 (2005).
[Crossref] [PubMed]

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]

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]

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Manns, F.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

Marcos, S.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, “Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging,” Opt. Express 18(21), 21905–21917 (2010).
[Crossref] [PubMed]

Meemon, P.

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]

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett. 35(7), 1058–1060 (2010).
[Crossref] [PubMed]

P. Meemon and J. P. Rolland, “Swept-source based, single-shot, multi-detectable velocity range Doppler optical coherence tomography,” Biomed. Opt. Express 1(3), 955–966 (2010).
[PubMed]

Modi, V.

Moore, D. T.

Na, J.

Ohmi, M.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

Ohnishi, Y.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

Ortiz, S.

Parel, J. M.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

Park, B. H.

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]

Pierce, M. C.

Ponting, M.

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]

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (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]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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]

Rolland, J. 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]

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 and J. P. Rolland, “Swept-source based, single-shot, multi-detectable velocity range Doppler optical coherence tomography,” Biomed. Opt. Express 1(3), 955–966 (2010).
[PubMed]

K. S. Lee, P. Meemon, W. Dallas, K. Hsu, and J. P. Rolland, “Dual detection full range frequency domain optical coherence tomography,” Opt. Lett. 35(7), 1058–1060 (2010).
[Crossref] [PubMed]

K. S. Lee, A. C. Akcay, T. Delemos, E. Clarkson, and J. P. Rolland, “Dispersion control with a Fourier-domain optical delay line in a fiber-optic imaging interferometer,” Appl. Opt. 44(19), 4009–4022 (2005).
[Crossref] [PubMed]

Sarunic, M. V.

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Shirk, J. S.

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

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]

Siedlecki, D.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

A. de Castro, S. Ortiz, E. Gambra, D. Siedlecki, and S. Marcos, “Three-dimensional reconstruction of the crystalline lens gradient index distribution from OCT imaging,” Opt. Express 18(21), 21905–21917 (2010).
[Crossref] [PubMed]

Southern, J. F.

Statt, B.

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[Crossref]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

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]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Tai, H.

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]

Tang, S.

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]

Uhlhorn, S.

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

Uhlhorn, S. R.

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

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]

Yang, C.

Yao, J.

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]

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Yoden, K.

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

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]

Zhou, Y.

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 (2)

IEEE Trans. Biomed. Eng. (1)

M. Ohmi, Y. Ohnishi, K. Yoden, and M. Haruna, “In vitro simultaneous measurement of refractive index and thickness of biological tissue by the low coherence interferometry,” IEEE Trans. Biomed. Eng. 47(9), 1266–1270 (2000).
[Crossref] [PubMed]

J. Appl. Polym. Sci. (1)

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]

J. Mod. Opt. (2)

A. de Castro, D. Siedlecki, D. Borja, S. Uhlhorn, J. M. Parel, F. Manns, and S. Marcos, “Age-dependent variation of the Gradient Index profile in human crystalline lenses,” J. Mod. Opt. 58(19-20), 1781–1787 (2011).
[Crossref] [PubMed]

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. Commun. (1)

A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Opt. Commun. 117(1-2), 43–48 (1995).
[Crossref]

Opt. Eng. (2)

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 refractive index ball lenses,” Opt. Eng. 52(11), 112105 (2013).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Proc. SPIE (3)

P. de Groot, “Optical thickness measurement of substrates using a transmitted wavefront test at two wavelengths to average out multiple reflection errors,” Proc. SPIE 4777, 177–183 (2002).
[Crossref]

D. W. Diehl, C. Cotton, C. J. Ditchman, and B. Statt, “Transmitted wavefront metrology of hemispheric domes using scanning low-coherence dual-interferometry (SLCDI),” Proc. SPIE 6545, 65450N (2007).
[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]

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]

Science (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Vision Res. (1)

S. R. Uhlhorn, D. Borja, F. Manns, and J. M. Parel, “Refractive index measurement of the isolated crystalline lens using optical coherence tomography,” Vision Res. 48(27), 2732–2738 (2008).
[Crossref] [PubMed]

Other (1)

J. C. Wyant and K. Creath, “Basic wavefront aberration theory for optical metrology,” in Applied Optics and Optical Engineering, Vol. XI, (Academic, 1992), Chap. 1.

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Figures (11)

Fig. 1
Fig. 1 (a) Estimated group index profile at 1318 nm of the first preform over its nominal thickness of 3.2 mm. (b) A photograph of the first preform. (c) Physical dimensions of the first preform (the color scheme is to indicate its S-GRIN profile as opposed to a uniform index).
Fig. 2
Fig. 2 (a) Estimated group index profile at 1318 nm of the second preform over its nominal thickness of 3.84 mm. (b) A photograph of the second preform. (c) Physical dimensions of the second preform.
Fig. 3
Fig. 3 Angular scan OCT system layout.
Fig. 4
Fig. 4 (a) The schematic and (b) the actual photograph of the angularly scanning sample arm.
Fig. 5
Fig. 5 (a) A top view of a schematic preform with the lines denoting the azimuthal positions where the sequence of raw cross-sectional OCT imaging frames shown in (b) is taken. (c) The cross-sectional frames each remapped in Cartesian coordinates. (d) A schematic showing the angular scan of the preform.
Fig. 6
Fig. 6 (a) An optomechanical cage is placed on the sample platform (not shown) in the angular-scan sample arm to set up a preform and to image a calibration sphere simultaneously. (b) A sequence of cross-sectional images of the preform and the calibration sphere. (c) A sequence of cross-sectional images of the calibration sphere alone after the preform has been removed.
Fig. 7
Fig. 7 (a) and (b) are cross-sectional images of the first preform in polar and Cartesian coordinates, respectively. (c) and (d) are cross-sectional images of the second preform in polar and Cartesian coordinates, respectively.
Fig. 8
Fig. 8 (a), (b) and (c) are the group optical thickness, physical thickness and group refractive index averaged radially for the first preform up to 30 ̊ polar angle. (d) The transmitted wavefront of the first preform across 30 ̊ polar angle and (e) the first 9-term Fringe Zernike fit across the reduced aperture encircled by the blue dashed line in (d) with piston, tilt and power terms removed.
Fig. 9
Fig. 9 (a), (b) and (c) are the group optical thickness, physical thickness and group refractive index averaged radially of the second preform up to 30 ̊ polar angle. (d) The transmitted wavefront of the second preform across 30 ̊ polar angle and (e) the first 9-term Fringe Zernike fit across the reduced aperture encircled by the blue dashed line in (d) with piston, tilt and power terms removed. (f) and (g) are the inner and outer surface figures of the preform measured on a Zygo GPI interferometer.
Fig. 10
Fig. 10 Measured azimuthally-averaged thicknesses of the first (blue) and the second (red) preforms are plotted as a function of the polar angle.
Fig. 11
Fig. 11 A schematic of the cross section of a preform at a given azimuthal angle ϕ = ϕ 0 , cut through the centers of curvature of the outer and inner surfaces ( c 1 and c 2 ) and the vertex of the outer surface ( B ).

Equations (22)

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< n g ( θ , ϕ )> r = i = 1 m n i ( r , θ , ϕ ) t i ( r , θ , ϕ ) t ( θ , ϕ ) ,
O P L ( θ , ϕ ) = < n g ( θ , ϕ ) > r t ( θ , ϕ ) .
Δ w ( θ , ϕ ) = ( < n g ( θ , ϕ ) > r n a i r ) t ( θ , ϕ ) ,
t ( θ , ϕ ) = O P L ( θ , ϕ ) Δ w ( θ , ϕ ) n a i r ,
< n g ( θ , ϕ ) > r = O P L ( θ , ϕ ) O P L ( θ , ϕ ) Δ w ( θ , ϕ ) n a i r .
Δ l = 1 θ max t w e d g e ,
Δ z = 2 θ max 2 t p o w e r ,
Δ z = 2 d 0 t p o w e r θ max 2 d 0 + 2 t p o w e r ,
t ( θ , ϕ 0 ) + d ( θ , ϕ 0 ) = t 0 + d 0 = R 1 ,
Δ l = c 1 c 2 ¯ sin ( θ 0 ) ,
Δ z = c 1 c 2 ¯ cos ( θ 0 ) .
[ d ( θ , ϕ 0 ) ] 2 + ( c 1 c 2 ¯ ) 2 2 cos ( θ + θ 0 ) d ( θ , ϕ 0 ) c 1 c 2 ¯ = R 2 2 ,
d 0 2 + ( c 1 c 2 ¯ ) 2 2 cos ( θ 0 ) d 0 c 1 c 2 ¯ = R 2 2 .
t ( θ , ϕ 0 ) = t 0 + Δ l sin θ Δ z cos θ + d 0 d 0 1 + ( Δ l sin θ Δ z cos θ d 0 ) 2 2 Δ z d 0 .
t ( θ , ϕ 0 ) t 0 + Δ l sin θ Δ z cos θ + d 0 d 0 ( 1 Δ z d 0 ) .
t ( θ , ϕ 0 ) t 0 + Δ l θ + Δ z 2 θ 2 Δ l 6 θ 3 .
t ( θ , ϕ ) t 0 + Δ l θ cos ( ϕ ϕ 0 ) + Δ z 2 θ 2 Δ l 6 θ 3 cos ( ϕ ϕ 0 ) .
Δ l = 1 θ max t w e d g e ,
Δ z = 2 θ max 2 t p o w e r ,
t ( θ , ϕ 0 ) t 0 + Δ l sin θ Δ z cos θ + d 0 d 0 ( 1 Δ z d 0 ) 2 [ 1 ( Δ z sin θ d 0 Δ z ) 2 ] .
t ( θ , ϕ 0 ) t 0 + Δ l θ + [ Δ z 2 + ( Δ z ) 2 2 ( d 0 Δ z ) ] θ 2 Δ l 6 θ 3 .
Δ z = 2 d 0 t p o w e r θ max 2 d 0 + 2 t p o w e r ,

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