Abstract

A hybrid confocal-scan swept-source optical coherence tomography metrology system was conceived for simultaneous measurements of the refractive index and thickness profiles of polymeric layered gradient refractive index (GRIN) optics. An uncertainty analysis predicts the metrology capability of the system and guides the selection of an optimum working numerical aperture. Experimental results on both a monolithic and a GRIN layered sheet are demonstrated to be in close agreement with theoretical predictions. Index measurement precision reached 0.0001 and 0.0008 for measuring 2.8 mm and ~300 µm thick layers, respectively. The thicknesses of these layers were simultaneously measured with a precision of 0.28 and 0.17 µm, respectively.

© 2015 Optical Society of America

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2015 (2)

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. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

2013 (3)

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]

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]

2010 (3)

2008 (2)

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]

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]

2007 (2)

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]

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]

2005 (1)

2003 (1)

2001 (1)

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

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 (1)

1993 (1)

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

1991 (2)

M. Gu, C. Sheppard, and X. Gan, “Image formation in a fiber-optical confocal scanning microscope,” J. Opt. Soc. Am. A 8(11), 1755–1761 (1991).
[Crossref]

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

1966 (1)

H. H. Ku, “Notes on use of propagation of error formulas,” J. Res. Nbs. C Eng. Inst. C 70, 263–273 (1966).

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]

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

Birch, K. P.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Borja, D.

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.

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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Choma, M.

Cirucci, N.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

Clarkson, E.

de Castro, A.

Delemos, T.

Downs, M. J.

K. P. Birch and M. J. Downs, “An updated Edlen equation for the refractive index of air,” Metrologia 30(3), 155–162 (1993).
[Crossref]

Drexler, W.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Fujimoto, J. G.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

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]

Gambra, E.

Gan, X.

Ghanta, R. K.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Gu, M.

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, and 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]

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]

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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Huang, J.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

Ivanov, T.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[PubMed]

Izatt, J.

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]

Kärtner, F. X.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

Kim, M. J.

Kim, S.

Ku, H. H.

H. H. Ku, “Notes on use of propagation of error formulas,” J. Res. Nbs. C Eng. Inst. C 70, 263–273 (1966).

Kuhn, W. 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]

S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (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]

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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Manns, F.

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.

Meemon, P.

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]

S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (2010).
[Crossref] [PubMed]

Morgner, U.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[Crossref] [PubMed]

Murali, S.

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.

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]

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]

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]

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]

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, and 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.

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
[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]

S. Murali, P. Meemon, K. S. Lee, W. P. Kuhn, K. P. Thompson, and J. P. Rolland, “Assessment of a liquid lens enabled in vivo optical coherence microscope,” Appl. Opt. 49(16), D145–D156 (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.

Schuman, J. S.

W. Drexler, U. Morgner, R. K. Ghanta, F. X. Kärtner, J. S. Schuman, and J. G. Fujimoto, “Ultrahigh-resolution ophthalmic optical coherence tomography,” Nat. Med. 7(4), 502–507 (2001).
[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, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Sheppard, C.

Shirk, J. S.

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.

Southern, J. F.

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, and 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).
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D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, and C. A. Puliafito, and et, “Optical coherence tomography,” Science 254(5035), 1178–1181 (1991).
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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).
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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).
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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).
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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).
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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).
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Biomed. Opt. Express (1)

IEEE Trans. Biomed. Eng. (1)

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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. Biomed. Opt. (1)

J. Huang, J. Yao, N. Cirucci, T. Ivanov, and J. P. Rolland, “Performance analysis of optical coherence tomography in the context of a thickness estimation task,” J. Biomed. Opt. 20(12), 121306 (2015).
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Opt. Eng. (1)

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).
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Opt. Express (4)

Opt. Lett. (1)

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, and 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).
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Figures (11)

Fig. 1
Fig. 1 (a) Illustration of a confocal-scan FD-OCT measurement through a single layer (or a homogeneous block). (b) An example of an FD-OCT depth profile acquired when the objective is focused between the top and bottom surfaces. (c) Confocal intensity profiles of both the top and bottom surfaces reconstructed from a sequence of depth profiles acquired simultaneously with the objective lens being translated to focus through the top and bottom surfaces.
Fig. 2
Fig. 2 Guideline (top) and procedures (bottom) of an analysis method carried out to estimate the np (similar for t) measurement uncertainty (i.e., bias and precision, respectively) by the confocal-scan SS-OCT.
Fig. 3
Fig. 3 (a) Experimentally measured sensitivity decay in the confocal-scan SS-OCT system over the measurement range of 5 mm depth. (b) Theoretical and experimentally-measured signal decay of the top surface of a BK7 flat with the increased defocus distance up to 2500 µm from the focus of the objective lens (working NA of 0.1782).
Fig. 4
Fig. 4 (a) and (b) are the estimated precision and bias in measuring group OPD (ΔD) up to 5 mm. (c) and (d) are the estimated np and t measurement precisions, respectively, attributable to the ΔD precision at different NAs.
Fig. 5
Fig. 5 (a) Theoretical confocal intensity profiles of a surface of a 10/90% PMMA/SAN17 layer at different NAs. (b) An example of a raw noisy confocal intensity profile (black) at 0.2 NA and with Lorentzian fit applied (magenta). (c) Simulated peak detection error of confocal PSFs at different NAs with σ = 0.5% Gaussian random intensity noise before and after Lorentzian fitting.
Fig. 6
Fig. 6 (a) Estimated precision of the Δz measurement, and the resulted (b) np precision and (c) t precision at different NAs. (d) Estimated bias limit of the Δz measurement, and the resulted (e) np bias limit and (f) t bias limit at different NAs.
Fig. 7
Fig. 7 np and relative t biases as a function of (a) NA bias and (b) nair bias, respectively.
Fig. 8
Fig. 8 Confocal-scan SS-OCT system layout and experimental setup of the sample arm. CL: collimating lens; OL: objective lens; PC: polarization controller; FC: fiber circulator; MLS: motorized linear stage; BP: balanced photodetector; ADC: analog-to-digital converter; MZI: Mach-Zehnder interferometer.
Fig. 9
Fig. 9 (a) Theoretical and OCT-measured phase index and cumulative thickness of a monolithic 108-layer 10/90% PMMA/SAN17 sheet measured across increasing numbers of layers. (b) Nominal and OCT-measured thickness of each layer.
Fig. 10
Fig. 10 Metricon-measured and OCT-measured phase refractive indices, and nominal and OCT-measured thicknesses of each stack of layers sharing the same material composition within a 102-layer GRIN sheet.
Fig. 11
Fig. 11 (a) np precision, (b) t precision, and (c) np bias of sample layers of thicknesses ranging from 50 – 3000 µm predicted theoretically and measured experimentally.

Equations (13)

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ΔD= n g t,
n p = N A 2 +( n air 2 N A 2 ) ( t Δz ) 2 ,
n g = n p Δ n disp = n p λ n p λ .
A n p 4 +B n p 3 +C n p 2 +D n p +E=0, A= ( Δz ) 2 ,B=2Δ n disp ( Δz ) 2 ,C=[ ( Δ n disp ) 2 ( NA ) 2 ] ( Δz ) 2 , D=2Δ n disp ( Δz ) 2 ( NA ) 2 ,E= ( Δ n disp ) 2 ( Δz ) 2 ( NA ) 2 [ n air 2 ( NA ) 2 ] ( ΔD ) 2 .
n p =f(ΔD,Δz,NA, n air ).
| B n p |= | ( f ΔD ) B ΔD | 2 + | ( f Δz ) B Δz | 2 + | ( f NA ) B NA | 2 + | ( f n air ) B n air | 2 ,
| B n p |= | B n p ,ΔD | 2 + | B n p ,Δz | 2 + | B n p ,NA | 2 + | B n p , n air | 2 .
S n p = S n p ,ΔD 2 + S n p ,Δz 2 + S n p ,NA 2 + S n p , n air 2 .
λ sim Normal( λ ¯ ,Δ λ 2 ),
N g ( λ sim )Normal( N g ( λ sim ) , K N g ( λ sim ) ),
K Ng ( λ sim )= C 1 N g ( λ sim ) 2 + C 2 N g ( λ sim ) + C 3 .
K I c ( z )= C 1 [ I c ( z ) ] 2 + C 2 I c (z)+ C 3 .
NA= n air 2 t cal 2 n p,cal 2 Δ z 2 t cal 2 Δ z 2 .

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