Abstract

Full-field optical coherence tomography (FF-OCT) is a widely used technique for applications such as biological imaging, optical metrology, and materials characterization, providing structural and spectral information. By spectral analysis of the backscattered light, the technique of spectroscopic-OCT enables the differentiation of structures having different spectral properties, but not the determination of their reflectance spectrum. For surface measurements, this can be achieved by applying a Fourier transform to the interferometric signals and using an accurate calibration of the optical system. An extension of this method is reported for local spectroscopic characterization of transparent samples and in particular for the determination of depth-resolved reflectance spectra of buried interfaces. The correct functioning of the method is demonstrated by comparing the results with those obtained using a program based on electromagnetic matrix methods for stratified media. Experimental measurements of spatial resolutions are provided to demonstrate the smallest structures that can be characterized.

© 2017 Optical Society of America

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2016 (1)

R. Claveau, P. C. Montgomery, M. Flury, and D. Montaner, “Local reflectance spectra measurements of surfaces using coherence scanning interferometry,” Proc. SPIE 9890, 98900Q (2016).
[Crossref]

2015 (3)

2014 (2)

2013 (1)

I. Amenabar, S. Poly, W. Nuansing, E. H. Hubrich, A. A. Govyadinov, F. Huth, R. Krutokhvostov, L. Zhang, M. Knez, J. Heberle, A. M. Bittner, and R. Hillenbrand, “Structural analysis and mapping of individual protein complexes by infrared nanospectroscopy,” Nat. Commun. 4, 2890 (2013).
[Crossref] [PubMed]

2012 (5)

A. R. Badireddy, M. R. Wiesner, and J. Liu, “Detection, characterization, and abundance of engineered nanoparticles in complex waters by hyperspectral imagery with enhanced Darkfield microscopy,” Environ. Sci. Technol. 46(18), 10081–10088 (2012).
[PubMed]

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
[Crossref] [PubMed]

P. C. Montgomery, D. Montaner, and F. Salzenstein, “Tomographic analysis of medium thickness transparent layers using white light scanning interferometry and XZ fringe image processing,” Proc. SPIE 8430, 843014 (2012).
[Crossref]

A. Morin and J.-M. Frigerio, “Aperture effect correction in spectroscopic full-field optical coherence tomography,” Appl. Opt. 51(16), 3431–3438 (2012).
[Crossref] [PubMed]

2011 (1)

P. D. Woolliams and P. H. Tomlins, “Estimating the resolution of a commercial optical coherence tomography system with limited spatial sampling,” Meas. Sci. Technol. 22(6), 065502 (2011).
[Crossref]

2010 (1)

G. Latour, J. Moreau, M. Elias, and J.-M. Frigerio, “Micro-spectrometry in the visible range with full-field optical coherence tomography for single absorbing layers,” Opt. Commun. 283(23), 4810–4815 (2010).
[Crossref]

2009 (3)

2008 (2)

2006 (3)

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of normal skin and melanoma using high resolution hyperspectral imaging,” Cancer Biol. Ther. 5(8), 1033–1038 (2006).
[Crossref] [PubMed]

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

A. Dubois, G. Moneron, and C. Boccara, “Thermal-light full-field optical coherence tomography in the 1.2μm wavelength region,” Opt. Commun. 266(2), 738–743 (2006).
[Crossref]

2005 (2)

M. Fauver, E. Seibel, J. R. Rahn, M. Meyer, F. Patten, T. Neumann, and A. Nelson, “Three-dimensional imaging of single isolated cell nuclei using optical projection tomography,” Opt. Express 13(11), 4210–4223 (2005).
[Crossref] [PubMed]

D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
[Crossref]

2004 (3)

2002 (2)

A. Dubois, L. Vabre, A.-C. Boccara, and E. Beaurepaire, “High-Resolution Full-Field Optical Coherence Tomography with a Linnik Microscope,” Appl. Opt. 41(4), 805–812 (2002).
[Crossref] [PubMed]

K. J. Zuzak, M. D. Schaeberle, E. N. Lewis, and I. W. Levin, “Visible Reflectance Hyperspectral Imaging: Characterization of a Noninvasive, in Vivo System for Determining Tissue Perfusion,” Anal. Chem. 74(9), 2021–2028 (2002).
[Crossref] [PubMed]

2000 (4)

1999 (4)

S.-W. Kim and G.-H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38(28), 5968–5973 (1999).
[Crossref] [PubMed]

P. C. Montgomery and D. Montaner, “Deep submicron 3D surface metrology for 300 mm wafer characterization using UV coherence microscopy,” Microelectron. Eng. 45(2-3), 291–297 (1999).
[Crossref]

L. A. A. Pettersson, L. S. Roman, and O. Inganäs, “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films,” J. Appl. Phys. 86(1), 487–496 (1999).
[Crossref]

H. Zhou, A. Midha, G. Mills, L. Donaldson, and J. M. R. Weaver, “Scanning near-field optical spectroscopy and imaging using nanofabricated probes,” Appl. Phys. Lett. 75(13), 1824–1826 (1999).
[Crossref]

1997 (1)

P. Montgomery, D. Benhaddou, and D. Montaner, “Interferometric roughness measurement of Ohmic contact/III–V semiconductor interfaces,” Appl. Phys. Lett. 71(13), 1768–1770 (1997).
[Crossref]

1993 (1)

G. Vuye, S. Fisson, V. N. Van, Y. Wang, J. Rivory, and F. Abeles, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1-2), 166–170 (1993).
[Crossref]

1992 (2)

G. E. Jellison., “Optical functions of silicon determined by two-channel polarization modulation ellipsometry,” Opt. Mater. 1(1), 41–47 (1992).
[Crossref]

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

1989 (1)

1988 (1)

1977 (1)

J. Kirschner, “On the influence of backscattered electrons on the lateral resolution in scanning auger microscopy,” Appl. Phys. (Berl.) 14(4), 351–354 (1977).
[Crossref]

1956 (1)

F. R. Tolmon and J. G. Wood, “Fringe spacing in interference microscopes,” J. Sci. Instrum. 33(6), 236–238 (1956).
[Crossref]

Abeles, F.

G. Vuye, S. Fisson, V. N. Van, Y. Wang, J. Rivory, and F. Abeles, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1-2), 166–170 (1993).
[Crossref]

Adler, D.

Aggarwal, I. D.

D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
[Crossref]

Alvarez, D. F.

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
[Crossref] [PubMed]

Amarie, S.

F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
[Crossref] [PubMed]

S. Amarie, T. Ganz, and F. Keilmann, “Mid-infrared near-field spectroscopy,” Opt. Express 17(24), 21794–21801 (2009).
[Crossref] [PubMed]

Amenabar, I.

I. Amenabar, S. Poly, W. Nuansing, E. H. Hubrich, A. A. Govyadinov, F. Huth, R. Krutokhvostov, L. Zhang, M. Knez, J. Heberle, A. M. Bittner, and R. Hillenbrand, “Structural analysis and mapping of individual protein complexes by infrared nanospectroscopy,” Nat. Commun. 4, 2890 (2013).
[Crossref] [PubMed]

Annamdevula, N.

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
[Crossref] [PubMed]

Anstotz, F.

A. Leong-Hoï, R. Claveau, M. Flury, W. Uhring, B. Serio, F. Anstotz, and P. C. Montgomery, “Detection of defects in a transparent polymer with high resolution tomography using white light scanning interferometry and noise reduction,” Proc. SPIE 9528, 952807 (2015).
[Crossref]

Badireddy, A. R.

A. R. Badireddy, M. R. Wiesner, and J. Liu, “Detection, characterization, and abundance of engineered nanoparticles in complex waters by hyperspectral imagery with enhanced Darkfield microscopy,” Environ. Sci. Technol. 46(18), 10081–10088 (2012).
[PubMed]

Barth, S. F.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of normal skin and melanoma using high resolution hyperspectral imaging,” Cancer Biol. Ther. 5(8), 1033–1038 (2006).
[Crossref] [PubMed]

Beadie, G.

Beaurepaire, E.

Benhaddou, D.

P. Montgomery, D. Benhaddou, and D. Montaner, “Interferometric roughness measurement of Ohmic contact/III–V semiconductor interfaces,” Appl. Phys. Lett. 71(13), 1768–1770 (1997).
[Crossref]

Betzig, E.

E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257(5067), 189–195 (1992).
[Crossref] [PubMed]

Biegen, J. F.

Bittner, A. M.

I. Amenabar, S. Poly, W. Nuansing, E. H. Hubrich, A. A. Govyadinov, F. Huth, R. Krutokhvostov, L. Zhang, M. Knez, J. Heberle, A. M. Bittner, and R. Hillenbrand, “Structural analysis and mapping of individual protein complexes by infrared nanospectroscopy,” Nat. Commun. 4, 2890 (2013).
[Crossref] [PubMed]

Boccara, A. C.

Boccara, A.-C.

Boccara, C.

Boni, J.

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
[Crossref] [PubMed]

Boppart, S. A.

J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2(1-2), 9–25 (2000).
[Crossref] [PubMed]

Brehm, M.

M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
[Crossref] [PubMed]

Brezinski, M. E.

J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2(1-2), 9–25 (2000).
[Crossref] [PubMed]

Brindza, M.

Brown, W. J.

Claveau, R.

R. Claveau, P. C. Montgomery, M. Flury, and D. Montaner, “Local reflectance spectra measurements of surfaces using coherence scanning interferometry,” Proc. SPIE 9890, 98900Q (2016).
[Crossref]

A. Leong-Hoï, R. Claveau, M. Flury, W. Uhring, B. Serio, F. Anstotz, and P. C. Montgomery, “Detection of defects in a transparent polymer with high resolution tomography using white light scanning interferometry and noise reduction,” Proc. SPIE 9528, 952807 (2015).
[Crossref]

Cricenti, A.

D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
[Crossref]

da Costa, H. S.

David, G.

Dicker, D. T.

D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of normal skin and melanoma using high resolution hyperspectral imaging,” Cancer Biol. Ther. 5(8), 1033–1038 (2006).
[Crossref] [PubMed]

Donaldson, L.

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Hubrich, E. H.

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L. A. A. Pettersson, L. S. Roman, and O. Inganäs, “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films,” J. Appl. Phys. 86(1), 487–496 (1999).
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Ivanov, B.

D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
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Latour, G.

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Lewis, E. N.

K. J. Zuzak, M. D. Schaeberle, E. N. Lewis, and I. W. Levin, “Visible Reflectance Hyperspectral Imaging: Characterization of a Noninvasive, in Vivo System for Determining Tissue Perfusion,” Anal. Chem. 74(9), 2021–2028 (2002).
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R. Claveau, P. C. Montgomery, M. Flury, and D. Montaner, “Local reflectance spectra measurements of surfaces using coherence scanning interferometry,” Proc. SPIE 9890, 98900Q (2016).
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G. Latour, J. Moreau, M. Elias, and J.-M. Frigerio, “Micro-spectrometry in the visible range with full-field optical coherence tomography for single absorbing layers,” Opt. Commun. 283(23), 4810–4815 (2010).
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I. Amenabar, S. Poly, W. Nuansing, E. H. Hubrich, A. A. Govyadinov, F. Huth, R. Krutokhvostov, L. Zhang, M. Knez, J. Heberle, A. M. Bittner, and R. Hillenbrand, “Structural analysis and mapping of individual protein complexes by infrared nanospectroscopy,” Nat. Commun. 4, 2890 (2013).
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F. Huth, A. Govyadinov, S. Amarie, W. Nuansing, F. Keilmann, and R. Hillenbrand, “Nano-FTIR absorption spectroscopy of molecular fingerprints at 20 nm spatial resolution,” Nano Lett. 12(8), 3973–3978 (2012).
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D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
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L. A. A. Pettersson, L. S. Roman, and O. Inganäs, “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films,” J. Appl. Phys. 86(1), 487–496 (1999).
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D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
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J. G. Fujimoto, C. Pitris, S. A. Boppart, and M. E. Brezinski, “Optical coherence tomography: an emerging technology for biomedical imaging and optical biopsy,” Neoplasia 2(1-2), 9–25 (2000).
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I. Amenabar, S. Poly, W. Nuansing, E. H. Hubrich, A. A. Govyadinov, F. Huth, R. Krutokhvostov, L. Zhang, M. Knez, J. Heberle, A. M. Bittner, and R. Hillenbrand, “Structural analysis and mapping of individual protein complexes by infrared nanospectroscopy,” Nat. Commun. 4, 2890 (2013).
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Rich, T. C.

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
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D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
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G. Vuye, S. Fisson, V. N. Van, Y. Wang, J. Rivory, and F. Abeles, “Temperature dependence of the dielectric function of silicon using in situ spectroscopic ellipsometry,” Thin Solid Films 233(1-2), 166–170 (1993).
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L. A. A. Pettersson, L. S. Roman, and O. Inganäs, “Modeling photocurrent action spectra of photovoltaic devices based on organic thin films,” J. Appl. Phys. 86(1), 487–496 (1999).
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Salzenstein, F.

P. C. Montgomery, D. Montaner, and F. Salzenstein, “Tomographic analysis of medium thickness transparent layers using white light scanning interferometry and XZ fringe image processing,” Proc. SPIE 8430, 843014 (2012).
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Sanghera, J. S.

D. Vobornik, G. Margaritondo, J. S. Sanghera, P. Thielen, I. D. Aggarwal, B. Ivanov, N. H. Tolk, V. Manni, S. Grimaldi, A. Lisi, S. Rieti, D. W. Piston, R. Generosi, M. Luce, P. Perfetti, and A. Cricenti, “Spectroscopic infrared scanning near-field optical microscopy (IR-SNOM),” J. Alloys Compd. 401(1-2), 80–85 (2005).
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K. J. Zuzak, M. D. Schaeberle, E. N. Lewis, and I. W. Levin, “Visible Reflectance Hyperspectral Imaging: Characterization of a Noninvasive, in Vivo System for Determining Tissue Perfusion,” Anal. Chem. 74(9), 2021–2028 (2002).
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Selb, J.

Serio, B.

A. Leong-Hoï, R. Claveau, M. Flury, W. Uhring, B. Serio, F. Anstotz, and P. C. Montgomery, “Detection of defects in a transparent polymer with high resolution tomography using white light scanning interferometry and noise reduction,” Proc. SPIE 9528, 952807 (2015).
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Sticker, M.

Stocker, S.

S. J. Leavesley, N. Annamdevula, J. Boni, S. Stocker, K. Grant, B. Troyanovsky, T. C. Rich, and D. F. Alvarez, “Hyperspectral imaging microscopy for identification and quantitative analysis of fluorescently-labeled cells in highly autofluorescent tissue,” J. Biophotonics 5(1), 67–84 (2012).
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N. Sultanova, S. Kasarova, and I. Nikolov, “Dispersion proper ties of optical polymers,” Acta Phys. Pol.-. Ser. Gen. Phys. 116, 585 (2009).

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M. Brehm, T. Taubner, R. Hillenbrand, and F. Keilmann, “Infrared spectroscopic mapping of single nanoparticles and viruses at nanoscale resolution,” Nano Lett. 6(7), 1307–1310 (2006).
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P. D. Woolliams and P. H. Tomlins, “Estimating the resolution of a commercial optical coherence tomography system with limited spatial sampling,” Meas. Sci. Technol. 22(6), 065502 (2011).
[Crossref]

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D. T. Dicker, J. Lerner, P. Van Belle, S. F. Barth, D. Guerry, M. Herlyn, D. E. Elder, and W. S. El-Deiry, “Differentiation of normal skin and melanoma using high resolution hyperspectral imaging,” Cancer Biol. Ther. 5(8), 1033–1038 (2006).
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A. R. Badireddy, M. R. Wiesner, and J. Liu, “Detection, characterization, and abundance of engineered nanoparticles in complex waters by hyperspectral imagery with enhanced Darkfield microscopy,” Environ. Sci. Technol. 46(18), 10081–10088 (2012).
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Figures (11)

Fig. 1
Fig. 1

Schematic representation of the phase shifts and the interferometric signal along the Z-axis in a transparent layer. Interferograms from the surface and the rear interface are shown.

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Fig. 2
Fig. 2

Schematic representation of the experimental microscopes. (a) Mirau-based interference microscope and (b) Linnik-based interference microscope. A.D, aperture diaphragm; F.D, field diaphragm; RM, reference mirror; B-S, beamsplitter; PZT, piezoelectric device.

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Fig. 3
Fig. 3

Results of reflectance spectra for (a) Air-PMMA surface. (b) PMMA-silicon interface. (c) Combined layer (total reflectance spectrum) at a NA of 0.32. The black and blue curves are respectively obtained from the S-matrix program and from the OCT experimental data. The grey area shows the standard deviation of the measurements at each wavelength defined by Eq. (4).

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Fig. 4
Fig. 4

Experimental and simulated source spectra. The spectrum in the solid line is obtained from the FT of one interferogram for a simple silicon substrate. The spectrum in the dashed line is obtained from Eq. (6).

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Fig. 5
Fig. 5

Effect of the numerical aperture on both the total reflectance spectrum (a), (b), (c), (d) and the buried PMMA-silicon interface reflectance spectrum (e), (f), (g), (h), and comparison between the results obtained using an electromagnetic program (S-matrix; black curves) and from the processing of interference fringes (blue curves).

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Fig. 6
Fig. 6

(a) Derivative of z with respect to θ: variation of position of the third white fringe (m = 3) as a function of the angle of incidence for different wavelengths. The result is compared to that obtained by assuming no refraction, i.e. θ'=θ (blue curves). The sample is assumed to be non-dispersive with a constant refractive index of 1.49. (b) Derivative of z with respect to λ: variation of position of the white fringe (m = 1) as a function of the wavelength for different angles of incidence. The result is compared to that obtained by assuming no dispersion (blue curves). (c)-(d) Simulated fringes with a NA of 0.5 with the refraction taken into account (c), and assuming no refraction, i.e. θ'=θ(d). In each case, the signals are normalized with respect to the maximum intensity.

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Fig. 7
Fig. 7

Influence of the spatial coherence on the interference signal when a dispersion mismatch occurs. (a) The coherence plane is assumed to match with the focal plane. (b) The planes are separated by a distance of Δg = 4.06 µm. The NA is set to 0.4. (c) Modification of the PMMA-silicon interface reflectance spectrum.

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Fig. 8
Fig. 8

a) PMMA-silicon interface reflectance spectrum. b) Total reflectance spectrum. The black and blue curves are respectively obtained from the WILIS program and from the measured OCT data.

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Fig. 9
Fig. 9

(a)-(b) Comparison between experimental (blue curves) and theoretical spectra (black curves) for depth-resolved and total reflectance spectrum measurements for very low NA (∼0.1). (a) PMMA-silicon interface reflectance spectrum. (b) Total reflectance spectrum. For simulations, the NA is adjusted to 0.1. (c) Signal to noise ratio measured over the spectral band considered. The two vertical dotted lines define the domain where the measurement is reliable.

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Fig. 10
Fig. 10

(a) CTFs (Contrast Transfer Function) of the Leitz-Linnik setup for two positions of the aperture diaphragm. (b) Intensity profile of the 0.8 µm period grating obtained in the open (black line) and closed (blue line) positions of the diaphragm. The square curve in the dotted line represents the theoretical results.

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Fig. 11
Fig. 11

(a) Theoretical axial resolution as a function of the effective NA for two source bandwidths. The illumination spectrum is centered at 800 nm. (b)-(c) Experimental axial resolution obtained for two extreme aperture positions of the diaphragm. (b) Fully open. (c) Closed as much as possible. The interferograms are obtained from a silicon substrate.

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Equations (12)

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I( z )∝ ∫ θ min θ max ∫ 0 +∞ 1 2 S( λ ) R ref ( λ ) [ R s 1 ( λ ) cos( Δ φ 1 ( λ,z,θ ) )+ R s 2 ( λ ) T s 1 ( λ )exp( −2keκ )cos( Δ φ 2 ( λ,z,θ ) ) ]dθdλ
| FT { I( δ ) } s 2 |= 1 2 S( σ ) R ref ( σ ) R s 2 ( σ ) ( 1− R s 1 ( σ ) ) exp( −4πσeκ )⋅SpecRes p cam ⋅ T sys
R s 2 ( σ )= | FT { I( δ ) } s 2 FT { I( δ ) } cal | 2 R cal ( σ ) ( 1− R s 1 ( σ ) ) 2
σ( λ )= 1 N ∑ i=1 N ( R i ( λ )− R ¯ ( λ ) ) 2
R ¯ ( λ )= 1 N ∑ i=1 N R i ( λ ) .
S( σ )= I 0 1+4 ( σ− σ 0 ) 2 Δ σ 2 with σ= 1 λ and Δσ= Δλ λ 0 2
z( λ,θ )= mλ 2cos( θ ) +en cos( θ' ) cos( θ ) ;   m∈ℤ
SCE( Z )= ( sin( Z ) Z ) 2 ,      Z= πN A 2 z 2 λ 0 n
SNR( dB )=20 log 10 ( A signal σ )
h(u)= [ 2 J 1 ( u ) u ] 2 ,       u= 2π λ r NA
V= V 0 | μ || γ |
Δ z temp = 2ln2 nπ λ 0 2 Δλ ;             Δ z spat = 7.6 λ 0 πN A eff 2