Abstract

A circularly polarized ellipsometer was developed to enable real-time measurements of the optical properties of materials. Using a four photo-detector quadrature configuration, a phase modulated ellipsometer was substantially miniaturized which has the ability to achieve a high precision detection limit. With a proven angular resolution of 0.0001 deg achieved by controlling the relative positions of a triangular prism, a paraboloidal and a spherical mirror pair, this new ellipsometer possesses a higher resolution than traditional complex mechanically controlled configurations. Moreover, the addition of an algorithm, FTA (fault tolerance algorithm) was adopted to compensate for the imperfections of the opto-mechanical system which can decrease system measurement reliability. This newly developed system requires only one millisecond or less to complete the measurement task without having to adopt any other modulation approach. The resolution achieved can be as high as 4x10−7 RIU (refractive index unit) which is highly competitive when compared with other commercially available instruments. Our experimental results agreed well with the simulation data which confirms that our quadrature-based circularly polarized ellipsometer with FTA is an effective tool for precise detection of the optical properties of thin films. It also has the potential to be used to monitor the refractive index change of molecules in liquids.

© 2011 OSA

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2010 (1)

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010).
[CrossRef]

2009 (2)

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009).
[CrossRef] [PubMed]

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

2008 (2)

2007 (1)

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

2005 (2)

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005).
[CrossRef]

2002 (2)

Q. W. Zhan and J. R. Leger, “High-resolution imaging ellipsometer,” Appl. Opt. 41(22), 4443–4450 (2002).
[CrossRef] [PubMed]

P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002).
[CrossRef]

2001 (1)

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001).
[CrossRef]

1999 (1)

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999).
[CrossRef]

1996 (1)

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996).
[CrossRef]

1993 (2)

W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993).
[CrossRef]

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

1991 (2)

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[CrossRef]

1987 (1)

1985 (2)

Y. Y. Cheng and J. C. Wyant, “Phase shifter calibration in phase-shifting interferometry,” Appl. Opt. 24(18), 3049–3052 (1985).
[CrossRef] [PubMed]

H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985).
[CrossRef] [PubMed]

1978 (1)

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978).
[CrossRef] [PubMed]

1974 (1)

Adachi, E.

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001).
[CrossRef]

An, I.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[CrossRef]

Arwin, H.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996).
[CrossRef]

Azzam, R. M. A.

Bashara, N. M.

Bornmann, A.

P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002).
[CrossRef]

Butler, S. W.

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

Chang, C. K.

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

Chen, J. Y.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

Chen, Z. D.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

Cheng, T. D.

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

Cheng, Y. Y.

Chou, T. K.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

Collins, R. W.

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[CrossRef]

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

Cong, Y.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

Cuypers, P. A.

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978).
[CrossRef] [PubMed]

Duncan, W. M.

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993).
[CrossRef]

Eiju, T.

Hariharan, P.

Hemker, H. C.

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978).
[CrossRef] [PubMed]

Henck, S. A.

W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993).
[CrossRef]

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

Hermens, W. T.

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978).
[CrossRef] [PubMed]

Homola, J.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

Hong, C. T.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

Hsieh, C. T.

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999).
[CrossRef]

Hsu, W. L.

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009).
[CrossRef] [PubMed]

Jan, C. M.

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010).
[CrossRef]

Jansson, R.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996).
[CrossRef]

Jin, G.

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996).
[CrossRef]

Kabashin, A. V.

Kajikawa, K.

R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005).
[CrossRef]

Lee, C. K.

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010).
[CrossRef]

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009).
[CrossRef] [PubMed]

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999).
[CrossRef]

Lee, J. Y.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

Lee, S. S.

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009).
[CrossRef] [PubMed]

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

Lee, Y. H.

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010).
[CrossRef]

Leger, J. R.

Li, C. L.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

Lowenstein, L. M.

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

Maisonneuve, M.

Meunier, M.

Nagayama, K.

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001).
[CrossRef]

Naraoka, R.

R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005).
[CrossRef]

Nguyen, N. V.

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[CrossRef]

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

Nygren, H.

H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985).
[CrossRef] [PubMed]

Oreb, B. F.

Patskovsky, S.

Pudliner, B. S.

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

N. V. Nguyen, B. S. Pudliner, I. An, and R. W. Collins, “Error correction for calibration and data reduction in rotating-polarizer ellipsometry - applications to a novel multichannel ellipsometer,” J. Opt. Soc. Am. A 8(6), 919–931 (1991).
[CrossRef]

Shih, H. C.

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

Stenberg, M.

H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985).
[CrossRef] [PubMed]

Tanooka, D.

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001).
[CrossRef]

Westphal, P.

P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002).
[CrossRef]

Wu, G. Y.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

Wu, W. J.

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999).
[CrossRef]

Wyant, J. C.

Zhan, Q. W.

Anal. Biochem. (1)

P. A. Cuypers, W. T. Hermens, and H. C. Hemker, “Ellipsometry as a tool to study protein films at liquid-solid interfaces,” Anal. Biochem. 84(1), 56–67 (1978).
[CrossRef] [PubMed]

Appl. Opt. (3)

Appl. Surf. Sci. (1)

W. M. Duncan and S. A. Henck, “In situ spectral ellipsometry for real-time measurement and control,” Appl. Surf. Sci. 63(1-4), 9–16 (1993).
[CrossRef]

Chem. Rev. (1)

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

W. L. Hsu, S. S. Lee, and C. K. Lee, “Ellipsometric surface plasmon resonance,” J. Biomed. Opt. 14(2), 024036 (2009).
[CrossRef] [PubMed]

J. Immunol. Methods (1)

H. Nygren and M. Stenberg, “Calibration by ellipsometry of the enzyme-linked immunosorbent assay,” J. Immunol. Methods 80(1), 15–24 (1985).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Vac. Sci. Technol. A (1)

S. A. Henck, W. M. Duncan, L. M. Lowenstein, and S. W. Butler, “In situ spectral ellipsometry for real-time thickness measurement: etching multilayer stacks,” J. Vac. Sci. Technol. A 11(4), 1179–1185 (1993).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (2)

W. J. Wu, C. K. Lee, and C. T. Hsieh, “Signal processing algorithms for Doppler effect based nanometer positioning systems,” Jpn. J. Appl. Phys., Part 1 38(3B), 1725–1729 (1999).
[CrossRef]

D. Tanooka, E. Adachi, and K. Nagayama, “Color-imaging ellipsometer: high-speed characterization of in-plane distribution of film thickness at nano-scale,” Jpn. J. Appl. Phys., Part 1 40(2A), 877–880 (2001).
[CrossRef]

Opt. Commun. (1)

J. Y. Lee, H. C. Shih, C. T. Hong, and T. K. Chou, “Measurement of refractive index change by surface plasmon resonance and phase quadrature interferometry,” Opt. Commun. 276(2), 283–287 (2007).
[CrossRef]

Opt. Eng. (1)

C. K. Lee, W. J. Wu, G. Y. Wu, C. L. Li, Z. D. Chen, and J. Y. Chen, “Design and performance verification of a microscope-based interferometer for miniature-specimen metrology,” Opt. Eng. 44(8), 085602 (2005).
[CrossRef]

Opt. Express (1)

Opt. Rev. (1)

C. K. Lee, T. D. Cheng, S. S. Lee, and C. K. Chang, “Opto-mechatronic configurations to maximize dynamic range and optimize resolution of optical instruments,” Opt. Rev. 16(2), 133–140 (2009).
[CrossRef]

Proc. SPIE (1)

C. M. Jan, Y. H. Lee, and C. K. Lee, “The circular polarization interferometer based surface plasmon biosensor,” Proc. SPIE 7577, 75770B, 75770B-12 (2010).
[CrossRef]

Rev. Sci. Instrum. (1)

G. Jin, R. Jansson, and H. Arwin, “Imaging ellipsometry revisited: developments for visualization of thin transparent layers on silicon substrates,” Rev. Sci. Instrum. 67(8), 2930–2936 (1996).
[CrossRef]

Sens. Actuators B Chem. (2)

P. Westphal and A. Bornmann, “Biomolecular detection by surface plasmon enhanced ellipsometry,” Sens. Actuators B Chem. 84(2-3), 278–282 (2002).
[CrossRef]

R. Naraoka and K. Kajikawa, “Phase detection of surface plasmon resonance using rotating analyzer method,” Sens. Actuators B Chem. 107(2), 952–956 (2005).
[CrossRef]

Thin Solid Films (1)

I. An, Y. Cong, N. V. Nguyen, B. S. Pudliner, and R. W. Collins, “Instrumentation considerations in multichannel ellipsometry for real-time spectroscopy,” Thin Solid Films 206(1-2), 300–305 (1991).
[CrossRef]

Other (3)

R. M. A. Azzam, and N. M. Bashara, Ellipsometry and Polarized Light (North-Holland Pub. Co., 1977).

H. G. Tompkins, and E. A. Irene, Handbook of Ellipsometry (William Andrew Pub., Springer, 2005).

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).

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Figures (7)

Fig. 1
Fig. 1

Circularly polarized ellipsometer.

Fig. 2
Fig. 2

Schematic diagram of quadrature configuration with PD1~4.

Fig. 3
Fig. 3

Re-mapping schematic diagram of FTA (fault tolerance algorithm).

Fig. 4
Fig. 4

Experimental results of a Lissajous curve utilizing FTA. (Note: dark circle denotes data before FTA; light circle denotes data after FTA.)

Fig. 5
Fig. 5

Measurement of Δ in liquid phase environments. (Note: dark triangle denotes data before FTA; circle denotes data after FTA.) (The simulation curve of the fixed incident angle at 65 deg characterizes the variation of Δ versus the refractive index of the sample.)

Fig. 6
Fig. 6

Relationship between the specific angle ζof the minimum reflectance and effective refractive index of samples. (Note: solid triangle denotes the experimental results (N = 1.332, 1.3359, 1.3386, 1.3404, and 1.3505); circle denotes the simulation data (N = 1 ~1.4).)

Fig. 7
Fig. 7

Measurement of ellipsometry parameters in (a) Sample #1 (50 nm Au/1 nm Cr) (b) Sample #2 (46 nm Au/4 nm Ti/40 nm ITO) (Note: dark circle denotes the Δ measured by CPE, and dark diamond denotes the Ψ measured by CPE; light circle denotes the Δ measured by EP3, and light diamond denotes the Ψ measured by EP3.) (The simulation curve was based on the real model with adopted incidences from 20 to 70 deg.)

Equations (13)

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tan ( Δ ϕ ) = 1-cos ( ) sinβ ( I 2 -I 4 ) ( 2I 3 -I 1 -I 5 ) .
[ e cos 2 M + e sin 2 M 2 isinMcosMsinδ 2 isinMcosMsinδ e sin 2 M + e cos 2 M ] = 2 2 [ 1 i i 1 ] .
E = [ E x E y ] = [ cos 2 θ cosθsinθ cosθsinθ sin 2 θ ] 2 2 [ 1 i i 1 ] [ r p 2 exp [ i ( ϕ 0p + ϕ p ) ] r s 2 exp [ i ( ϕ 0s + ϕ s ) ] ] = [ cos 2 θ cosθsinθ cosθsinθ sin 2 θ ] 2 2 [ 1 i i 1 ] [ r p 2 exp ( i 2 Δ ) r s 2 ] .
I 1 = 1 2 ( r p 4 + r s 4 + 2r p 2 r s 2 sin2Δ )                   I 2 = 1 2 ( r p 4 + r s 4 + 2r p 2 r s 2 cos2Δ ) I 3 = 1 2 ( r p 4 + r s 4 2r p 2 r s 2 sin2Δ )                   I 4 = 1 2 ( r p 4 + r s 4 2r p 2 r s 2 cos2Δ )
Δ= 1 2 tan -1 ( I 1 -I 3 I 2 -I 4 ) ,           π Δ π .
I 1 +I 3 I 1 -I 3 = ( tan 2 Ψ ) 2 +1 2 ( tan 2 Ψ ) sin2Δ ,     0 Ψ π 4 .
[ q p ] = [ cos ( ϕ * ) -sin ( ϕ * ) sin ( ϕ * ) cos ( ϕ * ) ] [ R A cos( ϕ + ϕ 0 ) R B sin ( ϕ + ϕ 0 ) ] + [ B q B p ]
[ q p ] = [ A q sin ( ϕ q + ϕ ) A p sin ( ϕ p + ϕ ) ] + [ B q B p ]
[ A q 2 A p 2 ] = [ cos 2 ( ϕ * ) sin 2 ( ϕ * ) sin 2 ( ϕ * ) cos 2 ( ϕ * ) ] + [ R A 2 R B 2 ] , A p A q cos ( ϕ p - ϕ q ) =A p A q cos ( θ ) = ( R A 2 -R B 2 ) sin ( ϕ * ) cos ( ϕ * ) ,
[ cos ϕ sin ϕ ] = [ 0 A q C p D p ] -1 [ q i -B q p i -B p ] = [ C q ¯ D q ¯ C p ¯ 0 ] [ q i -B q p i -B p ] = [ C q ¯ D q ¯ B q ¯ C p ¯ 0 B p ¯ ] [ q i p i 1 ]
[ C p ¯ D q ¯ B q ¯ C q ¯ B p ¯ ] = ( i=1 N [ q i sin ϕ i p i cos ϕ i cos ϕ i q i cos ϕ i sin ϕ i ] [ cos ϕ i sin ϕ i ] T [ 0 p i 1 q i 0 q i 0 0 0 1 ] ) -1 ( i=1 N [ q i sin ϕ i p i cos ϕ i cos ϕ i q i cos ϕ i sin ϕ i ] )
ϕ i = tan -1 ( p i - B p q i - B q ) ,
[ cos ϕ sin ϕ ] = [ C ¯ q D ¯ q B ¯ q C ¯ p 0 B ¯ p ] [ q p 1 ] | [ C ¯ q D ¯ q B ¯ q C ¯ p 0 B ¯ p ] [ q p 1 ] | .

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